Studying and diagnosing psychiatric disorders is always difficult due to their wide range of criteria and different ways they can apply to each individual. We have trouble diagnosing a lot of mental illnesses on their own due to the fact that each person displays symptoms in their own way.

A larger study is needed and thats important for us to know, we can take the data as seen but with the background knowledge that a bigger study is in order.

Its important to recognize the failings in the data and that some criteria simply don't work for these sources.

When I read this I got a wake up call into how I could seriously improve my writing. I think that I have fallen trap to grabbing any case that has a good line. In order to move past that surface level writing in which my network of cases fails to connect and its all just great one-liners: I need to focus on taking the time to collect cases relevant to my research. I also think this mainly points out that good research takes time. Legal research and building a network of cases for a research project takes more than one night right before the deadline.

One way I’ve noticed associative reasoning playing a role in my law school experience is when I try to connect a case we’ve studied in class to a practice problem or exam question. I often attempt to relate the facts of the case to those presented in the question. While this approach can be helpful, it’s more crucial to focus on the rules established by multiple cases and the key issues they addressed. Sometimes, cases may share similar facts, but if I rely too heavily on those surface similarities and overlook the underlying legal principles, I can end up arriving at the wrong answer. For example, my associative reasoning can't be so surface level that I begin associating any new case that involves a house to be a valid contract, etc.

The United States was at peace with that nation and, at the solicitation of Japan, was still in conversation with its government and its emperor looking toward the maintenance of peace in the pacific. Indeed, one hour after Japanese air squadrons had commenced combing in the American Island of Oahu, The Japanese ambassador to the United States and his colleague delivered to our secretary of state a formal reply to a recent American message.

I know we are just recently learning about how these tools are accessible to students, but how long has AI been a thing but we just didn't know how to utilize it?

Every student should be able to have the opportunity to an education, whether they have learning disabilities or not

This sounds like Duolingo

This is a huge thing in education. I think teachers can get good ideas from AI and can help with lesson planning and learn about different ways to keep students engaged

I really like this idea. If there are robots like this to be able to help people in situations like this, I strongly support.

AI tools like this are very useful in cases like this. Kids being able to engage with classwork when they are neurodivergent is important so they don't feel like they are behind on anything school related. These are the types of tools that can help encourage active engagement

The division between designers and handicapped people—who are frequently viewed as passive recipients rather than active creators—is a problem in accessible design that is brought to light in this paragraph. The framing of design discussions frequently suggests that non-disabled designers are the creators and handicapped people are just users. According to Dr. Cynthia Bennett, it is problematic when disabled persons are excluded from the design process because it ignores their lived experience and knowledge of their own needs. The opinions of disabled people may not be given the same weight as those of "professional" designers, even when they do contribute. This highlights a problem in many domains where underrepresented groups are viewed as recipients rather than collaborators, which can result in designs that don't completely meet their needs or reflect their perspectives.

It's important to make sure you are designing the product for people who are going to be using your product thoughtfully. If you design it for yourself, you'll usually end up forgetting important details that will affect how others using your design will perceive.

Because it perpetuates the notion that disability is something to be "fixed" rather than accommodated, this emphasis on normalcy can be harmful. The high costs of many assistive devices are also mentioned in the text, which can be a barrier for people who require them and reflect larger problems of unequal access to help. By highlighting how attempts to make people "normal" can occasionally backfire, the mention of abusive practices like gay conversion therapy or ABA therapy for autistic persons broadens the discussion.

After reading this, I realized that coping mechanisms such as masking place the whole weight on people with impairments to adapt to situations that were not meant for them. However, I believe it underscores a wider issue: when systems are inaccessible, disabled people are unfairly expected to find ways to fit in, often at considerable personal cost. And I'm wondering if there's a better way for society to support people with invisible disabilities so they don't feel compelled to hide or adapt alone.

To my observations, society is still experimenting with universal design as it is harder to notice features that make certain actions or services accessible to all people, especially in the physical sense. However, I have noticed software companies releasing new features that make their products usable for all, for example, Apple's accessibility feature that reads out text and options for the user to interact with without having the need to read the screen.

This is me. I have a few disabilities that I struggle with, and I think this is excellent to remind others of something they might take for granted. It's funny for quite a while I learned to just adapt before I went out and got diagnosed and was able to receive help for some of my disabilities. I believe human beings are like that and can make do when they need to that's what makes us so resilient.

anthropocene - era when human actions have become the main driver of environmental change. (Ford et al)

there should have been weekly/daily data points on this

The quote, "Room for Error", means that there is more of an allowance for imperfection and it shows a complexity of life. This quote shows compassion, patience, and adaptability in our lives.

This section encourages us to evaluate disability as a social construct shaped by preconceived beliefs about what abilities are "normal." For example, trichromats are not considered "disabled," despite the fact that they lack the additional color sensitivity that tetrachromats do. It serves as a powerful reminder that disabilities are frequently imposed barriers rather than inherent limitations. This makes me wonder how much more inclusive our environments could be if they accommodated a broader spectrum of talents from the outset.

This paragraph calls upon the reasons why we consider some people to be disabled. We do not classify certain people solely on their physical or mental differences but due to the low accommodation or opportunities present for them in society.

I really appreciate that this reading gave me that view of this issue. You always look at things from a certain scope and never venture to look at things from a different viewpoint. The fact that tetrachromats exist is something I never knew, and I think there should absolutely be special accommodations made for them as well.

This is a good amount of people without legal papers and i can say that even for a fact theyre the most hard working people who push hard for an education but are let down because of the support system of society. I know that they don't fully get the opportunity to finish school and are pushed out to work.

To those families who maintain their culture and certain traditions in their households can be a good thing to a certain extent. I think being open to learning different cultures is a good thing except for when people try to bash and change aspects and perceptions. People tend to bash the cultures that they believe are not the correct ones or what they dont expect, but at the end of the day the correct ones start from native americans.

This is actually true and it is something that still continues. In families they will look for the next girl to be the most nurturing or show care to the rest of the siblings because the parents are at work. It shows different perspectives having them grow up a little faster. It gives and holds back little girls from different experience because they're put into a different stress.

On what I've learned and seeing the stress a child takes upon in situations usually starts with families. The built up anger, not being able to sleep, feeling the stress of their parents having them do extra things. From what i've been told from Asian cultures is how much pressure they add to a kid to be able to be "perfect" through education having them meet extra standards and going above and beyond adding them in extra forms of help/ tutors. This is when it comes down too having to meet a standard and over working themselves,

Throughout the story, Frost uses beautiful imagery as a metaphor to communicate his longing to return to care free adolescence.

Frost talks about the concept of "ignorance is bliss" and how you should be patient and not grow up too fast. The whole tone of the poem is imaginative and nostalgic. Explores the "coming of age" theme.

I believe this section of the poem emphasizes the modernism characteristic of having "confidence in the power of the imagination to construct meaning where there is none." We see this here with the girl's hair and above with the boy swinging on the trees. Through imagination, Frost takes something that most people would have over looked, and uses it to symbolize something else with a deeper meaning.

Here, Frost compares potential causes of the bending of the trees. He'd like to assume it was because a boy had been swinging on them instead of it being due to an ice storm.

Ways to discover music organically: - 1) Check out the producer of the song - 2) Check out artist features (who features on them and who they feature for. - 3) Check out playlists by favorite artist. - 4) Keep up with critics/publications of music - 5) Genre Reddit communities - 6) Rate Your Music -> IMDB for music - 7) AlbumOfTheYear - 8) Physical Record Stores - 9) Discover Music through Friends Warning: Not for Loners!!! - 10) Local Music Venues

Theres always a story behind how one acts or how they learn. Here benny knows that he has always been neglected and even though he had someone to take care of him, hes going to remember that even his mom left him from the start. It puts a bigger role on him of having to look at things different. He was able to grow up in a house hold where his grandmother was able to get her high school dimploma giving him an advantage.

The advantage given based on being able to be bilingual and not only being able to read or write but being able to speak both languages gives you a push. As a child you learn their capacities of being able to learn them but the point is being open to learn and not forget. It is a struggle when you can not communicate with others because of a language barrier but also seeing the effort that they put in to learn. It opens them up to a broad range of readings.

I liked reading that the research was based on their strenghts and resources because in a kid we see all the bad they do and from those small comments it stivks to the kids for a long time. It reminds me to the different reading we had 2 weeks ago based on how comments stick to the kids at a young age of the "woah you're too tall for your age" "you're suppose to be smart"etc. I know they see their strengths and as they demonstrate it and someone acknowledges it they know and feel that they can do good.

Reading the title opens up many questions and realization of why literacy is not really a factor in certain households of the Latino community. It comes down to sometimes parents tend to not help out to offer books because thye themselves do not know how to read or understand the language. Then it is also that being in a household that have different priorities and its to work to be able to pay rent we know that they would not have time to sit down and help us learn.

key element here of desire

Highlighting its relevance in developing his perspective on life and knowledge, Descartes explains his fundamental belief in an all-powerful God who created him. A loving God guides his perspective since he would not fool others. Descartes emphasizes the ageless nature of this religion and how it shapes his intellectual efforts, especially his search of truth and certainty.

This chapter captures Descartes's attempt to link our mental images of the physical world with the actuality of those items. He highlights the difference between imagination and actuality and addresses doubt about existence by claiming that our concepts of bodily forms originate from actual entities. Aiming to provide a basis of knowledge that recognizes the truth of the physical universe while also being skeptical of sensory experience, this argument is important to his philosophical study.

Descartes considers the nature of reality and perception and the indistinctiveness of dreaming and waking life. His admission of falling for dreams sets off intense doubts about sensory knowledge. The chapter shows his approach of critical thinking and emphasizes the philosophical and emotional difficulties of looking for certainty in an uncertain environment. In essence, it captures the essence of his philosophical investigation on the meaning of life and the dependability of human perception.

Emphasizing how people could be caught in false beliefs resulting from a disordered state of mind, this chapter shows Descartes's investigation of mental clarity against delusion. By means of striking images and contrasts, he challenges the continuation of illusion, therefore highlighting the more general philosophical concerns of identity, perception, and the character of reality. This is a sobering meditation on the need of clear thinking and the perils of letting irrationality or negativity color one's impressions.

This chapter, taken as a whole, shows Descartes's critical analysis of sensory experience, stressing its constraints and therefore confirming the presence of trustworthy experiences. It represents his larger philosophical quest for knowledge's basis among the complexity of human perception and for certainty.

Descartes is arguing that, just as we should be wary of accepting false things, so should we be of accepting doubtful things. Should one have any cause to question a belief, we should completely reject it. This method promotes absolutely certain knowledge building.

In forms of education i know that the best help is allowing them or talking through students about opportunities that can have especially when it comes down to high schoolers. Alowing students to know and if there is possible connects, it would automatically give them the advantage of wanting to try out something and go for it. Gving a student the reassurance of im here for you or im here to support you will always be a successful outcome.

Having the opportunity of being able to receive financial aid and this year being the hardest because of the new updates. Many people got unmotivated because they were in the air as to what was going to happen or what were going to be the outcomes. We try our best to work our way to receive grants or scholarships so getting that opportunity away is hard because we know how expensive it is. So for those who do not receive financial aid impacts them to know that they wont be able to afford it.

The financial status of one will always take a big toll especially when it comes down to education. You either choose the route to make money or work your way but in the process basically be suffering. This is when it comes down that having support from someone even with the minor help it would give you the advantages or the push of oh okay i got this!.

In life and i can speak for myself all i need sometimes is that push of guidance. Knowing that someone is there for you and willing to put time aside to help you out. Even when it comes down you just want that reassurance of the Hey im here for you or if theres anything they can do or even the you got this! Listening to this honestly support goes a long way.

Its sad that her realization was at a young age just like someone elses comments stated and its true, you feel the inequality based on the standards of society the moment youre forced to grow up young. Even today the people who have the privelege to get an education deny that route and the people who want that route can't have it because society doesnt provide or allow them to. Here is with undocumented and her knowing that without papers she won't have that and others is knowing now that can get protected by DACA will help them out a little more.

The American Dream is always something that stays in the air that people tend to take differently. The American dream has been implemented forcefully to say education is the way to go but everything comes down to perception of what you think success means to someone. For me success means going to school, graduating, and getting the job i've always strived for or having a degree to rely on. Success for others can be getting a job as long as they're able to support their family. Now i wonder what Flors ideal would be.

I think that this piece of advice is among the most effective in the article, because audience members certainly have a tendency to focus on "me" questions. I think that knowing that "me" questions often defer from the speech can help people to reshape questions that they may have asked as is otherwise.

I believe that this is very important to know because its an organized way to be an audience member.

This quote really hits home for me because I used to be someone who was pretty regularly late for calculus. Because I was late, I would always be flustered and so lost when I got to class, and my grade suffered because of it. This year I have made an effort to be early to all my classes, and I feel like I have definitely understood more of what I have been learning.

I like how you mentioned these words of Jackie Robinson. It really emphasizes his quiet but powerful determination, as he states that patience is necessary, especially it times where progress seems to be slow.

I appreciate the way you contrasted this idea in words. It was interesting to see how she finally felt valued as a writer, even through such illegal actions.

I like how you mentioned this quote by Jackie Robinson. It really highlights the determined mindset that Robinson had, showing that he was always focused on progress and future achievements, and not just past milestones.

Recognizing implicit bias is hard for some teachers. Being aware is half way there.

This is insightful! I think that a coach that is given to a teacher almost negates the whole growing and learning process

The unity of the American grew through shared sacrifice and resistance to imperial controls, creating a distinct political identity.

This reveal a society fighting with the contradictions of freedom and enslavement

The text highlights how Quaker beliefs in equality and nonviolence began to shape anti-slavery sentiments by the mid-18th century, particularly in Pennsylvania. This period represents a turning point in how some colonists began to question the legitimacy of slavery as an institution.

Voices that are marginalized in this quote include those of the enslaved individuals themselves, whose perspectives and motivations for rebellion are often overlooked.

**Questions in this section: ** 1. How did religious beliefs influence societal attitudes toward slavery? 2. Are there parallels between Quaker activism and modern movements against systemic injustice?

Answering Historical Questions The audience that would have become interested in reading accounts detailing the Stono Rebellion would have been primarily the colonial masters and the white settlers. The accounts were prescribed to cordon off rebellion and fear in the enslaved people. The rebellion’s importance was to show that the enslaved people would fight to be free and thereby show the moral of slavery.

Asking Questions 1. How does the response to the Stono Rebellion reflect the attitudes toward enslaved people at the time? 2. How do these events connect to the legal and social frameworks surrounding slavery in other colonies, such as Pennsylvania?

The mid-Atlantic colonies relied heavily on enslaved labor, especially in urban areas like New York City, where over 40% of the population was enslaved by 1700.

I agree that skeptical arguments rely on the existence of doubt but I also do agree that not everything can be examined so we truly do not know if it is real or just skeptical.

I always wonder about this because, in some dreams, I genuinely feel like I am part of the dream, but as soon as I wake up, I automatically assume I am awake. But what if the dream is just continuing, and it's like a never-ending loop?

I find global skepticism fascinating to get into because everyone just knows like the why but never like the real reason why or if we are in a reality where everything is real or fake.

This reminds me of the I do, We do, You do process. The productive group work is an added component that resonates with me such as a small group.

Despite this being a sentiment from 1937 this is still a very real battle against women and children. One demonstration of this battle that has stuck with me is the fashion exhibit "What Were You Wearing?" This exhibit consists of outfits that were worn by SA survivors when they were attacked. Many of the exhibitions are children's clothing and some are just diapers. The sex criminal is still a terrifying threat but has only been taken less seriously by men.

Does the white fear of violent slave uprisings contribute to inherent subconscious prejudice towards black people?

I believe this blase attitude towards major stories has worsened with the age of social media. Many people have forgotten, or worse, were never aware, that Russia and Ukraine are at war, and the same for Israel and Palestine now that the genocide has been ongoing for over a year. Social media has simultaneously made people more nosey and forgetful. Social media users go from one outrageous story to another with no real empathy or care for those involved, only interested in the drama they provide. Overstimulation has dulled people's sense of reality and empathy.

As someone who is not very artistic, I'm not sure that this strategy would be that effective for me. I might get too caught up in making it look recognizable or overly explaining what it is, which detracts from the goal. I also think it's difficult to come up with this many ideas that also have some kind of visual element, and it requires a lot more effort and energy. With words, it can be easy to generate lists of dozens of things, but with drawings, creativity might start to drain halfway through the 8 pictures.

I think storyboarding is a great way to get into the mind of your target audience and build on the empathy phase of the process. It can be easy to come up with an idea and then realize it doesn't actually fit into the situation you had hoped. Storyboarding helps give context as to why some things do/don't work and helps focus ideas.

Is it often that ideas start to get similar by the end if ideas are working off of each other?

I think this is really important because a lot of times people have really good ideas but they are too scared to speak up. That's why I think writing things out makes it easier for less confident people to share their ideas

Honestly, I don't really understand this strategy. In general, this one seems the most confusing, but I also think the other strategies (opportunity redefinition, triggered brainwalking, and worst idea) do what it does better and in a more clear way. I just don't see a need to use this one over the others.

I think that this can be a great way to keep the energy up when brainstorming. I often feel like my first few ideas have to be the "right" ones, so purposefully being wrong can help take off some pressure and be fun.

Is this the best way to go about it from the start or could it be more helpful if no one can really think of any good ideas?

I think that this is very helpful because you can write down anything without having to think hard about it being a perfect idea or what others might think about it!

the greater the extent that you too possess this equipment, the more likely you will be to succeed (in anything). This doesn't just apply to those in the "entrepreneurial field" -- but that said, acquiring (and then knowing how to use) this equipment is much easier said than done.

what are your thoughts on this?

the 'pro' and the 'con' side

ground that we've covered before ... should be very familiar...

!!

exploited, as a good thing (as it seems in capitalism and resource extraction models in general...)

a vision for not just the future (but a better future, an improved tomorrow based on your innovation(s), today)

ecclesial imagery

No, I hate the idea of boxing in any ideas of communication by putting them in our made up term used to identify concepts used within a community. I think communication is a much larger idea and language just try’s to narrow down and define. Communication is a living, breathing idea and the rules are loose- changing all the time.

client only data

hierarchical object store

that;s what Peergos is for IndyWeb

I believe creating is so powerful and I like to use Book creator to do that,

Great definition or explanation of why we use digital tools.

I definitely agree that it is not about the shiniest but about what accomplished the learning goal and sometimes it is not technology that does it.

Mark Schrad discusses his German typewriter in episode 31 of the Austin Typewriter Ink Podcast<br /> https://www.podomatic.com/podcasts/austintypewriterink/episodes/2021-02-01T21_49_07-08_00

This is some really neat work. This is a wonderful resource for the community! I really appreciated the logic and decision making highlighted throughout the paper leading to an optimal protocol for 4- or 5- color imaging in dicty! Very cool work and beautiful images!!!

Why did y'all shift from mNeonGreen comparisons to GFP?

Very neat & exciting finding!!!

Is there any data comparing Dox-GFP with a Dox-mNeonGreen FP? If so, are the two probes comparable in their response times?

Was the cytoplasmic background also brighter here (not just the localized signal)? I'm just naively wondering if the achilles tag is causing some stress that is increasing background autofluorescence in the cell (given the onset of uniform cytoplasmic fluorescence in Fig 1).

Interesting that there is a significant difference in the distribution of mNeonGreen (anterior vs posterior) but not with Achilles. Do you have any ideas why this would be the case? Are there any observable physiological defects caused by either of these FPs?

Like sentence structures and outlines??

Analyze, analyze, analyze!!

I don't understand.

1. build confidence and voice as a writer
2. connect with the reading audience

You gotta snatch up the audience so then they will read the writing or something.

Yes!! Imagine if William Shakespeare wrote with zero emotion. Then it would twice as boring as it already is.

100% agree and I just love this sentence.

The title "Leave Yourself Out of Your Writing" has me confused because I thought that writing was a form of self expression??

He specifically mentions teaching here.

Reflect on this. Why do we need to be aware of this as teachers?

What are some complications he points to here?

What does ontological mean? What is the relationship between history and identity? How does that influence ontological satisfaction?

Note this. It's a long established practiced, and the pagans mock it.

Do we know that? Source?

Agents personal servers

to Agents personal servers

Flip the Web

I know on an intellectual level that the cultural implications of this practice are incredibly complex but emotionally I find it completely shocking that only a fifth of the women offered it choose reconstructive surgery.

The paper describes direct addition of amines to alkenes.

The authors present a novel iridium-catalyzed borylation method for aryl C–H bonds, allowing direct functionalization of unactivated arenes.

The authors demonstrate a palladium-catalyzed method for the amination of aromatic C–H bonds, enabling direct incorporation of nitrogen.

The paper discusses mechanistic insights and strategies that have broadened applications for C–H activation in synthetic organic chemistry.

The authors present a detailed computational and experimental study on the mechanistic pathways of iridium-catalyzed borylation of C–H bonds.

The authors introduce a photoredox-catalyzed cross-coupling reaction enabling the formation of C–C bonds without traditional organometallic reagents.

The authors explore the mechanisms of selective C–H activation catalysis involving transition metals through detailed computational studies.

https://phys.org/news/2020-10-approach-chemistry-enables-boron-added.html

Researchers have developed a new method to add boron atoms to organic molecules using light-driven chemistry, eliminating the need for transition metals. This approach is expected to simplify synthesis processes and reduce environmental impact by making boron addition more accessible and eco-friendly.

https://cen.acs.org/synthesis/c-h-activation/Alkane-borylation-reaction-kicks-metals/98/i42

Researchers have developed a novel alkane borylation reaction that bypasses the need for transition metal catalysts, traditionally essential in such reactions. This approach utilizes photoredox chemistry to enable borylation with milder conditions and reduced environmental impact, making the process greener and more sustainable. The reaction opens new possibilities for functionalizing hydrocarbons in pharmaceutical and material science applications by avoiding the cost and toxicity associated with metal catalysts.

https://news.berkeley.edu/2020/05/21/scientists-finally-crack-natures-most-common-chemical-bond/ Scientists finally crack nature’s most common chemical bond

https://phys.org/news/2023-12-catalyst-electronically-ch-functionalization.html

The Chirik Lab at Princeton has developed a cobalt-based catalyst that enables electronically controlled C–H functionalization, allowing for precise borylation in fluoroarenes without the need for directing groups. The catalyst offers potential applications in pharmaceutical and materials synthesis by expanding the toolkit for site-selective modifications.

2.5 M butyl lithium was added to a solution of furan at -78 deg Celsius under inert atmosphere. The reaction mixture was stirred at room temperature for 1 h. The reaction mixture was cooled to -78 deg Celsius and 43 was added. Then NBS was added. The reaction was warmed to room temperature and 10 mL of water was added. Extraction with ethyl acetate and followed by vacuum evaporation afforded a residue. This was purified by silica gel column chromatography to give 48 as a colorless oil.

Copper-Catalyzed Oxidation: To a premixed 2.0 M NaOH and 30% hydrogen peroxide and 15 was added in THF at 0 deg Celsius. The mixture was stirred at room temperature for 11 hours. 1.0 M aqueous hydrochloric acid was added and reaction mixture was extracted with ethyl acetate. The organic layer was washed with brine. Volatiles were evaporated with rotary evaporator and the residue was purified by silica gel column chromatography. 45 was obtained as a yellow solid.

Suzuki Coupling Reaction: 15, boronic acid, potassium phosphate, Pd(dppf)Cl2 and dioxane were added to a vial in a glove box. Then, the vial was removed from the glove box and water was added. The reaction mixture was heated to 100 deg Celsius for 2.5 hours. Volatiles were rotary evaporated and the residue was purified by silica gel column chromatography to give 37 as a colorless oil.

Deboronation and Deuterium Exchange: To a reaction vial, 15, [Ir(cod)OMe]2 and THF were added. The vial was sealed, removed out of the dry box and D2O was syringed. The reaction mixture was heated to 80 deg Celsius for ~3 h. The volatiles were removed by rotary evaporator and the residue was purified by column chromatography. 39 was obtained as a colorless oil.

To a reaction vial, cyclopropane carboxylate, B2Pin2, 6.3 micromol of [Ir(cod)(OMe)]2, 2-mphen and cyclooctane (solvent) were added. The reaction mixture was heated at 100 degrees Celsius for 20 h. The product mixture was purified by silica gel column chromatography. CH2Br2 was added as the internal standard and the product was characetrized by H-NMR spectroscopy

Diisopropylbenzene, B2PIn2, [Ir(cod)(OMe)]2, 2.5 mg of 2-mphen and cyclooctane were added to a reaction vial. The reaction mixture was heated to 100 deg Celsius, cooled and then stirred for 20 h under inert atmosphere. The reaction progress was monitored with GC-MS. Crude product was purified by silica gel column chromatography.

Metallophotoredox Reaction: In a glove-box, 4,4’-di-tert-butyl-2-2`-bipyridine and NiCl2.DME were added to a reaction vial, followed by addition of THF. The mixture was heated on a heating plate for 10 min. The vial was taken back into the glove-box, and the volatile materials were removed, followed by addition of Ir[dFCF3ppy]2(bpy)PF6, 4-bromobenzonitrile, Cs2CO3, potassium triflluoroborate and dioxane. The vial was capped and stirred under irridation of a 34 W blue LED lamp for 48 h. The crude reaction mixture was extracted with ethyl acetate. The resulting solution was concentrated under reduced pressure, and the residue was purified by column chromatography to give the product 52 as a colorless oil.

0.250 mol of the substrate, 3 equivalents of B2Pin2, 6.3 micromol of [Ir(cod)(OMe)]2, 13 micromol of 2-mphen and 200 microliter of cycloctane were added to a vial. The reaction mixture was heated to 100 degrees Celsius for 20 hours. Product was purified by column chromatography and characterized by proton NMR spectroscopy.

Carbocycles underwent borylation at the most accessible bond which is the bond with least steric hindrance. The secondary C-H bond was found to undergo borylation.

Heat was applied outside of dry box in this procedure. Then, the reaction vial is taken back into the glove box for further manipulations.

To a vial, an alcohol of interest was added inside a dry box. This was followed by 1.3 equivalents of HBPin and stirred for ~ 10 minutes to convert the alcohol to the borate ester. The vial was fitted with a cap and heated to 100 degrees Celsius outside the dry box. The vial was cooled and then 2.5 mol % of [Ir(cod)(OMe)]2, B2Pin2 and cyclooctane (solvent) were added under inert conditions. Heated to 80 degree Celsius (outside dry box) to activate the catalyst. Cooled to room temperature and charged with remaining B2Pin2 and more cyclooctane under inert conditions. Reaction mixture was stirred for 20 hours. CH2Br2 was added as an internal standard. Product was analyzed by proton NMR spectroscopy.

In a nitrogen filled glove box, a vial was charged with (MsSH)IrBPin3, a ligand, B2Pin2 (bis-pinacolatodiboron) and THF. Ligands are phenanthroline derived. Dodecane was used as the internal standard. The reaction vial was sealed with a Teflon cap. The mixture was heated to 100 degrees Celsius. Reaction was monitored by GC.

The same reaction was repeated replacing THF with diethyl ether.

The ligands used are 2-methylphananthroline (mphen), 2,9-dimethylphenanthroline (2,9-dmphen) and 3,4,7,8-tetramethylphanathroline (tmphen).

Borylations of heterocycles occured at C-H bonds closer to the heteroatom.

Acyl groups attached to the nitrogen atom are derived from non-aromatic carbon chains

Although several studies were carried out, the exact reason for the high reactivity of m-phen ligand is unclear. However, it can be concluded that the change in the methyl goup leads to the higher activity of the catalyst in borylation.

Borylation of primary C-H bond is irreversible leading to exclusivity in the product formed.

Borylation enabled placement of bromine atom at the strogest C-H bond instead of the weaker C-H bond that is typically observed.

Exclusive borylation occurred at the position beta to nitrogen.

Reaction preferentially occurred at the equatorial C-H over the axial C-H bond because reaction at the equatorial C-H bond is irreversible whereas the reaction at the axial C-H bond occurs but is reversible.

to key concepts

only shared by explicit invite

no need for server

built for customization

Students learn best when they are active participants, constructing new knowledge rather than passively receiving information. Why It Matters: Learning becomes more meaningful when students are encouraged to explore, reflect, and build connections to what they already know.

Self-reflection: Teachers develop the ability to reflect on their own practice and make adjustments independently.

Clinical supervision is a powerful tool for promoting effective teaching by focusing on growth through observation and reflection. When implemented with trust and consistency, it helps teachers build the skills needed to enhance student learning and achieve their instructional goals. The collaborative nature of the process encourages ongoing self-improvement and strengthens the partnership between teachers and supervisors.

This is a very big deal. The mentor needs to remember that this is the teacher's space and to be very respectful when being in that space.

argument

argument

DXOS

https://hyp.is/3sQOPuHyEe6_fLPUjKK-Vw/dxos.org/

Trexler's brains exhaustive on Climata Change

pinterestish

Plex magic

Plex format

Fellowship of the Link

Chris Aldrich

Love this scale for measuring student progress. I don't think it's linear either. I think there are times where teachers are in and out of the continuum depending on new content, etc.

I feel like I definitely fall into filter bubbles, and I try to listen to other people's points of view. Sometimes I agree with what they say and other times I don't. The part I find annoying is once you open yourself up to hearing the other side you then get bombarded with that propaganda and it immediately pushes me back to the other side. there needs to be a slower filter.

A telling story

This right here confuses me and terrifies and somehow comforts me at the same time. This "feature " or whatever it is makes most people uncomfortable and paranoid. I understand that it is a program but I think a lot of people think its a team of people listening in on their life and making them chose things based off of what the listener wants. It's odd and eerie.

Argument

Problem??/ end of beginning

Problem?

should schools be rolling out zero tolerance policies without full consideration of how they might contradict with their "diversity and inclusion" related policies, too?

Is full, complete tolerance and acceptance even possible in schools, if when in the context of making general safety measures, it could lead to contradicting values amongst differing beliefs, ideaologies and faith practices of students and staff?

Is this even achieveable without any form of discrimination?

Is discrimination inherently bad?

And what about the kinds of restrictions to other practicing faiths, where certain symbols and/or expressions of the faith could be deemed inappropriate for a public school setting with other students of varying faiths and value sets?

There are also other ways that Sikhs can express their faith through this specific symbol, without carrying a concealed weapon in public spaces. (ie. decorative, mini versions of the kirpan, kirpans made of wood or plastic instead of metal, focusing on the VALUES that the symbol represents instead of the weapon itself)

school admin learned about a sikh student wearing religious attire - what's kirpan?

• ceremonial dagger in the sikh religion
• symbol that's very important to their religious faith, that represents their commitment to the faith, but ALSO their commitment to PROTECTING and DEFENDING the weak, and upholding justice
• it's a SYMBOL, not meant to be used in the traditional sense
• only to be used for defense in the case of injustice (but who decides what is just and what is not, and how do you measure when and how those injustices are to be handled in response to them? Does this practice of taking matters of justice and injustice into anyone's hands align with the practices of the school measures in dealing with escalations of injustice? And what about simple matters of religious freedom in schools? Is that enough to protect and defend the entire ownership of the weapon altogether, nevermind it's implications? should this be an opportunity for the school administrator to learn more about the religion to be better informed about how they make their policies, especially if within those policies, freedom of religion is included?

MLE are not in the bayesian tradition

what is this mixing time ?

This page sold me on clay bricks; they are easier to build with, and provide better strength, and insulation, once construction is completed. These benefits outweigh the increased cost, for me.

You don't want your bricks to absorb water.

What does he mean while Blore Leave by himself？ Was Lambard implying Blore’s death？

In the previous chapters, Mr. Justice Wargrave acted suspicious, but it turned out that he died.

Scare factors played a huge part in the entire war.

Is this an example of another proxy war?

This is interesting.

How did the people feel about this????

Did the communism scare the people as badly as it scared he US and Uk governments?

I love this section. Allowing teachers to grapple with their thoughts and practice is giving them the freedom to come to their own conclusions and therefore master their craft.

I'm noticing that there are a few differences in philosophies regarding what children can and can't do. It's a mindset really. The approach that I've taken is one where I mention the difference in our thinking and then ground that in child development or the assessment tool we utilize.

I am working on honing in on being curious and asking the right questions to provoke thought. In my role, I'm often in the position to 'have all the answers' and I am carefully moving away from that.

because theyre still considered objects

Author response:

The following is the authors’ response to the original reviews.

A summary of changes

(1) Line 93: “positive effect” to “positive contribution”, as suggested by reviewer 2.

(2) Line 147-148: the null hypothesis to test “equal interspecific and intraspecific interactions”, as indicated by reviewers 2 and 4.

(3) Lines 155-162: removed to reduce duplication with the additive partitioning, as suggested by reviewer 2.

(4) Lines 186-188: added “the estimated competitive growth response would also include the effects of density-dependent pests, pathogens, or microclimates”, as suggested by reviewer 3.  

(5) Lines 219-222: added “The community positive effect can be further partitioned by mechanisms of positive interactions (resource partitioning and facilitation), and facilitative effect can be classified as mutualism (+/+), commensalism (+/0), or parasitic (+/–) based on species specific assessments”.  

(6) Lines 377-386: added options for determining maximum competitive growth response in some extreme scenarios of species mixtures.

(7) Figure 1: modified to show the variations of competitive growth response with relative competitive ability from minimum (null expectation) to maximum (competitive exclusion).    

A summary of four reviewers’ questions and authors’ response

(1) A summary of authors’ responses. Reviewers did not seem to understand our work. They indicated that our model is inadequate for hypothesis testing. The fact is, as we note below, that our model allows for more hypothesis testing than the additive partitioning model. They suggested that one of our model components, the competitive growth response, needs to be further partitioned. However, this term represents only the competition effect and can not be split any further. Reviewers criticized us for misunderstanding the additive components while they suggested the same logic to test some intuitive ideas. They did not seem to know that the effects of competitive interactions vary with assessment methods, which differ between competition and biodiversity research. Our work seeks to harmonise definitions between these two fields and bridge the gap. The reviewers acknowledged that the additive components (i.e., the selection effect and complementarity effect) do not have clear biological meanings; however, they did not acknowledge that the additive components are used extensively for determining mechanisms of species interactions in biodiversity research. There is hardly any research that uses the additive partitioning model without linking the additive components to specific mechanisms of species interactions (i.e., positive SE to competition and positive CE to positive interactions).

(2) Additive partitioning and underlying mechanisms. Some reviewers acknowledged that additive partitioning is not meant for determining mechanisms of species interactions and therefore argued that the additive partitioning should not be criticized for lack of biological meanings with the additive components. However, they insisted that additive partitioning is useful in quantifying net biodiversity effects against the null hypothesis that there is no difference between intraspecific and interspecific interactions or testing the idea that “niche complementarity mitigates competition” or “competitively superior species dominate mixtures”. Are these views contradictory each other? How can the additive partitioning that is not designed for determining mechanisms of species interactions provide meaningful explanations for outputs of species interactions, e.g., “niche complementarity mitigates competition” or “competitively superior species dominate mixtures”?

Reviewers did not seem to realize that these ideas are equivalent to the suggestions that CE represents for the effects of positive interactions and SE for the effects of competitive interactions, that the quantification of net biodiversity effects does not require the two additive components, and that the null hypothesis exists long before the additive partitioning (see de Wit, 1960, de Wit et al., 1966). It is generally agreed that CE and SE result from mathematical calculations and do not have clear biological meanings in terms of linkages to specific mechanisms of species interactions responsible for observed net biodiversity effects or changes in ecosystem function (Loreau and Hector, 2012; Bourrat et al., 2023). Calling some mixed effects of species interactions as mechanisms (e.g., CE and SE) is misleading.        

Model structure: incomplete or inadequate for hypothesis testing. Other than positive, negative, and competition interactions, two reviewers wanted to have more specific interactions such as microclimate amelioration and negative feedback from species-specific pests and pathogens. The determination of these specific mechanisms requires more investigations and cannot be simply made through partitioning growth and yield data. However, the effects of these interactions will be captured in our definition of species interactions.  Reviewers did not seem to know that the additive partitioning would also not allow identifying these specific positive species interactions.

Inspired by the mathematical form of additive partitioning, two reviewers suggested that our model (presumably equation 4) is incomplete and the second term, i.e., competitive growth response needs to be further explored or partitioned. The second term represents deviations from the null expectation, due to species differences in growth and competitive ability or competition effect. We do not know why and how this term can be further partitioned and what any subcomponents would mean.   

Our competitive partitioning model is based on two hypotheses: first, the null hypothesis to test the equivalence of interspecific and intraspecific interactions. This hypothesis is the same as the additive partitioning model. Second, the competitive hypothesis, which tests the dominance of positive or negative species interactions in a community. Thus, our model allows for more hypothesis testing than the current additive partitioning model.     

(3) Types of species interactions. We follow the definition of species interactions generally used in biodiversity research (see Loreau and Hector, 2001), i.e., positive interactions (or complementarity) include resource partitioning and facilitation, negative interactions include interference competition, and competitive interactions include resource competition. One reviewer suggested that resource partitioning is byproduct of competition and should not be part of positive species interactions, which may be true for long-term evolution of species co-existence but not for biodiversity experiments of decade duration at most. Two reviewers suggested that positive interactions should also include microclimate amelioration or negative feedback from species-specific pests and pathogens. We agree and these are included in our definition. 

(4) Significance of partial density monocultures. We used partial and full density monocultures and species competitive ability to determine what species can possibly achieve in mixture under the competitive hypothesis that constituent species share an identical niche but differ in growth and competitive ability. We did not use partial monocultures to test the effects of density on biodiversity effects. As with the additive partitioning, the competitive partitioning model is not designed for comparing yields across different densities. We added at lines 186-188 to indicate that the estimated competitive growth response would also include the effects of density-dependent pests, pathogens, or microclimates.  

Similarly, we do not use the partial density monoculture to  supplant the replacement series design. Partial density monocultures only supplement the “replacement series” design that does not provides estimates of facilitative effects and competitive growth responses that would occur in mixtures. It is crucial to know that one experimental approach is simply not enough for determining underlying mechanisms of species interactions responsible for changes in ecosystem function.  

(5) Competition effect in competition and biodiversity research. Due to different methods used, competition effect in competition research has different ecological meanings from that in biodiversity research. In competition research, species performance in mixture are compared with their partial density monocultures and therefore competition effect is generally negative, as suggested by reviewer 4. In biodiversity research, comparison is between mixture and full density monocultures. The resulting competition effect can be positive or negative for both individual species and community productivity defined by species composition and full density monoculture yields.     

Therefore, we cannot use the results of competition research based on additive series design to describe effects of competitive interactions on ecosystem productivity based replacement series design.

Reviewer #1 (Public Review):

[Editors' note: this is an overall synthesis from the Reviewing Editor in consultation with the reviewers.]

The three reviews expand our critique of this manuscript in some depth and complementary directions. These can be synthesized in the following main points (we point out that there is quite a bit more that could be written about the flaws with this study; however, time constraints prevented us from further elaborating on the issues we see):

(1) It is unclear what the authors want to do.

As indicate by the title, our objective is to “partition changes in ecosystem productivity by effects of species interactions”, i.e., partitioning net biodiversity effects estimated from the null expectation into components associated with positive, negative, or competition interspecific interactions.

It seems their main point is that the large BEF literature and especially biodiversity experiments overstate the occurrence of positive biodiversity effects because some of these can result from competition.

We demonstrated through ecological theories and simulation/experiment data that competition is a major source of the net biodiversity effects estimated with additive partitioning model. We know that competition effect varies with mixture attributes. Future research will determine average effect of competitive interactions on biodiversity effects in large BEF literature.   

Because reduced interspecific relative to intraspecific competition in mixture is sufficient to produce positive effects in mixtures (if interspecific competition = 0 then RYT = S, where S is species richness in mixture -- this according to the reciprocal yield law = law of constant final yield), they have a problem accepting NE > 0 as true biodiversity effect (see additive partitioning method of Loreau & Hector 2001 cited in manuscript).

We have no problem to accept NE>0 as true positive biodiversity effect. However, NE>0 can also result from competitive interactions based on the null expectation and needs to be partitioned by effects of species interactions.

(2) The authors' next claim, without justification, that additive partitioning of NE is flawed and theoretically and biologically meaningless.

The additive partitioning model is based on Covariance equation (or Price equation) that has nothing to do with biodiversity partitioning (Bourrat et al., 2023). Biological meaning was arbitrarily assigned to CE and SE. We made clear that the additive partitioning model is mathematically sound but does not have biological meanings that it has been used for.   

They misinterpret the CE component as biological niche partitioning and the SE component as biological dominance.

We did not. Loreau and Hector (2001) clearly indicated positive CE for positive interactions and positive SE for competitive interactions, which is generally what has been used for in the last twenty years.

They do not seem to accept that the additive partitioning is a logically and mathematically sound derivation from basic principles that cannot be contested.

We do not have problem with mathematical form of additive partitioning but only oppose ecological meanings assigned to CE and SE, simply because CE and SE both result from all species interactions (see Loreau and Hector, 2001; Bourrat et al., 2023). The reviewer seemed to have a contradictory thinking that the additive components are biologically meaningless but derived from biological basic principles.       

(3) The authors go on to introduce a method to calculate species-level overyielding (RY > 1/S in replacement series experiments) as a competitive growth response and multiply this with the species monoculture biomass relative to the maximum to obtain competitive expectation. This method is based on resource competition and the idea that resource uptake is fully converted into biomass (instead of e.g. investing it in allelopathic chemical production).

Correct, but we did not assume “resource uptake is fully converted into biomass”.

(4) It is unclear which experiments should be done, i.e. are partial-density monocultures planted or simply calculated from full-density monocultures? At what time are monocultures evaluated? The framework suggests that monocultures must have the full potential to develop, but in experiments, they are often performing very poorly, at least after some time. I assume in such cases the monocultures could not be used.

Both partial and full density monocultures are needed, along with mixtures to separate NE by species interactions. Calculating competitive growth responses from density-size relationships can be an alternative, given the lack of partial density monocultures in current biodiversity experiments, but is not preferred.

Similar to additive partitioning, our model can (and should) be applied to all developmental stages of an experiment to examine how interactions evolve through time.   

(5) There are many reasons why the ideal case of only resource competition playing a role is unrealistic. This excludes enemies but also differential conversion factors of resources into biomass and antagonistic or facilitative effects. Because there are so many potential reasons for deviations from the null model of only resource competition, a deviation from the null model does not allow conclusions about underlying mechanisms.

The competitive expectation is only a hypothesis, just as the null expectation. The difference between competitive and null expectations represents a competitive effect resulting from species differences in growth and competitive ability, while the deviation of observed yields from the competitive expectation indicates positive or negative effect (see lines 201-219).

Furthermore, this is not a systematically developed partitioning, but some rather empirical ad hoc formulation of a first term that is thought to approximate competitive effects as understood by the authors (but again, there already are problems here). The second residual term is not investigated. For a proper partitioning approach, one would have to decompose overyielding into two (or more) terms and demonstrate (algebraically) that under some reasonable definitions of competitive and non-competitive interactions, these end up driving the respective terms.

The first term represents the null expectation assuming equal interspecific and intraspecific interactions, i.e., absence of positive, negative, and competition effects. The second residual term represents competition effect, due to species differences in growth and competitive ability. The meaning of second residual term is clear and does not need to be further partitioned or investigated.

In fact, our competitive partitioning also has several components including null expectation, competitive growth response, and observed yield, plus partial density monocultures for species assessment, or null expectations, competitive expectations, and observed yields for community level assessment, although different from the additive partitioning.

(6) Using a simplistic simulation to test the method is insufficient. For example, I do not see how the simulation includes a mechanism that could create CE in additive partitioning if all species would have the same monoculture yield. Similarly, they do not include mechanisms of enemies or antagonistic interactions (e.g. allelopathy).

The simulation model we used is developed from real world data and can only do what are available in the model in terms of species and their growth under different conditions. We can not go beyond data limitation. The model is empirical and has been shown to accurately estimate yield in the aspen-spruce forest condition. We would also note that we do also use experimental data (Table 2).  

(7) The authors do not cite relevant literature regarding density x biodiversity experiments, competition experiments, replacement-series experiments, density-yield experiments, additive partitioning, facilitation, and so on.

We cited literature relevant to biodiversity partitioning since we are not aiming to cover everything. The reviewer may not be aware that most of the research areas listed are actually included in our work, such as additive and replacement-series experiment designs, additive partitioning, facilitation, competition studies, and density-yield relationships. Our competitive model partitioning is based on biological principles, while the additive partitioning model is based only on a mathematical equation.   

Overall, this manuscript does not lead further from what we have already elaborated in the broad field of BEF and competition studies and rather blurs our understanding of the topic.

The results of competition studies based on additive series design are not really used in the broad field of BEF based on replacement series design. The effects of competitive interactions on BEF are never clearly defined using the results of competition studies. Our work is filling that gap.  

Reviewer #2 (Public Review):

This manuscript is motivated by the question of what mechanisms cause overyielding in mixed-species communities relative to the corresponding monocultures. This is an important and timely question, given that the ultimate biological reasons for such biodiversity effects are not fully understood.

As a starting point, the authors discuss the so-called "additive partitioning" (AP) method proposed by Loreau & Hector in 2001. The AP is the result of a mathematical rearrangement of the definition of overyielding, written in terms of relative yields (RY) of species in mixtures relative to monocultures. One term, the so-called complementarity effect (CE), is proportional to the average RY deviations from the null expectations that plants of both species "do the same" in monocultures and mixtures. The other term, the selection effect (SE), captures how these RY deviations are related to monoculture productivity. Overall, CE measures whether relative biomass gains differ from zero when averaged across all community members, and SE, whether the "relative advantage" species have in the mixture, is related to their productivity. In extreme cases, when all species benefit, CE becomes positive. When large species have large relative productivity increases, SE becomes positive. This is intuitively compatible with the idea that niche complementarity mitigates competition (CE>0), or that competitively superior species dominate mixtures and thereby driver overyielding (SE>0).

The reviewer needs to know that these ideas are based on the same logic that positive CE represents the effects of positive interactions and positive SE represents the effects of competitive interactions. CE>0 or SE>0 can result from many different scenarios of species interactions, not necessarily “niche complementarity mitigates competition” or “competitively superior species dominate mixtures”. CE>0 and SE>0 can occur alone or together. We simply can not tell underlying mechanisms of overyielding from mathematical calculations (CE and SE), as suggested by this reviewer later.

The reviewer criticizes us while using the same logic themselves.

However, it is very important to understand that CE and SE capture the "statistical structure" of RY that underlies overyielding. Specifically, CE and SE are not the ultimate biological mechanisms that drive overyielding, and never were meant to be. CE also does not describe niche complementarity. Interpreting CE and SE as directly quantifying niche complementarity or resource competition, is simply wrong, although it sometimes is done. The criticism of the AP method thus in large part seems unwarranted. The alternative methods the authors discuss (lines 108-123) are based on very similar principles.

The reviewer actually supports our point. However, CE and SE have been largely used as biological mechanisms, positive CE as the results of complementary interactions and positive SE as the results of competitive interactions (see Loreau and Hector, 2001).  

We do not have problem with the "statistical structure" of AP; it is simply a covariance equation. It is important to know that CE and SE do not provide additional information on overyielding than NE in terms of underlying mechanisms of species interactions. Any attempt to investigate mechanism of overyielding with CE or SE can easily go wrong.

Our competitive partitioning model incorporates effects of competitive interactions into the conventional null expectation and allows for separating different effects of species interactions. In comparison, the additive partitioning model does not have this capacity, not even designed for this purpose, as suggested by this and other reviewers.         

The authors now set out to develop a method that aims at linking response patterns to "more true" biological mechanisms.

Assuming that "competitive dominance" is key to understanding mixture productivity, because "competitive interactions are the predominant type of interspecific relationships in plants", the authors introduce "partial density" monocultures, i.e. monocultures that have the same planting density for a species as in a mixture. The idea is that using these partial density monocultures as a reference would allow for isolating the effect of competition by the surrounding "species matrix".

Correct.

The authors argue that "To separate effects of competitive interactions from those of other species interactions, we would need the hypothesis that constituent species share an identical niche but differ in growth and competitive ability (i.e., absence of positive/negative interactions)." - I think the term interaction is not correctly used here, because clearly competition is an interaction, but the point made here is that this would be a zero-sum game.

We did not say that competition is not an interaction; we only want to separate the effect of competition from those of other species interactions.

The authors use the ratio of productivity of partial density and full-density monocultures, divided by planting density, as a measure of "competitive growth response" (abbreviated as MG). This is the extra growth a plant individual produces when intraspecific competition is reduced.

Correct.

We added at lines 377-386 to discuss options to determine MG in some uncommon scenarios of species mixtures.

Here, I see two issues: first, this rests on the assumption that there is only "one mode" of competition if two species use the same resources, which may not be true, because intraspecific and interspecific competition may differ. Of course, one can argue that then somehow "niches" are different, but such a niche definition would be very broad and go beyond the "resource set" perspective the authors adopt. Second, this value will heavily depend on timing and the relationship between maximum initial growth rates and competitive abilities at high stand densities.

First, the "competitive effect" focusses on resource competition and other forms of competition (presumably interference competition) are included in the negative interactions.

Second, competitive growth response varies over time and with density, and so do NE, CE, SE, and interspecific interactions.

The authors then progress to define relative competitive ability (RC), and this time simply uses monoculture biomass as a measure of competitive ability. To express this biomass in a standardized way, they express it as different from the mean of the other species and then divide by the maximum monoculture biomass of all species.

I have two concerns here: first, if competitive ability is the capability of a species to preempt resources from a pool also accessed by another species, as the authors argued before, then this seems wrong because one would expect that a species can simply be more productive because it has a broader niche space that it exploits. This contradicts the very narrow perspective on competitive ability the authors have adopted. This also is difficult to reconcile with the idea that specialist species with a narrow niche would outcompete generalist species with a broad niche. Second, I am concerned by the mathematical form. Standardizing by the maximum makes the scaling dependent on a single value.

First, growth conditions are controlled in biodiversity experiments, i.e., both monocultures and mixtures are the same in resource space. Species do not have opportunity to exploit resources outside experimental area. For example, if less productive species on normal soils outperform more competitive species on saline/alkaline soil, these “less productive species” are considered “more productive”.    

Second, as discussed in our paper (lines 367-376; Figure 1), more research is needed to determine relationships between species traits (biomass or height) and relative competitive ability. By then, scaling by the maximum would not be needed. There has been quite a lot of research on such relationships; we should leave this to subject experts to determine what would be mostly appropriate for species studied.

As a final step, the authors calculate a "competitive expectation" for a species' biomass in the mixture, by scaling deviations from the expected yield by the product MG ⨯ RC. This would mean a species does better in a mixture when (1) it benefits most from a conspecific density reduction, and (2) has a relatively high biomass.

Put simply, the assumption would be that if a species is productive in monoculture (high RC), it effectively does not "see" the competitors and then grows like it would be the sole species in the community, i.e. like in the partial density monoculture.

Correct, if species competitive ability differs substantially, the more competitive species in the mixture would grow like partial density monoculture. This extra growth should not be treated as sources of positive biodiversity effects, simply because it does not result from positive species interactions.   

Overall, I am not very convinced by the proposed method.

(1) The proposed method seems not very systematic but rather "ad hoc". It also is much less a partitioning method than the AP method because the other term is simply the difference. It would be good if the authors investigated the mathematical form of this remainder and explored its properties.. when does complementarity occur? Would it capture complementarity and facilitation?

AP is, by no means, systematic. Remember, AP is based on covariance equation (or Price equation) that has nothing to do with species interactions, other than nice-looking mathematical form (Bourrat et al., 2023). Ecological meanings are subjectively given to CE and SE. Therefore,  CE and SE reflect what we call them, not what they really mean.    

The remainder measures deviations from the null expectation, due to only competition effect, and can not be partitioned any further. The remainder would be positive for more competitive species and negative for less competitive species in mixture relative to their full density monoculture. The deviation of observed yields from competitive expectations indicates dominance of positive or negative species interactions. All these are clearly outlined at lines 201-221.   

(2) The justification for the calculation of MG and RC does not seem to follow the very strict assumptions of what competition (in the absence of complementarity) is. See my specific comments above.

We do not see why not.

(3) Overall, the manuscript is hard to read. This is in part a problem of terminology and presentation, and it would be good to use more systematic terms for "response patterns" and "biological mechanisms".

To help understand the variations of competitive growth response with relative competitive ability, the x axis of Figure 1 is labelled with null expectation, competitive expectation, and competitive exclusion from minimum to maximum deviation of competitive ability from community average.

We have followed terms used in biodiversity partitioning and changing terms can be confusing.  

Examples:

- on line 30, the authors write that CE is used to measure "positive" interactions and SE to measure "competitive interactions", and later name "positive" and "negative" interactions "mechanisms of species interactions". Here the authors first use "positive interaction" as any type of effect that results in a community-level biomass gain, but then they use "interaction" with reference to specific biological mechanisms (e.g. one species might attract a parasite that infests another species, which in turn may cause further changes that modify the growth of the first and other species).

There are some differences in meaning, but that is what CE and SE have been generally used for. Using different terms can be confusing and does not help understanding the problems with AP.

- on line 70, the authors state that "positive interaction" increases productivity relative to the null expectation, but it is clear that an interaction can have "negative" consequences for one interaction partner and "positive" ones for the other. Therefore, "positive" and "negative" interactions, when defined in this way, cannot be directly linked to "resource partitioning" and "facilitation", and "species interference" as the authors do. Also, these categories of mechanisms are still simple. For example, how do biotic interactions with enemies classify, see above?

We are explaining effects of competitive interactions on species yield, and ultimately on community yield that can be linked to “resource partitioning" and "facilitation", and "species interference".

More specific species interactions require detailed biological investigation and cannot be determined through partitioning of biomass production.  

- line 145: "Under the null hypothesis, species in the mixture are assumed to be competitively equivalent (i.e., absence of interspecific interactions)". This is wrong. The assumption is that there are interspecific interactions, but that these are the same as the intraspecific ones. Weirdly, what follows is a description of the AP method, which does not belong here. This paragraph would better be moved to the introduction where the AP method is mentioned. Or omitted, since it is basically a repetition of the original Loreau & Hector paper.

As suggested, “absence of interspecific interactions” was replaced with “equal interspecific and intraspecific interactions”.

We have removed lines 155-162 to reduce duplication. However, our method is based on null expectation that needs to be introduced, despite it is part of AP.

Other points:

- line 66: community productivity, not ecosystem productivity.

Both community productivity and ecosystem productivity are used in biodiversity research, although meaning can be slightly different. Comparatively, ecosystem productivity is more common.

- line 68: community average responses are with respect to relative yields - this is important!

- line 64: what are "species effects of species interactions"?

We searched and did not find “species effects of species interactions”.

- line 90: here "competitive" and "productive" are mixed up, and it is important to state that "suffers more" refers to relative changes, not yield changes.

It, in fact, refers to yield changes. For example, less productive species, at active growth, are more responsive to changes in competition, while more productive species, at inactive growth (i.e., aging), are less responsive to changes in competition.   

- line 92: "positive effect of competitive dominance": I don't understand what is meant here.

The phrase was modified to “positive contribution of competitive dominance to ecosystem productivity based on the null expectation”.

Reviewer #3 (Public Review):

Summary:

This manuscript by Tao et al. reports on an effort to better specify the underlying interactions driving the effects of biodiversity on productivity in biodiversity experiments. The authors are especially concerned with the potential for competitive interactions to drive positive biodiversity-ecosystem functioning relationships by driving down the biomass of subdominant species. The authors suggest a new partitioning schema that utilizes a suite of partial density treatments to capture so-called competitive ability. While I agree with the authors that understanding the underlying drivers of biodiversity-ecosystem functioning relationships is valuable - I am unsure of the added value of this specific approach for several reasons.

Strengths:

I can find a lot of value in endeavouring to improve our understanding of how biodiversity-ecosystem functioning relationships arise. I agree with the authors that competition is not well integrated into the complementarity and selection effect and interrogating this is important.

Weaknesses:

(1) The authors start the introduction very narrowly and do not make clear why it is so important to understand the underlying mechanisms driving biodiversity-ecosystem functioning relationships until the end of the discussion.

There are different ways to start introduction; we believe that starting with the problems of the current approach is the most effective for outlining the study’s objective.  

(2) The authors criticize the existing framework for only incorporating positive interactions but this is an oversimplification of the existing framework in several ways:

We did not criticize the existing framework for only incorporating positive interactions. We criticize the existing framework, because it is not based on mechanisms of species interactions, but is extensively used to determine underlying mechanisms driving biodiversity-ecosystem functioning relationships.

a. The existing partitioning scheme incorporates resource partitioning which is an effect of competition.

Resource partitioning means that species utilize resources differently, while competition means species use the same resources. “resource partitioning is an effect of competition” is not true in biodiversity experiments that are often short in duration and controlled in conditions.  

b. The authors neglect the potential that negative feedback from species-specific pests and pathogens can also drive positive BEF and complementarity effects but is not a positive interaction, necessarily. This is discussed in Schnitzer et al. 2011, Maron et al. 2011, Hendriks et al. 2013, Barry et al. 2019, etc.

We did not. The feedback effect will be reflected in the differences between observed yields and competitive expectations if species in mixtures have different pests and pathogens relative to monocultures. The additive partitioning does not identify these feedback effects either.

c. Hector and Loreau (and many of the other citations listed) do not limit competition to SE because resource partitioning is a byproduct of competition.

Positive SE has been largely interpreted as the result of competition including Hector and Loreau (2001) and many others. It needs to be clear that neither of the additive components can be linked to specific mechanisms of species interactions. 

Does “resource partitioning is a byproduct of competition” mean that species change their niche to avoid competition? If this is what the reviewer means, it may occur through long-term evolution, but not in short-term biodiversity experiments. Hector and Loreau (2001) clearly indicated that their complementarity effect includes both resource partitioning and facilitation.   

(3) It is unclear how this new measure relates to the selection effect, in particular. I would suggest that the authors add a conceptual figure that shows some scenarios in which this metric would give a different answer than the traditional additive partition. The example that the authors use where a dominant species increases in biomass and the amount that it increases in biomass is greater than the amount of loss from it outcompeting a subdominant species is a general example often used for a selection effect when exactly would you see a difference between the two?:<br /> a. Just a note - I do think you should see a difference between the two if the species suffers from strong intraspecific competition and has therefore low monoculture biomass but this would tend to also be a very low-density monoculture in practice so there would potentially be little difference between a low density and high-density monoculture because the individuals in a high-density monoculture would die anyway. So I am not sure that in practice you would really see this difference even if partial density plots were incorporated.

Linking new measure to SE or CE would be difficult (see many comparisons in Tables and Figures in our manuscript), as SE and CE are derived from mathematical equation and do not represent specific mechanisms of species interactions (Hector and Loreau 2012; Bourrat et al., 2023).

(4) One of the tricky things about these endeavors is that they often pull on theory from two different subfields and use similar terminology to refer to different things. For example - in competition theory, facilitation often refers to a positive relative interaction index (this seems to be how the authors are interpreting this) while in the BEF world facilitation often refers to a set of concrete physical mechanisms like microclimate amelioration. The truth is that both of these subfields use net effects. The relative interaction index is also a net outcome as is the complementarity effect even if it is only a piece of the net biodiversity effect. Trying to combine these two subfields to come up with a new partitioning mechanism requires interrogating the underlying assumptions of both subfields which I do not see in this paper.

Agree, microclimate amelioration is also part of positive effect and will be reflected in the difference between observed yield and competitive expectation. We can not separate the two mechanisms of positive species interactions without investigating influences of microclimate on growth and yield.

(5) The partial density treatment does not isolate competition in the way that the authors indicate. All of the interactions that the authors discuss are density-dependent including the mechanism that is not discussed (negative feedback from species-specific pests and pathogens). These partial density treatment effects therefore cannot simply be equated to competition as the authors indicate.:

We use partial density monoculture to determine maximum competitive growth response, effect of density-dependent intraspecific interactions, and species competitive ability to determine the level of maximum competitive growth response species can achieve in mixtures. There may be changes in species-specific pests and pathogens from partial to full density monocultures, which will be captured in competitive growth responses of individuals. We added at lines 186-188 to indicate that the maximum competitive growth response estimated would also include the effects of density-dependent pests, pathogens, or microclimates.   

a. Additionally - the authors use mixture biomass as a stand-in for competitive ability in some cases but mixture biomass could also be determined by the degree to which a plant is facilitated in the mixture (for example).

We used monoculture biomass, not mixture biomass, to assess competitive ability

(6) I found the literature citation to be a bit loose. For example, the authors state that the additive partition is used to separate positive interactions from competition (lines 70-76) and cite many papers but several of these (e.g. Barry et al. 2019) explicitly do not say this.

Barry et al. (2019) defined CE as overproduction from monocultures, an effect of positive interactions.  

(7) The natural take-home message from this study is that it would be valuable for biodiversity experiments to include partial density treatments but I have a hard time seeing this as a valuable addition to the field for two reasons:

a. In practice - adding in partial density treatments would not be feasible for the vast majority of experiments which are already often unfeasibly large to maintain.

The reviewer suggested that quantity is more important than quality. Without partial density monocultures no one can separate different effects of species interactions, as suggested by Loreau and Hector, reviewers, and many others that effects of species interactions can not be clearly differentiated with replacement series design. Unreliable scientific findings are not valuable.

b. The density effect would likely only be valuable during the establishment phase of the experiment because species that are strongly limited by intraspecific competition will die in the full-density plots resulting in low-density monocultures. You can see this in many biodiversity experiments after the first years. Even though they are seeded (or rarely planted) at a certain density, the density after several years in many monocultures is quite low.

True. High or low density also depends on individual size; if individuals do not get enough resources, density is high. Therefore, density effect can be strong even as density drops substantially from initial levels.  

Reviewer #4 (Public Review):

Summary:

This manuscript claims to provide a new null hypothesis for testing the effects of biodiversity on ecosystem functioning. It reports that the strength of biodiversity effects changes when this different null hypothesis is used. This main result is rather inevitable. That is, one expects a different answer when using a different approach. The question then becomes whether the manuscript’s null hypothesis is both new and an improvement on the null hypothesis that has been in use in recent decades.

It needs to be clear that we use two hypotheses, null hypothesis that is currently used with AP, and competitive hypothesis that is new with this manuscript. The null hypothesis helps determine changes in ecosystem productivity from all species interactions, while the competitive hypothesis helps partition changes in ecosystem productivity by mechanisms of species interactions, i.e., positive, negative, or competitive interactions.    

Strengths:

In general, I appreciate studies like this that question whether we have been doing it all wrong and I encourage consideration of new approaches.

Weaknesses:

Despite many sweeping critiques of previous studies and bold claims of novelty made throughout the manuscript, I was unable to find new insights. The manuscript fails to place the study in the context of the long history of literature on competition and biodiversity and ecosystem functioning. The Introduction claims the new approach will address deficiencies of previous approaches, but after reading further I see no evidence that it addresses the limitations of previous approaches noted in the Introduction. Furthermore, the manuscript does not reproducibly describe the methods used to produce the results (e.g., in Table 1) and relies on simulations, claiming experimental data are not available when many experiments have already tested these ideas and not found support for them. Finally, it is unclear to me whether rejecting the ‘new’ null hypothesis presented in the manuscript would be of interest to ecologists, agronomists, conservationists, or others. I will elaborate on each of these points below.

First, there are many biodiversity experiments but those with partial density monocultures are rare. We found only one greenhouse experiment. We have to use simulation to illustrate different scenarios of species interactions to demonstrate how our approach works and how different it is from the AP.  

Because of different methods used, the results of long history competition research (generally based on additive series design) cannot be used to define effects of competitive interactions in biodiversity research (generally based on replacement series design). This may be the reason that few competition researchers were cited in Loreau and Hector (2001).

Our approach requires two hypotheses, null and competitive, and the meaning of deviation from these hypotheses are outlined at lines 201-221 for both individual species and community level assessments. Distinguishing changes in ecosystem productivity by species interactions would be of great interest to “ecologists, agronomists, conservationists, or others”.

The critiques of biodiversity experiments and existing additive partitioning methods are overstated, as is the extent to which this new approach addresses its limitations. For example, the critique that current biodiversity experiments cannot reveal the effects of species interactions (e.g., lines 37-39) isn't generally true, but it could be true if stated more specifically. That is, this statement is incorrect as written because comparisons of mixtures, where there are interspecific and intraspecific interactions, with monocultures, where there are only intraspecific interactions, certainly provide information about the effects of species interactions (interspecific interactions). These biodiversity experiments and existing additive partitioning approaches have limits, of course, for identifying the specific types of interactions (e.g., whether mediated by exploitative resource competition, apparent competition, or other types of interactions). However, the approach proposed in this manuscript gets no closer to identifying these specific mechanisms of species interactions. It has no ability to distinguish between resource and apparent competition, for example. Thus, the motivation and framing of the manuscript do not match what it provides. I believe the entire Introduction would need to be rewritten to clarify what gap in knowledge this proposed approach is addressing and what would be gained by filling this knowledge gap.

Our approach helps determine underlying mechanisms of species interactions, i.e., positive (resources partitioning or facilitation), negative, or competitive interactions. I am not sure how much we need to go further in identifying more specific mechanisms. If resource and apparent competition refers to resource and interference competition, our approach can tease apart them.

I recommend that the Introduction instead clarify how this study builds on and goes beyond many decades of literature considering how competition and biodiversity effects depend on density. This large literature is insufficiently addressed in this manuscript. This fails to give credit to previous studies considering these ideas and makes it unclear how this manuscript goes beyond the many previous related studies. For example, see papers and books written by de Wit, Harper, Vandermeer, Connolly, Schmid, and many others. Also, note that many biodiversity experiments have crossed diversity treatments with a density treatment and found no significant effects of density or interactions between density and diversity (e.g., Finn et al. 2013 Journal of Applied Ecology). Thus, claiming that these considerations of density are novel, without giving credit to the enormous number of previous studies considering this, is insufficient.

A misunderstanding here. Our approach is not designed to test density effect. The same density is held across full density monocultures and mixtures. We use partial density monocultures to determine what species may competitively achieve in full density mixture, without positive or negative interspecific interactions.  

Replacement series designs emerged as a consensus for biodiversity experiments because they directly test a relevant null hypothesis. This is not to say that there are no other interesting null hypotheses or study designs, but one must acknowledge that many designs and analyses of biodiversity experiments have already been considered. For example, Schmid et al. reviewed these designs and analyses two decades ago (2002, chapter 6 in Loreau et al. 2002 OUP book) and the overwhelming consensus in recent decades has been to use a replacement series and test the corresponding null hypothesis.

Some wrong impressions. We are not trying to supplant “replacement series” with “additive series”; we use “additive series” designs to supplement “replacement series” design for partitioning changes in ecosystem productivity by mechanisms of species interactions, which would not be possible with “replacement series” design alone, as suggested by many including reviewers.   

It is unclear to me whether rejecting the 'new' null hypothesis presented in the manuscript would be of interest to ecologists, agronomists, conservationists, or others. Most biodiversity experiments and additive partitions have tested and quantified diversity effects against the null hypothesis that there is no difference between intraspecific and interspecific interactions. If there was no less competition and no more facilitation in mixtures than in monocultures, then there would be no positive diversity effects. Rejecting this null hypothesis is relevant when considering coexistence in ecology, overyielding in agronomy, and the consequences of biodiversity loss in conservation (e.g., Vandermeer 1981 Bioscience, Loreau 2010 Princeton Monograph). This manuscript proposes a different null hypothesis and it is not yet clear to me how it would be relevant to any of these ongoing discussions of changes in biodiversity.

Our method begins with the null expectation: that intraspecific and interspecific interactions are equivalent. We then propose the competitive hypothesis as a second non-exclusive hypothesis which tests the dominance of positive or negative specific interactions. As shown by its name, the additive partitioning model has been advocated for partitioning biodiversity effects by some ecological mechanisms (CE and SE). The ecological meaning of deviation from the two hypotheses are outlined at lines 201-221 for both individual species and community level assessments.   

The claim that all previous methods 'are not capable of quantifying changes in ecosystem productivity by species interactions and species or community level' is incorrect. As noted above, all approaches that compare mixtures, where there are interspecific interactions, to monocultures, where there are no species interactions, do this to some extent. By overstating the limitations of previous approaches, the manuscript fails to clearly identify what unique contribution it is offering, and how this builds on and goes beyond previous work.

The reviewer implies that a partial truth equals the whole truth. The same argument can also be applied to the additive partitioning if relative yield total or response ratio provides a kind of comparison between mixture and monocultures. Our statement is correct in the way that previous approaches are not designed to separate changes in ecosystem productivity by species interactions, as indicated by other reviewers. The additive partitioning is built on Price equation (covariance equation) that has never been biologically demonstrated for relevance in biodiversity partitioning (Bourrat et al., 2023).  

We made clear that our work is built on and beyond the null expectation with addition of competitive expectation.

The manuscript relies on simulations because it claims that current experiments are unable to test this, given that they have replacement series designs (lines 128-131). There are, however, dozens of experiments where the replacement series was repeated at multiple densities, which would allow a direct test of these ideas. In fact, these ideas have already been tested in these experiments and density effects were found to be nonsignificant (e.g., Finn et al. 2013).

Out of point. Again, we are not testing density effect. Partial density is used to determine competitive growth responses that species may achieve in mixture based on their relative competitive ability. We used simulations, as partial density monocultures are used only in one experimental study that has been included in our study.  

It seems that the authors are primarily interested in trees planted at a fixed density, with no opportunity for changes in density, and thus only changes in the size of individuals (e.g., Fig. 1). In natural and experimental systems, realized density differs from the initial planted density, and survivorship of seedlings can depend on both intraspecific and interspecific interactions. Thus, the constrained conditions under which these ideas are explored in this manuscript seem narrow and far from the more complex reality where density is not fixed.

We use fixed density only for convenience. In biodiversity experiments, density can increase or decrease over time from initial levels. However, initial density is generally used in evaluation of species interactions. If interest is community productivity, density change does not need to be considered. Again, we are not testing density effects.    

Additional detailed comments:

It is unclear to me which 'effects' are referred to on line 36. For example, are these diversity effects or just effects of competition? What is the response variable?

It means the effect of competitive interactions on productivity and should be clear based on previous sentences.

The usefulness of the approach is overstated on line 52. All partitioning approaches, including the new one proposed here, give the net result of many types of species interactions and thus cannot 'disentangle underlying mechanisms of species interactions.'

Not sure how many types of species interactions the reviewer referred to. If mechanisms of species interactions are grouped in three categories (positive, negative, and competitive) as has been in biodiversity research, our approach can tease them apart.   

The weaknesses of previous approaches are overstated throughout the manuscript, including in lines 60-61. All approaches provide some, but not all insights. Sweeping statements that previous approaches are not effective, without clarifying what they can and can't do, is unhelpful and incorrect. Also, these statements imply that the approach proposed here addresses the limitations of these previous approaches. I don't yet see how it does so.

The weaknesses of previous approaches are not overstated in terms of separating changes in ecosystem productivity by species interactions. As pointed by other reviewers, none of the previous approaches are designed for quantifying changes in ecosystem productivity by species interactions.   

The definitions given for the CE and SE on line 71 are incorrect. Competition affects both terms and CE can be negative or have nothing to do with positive interactions, as noted in many of the papers cited.

We are not trying to define CE and SE but only point out how CE and SE have been generally used in biodiversity research (see recent publication by Feng et al., 2022).

The proposed approach does not address the limitations noted on lines 73 and 74.

It does in terms of sources of net biodiversity effect, whether from positive, negative or competitive interactions.

The definition of positive interactions in lines 77 and 78 seems inconsistent with much of the literature, which instead focuses on facilitation or mutualism, rather than competition when describing positive interactions.

Much of the literature supports our definition (see Loreau and Hector, 2001). In biodiversity research, positive interactions include resource partitioning and facilitation. What we are trying to point out is that competition affects species and community level assessments based on the null expectation and needs to be separated.

Throughout the manuscript, competition is often used interchangeably with resource competition (e.g., line 82) and complementarity is often attributed to resource partitioning (e.g., line 77). This ignores apparent competition and partitioning enemy-free niche space, which has been found to contribute to biodiversity effects in many studies.

If apparent competition refers to interference competition, it is included in negative interaction. Changes in species-specific pests and pathogens in mixture will be captured in positive or negative effects through facilitation or interference.  

In what sense are competitive interactions positive for competitive species (lines 82-83)? By definition, competition is an interaction that has a negative effect. Do you mean that interspecific competition is less than intraspecific competition? I am having a very difficult time following the logic.

I am glad the reviewer raised this question that may confuse many others and has never been clearly discussed. It all depends on how comparison is made. If species performance in mixture are compared with that in partial density monocultures, as is in competition research, competition effect is negative for all species. If comparison is made between mixture and full density monocultures, as is done in biodiversity research, competition effect should be positive for more competitive species and negative for less competitive species, with resources flowing from less to more competitive species in mixture relative to full density monocultures.   

Therefore, the definitions of competitive interactions based on additive series design in competition research cannot be used to describe competitive interactions based on replacement series design in biodiversity research. In biodiversity research, the effects of competitive interactions are never clearly defined at species or community level and mixed up with those of other species interactions.      

Results are asserted on lines 93-95, but I cannot find the methods that produced these results. I am unable to evaluate the work without a repeatable description of the methods.

We have added references on sources of these data.

The description of the null hypothesis in the common additive partitioning approach on lines 145-146 is incorrect. In the null case, it does not assume that there are no interspecific interactions, but rather that interspecific and intraspecific interactions are equivalent.

Correct, changes have been made as suggested.

Recommendations for the authors:

Reviewer #2 (Recommendations For The Authors):

I recommend to:

- re-organize the presentation of the material (see my concerns in the public review section). The manuscript is very difficult to read.

Changes have been made to help with understanding of our approach. Figure 1 was modified to show the variations of competitive growth response with relative competitive ability from minimum (null expectation) to maximum (competitive exclusion).

- explore the mathematical form the the remainder term. It seems important to understand that the remainder capture terms unrelated to competition as defined in the present scope.

The remainder measures deviations from the null expectation, due to species differences in growth and competitive ability or competition effect. The term has clear meaning, positive for more competitive species and negative for less competitive species (lines 202-204), and does not need to be further explored or partitioned. The deviations of observed yields from competitive expectations are outlined in lines 205-221.  

Reviewer #4 (Recommendations For The Authors):

The authors should be sure to include reproducible methods and share any data and code.

Both simulation and experimental data are shared through supplementary tables. Calculations are included in excel spreadsheets and do not require program coding.

eLife Assessment

The authors propose that positive biodiversity-ecosystem functioning relationships found in experiments have been exaggerated because commonly used statistical analyses are flawed. To remedy this, a new type of analysis based on a concept of "partial density monoculture yield" is proposed. However, the presented concept and analysis methods are not reproducibly described, do not appear to be complete, and are inadequate for hypothesis testing. The reviewers found that the authors misinterpret current research in the field and made limited efforts to understand or address the reviewer comments on a previous version of the study.

Reviewer #1 (Public review):

As a starting point, the authors discuss the so-called "additive partitioning" (AP) method proposed by Loreau & Hector in 2001. The AP is the result of a mathematical rearrangement of the definition of overyielding, written in terms of relative yields (RY) of species in mixtures relative to monocultures. One term, the so-called complementarity effect (CE), is proportional to the average RY deviations from the null expectations that plants of both species "do the same" in monocultures and mixtures. The other term, the selection effect (SE), captures how these RY deviations are related to monoculture productivity. Overall, CE measures whether relative biomass gains differ from zero when averaged across all community members, and SE, whether the "relative advantage" species have in the mixture, is related to their productivity. In extreme cases, when all species benefit, CE becomes positive. When large species have large relative productivity increases, SE becomes positive. This is intuitively compatible with the idea that niche complementarity mitigates competition (CE>0), or that competitively superior species dominate mixtures and thereby driver overyielding (SE>0).

However, it is very important to understand that CE and SE capture the "statistical structure" of RY that underlies overyielding. Specifically, CE and SE are not the ultimate biological mechanisms that drive overyielding, and never were meant to be. CE also does not describe niche complementarity. Interpreting CE and SE as directly quantifying niche complementarity or resource competition, is simply wrong, although it sometimes is done. The criticism of the AP method thus in large part seems unwarranted. The alternative methods the authors discuss (lines 108-123) are based on very similar principles.

The authors now set out to develop a method that aims at linking response patterns to "more true" biological mechanisms.

Assuming that "competitive dominance" is key to understanding mixture productivity, because "competitive interactions are the predominant type of interspecific relationships in plants", the authors introduce "partial density" monocultures, i.e. monocultures that have the same planting density for a species as in a mixture. The idea is that using these partial density monocultures as a reference would allow for isolating the effect of competition by the surrounding "species matrix".

The authors argue that "To separate effects of competitive interactions from those of other species interactions, we would need the hypothesis that constituent species share an identical niche but differ in growth and competitive ability (i.e., absence of positive/negative interactions)." - I think the term interaction is not correctly used here, because clearly competition is an interaction, but the point made here is that this would be a zero-sum game.

The authors use the ratio of productivity of partial density and full-density monocultures, divided by planting density, as a measure of "competitive growth response" (abbreviated as MG). This is the extra growth a plant individual produces when intraspecific competition is reduced.

Here, I see two issues: first, this rests on the assumption that there is only "one mode" of competition if two species use the same resources, which may not be true, because intraspecific and interspecific competition may differ. Of course, one can argue that then somehow "niches" are different, but such a niche definition would be very broad and go beyond the "resource set" perspective the authors adopt. Second, this value will heavily depend on timing and the relationship between maximum initial growth rates and competitive abilities at high stand densities.

The authors then progress to define relative competitive ability (RC), and this time simply uses monoculture biomass as a measure of competitive ability. To express this biomass in a standardized way, they express it as different from the mean of the other species and then divide by the maximum monoculture biomass of all species.

I have two concerns here: first, if competitive ability is the capability of a species to preempt resources from a pool also accessed by another species, as the authors argued before, then this seems wrong because one would expect that a species can simply be more productive because it has a broader niche space that it exploits. This contradicts the very narrow perspective on competitive ability the authors have adopted. This also is difficult to reconcile with the idea that specialist species with a narrow niche would outcompete generalist species with a broad niche. Second, I am concerned by the mathematical form. Standardizing by the maximum makes the scaling dependent on a single value.

As a final step, the authors calculate a "competitive expectation" for a species' biomass in the mixture, by scaling deviations from the expected yield by the product MG ⨯ RC. This would mean a species does better in a mixture when (1) it benefits most from a conspecific density reduction, and (2) has a relatively high biomass.

Put simply, the assumption would be that if a species is productive in monoculture (high RC), it effectively does not "see" the competitors and then grows like it would be the sole species in the community, i.e. like in the partial density monoculture.

Overall, I am not very convinced by the proposed method.

Comments on revised version:

Only minimal changes were made to the manuscript, and they do not address the main points that were raised.

Reviewer #2 (Public review):

This manuscript by Tao et al. reports on an effort to better specify the underlying interactions driving the effects of biodiversity on productivity in biodiversity experiments. The authors are especially concerned with the potential for competitive interactions to drive positive biodiversity-ecosystem functioning relationships by driving down the biomass of subdominant species. The authors suggest a new partitioning schema that utilizes a suite of partial density treatments to capture so-called competitive ability. While I agree with the authors that understanding the underlying drivers of biodiversity-ecosystem functioning relationships is valuable - I am unsure of the added value of this specific approach for several reasons.

Comments on revised version:

The authors changed only one minor detail in response to the last round of reviews.

Reviewer #3 (Public review):

Summary:

This manuscript claims to provide a new null hypothesis for testing the effects of biodiversity on ecosystem functioning. It reports that the strength of biodiversity effects changes when this different null hypothesis is used. This main result is rather inevitable. That is, one expects a different answer when using a different approach. The question then becomes whether the manuscript's null hypothesis is both new and an improvement on the null hypothesis that has been in use in recent decades.

Strengths:

In general, I appreciate studies like this that question whether we have been doing it all wrong and I encourage consideration of new approaches.

Weaknesses:

Despite many sweeping critiques of previous studies and bold claims of novelty made throughout the manuscript, I was unable to find new insights. The manuscript fails to place the study in the context of the long history of literature on competition and biodiversity and ecosystem functioning. The Introduction claims the new approach will address deficiencies of previous approaches, but after reading further I see no evidence that it addresses the limitations of previous approaches noted in the Introduction. Furthermore, the manuscript does not reproducibly describe the methods used to produce the results (e.g., in Table 1) and relies on simulations, claiming experimental data are not available when many experiments have already tested these ideas and not found support for them. Finally, it is unclear to me whether rejecting the 'new' null hypothesis presented in the manuscript would be of interest to ecologists, agronomists, conservationists, or others.

Comments on revised version:

Please see review comments on the previous version of this manuscript. The authors have not revised their manuscript to address most of the issues previously raised by reviewers.

I wish we were able to know the best thing for our students before we met them. I feel like we can't truly know what is best for our students unless we meet them. It doesn't matter how much paperwork we read on them.

claim: local volumetric reductions in gray matter associated with certain psychiatric disorders may be reversible in adequate training. 1 march 2011 : no studies have examined this according to doi:10.1002/hbm.21143

suprising: the capacity of the nervous system for rapid morphological adjustments in response to environmental triggers

similar to US Constitution

What if this is unsafe

Religion is placed back into government

Restricting religion in this area

Author response:

The following is the authors’ response to the original reviews.

Public Reviews:

Reviewer 1 (Public Review):

Summary:

The authors present a mean-field model that describes the interplay between (protein) aggregation and phase separation. Different classes of interaction complexity and aggregate dimensionality are considered, both in calculations concerning (equilibrium) phase behavior and kinetics of assembly formation.

Strengths:

The present work is, although purely theoretical, of high interest to understanding biological processes that occur as a result of a coupling between protein aggregation and phase separation. Of course, such processes are abundant, in the living cell as well as in in-vitro experiments. I appreciate the consideration of aggregates with various dimensionality, as well as the categorization into different ”interaction classes”, together with the mentioning of experimental observations from biology. The model is convincing and underlines the complexity associated with the distribution of proteins across phases and aggregates in the living cell.

Weaknesses:

There are a few minor weaknesses.

Reviewer 2 (Public Review):

This work deals with a very difficult physical problem: relating the assembly of building blocks on a molecular scale to the appearance of large, macroscopic assemblies. This problem is particularly difficult to treat, because of the large number of units involved, and of the complex way in which these units-monomers-interact with each other and with the solvent. In order to make the problem treatable, the authors recur to a number of approximations: Among these, there is the assumption that the system is spatially homogeneous, i.e., its features are the same in all regions of space. In particular, the homogeneity assumption may not hold in biologically relevant systems such as cells, where the behavior close to the cell membrane may strongly differ from the one in the bulk. As a result, this hypothesis calls for a cautious consideration and interpretation of the results of this work. Another notable simplification introduced by the authors is the assumption that the system can only follow two possible behaviors: In the first, each monomer interacts equally with the solvent; no matter the size of the cluster of which it is part. In the second case, monomers in the bulk of a cluster and monomers at the assembly boundary interact with the solvent in a different way. These two cases are considered not only because they simplify the problem, but also because they are inspired by biologically relevant proteins.

With these simplifications, the authors trace the phase diagram of the system, characterizing its phases for different fractions of the volume occupied by the monomers and solvent, and for different values of the temperature. The results qualitatively reproduce some features observed in recent experiments, such as an anomalous distribution of cluster sizes below the system saturation threshold, and the gelation of condensed phases above such threshold.

Reviewer 3 (Public Review):

Summary:

The authors combine classical theories of phase separation and self-assembly to establish a framework for explaining the coupling between the two phenomena in the context of protein assemblies and condensates. By starting from a mean-field free energy for monomers and assemblies immersed in solvent and imposing conditions of equilibrium, the authors derive phase diagrams indicating how assemblies partition into different condensed phases as temperature and the total volume fraction of proteins are varied. They find that phase separation can promote assembly within the protein-rich phase, providing a potential mechanism for spatial control of assembly. They extend their theory to account for the possibility of gelation. They also create a theory for the kinetics of self-assembly within phase separated systems, predicting how assembly size distributions change with time within the different phases as well as how the volumes of the different phases change with time.

Strengths:

The theoretical framework that the authors present is an interesting marriage of classic theories of phase separation and self-assembly. Its simplicity should make it a powerful general tool for understanding the thermodynamics of assembly coupled to phase separation, and it should provide a useful framework for analyzing experiments on assembly within biomolecular condensates.

The key advance over previous work is that the authors now account for how self-assembly can change the boundaries of the phase diagram.

A second interesting point is the explicit theoretical consideration for the possibility that gelation (i.e. self-assembly into a macroscopic aggregate) could account for widely observed solidification of condensates. While this concept has been broadly discussed, to date I have yet to see a rigorous theoretical analysis of the possibility.

The kinetic theory in sections 5 and 6 is also interesting as it extends on previous work by considering the kinetics of phase separation as well as those of self-assembly.

Weaknesses:

A key point the authors make about their theory is that it allows, as opposed to previous research, to study non-dilute limits. It is true that they consider gelation when the 3D assemblies become macroscopic. However, dilute solution theory assumptions seem to be embedded in many aspects of their theory, and it is not always clear where else the non-dilute limits are considered. Is it in the inter-species interaction χij? Why then do they never explore cases for which χij is nonzero in their analysis?

We explicitly consider that monomers and aggregates are non-dilute with respect to solvent. This is evident in accounting for the mixing entropy of all components, including the solvent. Moreover, we account for interactions among the monomers and the different aggregates with the solvent. We consider the case where each monomeric unit, independent in aggregate it is part of, interacts the same way with the solvent. Please note that this case corresponds to a non-dilute scenario where interactions indeed drive phase separation.

The connection between this theory and biological systems is described in the introduction but lost along the main text. It would be very helpful to point out, for instance, that the presence of phase separation might induce aggregation of proteins. This point is described formally at the end of Section 3, but a more qualitative connection to biological systems would be very useful here.

We thank the referee for the useful comment, we now mention this in the introduction (line 80) and point out the biological relevance of assembly formation and localization via the presence of phase separation (lines 268 and 283).

Building on the previous point, it would be helpful to give an intuitive sense of where the equations derived in the Appendices and presented in the main text come from and to spell out clear physical interpretations of the results. For example, it would be helpful to point out that Eq. 4 is a form of the law of mass action, familiar from introductory chemistry. It would be useful to better explain how the current work extends on existing previous work from these authors as well as others. Along these lines, closely related work by W. Jacobs and B. Rogers [O. Hedge et al. 2023, https://arxiv.org/abs/2301.06134; T. Li et al. 2023, https://arxiv.org/abs/2306.13198] should be cited in the introduction. The results discussed in the first paragraph of Section 3 on assembly size distributions in a homogeneous system are well-known from classic theories of self-assembly. This should be acknowledged and appropriate references should be added; see for instance, Rev. Mod. Phys. 93, 025008 and Statistical Thermodynamics Of Surfaces, Interfaces, And Membranes by Sam Safran. Equation 14 for the kinetic of volume fractions is given with reference to Bauermann et al. 2022, but it should be accompanied by a better intuitive interpretation of its terms in the main text. In particular, how should one understand the third term in this equation? Why does the change in volume impact the change of volume fraction in this way?

We thank the referee for the suggestions. We have included the missing references, with a particular emphasis on DNA nanostars that inhibit phase separation in DNA liquids in the definition of class II. We added intuitive explanations of the main equations, such as Eqs. (4),(8),(14), (17), and (18). Notice that, according to Mysels, Karol J., J. Chem. Educ., 33, 178 (1956) (https://pubs-acs-org.sire.ub.edu/doi/epdf/10.1021/ed033p178) we refer to (18) as the law of mass action.

The discussion in the last paragraph of Section 6 should be clarified. How can the total amount of protein in both phases decrease? This would necessarily violate either mass or volume conservation. Also, the discussion of why the volume is non-monotonic in time is not clear.

A decrease in the total amount of protein in both phases does not violate mass conservation, if the volume of the phases varies accordingly. In particular, the volume of the denser phase should grow. This given, in the case presented the total protein amount in the dense phase decreases, while in the dilute phase increases. For this reason, we revised the paragraph and now explain the results in more detail (see lines starting from 407). The nonmonotonic volume change is indeed a puzzling finding that, as we now state in the manuscript, requires further investigation. Given the lack of analytical approaches available to tackle the complex kinetics in the presence of coexisting phases, we believe that this analysis goes beyond the scope of the present paper.

Recommendations for the authors

Reviewer 1 (Recommendations For The Authors):

Line 96: I feel a mentioning/definition/explanation and perhaps some discussion on the parameter M (limiting aggregate size) would have been in place in the introduction of Equation (1). Furthermore, in the usual interpretation, Flory interaction parameters (symbolized χ) are dimensionless, as, classically, they represent an exchange energy (normalized by kT), defined on a monomeric basis. Here they seem to carry the dimension of energy.

We thank the reviewer for the observation. We have included a brief comment on M and mentioned that we use χ parameters that carry the dimension of energy such that, varying kBT, we scale at the same time the term containing interaction propensities (χ) and the one containing internal energies (_e_int). See the comment on line 127

Line 150: The choice of ρi \= i physically implies that a single protein is assumed to have the same as a solvent molecule. This may be a bit of a stretch. This assumption leads to an overestimation of the translational entropy of the aggregates (first term in Equation (1)). Acknowledging that ρ_1 >> ρs_ would give a pronounced desymmetrization of the phase diagram (I suspect).

Indeed, in the case of monomers only, the assumption leads to a symmetric phase diagram which may be unrealistic. Once assemblies form, however, the phase diagram becomes asymmetric and for this reason we decided to assume ρi \= i, simplifying the theoretical analysis. We have added a clarifying sentence in the manuscript, see line 163

Furthermore, the pictures in Figure 1a-c suggest the presence of a disordered residue, the degree of swelling of which might affect binding strength (see for instance: https://doi.org/10.3389/fnmol.2022.962526).

We added a comment on the possible coupling between internal free energies and interaction propensities, such as the swelling mechanism that affects binding sites, and included the reference above (line 215).

Line 154-156: It’s unclear what is meant with ”an internal bond that keeps each assembly together”. How should this be interpreted on an intuitive physical level?

We apologise for being unclear. We meant the internal bonds that lead to the formation of assemblies. We have now rephrased this sentence in the main text (lines starting from 169).

Line 254: The fact that ϕsg is defined below does not mean it does not fall out of the air here. The same holds for the consideration of the limit M →∞. Ideally, the main text should stand on its own, in particular with respect to physical intuitiveness, as well as the necessity and interest of discussion topics. Technical details, derivations and additional information can be in an appendix.

We agree with the referee and added some physical insights about the limit. We now also state clearly in the main text (line 298) that _ϕ_sg is affected by temperature and the free energy of internal bonds.

Line 257: ”Since we do not explicitly include the solvent in assembly formation we will consider the gel as a phase without solvent and thus ϕtot \= 1”. I’m not sure if I can agree with this. I would say, a gel, certainly in biological context, almost per definition contains a large fraction of solvent, i.e. here water. The situation ”ϕtot \= 1” would rather be a solid precipitate. Is gelation properly captured by this model?

We thank the referee for this very relevant observation. We now state in the main text that the model predicts a macroscopic assembly which we call ’the gel phase’, in agreement with previous literature. Then, to clarify, we added the sentence ”Please note that, since we do not explicitly include the solvent in assembly formation (see reaction scheme in Fig.1a), in our model the gel corresponds to a phase without solvent, _ϕ_tot \= 1. To account for biological gels that can be rich in water, our theory can be straightforwardly extended by incorporating the solvent into the reaction scheme.”, see main text line 300.

Line 268: Shouldn’t ”solvent” be ”solution”? If fsol is given by Equation (1), surely not only the solvent is considered.

Indeed, this is a typo, and we now use the term ’solution’ instead of ’solvent.’

Line 273: At this stage, the only information provided in the main text is that ω∞ is ”a constant that does not affect chemical nor phase equilibrium, except in the limit M →∞” (see lines 153-154). This is a little bit too abstract for me. Again, the main text should stand on its own, meaning the reader should not have to rely on an appendix to at least have an intuitive physical understanding of any modeling or input parameter discussed in the main text.

We thank the reviewer for pointing this out. We now comment on the physical interpretation of ω∞ in the main text, see lines from 320 on.

Figure 4. appears in Equation (39) but it is not defined.

We thank the reviewer for pointing this out. We have reshaped appendix 6A, making use of chemical activities and clarified the origin of the rate .

Line 317. I don’t fully understand the intention of the remark on the model being adaptable for ”primary and secondary nucleation”. How/in what way is this different from association and dissociation? For instance, classical nucleation theory is based on association and dissociation of monomeric units to and from clusters.

We agree that the kinetic rate coefficients kij (appearing in the association and dissociation rates ∆rij, Eq. 17) in our manuscript already depend on assembly length, see Appendix 6 B, where we now clarified their definition. Please note that, however, that secondary nucleation is a special kind of association, for which the kinetic rate coefficients corresponding to associations of small assemblies, i.e. kij with_i,j_ ≪ M, explicitly depend on the presence of large assemblies with sizes l ≫ 1. In our manuscript, we have not accounted for such a dependence. We now make this aspect clear in the manuscript, see Appendix 6 B.

Line 321. Why is ∆rij called the ”monomer exchange rate”? In line 318 the same parameter is defined as the ”reaction rate for the formation of a (i+j)-mer”. Why should these be the same?

We thank the reviewer for spotting this typo.

Line 323. Why do these calculations use M = 15?

The exploration of a 15-dimensional phase space is already numerically challenging. We are currently working on a generalization of the numerical scheme to work with larger values of M but, to discuss the fundamental physical principles, we kept M \= 15.

Reviewer 2 (Recommendations For The Authors):

The manuscript presents several issues, on both the scientific and presentational level, which need to be carefully addressed. Please find below a list of the points that need to be addressed by the authors, divided into major and minor points. Major issues:

• A general, major concern about the results in the paper is the homogeneity assumption. I do understand that repeating the whole analysis presented in the manuscript by allowing for spatial inhomogeneities partially goes beyond the scope of this paper. However, the authors should at least discuss how such inhomogeneities may alter the results in a qualitative way, and treat explicitly the presence of inhomogeneity in one prototypical case treated in the manuscript. Namely, what happens if the volume fractions and relative molecular volumes in the free energy (1) depend on space, e.g., ϕi → ϕi(x)?

We would like to stress that, in the present paper, we do account for spatial inhomogeneities. Indeed, in the case of phase separation, we consider systems which are divided into two phases, characterized by different values of the assemblies’ volume fractions ϕi. We do, however, consider the system to be homogeneous inside the phases, implying a jump in the value of the volume fraction at the interface between the two phases. In this sense, the analysis we carry out is valid in the thermodynamic limit, where gradients of the volume fractions ϕi(x) within the phases, can be neglected. On the other hand, considering the full spatial problem, i.e. solving the equations for M \= 15 spatially varying fields, would be numerically extremely challenging.

• The authors’ results relate molecular assembly- a phenomenon at the molecular scale-to phase separation-a mesoscopic or macroscopic phenomenon. The authors should stress the conceptual importance of this connection between scales, and present their results from the perspective of a multi-scale model.

We thank the reviewer for pointing this out. We now emphasize the multi-scale feature of our model in the introduction (line 80).

• Starting from Section 1, the reader is not well guided through the sections that follow. The authors should provide an outline of the line of though that they are going to follow in the following sections, and logically connect each section to the next one with a short paragraph at the end of each section. This paragraph should resume what has been addressed in the current section, and the connection with the topic that will be addressed in the next one.

We agree with the reviewer and have added a transitioning sentence at the end of each paragraph.

• ’We focus on linear assemblies (d = 1)’: Given the striking differences of the results between d = 1 and d > 1 shown above, the authors should discuss what happens for d > 1 as well.

• ’In figure Fig. 5a, we show the initial and final equilibrium binodals (black and coloured curve, respectively), for the case of linear assemblies (d = 1) belonging to class 1’: Again, show what happens for d > 1.

We agree with the reviewer, the kinetics in d > 1 would be definitely interesting. However, in this case, one assembly can become macroscopic (i.e. M must be set to ∞). This requires some substantial modification in the kinetic scheme, like introducing an absorbing boundary condition for monomers ’sucked in’ the gel. We prefer to leave this for future work, and now state it explicitly in the manuscript (line 383).

• ’This difference arises because, within class 2, monomers in the bulk of an assembly have reduced interaction propensity with respect to the boundary ones. As a consequence, the formation of large clusters shifts the onset of phase separation to higher ϕtot values.’: To prove this argument, the authors should show Fig. 2g and h for d > 1. In fact, by varying d, the effect of the boundary vs. bulk also varies.

We prefer to discuss the thermodynamics of d > 1 in section 4 on gelation. There we present only a single phase diagram so as not to blow up the discussion on equilibrium too much.

• ’referring for simplicity to systems belonging to Class 1’: The authors should do the same analysis for Class 2.

We agree with the reviewer. However, again not to blow up the discussion on equilibrium, we leave it for future work.

• ’other, implying that the corresponding Flory-Huggins parameter χij vanishes’: Why?

The explanation based on a lattice model is reported in Appendix 2, and is now more clearly referenced (line 185).

Minor issues:

• Eq. (10): Here the authors should explain in the main text, possibly in a simple and intuitive way, why the number of monomers i and the space dimension d enter the righthand side of this equation in this particular way.

We thank the reviewer for pointing this out. We added the physical origin of the scaling with dimension in Eq. (10) and in Eq. (8), as pointed out by reviewer 3.

• ’The second and fifth terms of fsol characterize the internal free energies’: What do you mean by ’characterize the internal free energies’? Please clarify.

As we now state more clearly (lines 114-120), these two contributions include the internal free energies ω_s and _ωi, stemming from the free energy of internal bonds that lead to assembly formation.

• ’depend on the scaling form of the’: Scaling with respect to what ? Please clarify.

We have now clarified that the scaling is with respect to the assembly size i.

• Figure 2 is way too dense: it should be split into two figures, and the legend of each of the two figures should be expanded to properly guide the reader to understand the figures.

We understand the reviewer’s point of view. To avoid altering the present flow, we decided not to split the figure, but we have included shaded boxes to better guide the reader.

• ’this is a consequence of the gelation transition’: Please clarify

• ’and this limitation can be dealt with by introducing explicitly the infinite-sized gel in the free energy’: Why? Please clarify.

We have now rephrased these sentences, hopefully in a clearer way. We now state: ’We know that this divergence is physical, and is caused by the gelation transition. This limitation can be dealt with by introducing explicitly a term in the free energy that accounts for an infinite-sized assembly (the gel)’, see lines 320-322.

• Figure 4: Add plots of panels d, e, h and i with log scale on the y axis to make explicit an eventual exponential behavior, and revise the text accordingly

Not to further complicate Figure 4, we preferred to display the logarithmic plots of the equilibrium distribution in the appendix, see Figure A3-1.

• ’... an equilibrium distribution which monotonously decreases with assembly size’: It is not the distributions that decreases but the cluster volume fraction, please rephrase.

We thank the reviewer for pointing this out and have now rephrased this sentence (line 394).

Reviewer 3 (Recommendations For The Authors):

I could not obtain the exact form of Eq 29 in App 3, can the authors elaborate on this calculation. App 3: What does it mean binodal agrees well with ϕsg? And doesn’t ϕsg depend on temperature through phi tilde? What temperature is this result for?

We apologise for the unclear explanation. We now state in detail that Eq. (29) is obtained by plugging the expression of ϕi given in Eq. (24) into Eq. (1), in the main text. The dependence of ϕ₁ on ϕ_tot is expressed in Eq. (26), and we have omitted linear terms in ϕ_tot, since they do not affect phase equilibrium (see lines 802-809). Moreover, ϕsg depends indeed on k_BT. We refer to the comparison between the full curve ϕsg in the k_BT−ϕ_tot plane, and the branch of the binodal between the triple point (indicated now with a cross) and ϕ_tot \= 1. The two curves are close, as expected since both correspond to the boundary between homogeneous mixtures and the gel state, obtained with different methods.

The references to Figures in the appendices are confusing. Please make it clear whether Figures in the main text or the appendices are being referenced. On a related note, the Appendix figures seem to be placed in appendices whose text describes something else - Appendix 2, Figure 1 should be moved to Appendix 3; Appendix 3, Figure 1 should be moved to Appendix 4; etc.

We revised the appendix, corrected the figure positions and clarified their references.