Reviewer #1 (Public Review):
Bera et al. study the response of vegetation in water-limited ecosystems to changes in the precipitation regime. Previous studies have shown that spatial processes, in particular the redistribution of (soil and surface) water, may play an important role in mediating the ecosystem response. An important consequence of this redistribution is the spatial self-organization of vegetation into regular spatial patterns, consisting of vegetation patches that act as sinks for (surface) water, and surrounding areas of bare soil that act as water sources. At the ecosystem level, the additional water input in vegetation patches may enable vegetation to persist at precipitation levels that are too low to sustain a spatially uniform cover.
While most model studies of spatial self-organization and pattern formation describe vegetation dynamics through 1-2 biomass variables, the current study extends this previous work by considering a trait diversity gradient, considering a large number (N=128) of discrete trait classes that range from stress-tolerant to fast-growing characteristics. The results show that in the absence of spatial pattern formation, a decrease in precipitation leads to a shift in the biomass distribution toward the more stress-tolerant trait classes. At the onset of pattern formation, however, soil water availability increases at the locations where vegetation patches form, enabling the more fast-growing trait classes to increase in biomass, and this shift is accompanied by an increase in functional diversity of trait classes as well. It is also shown that once these patterned ecosystem states are formed, the main adaptation to further decreases in precipitation occurs either through shrinking the size of existing patches, or by reducing the number of patches; in contrast, biomass and community composition of the patches remains relatively stable. Finally, it is shown that for certain precipitation conditions, functional diversity is maximized when the ecosystem is in a hybrid state, where part of the landscape has a spatially uniform vegetation cover, and part of the landscape is in a patterned state.
A potential strength of this paper is that the community assembly and biodiversity perspective on spatial self-organization may highlight the relevance of pattern formation in ecosystems more clearly to a broad audience. The formulation of a trait/strategy gradient of discrete classes is certainly an interesting suggestion to connect the typical single/few biomass variable(s) approach to a community-level approach. The community assembly process is modelled in a very specific way, and the manuscript would benefit from an expanded ecological motivation of the processes that are being mimicked, and thereby explain more clearly what taxonomic level of organization is being considered. In addition, it would be useful if the authors could provide further clarification as to what extent the community diversity dynamics can be separated from total biomass dynamics of patterned water-limited ecosystems given the current approach. These points are explained in further detail below.
• First, it was not entirely clear to this reviewer how the reaction parts of the model equations determine the optimal trait value χ, and how this value varies as a function of precipitation. Assuming a single trait class, and plotting the relevant equilibrium values of the three state variables shed some light on this issue. [Unfortunately, there does not seem to be a possibility to attach the figure with these plots to this review report]. Assuming the non-spatial equilibrium solution was derived correctly , the optimum biomass (B) value shifts across the trait spectrum with changing precipitation (in the non-spatial model version, solving the surface water equation for equilibrium will always yield that all precipitation infiltrates, i.e. regardless of the values of surface water, H, and χ). The equilibrium of soil water availability (W), which is the growth limiting resource of the vegetation, shows an inverse pattern with biomass. This result is in line with a classical results (e.g. Tilman 1982), in that the most successful strategy is the one that is able to reduce the limiting resource to the lowest equilibrium value. With all trait classes competing for the soil water resource, however, it is then not immediately clear why the most successful trait class is not outcompeting the other classes. This leads to a second point, about the way in which community trait adaptation is modelled.
• The authors model trait adaptation through a diffusion approximation between trait classes. That is, every timestep, a small amount of biomass flows from the class with higher biomass to the neighboring trait class with lower biomass. From an ecological point of view, it seems that this process is describing adaptation of vegetation that is already present, so this process seems to be limited to intraspecific phenotypic plasticity. From the text, however, it seems that the trait classes correspond to higher taxonomic levels of organization, when describing shifts from fast growing to stress-tolerant species, for example. It is not entirely clear, however, how biomass flows as assumed in the model could occur at these higher levels of organization.
• Combining the observations from the previous two points, there is a concern that for a given level of precipitation, there is a single trait class with optimal biomass/lowest soil water level that is dominant, with the neighboring trait classes being sustained by the diffusion of biomass from the optimal class to neighboring inferior classes. This would seem a bit problematic, as it would mean that most classes are not a true fit for the environment, and only persist due to the continuous inflow of biomass. Taking a clue from the previous papers of the authors, it seems this may not be the case, though. Specifically, in the paper by Nathan et al. (2016) it seems that all trait classes are started at low initial biomass density, and the resulting steady state (in the absence of biomass flows between classes) seems to show similar biomass profiles as shown in Figs. 4,5 and 7 of the current paper. While the current model formulation seems slightly different, similar results may apply here. Indeed, keeping all trait classes at non-zero (but low) density, and when the (abiotic and biotic) environment permits, let each class increase in biomass seems like the most straightforward approach to model community assembly dynamics. Given the above discussion about these trait classes competing for a single resource (soil water), and one trait class being able to drive this resource availability to the lowest level, it would then be useful to readers to explain why multiple trait classes can coexist here, and how (for spatial uniform solutions) the equilibrium soil water level with multiple trait classes present compares to the equilibrium soil water level when only the optimal trait class is present. Furthermore, if results as presented in Nathan et al. (2016) indeed hold in the current case, perhaps it means that the biomass profile responses as shown in e.g. Fig. 5 would also occur if there was no biomass flow between trait classes included, but that the time needed to adjust the profile would take much longer as compared to when the drift term/second trait derivative is included. In summary, further clarification of what the biomass flows between classes represent, and the role it plays in driving the presented results would be useful for readers.
• In addition, it would be useful for readers to understand to what extent the shifts in average trait values and functional diversity can be decoupled from the biomass and soil water responses to changes in precipitation that would occur in a model with only a single biomass variable. For example, early studies on self-organization in semi-arid ecosystems already showed that the shift toward a patterned state involved the formation of patches with higher biomass, and higher soil water availability, as compared to the preceding spatially uniform state, and that the biomass in these patches remains relatively stable under decreasing rainfall, while their geometry changes (e.g. Rietkerk et al. 2002). It has also been observed that for a given environmental condition, biomass in vegetation patches tends to increase with pattern wavelength (e.g. Bastiaansen and Doelman 2018; Bastiaansen et al. 2018). Given the model formulation, one wonders whether higher biomass in the single variable model is not automatically corresponding to higher abundance of faster growing species and a higher functional diversity (as the diffusion of biomass can cover a broader range when starting from higher mass in the optimal trait class). There are some indications in the current work that the linkage is more complicated, for example, the biomass peak in Fig. 7c is lower, but also broader as compared to the distribution of Fig. 7b, but it is currently not entirely clear how this result can be explained (for example, it might be the case that in the spatially patterned states, the biomass profiles also vary in space).
• The possibility of hybrid states, where part of the landscape is in a spatially uniform state, while the other part of the landscape is in a patterned state, is quite interesting. To better understand how such states could be leveraged in management strategies, it would be useful if a bit more information could be provided on how these hybrid states emerge, and whether one can anticipate whether a perturbation will grow until a fully patterned state, or whether the expansion will halt at some point, yielding the hybrid state. It seems that being able to distinguish these case would be necessary in the design of planning and management strategies. Also, in Fig. 3a, the region of parameter space in which hybrid states occur is not very large; it is not entirely clear whether the full range of hybrid states is left out here for visual considerations, or whether these states only occur within this narrow range in the vicinity of the Turing instability point.
References:
Bastiaansen R, Doelman A. 2018. The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space. Physica D 388: 45-72.
Bastiaansen R, Jaïbi O, Deblauwe V, Eppinga MB, Siteur K, Siero E, Mermoz S, Bouvet A, Doelman A, Rietkerk M. 2018. Multistability of model and real dryland ecosystems through spatial self-organization. Proceedings of the National Academy of Sciences USA 115:11256-11261.
Nathan J, Osem Y, Shachak M, Meron E. 2016. Linking functional diversity to resource availability and disturbance: a mechanistic approach for water limited plant communities. Journal of Ecology 104: 419-429.
Rietkerk M, Boerlijst MC, van Langevelde F, HilleRisLambers R, van de Koppel J, Kumar L, Prins HHT, De Roos AM. 2002. Self-organization of vegetation in arid ecosystems. American Naturalist 160: 524-530.
Tilman D. 1982. Resource competition and community structure. Princeton University Press, Princeton, NJ, USA.