The impact of process at different scales on diversity and ecosystem functioning: a huge challenge
Linking intrinsic scales of ecological processes to characteristic scales of biodiversity and functioning patterns
Recommendation: posted 12 September 2023, validated 12 September 2023
Scale is a big topic in ecology . Environmental variation happens at particular scales. The typical scale at which organisms disperse is species-specific, but, as a first approximation, an ensemble of similar species, for instance, trees, could be considered to share a typical dispersal scale. Finally, characteristic spatial scales of species interactions are, in general, different from the typical scales of dispersal and environmental variation. Therefore, conceptually, we can distinguish these three characteristic spatial scales associated with three different processes: species selection for a given environment (E), dispersal (D), and species interactions (I), respectively.
From the famous species-area relation to the spatial distribution of biomass and species richness, the different macro-ecological patterns we usually study emerge from an interplay between dispersal and local interactions in a physical environment that constrains species establishment and persistence in every location. To make things even more complicated, local environments are often modified by the species that thrive in them, which establishes feedback loops. It is usually assumed that local interactions are short-range in comparison with species dispersal, and dispersal scales are typically smaller than the scales at which the environment varies (I < D < E, see ), but this should not always be the case.
The authors of this paper  relax this typical assumption and develop a theoretical framework to study how diversity and ecosystem functioning are affected by different relations between the typical scales governing interactions, dispersal, and environmental variation. This is a huge challenge. First, diversity and ecosystem functioning across space and time have been empirically characterized through a wide variety of macro-ecological patterns. Second, accommodating local interactions, dispersal and environmental variation and species environmental preferences to model spatiotemporal dynamics of full ecological communities can be done also in a lot of different ways. One can ask if the particular approach suggested by the authors is the best choice in the sense of producing robust results, this is, results that would be predicted by alternative modeling approaches and mathematical analyses . The recommendation here is to read through and judge by yourself.
The main unusual assumption underlying the model suggested by the authors is non-local species interactions. They introduce interaction kernels to weigh the strength of the ecological interaction with distance, which gives rise to a system of coupled integro-differential equations. This kernel is the key component that allows for control and varies the scale of ecological interactions. Although this is not new in ecology , and certainly has a long tradition in physics ---think about the electric or the gravity field, this approach has been widely overlooked in the development of the set of theoretical frameworks we have been using over and over again in community ecology, such as the Lotka-Volterra equations or, more recently, the metacommunity concept .
In Physics, classic fields have been revised to account for the fact that information cannot travel faster than light. In an analogous way, a focal individual cannot feel the presence of distant neighbors instantaneously. Therefore, non-local interactions do not exist in ecological communities. As the authors of this paper point out, they emerge in an effective way as a result of non-random movements, for instance, when individuals go regularly back and forth between environments (see , for an application to infectious diseases), or even migrate between regions. And, on top of this type of movement, species also tend to disperse and colonize close (or far) environments. Individual mobility and dispersal are then two types of movements, characterized by different spatial-temporal scales in general. Species dispersal, on the one hand, and individual directed movements underlying species interactions, on the other, are themselves diverse across species, but it is clear that they exist and belong to two distinct categories.
In spite of the long and rich exchange between the authors' team and the reviewers, it was not finally clear (at least, to me and to one of the reviewers) whether the model for the spatio-temporal dynamics of the ecological community (see Eq (1) in ) is only presented as a coupled system of integro-differential equations on a continuous landscape for pedagogical reasons, but then modeled on a discrete regular grid for computational convenience. In the latter case, the system represents a regular network of local communities, becomes a system of coupled ODEs, and can be numerically integrated through the use of standard algorithms. By contrast, in the former case, the system is meant to truly represent a community that develops on continuous time and space, as in reaction-diffusion systems. In that case, one should keep in mind that numerical instabilities can arise as an artifact when integrating both local and non-local spatio-temporal systems. Spatial patterns could be then transient or simply result from these instabilities. Therefore, when analyzing spatiotemporal integro-differential equations, special attention should be paid to the use of the right numerical algorithms. The authors share all their code at https://zenodo.org/record/5543191, and all this can be checked out. In any case, the whole discussion between the authors and the reviewers has inherent value in itself, because it touches on several limitations and/or strengths of the author's approach, and I highly recommend checking it out and reading it through.
Beyond these methodological issues, extensive model explorations for the different parameter combinations are presented. Several results are reported, but, in practice, what is then the main conclusion we could highlight here among all of them? The authors suggest that "it will be difficult to manage landscapes to preserve biodiversity and ecosystem functioning simultaneously, despite their causative relationship", because, first, "increasing dispersal and interaction scales had opposing
effects" on these two patterns, and, second, unexpectedly, "ecosystems attained the highest biomass in scenarios which also led to the lowest levels of biodiversity". If these results come to be fully robust, this is, they pass all checks by other research teams trying to reproduce them using alternative approaches, we will have to accept that we should preserve biodiversity on its own rights and not because it enhances ecosystem functioning or provides particular beneficial services to humans.
 Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943–1967. https://doi.org/10.2307/1941447
 Yuval R. Zelnik, Matthieu Barbier, David W. Shanafelt, Michel Loreau, Rachel M. Germain. 2023. Linking intrinsic scales of ecological processes to characteristic scales of biodiversity and functioning patterns. bioRxiv, ver. 2 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2021.10.11.463913
 Baron, J. W. and Galla, T. 2020. Dispersal-induced instability in complex ecosystems. Nature Communications 11, 6032. https://doi.org/10.1038/s41467-020-19824-4
 Cushing, J. M. 1977. Integrodifferential equations and delay models in population dynamics
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 M. A. Leibold, M. Holyoak, N. Mouquet, P. Amarasekare, J. M. Chase, M. F. Hoopes, R. D. Holt, J. B. Shurin, R. Law, D. Tilman, M. Loreau, A. Gonzalez. 2004. The metacommunity concept: a framework for multi-scale community ecology. Ecology Letters, 7(7): 601-613. https://doi.org/10.1111/j.1461-0248.2004.00608.x
 M. Pardo-Araujo, D. García-García, D. Alonso, and F. Bartumeus. 2023. Epidemic thresholds and human mobility. Scientific reports 13 (1), 11409. https://doi.org/10.1038/s41598-023-38395-0
David Alonso (2023) The impact of process at different scales on diversity and ecosystem functioning: a huge challenge. Peer Community in Ecology, 100402. 10.24072/pci.ecology.100402
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article. The authors declared that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article.
YRZ, MB, DWS and ML were supported by the TULIP Laboratory of Excellence (ANR-668 10-LABX-41), and by the BIOSTASES Advanced Grant, funded by the European Research Council under the European Union’s Horizon 2020 research and innovation program 670 (grant agreement no.666971).
Evaluation round #1
DOI or URL of the preprint: https://doi.org/10.1101/2021.10.11.463913
Author's Reply, 08 Jun 2023
Decision by David Alonso, posted 23 Jan 2022
This paper studies how spatial patterns of species diversity and ecosystem function are affected by and emerged from the interaction among three different scales: the scale of dispersal, the scale of environmental spatial variability, and the scale of at which species typically interact. The question of scale in Ecology is extremely relevant. It is at the core of the discipline.
I think this ms in the present form has strengths but too many weaknesses. This preprint has been carefully read by three reviewers and myself. The reviewers make interesting and constructive comments from different angles. Please read them carefully and try to address them. They all agree this is not an easy paper to read and review. It took longer than expected to find reviewers. It requires solid expertise in theoretical/mathematical approaches in ecology, and even in this case, the reader needs to go through the material several times in order to get his/her head around. After reading the ms, and from reviewers' overall comments, I also have the impression the manuscript lacks clarity. Certain points need a better justitication. Methods need to be better explained. Parts of the discussion need to better emphasize the relevance of the contribution, particularly, in practical settings.
In addition to the specific issues raised by the reviewers, here I will highlight some general points where I find the paper has a lot of room for improvement. As you will see, coincidence with some of the major points raised by the reviewers emerge.
1. The connection of the main model in Eq (1) to previous literature should be better explained. I agree with one of the reviewers: this does not seem to be a metacommunity model in the typical sense. Eq (1) does not correspond to a set of local populations connected through dispersal and distributed over a discrete number of local sites. Metacommunity models inherit the discret nature of local populations (or patches), while Eq (1) considers space as a continuous variable. In my opinion, Eq (1) is better regarded as a S species generalization of the Fisher equation with non-local interactions . This comment makes me think that the analysis of the Eq (1) will be more robust if the authors could start by comparing first its dynamics agains a simpler bench mark, for instance, without considering environmental heterogeneity at all. What kind of spatial patterns emerge from the interaction of dispersal (the Laplace operator) and non-local interactions on a uniform environment? This question has been addressed before for a single species , and, recently, in the context of predator-prey interactions  without non-locality. To make the connections to this literature is fair and necessary. Spatio-temporal chaos and Turing instabilities naturally appear in this type of models in some areas of the parameter space.
2. I think the analysis of Eq (1) would also benefit from a dimensionless approach. What if in Eq (1) we expressed length in units of the typical scale of environmental heterogeneity? This dimensionless length would reduce the complexity of the problem to only two typical scales, the relative scale of dispersal and the relative scale of ecological interactions (both with respect to the environmental scale) . The authors implicitly take this approach when fixing the environmental scale to what it seems to be a magic number, and then present their results across diferent values of the other two scales, but a more explcit approach would be better and more elegant.
3. Although Eq (1) is deterministic, species parameter sets are drawn from certain probability distribuitions (see Table 1) , which amonts to different stochastic realizations of the same model. This is the approach initiated by May, further elaborated by Allesina, Grilli, and others, and recently extended to include dispersal by Baron and Gala . This approach focuses on the distribution of eigenvalues over the ensamble of species configurations defined through random realizations of the community matrix. In the case of this model, species are defined in a more complex way by drawing their defining parameters from certain distributions (Table 1). In this case, not only a competitive community matrix is chosen at random, but also the species optima, local carrying capacities, and niche widths. Although in this context analytic results might be impossible, stability analysis and some numerics can be used to better link probability of stability to the underlying parameter distributions.
4. Non-local interactions are somehow magical. I mean, in reality, information never travels at infinite speed. A focal individual at local position x never feels instantaneously the competition of a second individual located further away from the focal one. It remains to be proved that non-local interactions are the best way to represent a spatial scale not related to species dispersal, but to the shorter time scales associated to individual foraging behavior, and short-time scale movements underlying competitive interactions. In the case of trees, competition can be well represented by a spatial kernel taking into account the typical size of the tree crowns, while dispersal occurs at longer spatio-temporal scales. For animals, the interpretation of the a competition spatial kernel is less obvious. This comment is related to the one by one of the reviewers when saying that the results probably apply to horizontal competitive communities (sensu Vellend) in a straightfoward way, but it remains to be seen if they apply rightaway to all kind of communities, or further work will be needed to carefully extend these results to other types of community structures.
In sum, I believe this ms is potentially a great contribution. By addressing the points reviewers and I have raised I believe the paper will be more readable and understandable for wider audiences.
 M. A. Fuentes, M. N. Kuperman, and V. M. Kenkre (2004). Analytical Considerations in the Study of Spatial Patterns Arising from Nonlocal Interaction Effects. J. Phys. Chem. B 108 (29): 10505–10508
 Baron, J. W., & Galla, T. (2020). Dispersal-induced instability in complex ecosystems. Nature Communications, 11, 6032.