Scale is a big topic in ecology [1]. 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 [2]), but this should not always be the case. 

The authors of this paper [2] 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 [3]. 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 [4], 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 [5].

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 [6], 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 [2]) 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. 

References

[1] Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943–1967. https://doi.org/10.2307/1941447

[2] 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

[3] 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

[4] Cushing, J. M. 1977. Integrodifferential equations and delay models in population dynamics 
 Springer-Verlag, Berlin. https://doi.org/10.1007/978-3-642-93073-7

[5] 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

[6] 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

What predisposes two individuals to form and maintain a relationship is a fundamental question. Using facial recognition to see whether couples' faces change over time to become more and more similar, psychology researchers have concluded that couples tend to be formed from the start between people whose faces are more similar than average [1]. As the saying goes, birds of a feather flock together.

And what about in nature? Are these rules of assembly valid for communities of different species?

In his seminal contribution, Robert MacArthur (1984) wrote ‘To do science is to search for repeated patterns’ [2]. Identifying the mechanisms that govern the arrangement of life is a hot research topic in the field of ecology for decades, and an absolutely essential prerequisite to answer the outstanding question of what shape ecological patterns in multi-species communities such as species-area relationships, relative species abundances, or spatial and temporal turnover of community composition; amid others [3]. To explain ecological patterns in nature, some rely on the concept that every species - through evolutionary processes and the acquisition of a unique set of traits that allow a species to be adapted to its abiotic and biotic environment - occupies a unique niche: Species coexistence comes as the result of niche differentiation [4,5]. Such a view has been challenged by the recognition of the key role of neutral processes [6], however, in which demographic stochasticity contributes to shape multi-species communities and to explain why congener species coexist much more frequently than expected by chance [7,8]. While the niche-based and neutral theories appear seemingly opposed at first sight [9], the dichotomy may be more philosophical than empirical [4,5]. Many examples have come to support that both concepts are not incompatible as they together influence the structure, diversity and functioning of communities [10], and are simply extreme cases of a continuum [11]. From this perspective, extrinsic factors, i.e., environmental heterogeneity, may influence the location of a given community along the niche-neutrality continuum. 

The walk of species in nature is therefore neither random nor ecologically predestined. In microbial assemblages, the co-existence of these two antagonistic mechanisms has been shown both theoretically and empirically. It has been shown that a combination of stabilising (niche) and equalising (neutral) mechanisms was responsible for the existence of groups of coexistent species (clumps) in a phytoplankton rich community [12]. Analysing interannual changes (2003-2009) in the weekly abundance of diatoms and dinoflagellates located in a temperate coastal ecosystem of the Western English Channel, Mutshinda et al. [13] found a mixture of biomass dynamics consistent with the neutrality-niche continuum hypothesis. While niche processes explained the dynamic of phytoplankton functional groups (i.e., diatoms vs. dinoflagellates) in terms of biomass, neutral processes mainly dominated - 50 to 75% of the time - the dynamics at the species level within functional groups [13]. From one endpoint to another, defining the location of a community along the continuum is all matter of scale [4,11].

In their study, testing predictions made by an emergent neutrality model, Graco-Roza et al. [14] provide empirical evidence that neutral and niche processes joined together to shape and drive planktonic communities in a riverine ecosystem. Body size - the 'master trait' - is used here as a discriminant ecological dimension along the niche axis. From their analysis, they not only show that the specific abundance is organised in clumps and gaps along the niche axis, but also reveal that different clumps exist along the river course. They identify two main clumps in body size - with species belonging to three different morphologically-based functional groups - and characterise that among-species differences in biovolume are driven by functional redundancy at the clump level; species functional distinctiveness being related to the relative biovolume of species. By grouping their variables according to seasons (cold-dry vs. warm-wet) or river elevation profile (upper, medium and lower course), they hereby highlight how environmental heterogeneity contributes to shape species assemblages and their dynamics and conclude that emergent neutrality models are a powerful approach to explain species coexistence; and therefore ecological patterns.

References

[1] Tea-makorn PP, Kosinski M (2020) Spouses’ faces are similar but do not become more similar with time. Scientific Reports, 10, 17001. https://doi.org/10.1038/s41598-020-73971-8.

[2] MacArthur RH (1984) Geographical Ecology: Patterns in the Distribution of Species. Princeton University Press.

[3] Vellend M (2020) The Theory of Ecological Communities (MPB-57). Princeton University Press.

[4] Wennekes PL, Rosindell J, Etienne RS (2012) The Neutral—Niche Debate: A Philosophical Perspective. Acta Biotheoretica, 60, 257–271. https://doi.org/10.1007/s10441-012-9144-6.

[5] Gravel D, Guichard F, Hochberg ME (2011) Species coexistence in a variable world. Ecology Letters, 14, 828–839. https://doi.org/10.1111/j.1461-0248.2011.01643.x.

[6] Hubbell SP (2001) The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32). Princeton University Press.

[7] Leibold MA, McPeek MA (2006) Coexistence of the Niche and Neutral Perspectives in Community Ecology. Ecology, 87, 1399–1410. https://doi.org/10.1890/0012-9658(2006)87[1399:COTNAN]2.0.CO;2.

[8] Pielou EC (1977) The Latitudinal Spans of Seaweed Species and Their Patterns of Overlap. Journal of Biogeography, 4, 299–311. https://doi.org/10.2307/3038189.

[9] Holt RD (2006) Emergent neutrality. Trends in Ecology & Evolution, 21, 531–533. https://doi.org/10.1016/j.tree.2006.08.003. 

[10] Scheffer M, Nes EH van (2006) Self-organized similarity, the evolutionary emergence of groups of similar species. Proceedings of the National Academy of Sciences, 103, 6230–6235. https://doi.org/10.1073/pnas.0508024103.

[11] Gravel D, Canham CD, Beaudet M, Messier C (2006) Reconciling niche and neutrality: the continuum hypothesis. Ecology Letters, 9, 399–409. https://doi.org/10.1111/j.1461-0248.2006.00884.x.

[12] Vergnon R, Dulvy NK, Freckleton RP (2009) Niches versus neutrality: uncovering the drivers of diversity in a species-rich community. Ecology Letters, 12, 1079–1090. https://doi.org/10.1111/j.1461-0248.2009.01364.x.

[13] Mutshinda CM, Finkel ZV, Widdicombe CE, Irwin AJ (2016) Ecological equivalence of species within phytoplankton functional groups. Functional Ecology, 30, 1714–1722. https://doi.org/10.1111/1365-2435.12641.

[14] Graco-Roza C, Segura AM, Kruk C, Domingos P, Soininen J, Marinho MM (2021) Clumpy coexistence in phytoplankton: The role of functional similarity in community assembly. bioRxiv, 869966, ver. 6 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/869966

In this paper, Alan R. Rogers (2021) examines the dynamics of foraging strategies for a resource that gains value over time (e.g., ripening fruits), while there is a fixed cost of attempting to forage the resource, and once the resource is harvested nothing is left for other harvesters. For this model, not any pure foraging strategy is evolutionary stable. A mixed equilibrium exists, i.e., with a mixture of foraging strategies within the population, which is still evolutionarily unstable. Nonetheless, Alan R. Rogers shows that for a large number of competitors and/or high harvesting cost, the mixture of strategies remains close to the mixed equilibrium when simulating the dynamics. Surprisingly, in a large population individuals will less often attempt to forage the resource and will instead “go fishing”. The paper also exposes an experiment of the game with students, which resulted in a strategy distribution somehow close to the theoretical mixture of strategies.

The economist John F. Nash Jr. (1950) gained the Nobel Prize of economy in 1994 for his game theoretical contributions. He gave his name to the “Nash equilibrium”, which represents a set of individual strategies that is reached whenever all the players have nothing to gain by changing their strategy while the strategies of others are unchanged. Alan R. Rogers shows that the mixed equilibrium in the foraging game is such a Nash equilibrium. Yet it is evolutionarily unstable insofar as a distribution close to the equilibrium can invade.

The insights of the study are twofold. First, it sheds light on the significance of Nash equilibrium in an ecological context of foraging strategies. Second, it shows that an evolutionarily unstable state can rule the composition of the ecological system. Therefore, the contribution made by the paper should be most significant to better understand the dynamics of competitive communities and their eco-evolutionary trajectories. 

References

Nash JF (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 48–49. https://doi.org/10.1073/pnas.36.1.48

Rogers AR (2021) Beating your Neighbor to the Berry Patch. bioRxiv, 2020.11.12.380311, ver. 8 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2020.11.12.380311

The authors present a study typical of the field of belowground-aboveground interactions [1]. This framework has been extremely fruitful since the beginning of 2000s [2]. It has also contributed to bridge the gap between soil ecology and the rest of ecology [3]. The study also pertains to the rich field on the impacts of herbivores on soil functioning [4].

The study more precisely tested during two years the effect on nutrient cycling of the interaction between the type of grassland (along a gradient of biomass productivity) and the diet of the community of insect herbivores (5 treatments manipulating the grasshopper community on 1 m2 plots, with a gradient from no grasshopper to grasshoppers either specialized on forbs or grasses). What seems extremely interesting is that the study is based on a rigorous hypothesis-testing approach. They compare the predictions of two frameworks: (1) The “productivity model” predicts that in productive ecosystems herbivores consume a high percentage of the net primary production thus accelerating nutrient cycling. (2) The “diet model” distinguishes herbivores consuming exploitative plants from those eating conservative plants. The former (later) type of herbivores favours conservative (exploitative) plants therefore decelerating (accelerating) nutrient cycling. Interestingly, the two frameworks have similar predictions (and symmetrically opposite predictions) in two cases out of four combinations between ecosystem productivities and types of diet (see Table 1). An other merit of the study is to combine in a rather comprehensive way all the necessary measurements to test these frameworks in combination: grasshopper diet, soil properties, characteristics of the soil microbial community, plant traits, vegetation survey and plant biomass.

The results were in contradiction with the ‘‘diet model’’: microbial properties and nitrogen cycling did not depend on grasshopper diet. The productivity of the grasslands did impact nutrient cycling but not in the direction predicted by the “productivity model”: productive grasslands hosted exploitative plants that depleted N resources in the soil and microbes producing few extracellular enzymes, which led to a lower potential N mineralization and a deceleration of nutrient cycling. Because, the authors stuck to their original hypotheses (that were not confirmed), they were able to discuss in a very relevant way their results and to propose some interpretations, at least partially based on the time scales involved by the productivity and diet models.

Beyond all the merits of this article, I think that two issues remain largely open in relation with the dynamics of the studied systems, and would deserve future research efforts. First, on the ‘‘short’’ term (up to several decades), can we predict how the communities of plants, soil microbes, and herbivores interact to drive the dynamics of the ecosystems? Second, at the evolutionary time scale, can we understand and predict the interactions between the evolution of plant, microbe and herbivore strategies and the consequences for the functioning of the grasslands? The two issues are difficult because of the multiple feedbacks involved. One way to go further would be to complement the empirical approach with models along existing research avenues [5, 6]. 

References

[1] Ibanez S, Foulquier A, Brun C, Colace M-P, Piton G, Bernard L, Gallet C, Clément J-C (2022) The contrasted impacts of grasshoppers on soil microbial activities in function of primary production and herbivore diet. bioRxiv, 2022.07.04.497718, ver. 2 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2022.07.04.497718

[2] Hooper, D. U., Bignell, D. E., Brown, V. K., Brussaard, L., Dangerfield, J. M., Wall, D. H., Wardle, D. A., Coleman, D. C., Giller, K. E., Lavelle, P., Van der Putten, W. H., De Ruiter, P. C., et al. 2000. Interactions between aboveground and belowground biodiversity in terretrial ecosystems: patterns, mechanisms, and feedbacks. BioScience, 50, 1049-1061. https://doi.org/10.1641/0006-3568(2000)050[1049:IBAABB]2.0.CO;2

[3] Barot, S., Blouin, M., Fontaine, S., Jouquet, P., Lata, J.-C., and Mathieu, J. 2007. A tale of four stories: soil ecology, theory, evolution and the publication system. PLoS ONE, 2, e1248. https://doi.org/10.1371/journal.pone.0001248

[4] Bardgett, R. D., and Wardle, D. A. 2003. Herbivore-mediated linkages between aboveground and belowground communities. Ecology, 84, 2258-2268. https://doi.org/10.1890/02-0274

[5] Barot, S., Bornhofen, S., Loeuille, N., Perveen, N., Shahzad, T., and Fontaine, S. 2014. Nutrient enrichment and local competition influence the evolution of plant mineralization strategy, a modelling approach. J. Ecol., 102, 357-366. https://doi.org/10.1111/1365-2745.12200

[6] Schweitzer, J. A., Juric, I., van de Voorde, T. F. J., Clay, K., van der Putten, W. H., Bailey, J. K., and Fox, C. 2014. Are there evolutionary consequences of plant-soil feedbacks along soil gradients? Func. Ecol., 28, 55-64. https://doi.org/10.1111/1365-2435.12201

In this article, Saade et al. (2021) investigate how the rate of local extinctions and their spatial distribution affect recolonization dynamics in metacommunities. They use an elegant combination of microcosm experiments with metacommunities of freshwater ciliates and mathematical modelling mirroring their experimental system. Their main findings are (i) that local patch extinctions increase both local (α-) and inter-patch (β-) diversity in a transient way during the recolonization process, (ii) that these effects depend more on the spatial distribution of extinctions (dispersed or clustered) than on their amount, and (iii) that they may spread regionally.
Microcosm experiments are already quite cool just by themselves and have contributed largely to conceptual advances in community ecology (see Fraser and Keddy 1997, or Jessup et al. 2004 for reviews on this topic), but they are here exploited to a whole further level by the fitting of a metapopulation dynamics model. The model allows both to identify the underlying mechanisms most likely to generate the patterns observed (here, competitive interactions) and to assess the robustness of these patterns when considering larger spatial or temporal scales. This release of experimental limitations allows here for the analysis of quantitative metrics of spatial structure, like the distance to the closest patch, which gives an interesting insight into the functional basis of the effect of the spatial distribution of extinctions.

A major strength of this study is that it highlights the importance of considering the spatial structure explicitly. Recent work on ecological networks has shown repeatedly that network structure affects the propagation of pathogens (Badham and Stocker 2010), invaders (Morel-Journel et al. 2019), or perturbation events (Gilarranz et al. 2017). Here, the spatial structure of the metacommunity is a regular grid of patches, but the distribution of extinction events may be either regularly dispersed (i.e., extinct patches are distributed evenly over the grid and are all surrounded by non-extinct patches only) or clustered (all extinct patches are neighbours). This has a direct effect on the neighbourhood of perturbed patches, and because perturbations have mostly local effects, their recovery dynamics are dominated by the composition of this immediate neighbourhood. In landscapes with dispersed extinctions, the neighbourhood of a perturbed patch is not affected by the amount of extinctions, and neither is its recovery time. In contrast, in landscapes with clustered extinctions, the amount of extinctions affects the depth of the perturbed area, which takes longer to recover when it is larger. Interestingly, the spatial distribution of extinctions here is functionally equivalent to differences in connectivity between perturbed and unperturbed patches, which results in contrasted “rescue recovery” and “mixing recovery” regimes as described by Zelnick et al. (2019).
 
Furthermore, this study focuses on local dynamics of competition and short-term, transient patterns that may have been overlooked by more classical, equilibrium-based approaches of dynamical systems of metacommunities. Indeed, in a metacommunity composed of several competitors, early theoretical work demonstrated that species coexistence is possible at the regional scale only, provided that spatial heterogeneity creates spatial variance in fitness or precludes the superior competitor from accessing certain habitat patches (Skellam 1951, Levins 1969). In the spatially homogeneous experimental system of Saade et al., one of the three ciliate species ends up dominating the community at equilibrium. However, following local, one-time extinction events, the community endures a recolonization process in which differences in dispersal may provide temporary spatial niches for inferior competitors. These transient patterns might prove essential to understand and anticipate the resilience of natural systems that are under increasing pressure, and enduring ever more frequent and intense perturbations (IPBES 2019). Spatial autocorrelation in extinction events was previously identified as a risk for stability and persistence of metacommunities (Ruokolainen 2013, Kahilainen et al. 2018). These new results show that autocorrelated perturbations also have longer-lasting effects, which is likely to increase their overall impact on metacommunity dynamics. As spatial and temporal autocorrelation of temperature and extreme climatic events are expected to increase (Di Cecco and Gouthier 2018), studies that investigate how metacommunities respond to the structure of the distribution of perturbations are more necessary than ever.
 
References

Badham J, Stocker R (2010) The impact of network clustering and assortativity on epidemic behaviour. Theoretical Population Biology, 77, 71–75. https://doi.org/10.1016/j.tpb.2009.11.003
 
Di Cecco GJ, Gouhier TC (2018) Increased spatial and temporal autocorrelation of temperature under climate change. Scientific Reports, 8, 14850. https://doi.org/10.1038/s41598-018-33217-0
 
Fraser LH, Keddy P (1997) The role of experimental microcosms in ecological research. Trends in Ecology & Evolution, 12, 478–481. https://doi.org/10.1016/S0169-5347(97)01220-2
 
Gilarranz LJ, Rayfield B, Liñán-Cembrano G, Bascompte J, Gonzalez A (2017) Effects of network modularity on the spread of perturbation impact in experimental metapopulations. Science, 357, 199–201. https://doi.org/10.1126/science.aal4122
 
IPBES (2019) Summary for policymakers of the global assessment report on biodiversity and ecosystem services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. S. Díaz, J. Settele, E. S. Brondízio E.S., H. T. Ngo, M. Guèze, J. Agard, A. Arneth, P. Balvanera, K. A. Brauman, S. H. M. Butchart, K. M. A. Chan, L. A. Garibaldi, K. Ichii, J. Liu, S. M. Subramanian, G. F. Midgley, P. Miloslavich, Z. Molnár, D. Obura, A. Pfaff, S. Polasky, A. Purvis, J. Razzaque, B. Reyers, R. Roy Chowdhury, Y. J. Shin, I. J. Visseren-Hamakers, K. J. Willis, and C. N. Zayas (eds.). IPBES secretariat, Bonn, Germany. 56 pages. https://doi.org/10.5281/zenodo.3553579 
 
Jessup CM, Kassen R, Forde SE, Kerr B, Buckling A, Rainey PB, Bohannan BJM (2004) Big questions, small worlds: microbial model systems in ecology. Trends in Ecology & Evolution, 19, 189–197. https://doi.org/10.1016/j.tree.2004.01.008
 
Kahilainen A, van Nouhuys S, Schulz T, Saastamoinen M (2018) Metapopulation dynamics in a changing climate: Increasing spatial synchrony in weather conditions drives metapopulation synchrony of a butterfly inhabiting a fragmented landscape. Global Change Biology, 24, 4316–4329. https://doi.org/10.1111/gcb.14280

Levins R (1969) Some Demographic and Genetic Consequences of Environmental Heterogeneity for Biological Control1. Bulletin of the Entomological Society of America, 15, 237–240. https://doi.org/10.1093/besa/15.3.237
 
Morel-Journel T, Assa CR, Mailleret L, Vercken E (2019) Its all about connections: hubs and invasion in habitat networks. Ecology Letters, 22, 313–321. https://doi.org/10.1111/ele.13192

Ruokolainen L (2013) Spatio-Temporal Environmental Correlation and Population Variability in Simple Metacommunities. PLOS ONE, 8, e72325. https://doi.org/10.1371/journal.pone.0072325

Saade C, Kefi S, Gougat-Barbera C, Rosenbaum B, Fronhofer EA (2021) Spatial distribution of local patch extinctions drives recovery dynamics in metacommunities. bioRxiv, 2020.12.03.409524, ver. 4 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2020.12.03.409524
 
Skellam JG (1951) Random Dispersal in Theoretical Populations. Biometrika, 38, 196–218. https://doi.org/10.2307/2332328
 
Zelnik YR, Arnoldi J-F, Loreau M (2019) The three regimes of spatial recovery. Ecology, 100, e02586. https://doi.org/10.1002/ecy.2586