Landscape configuration can flip species–area relationships in dynamic meta-food-webs
Abstract
Spatial and trophic processes profoundly influence biodiversity, yet ecological theories often treat them independently. The theory of island biogeography and related theories on metacommunities predict higher species richness with increasing area across islands or habitat patches. In contrast, food-web theory explores the effects of traits and network structure on coexistence within local communities. Exploring the mechanisms by which landscape configurations interact with food-web dynamics in shaping metacommunities is important for our understanding of biodiversity. Here, we use a meta-food-web model to explore the role of landscape configuration in determining species richness and show that when habitat patches are interconnected by dispersal, more species can persist on smaller islands than predicted by classical theory. When patch sizes are spatially aggregated, this effect flattens the slope of the species–area relationship. Surprisingly, when landscapes have random patch-size distributions, the slope of the species–area relationships can even flip and become negative. This could be explained by higher biomass densities of lower trophic levels that then support species occupying higher trophic levels, which only persist on small and well-connected patches. This highlights the importance of simultaneously considering landscape configuration and local food-web dynamics to understand drivers of species–area relationships in metacommunities.
This article is part of the theme issue ‘Diversity-dependence of dispersal: interspecific interactions determine spatial dynamics’.
1. Introduction
Ecological theories on the maintenance of biodiversity have tended to bifurcate into those that focus on regional-scale spatial processes such as habitat heterogeneity and dispersal [1–4] and those that focus on local-scale interspecific interactions, ecological networks and their impact on coexistence [5–11]. More recently, understanding how these processes interact in shaping biodiversity patterns is becoming increasingly recognized as a key challenge (e.g. [12–15]). Combining these processes will be crucial to understanding how biodiversity patterns will change in the face of anthropogenic drivers that influence spatial processes, such as habitat fragmentation, as well as alterations to the structure of local food webs.
One of the earliest conceptualizations of the importance of spatial processes was the theory of island biogeography, which envisioned the number of species co-occurring on islands as a balance between species colonization rates and extinction rates [3]. These rates are, in turn, influenced by island size (larger islands have lower extinction rates and higher colonization rates) and island isolation (more distant islands have higher extinction rates and lower colonization rates). The theory of island biogeography, as well as related concepts, predicts a generally positive relationship between island size and the number of species on that island—the island species–area relationship (ISAR)—and this is frequently observed in natural systems [16,17]. We hereafter use ISAR for both island and island-like habitat patches to differentiate this type of species–area relationship from other types (e.g. nested species–area relationships) that are sometimes used synonymously [18,19].
The ISAR is typically positive (more species on larger islands) in mainland–island models and empirical observations [16,17]. This pattern often represents more than simple sampling effects for both natural islands and island-like habitat fragments, suggesting the importance of the underlying ecological mechanisms, such as local species interactions and dispersal [20,21]. However, the spatial distribution of patches in a landscape can influence the shape of the ISAR. For example, dispersal-mediated processes such as rescue effects [22] and source–sink dynamics [23] can often lead to flatter ISAR relationships because more species are able to persist on smaller islands than would have been possible without such metacommunity-level processes.
Species interactions, particularly trophic interactions in food webs, can also strongly influence community biodiversity and how it scales with area in manifold ways [5,8]. Moreover, trophic dynamics can influence abundances or densities of populations and affect extinction risks and dispersal fluxes, ultimately also affecting colonization rates. Traits such as body mass, for example, strongly influence interaction strengths and their distribution across food-web links that drive community biodiversity [9,24], and also influence spatial processes, such as how far animals can disperse [25,26]. Moreover, larger animals that tend to occupy higher trophic levels need larger habitats to meet their energetic demands [27–30] and tend to suffer most from habitat isolation [31]. As a result, the shape of the ISAR can be strongly influenced by trophic interactions and the manifold interactions between traits and dispersal (e.g. [32–34]).
The trophic theory of island biogeography [35] integrates spatial and trophic processes using food-web properties to predict ISARs and other patterns on islands of different sizes. In this approach, ISARs are generally shallower and depend on patch isolation and interisland dispersal rates. This finding rests on the idea that species are more likely to persist on large islands, but also need their prey species to be present, favouring generalist species and highly connected food webs. Based on the general pattern that species traits such as body mass impose strong constraints on possible dispersal distances [25,36,37] and trophic linkage patterns [38,39], a trait-based theory of island biogeography predicted that the distribution of traits also depended on island area and isolation [33].
Although the trophic theory of island biogeography increased the biological realism of the classical island biogeography by accounting for the consumer’s need to find resources, it still represents a rather simplified perspective of how landscape configurations and food-web structures interactively affect biodiversity. Here, we further integrate the theory of island biogeography with meta-food-web theory [15,31] and show that the species–area relationship depends on an interaction between landscape configurations and food-web structures. For example, patches within metacommunities can vary considerably in their spatial configuration—and thus dispersal links—in several ways (see figure 1 for the examples that we examined here). Patches can have a mainland–island structure such as that envisioned in the theory of island biogeography. Alternatively, they can have a ‘random graph’ structure, in which all patches have a similar number of dispersal connections (e.g. habitat networks of songbirds [40]). Like most naturally forming networks, they can also have a ‘small world’ structure, which has many short connections within a cluster of patches but not among clusters [40]. In addition, patch sizes within each of these three types of landscapes can be autocorrelated (larger patches near larger patches) or randomly distributed. For instance, in the case of forest fragments and wetlands, the distribution of patch sizes across the landscape can change systematically from random to autocorrelated distributions during the process of increasing fragmentation and human alteration of the landscape [41–45]. As such, the configurations of habitat patches determine different arrangements of possible dispersal routes. However, the realization of dispersal will depend on local processes because species dispersal often relates to local densities that are the outcome of a large set of interspecific interactions.

Figure 1. Conceptual figure of different landscape configurations. Patches in metacommunities can be distributed in different spatial configurations and therefore affect dispersal links in manyfold ways, as illustrated here. We simulated six different landscape configurations. In rows, three different landscape types named ‘Mainland–Island’ (with spatially autocorrelated distances between patches), 'Random Graph’ (random distributed patches) and ‘Small-World’ (clusters of patches with many short distances) that exhibit different distributions of patch locations, patch sizes and isolation. The sizes of patches can also be distributed differently. Here, in columns (1) spatially autocorrelated and (2) random distribution, each patch can potentially harbour a complete food web.
In this study, we use a simulation-based approach to meta-food-webs employing body-mass-driven trophic and spatial processes to address how landscape configurations affect ISARs. Specifically, we show how landscape configurations (distributions of patches and patch sizes across the landscape as shown in figure 1) drive: (1) the slope and intercept of the ISARs and (2) local food-web structures (here: trophic levels and distribution of biomass densities). Together, these analyses tackle how spatial and trophic processes drive biodiversity in multilayer networks (i.e. the combination of different types of networks such as spatial and trophic networks) that are complex in trophic and spatial topologies.
2. Methods
We created 120 distinct landscapes by manipulating the spatial network structures (figure 1, rows) and patch size distribution regimes (figure 1, columns). These landscapes belong to one of three primary network structures: mainland–island, random-graph and small-world. Each structure influenced the density and distribution of patches within the landscape. For instance, we created mainland–island landscapes characterized by skewed beta distributions, resulting in varying patch densities across the landscape. Similarly, we used random graph landscapes to exhibit uniform patch distributions, while small-world landscapes featured clustered patches. Furthermore, we varied the size of patches, ranging from 105 to 107, and distributed them either randomly or correlatedly based on the x-coordinate of the patch location.
We constructed food webs based on an allometric model by Schneider et al. [46], where each species was defined by its average adult body mass. We uniform randomly assigned log10 body masses within specified ranges for both plants [0, 3] and animals [2, 6]. The construction of diverse food web structures involved varying the number of species (between 10 and 60), fractions of basal species (between 0.2 and 0.5) and widths of species feeding niches (more or less generalistic consumers). These food webs represented potential trophic interactions among the species pool in the landscape.
In total, we conducted a total of 4800 meta-food-web simulations across the 120 landscapes to explore trophic and spatial dynamics. These dynamics were integrated into the model, encompassing local trophic interactions, emigration, immigration and nutrient dynamics. Dispersal was incorporated into the model as species-specific biomass flow between habitat patches. We executed the simulations for 50 000 time steps using numerical methods to capture the intricate dynamics of the landscapes.
To investigate the area effect on extinction, we examined species population extinction when biomass translated to less than one individual per species on a patch. The number of individuals per species on a patch was calculated based on the population density and patch area. For detailed methods and equations see the electronic supplementary material.
Simulations were done both with and without dispersal. Emigration rates were influenced by local biomass dynamics, while immigration rates were determined by emigration, the distance between patches and species-specific dispersal capacities.
(a) Analyses
We created three categories of isolation: ‘low’, ‘medium’ and ‘high’. To assign these categories, we binned log-transformed nearest neighbour distances with an equal number of data points in each bin. We binned according to the number of data points (as opposed to according to value ranges) to have comparable statistical power (sample size) in each category. Furthermore, we recorded the densities and trophic levels of all persistent populations at the end of the simulations.
For all landscapes and categories of isolation, we fitted species–area relationships with linear mixed effects models (lme4 in R, v. 3.6.2 [47]) of ln(species richness) (S) depending on ln(patch area) (A), thus expressing the linear relationship in log-space [17] (with c being the intercept and z the slope) according to
and the food-web ID of the initial structure as a random intercept. The averaged predictions were then plotted using ggplot [48].
3. Results
(a) Landscape configurations influence species–area relationships
In the model without dispersal (null model), species richness is affected only by extinction risks, which are higher on smaller patches relative to larger patches. Here, we found positive species–area relationships (figure 2, dashed lines, exponent z = 0.116, 95% CI = (0.109, 0.122)). Note that the absolute values of the exponents of species–area relationships presented here should only be interpreted in relation to each other because patch sizes and distances have artificial units.

Figure 2. Interaction of landscape configuration with species–area relationships. Species–area relationships in the different landscape configurations (see figure 1) (a–f) with different levels of isolation (colour-coded). Dashed lines (NULL) represent area effects obtained from the no-dispersal model.
For all models with dispersal, the different landscape configurations include three landscape types (figure 2, rows) across patch size distributions that are either random (figure 2, right column) or spatially correlated (figure 2, left column). In mainland–island landscapes and spatially correlated patch sizes (figure 1, correlated area), we also find positive species–area relationships and their slope is highest under high isolation (z = 0.070, 95% CI = (0.064, 0.075), figure 2, mainland–island: correlated, (a)). The species–area relationship for highly isolated patches is similar to the area effect on species richness in the model without dispersal, which suggests that species richness is mainly driven by area effects on extinction risks. Under decreasing isolation, the species–area curve flattens (i.e. the slope decreases; low isolation; z = 0.021, 95% CI = (0.016,0.026)) because small patches can harbour more species (i.e. the intercept c increases, figure 2a ). The other two landscape types with spatially correlated patch sizes (figure 2c , random graph; figure 2e , small-world) also show positive species–area relationships but less of an effect of isolation. The species–area relationships in small-world landscapes are shallower (i.e. have a smaller z; see electronic supplementary material, table S1 for all slopes).
Moreover, we found negative species–area relationships in landscapes with randomly distributed patch sizes for all three landscape types (increase in c, negative z, figure 2b,d and f ). These negative slopes are steepest for patches with low isolation. The large patches show a similar species richness (ln(S)~2.4) in the model without dispersal and all landscapes are independent of the patch size distribution, suggesting that the negative slopes arise from an increase in the intercept. In landscapes that have spatially correlated patch size distributions, small patches, however, support the fewest number of species. Here, species richness is generally not much higher than in the model without dispersal. Furthermore, we found that in landscapes with random patch size distributions, the highest number of species occur on small patches with low isolation. Here, species richness substantially exceeds the model without dispersal, as well as that of the large patches, causing the negative species–area relationships.
(b) Landscape configurations affect population densities and trophic levels
Our subsequent analysis aimed at understanding why small patches in landscapes with random patch size distributions have a substantially higher species richness than those in landscapes with correlated patch size distributions. Most species that exclusively persisted in landscapes with random patch size distributions occur on small patches and occupy high trophic levels (figure 3a ). This is especially the case for small patches at small or medium isolation (see electronic supplementary material, figure S1 for details). These small patches also harbour higher population densities across all trophic levels compared to small patches in landscapes with correlated patch sizes and larger patches in all landscapes (figure 3b ). Medium-sized and large patches harbour similar biomass densities in landscapes with either random or correlated patch size distributions.

Figure 3. Species occupying higher trophic levels occurring on small patches drive negative species–area relationships. (a) Trophic level of species that uniquely occur in landscapes with random patch-size distributions on small (red), medium (green) and large (blue) patches. This means that the average trophic level of species uniquely occurring there is around 3 and therefore consists mostly of large carnivores. With their almost 10-fold number (numbers on top represent the number of species) compared to medium- and large-sized patches, they contribute most to the increase in the ISARs intercept. (b) Total biomass of trophic levels on small, medium and large patches in landscapes with either correlated (blue) or random (red) patch size distributions.
4. Discussion
Here, we have extended ideas related to the trophic theory of island biogeography [32,33,35] to include meta-food-webs with interacting spatial and trophic dynamics. Overall, when there is no interpatch dispersal, our model recovers the expected strong and positive effect of patch size on species richness, with a relatively low intercept (low c, meaning few species on the smallest patches) that emerges from typical island biogeography theory [3]. However, when we allow for interpatch dispersal, the shape of the ISAR shifts considerably. First, in all cases, many more species persist on smaller patches than when there is no interpatch dispersal (higher c values). Second, the typically positive ISAR (positive z values) found in landscapes with spatially autocorrelated patch sizes switched to unexpected negative ISAR slopes in landscapes with random distributions of patch sizes. Together, these results show strong constraints of the patch configuration in the landscape on the slope of the ISAR. Our findings thus provide explanations and testable hypotheses on the variance in ISAR slopes across studies.
In our study, differences in ISAR slope and intercept are mainly driven by differences in the patch size distribution across the landscape and patch isolation. We found that large patches all have a similar species richness, independent of the type of landscape in which they are embedded, or with and without dispersal. This finding suggests that the decrease in the slope of ISAR with decreasing isolation and the switch to negative slopes in landscapes with a random patch size distribution arise because species richness in small areas (the intercept c) increases. This increase in c is driven by species densities arising from large immigration fluxes from neighbouring patches, which is driven by two main factors. First, lower isolation results in lower dispersal losses and therefore increased immigration. Second, the size of a patch relative to its neighbours drives the magnitude of immigration fluxes. Consistent with classical source–sink dynamics [49], a small patch receives a lot of immigrating biomass from a large patch, whereas a large patch receives relatively little biomass from a small patch. This difference explains the consistent increase in c with decreasing isolation and a further increase in c in landscapes with random patch size distributions because small patches can have large neighbours in such landscapes. Generally, these fluxes increase species richness in small patches, thus increasing c, via rescue effects that prevent extinctions or allow populations to recover after local extinctions [22]. In addition, we found that strong immigration fluxes from large to small patches can lead to higher species biomass densities in small patches in comparison to what is observed when only trophic processes occur. This highlights the importance of spatial processes for biodiversity at both local and regional levels: while species from high trophic levels go extinct in the scenarios with little or no immigration, dispersal in the landscape allows them to survive on small patches. This is due to a local bottom-up effect that arises from a positive net immigration of species from lower trophic levels toward small patches and that makes them able to support the energetic requirements of species from higher trophic levels. It is important to note that this effect arises from changed population densities (i.e. abundance per area), which is driving predator–prey encounter rates and thus trophic interactions. This means that large patches can have higher population abundances, but because of their size still have lower population densities than small islands, rendering large islands relatively resource-poorer (see figure 4). Higher abundances on larger patches are distributed across a wider area, which dilutes the prey to lower density. Thereby, the foraging becomes less efficient because the predators have to search longer for their food. In contrast, abundances on small patches are less diluted and the constant influx of prey individuals from large patches can lead to a subsidy effect of high prey densities.

Figure 4. Illustration of mechanism responsible for negative ISARs. While larger patches may hold higher abundances of prey species than small patches, the prey density (individuals or biomass per area) may still be lower than on small patches that receive a lot of immigration (dispersal arrows show the dispersal biomass fluxes of the intermediate trophic level). Since a consumer's consumption rates depend on its encounter rate with its prey, they are driven rather by the density of their prey than their total abundance. This in turn means that the consumption rate may be higher on small patches and thus support a consumer population, while the prey density on a larger patch may not be sufficient despite its higher total abundance. Icons from ©pixabay.
In summary, when neighbouring patches are of similar size under correlated patch-size distributions, they have similar extinction rates (owing to the similar patch area) and the net dispersal is low (immigration and emigration are of similar magnitude). In this context, local dynamics are mainly driven by inherent food-web dynamics. When neighbouring patches tend to be of different sizes under random patch-size distributions, small patches receive a net influx of biomass, and the effect of biomass immigration may become larger relative to the biomass fluxes that are driven by food-web dynamics. Consequently, the biomass fluxes in the food web interact with the spatial fluxes of biomass and thereby with the landscape configuration. Overall, the strength of the correlation between the sizes of neighbouring patches corresponds to a gradient from more food-web-driven communities (landscapes with correlated distributions of patch area) to more landscape-driven communities (landscapes with random distributions of patch area).
Many of the ISAR patterns that our meta-food-web simulations reveal are consistent with empirical findings, including decreasing ISAR slopes z and increasing intercepts c with lower island isolation [50–53]. Furthermore, there is increasing evidence that food-web structures can alter ISAR shapes (e.g. [13,32,54–56]). Much less is known about how food-web and landscape structures interact to drive ISARs. For example, Östman et al. [54] showed that ISARs of insects in landscapes of habitat patches (grasslands called ‘glades’ within forested openings) depended on the interaction between patch area, patch isolation and the presence of top predatory lizards. Our results suggest that the effects of food-web structures on ISAR slopes can be even more complex than these simple observations, which calls for further empirical evaluation.
The finding of negative ISARs in landscapes with random patch-size distributions is counterintuitive. An explanation for the predominance of positive species–area relationships in nature, despite the potential for negative ones in our model, may be that our model does not include other important mechanisms underlying the ISAR, which may override the effects we observed when dispersal fluxes are high. For instance, a prominent mechanism underlying natural ISAR is that larger patches tend to have higher within-patch habitat heterogeneity of abiotic parameters such as nutrient supply and habitat structure [16,57–61]. The positive effects of habitat heterogeneity on species richness can override the negative ISARs predicted by our model simulations that assumed patches were homogeneous. Extensions of our meta-food-web approach should more directly incorporate different levels of matrix hostility and habitat heterogeneity to tease apart these effects. Nevertheless, our results suggest that neutral or positive ISARs cannot be expected as a trophic-spatial null model.
However, there are also a few empirical examples of negative ISARs [62–64]. Furthermore, there is evidence of negative density–area relationships [65], which supports the mechanism that we assume to underlie negative ISARs (figure 4). For instance, Bowers & Matter [66] found that some mammal species tend to exhibit negative area–density relationships in landscapes with small and less-isolated patches, which switch to positive area–density relationships in landscapes with larger and more isolated patches. We also uncover higher densities on small patches in random landscapes that allow the persistence of higher trophic levels. Consistent with our simulations, a study in the Swiss Alps showed that wolves, as large top-predators, occur where their prey density is high [67]. Together, these studies indicate that negative ISAR relationships may result from density-dependent regulation of dispersal and trophic interactions.
A possible explanation for this very scarce empirical evidence for negative ISARs could be that ISARs are typically measured in island and island-like systems where the matrix resistance might be higher than in our model (e.g. islands surrounded by water). This should diminish the effects of spatial dynamics altering the strength and direction of species–area relationships as, for instance, exemplified in the extreme case of our strongly positive ISARs in simulations without dispersal. Another reason for the scarce evidence of negative ISARs might be that real landscapes (or at least investigated landscapes) are rarely random in their patch-size distribution from the perspective of organisms.
Overall, our use of a meta-food-web model revealed that the interaction between spatial processes (dispersal) and trophic fluxes (bottom-up resource supply) can influence the shape of the species–area relationship, including negative ISARs under some landscape configurations. While ecologists have long stressed the importance of either spatial processes or species interaction networks for biodiversity patterns, our meta-food-web approach has integrated both aspects of species dynamics. This has revealed that the landscape configuration can strongly determine whether biodiversity patterns on habitat patches mostly depend on dispersal, food-web dynamics or a combination of both. In particular, our results demonstrate that the largest differences in the shapes of ISARs occur between landscapes with random or correlated distributions of patch sizes across the landscape that in turn produce large immigration rates on small patches.
As biodiversity is increasingly threatened by global change and habitat fragmentation, it is a key challenge to understand how spatial processes and the structure of ecological networks interact in shaping biodiversity patterns [12,13,33]. Here, our results emphasize that considering landscape configuration and food-web structures simultaneously may be crucial in conservation decisions to develop habitat protection strategies that particularly include small patches. It is these small patches in landscapes with uncorrelated patch sizes that may harbour species that do not occur anywhere else. This surprising result can only be revealed and understood owing to the integration of spatial and trophic networks into meta-food-webs.
Ethics
This work did not require ethical approval from a human subject or animal welfare committee.
Data accessibility
Code is availabile for review at [68].
Supplementary material is available online at [69].
Declaration of AI use
We have not used AI-assisted technologies in creating this article.
Authors’ contributions
R.R.: conceptualization, data curation, formal analysis, investigation, methodology, project administration, visualization, writing—original draft, writing—review and editing; J.M.C.: writing—review and editing; B.G.: formal analysis, writing—review and editing; J.H.: software, writing—review and editing; M.R.H.: visualization, writing—review and editing; B.R.: formal analysis, writing—review and editing; U.B.: conceptualization, formal analysis, funding acquisition, methodology, project administration, supervision, visualization, writing—review and editing.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.
Conflict of interest declaration
We declare we have no competing interests.
Funding
We gratefully acknowledge the support of the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig funded by the German Research Foundation (DFG-FZT 118, 202548816) and funding by the German Research Foundation (DFG) in the framework of the research units FOR 1748 (BR 2315/16-2) and FOR 2716 (BR 2315/21-1).