Article

# Dispersal governs the reorganization of ecological networks under environmental change

• Nature Ecology & Evolution 1, Article number: 0162 (2017)
• doi:10.1038/s41559-017-0162
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## Abstract

Ecological networks, such as food webs, mutualist webs and host–parasite webs, are reorganizing as species abundances and spatial distributions shift in response to environmental change. Current theoretical expectations for how this reorganization will occur are available for competition or for parts of interaction networks, but these may not extend to more complex networks. Here we use metacommunity theory to develop new expectations for how complex networks will reorganize under environmental change, and show that dispersal is crucial for determining the degree to which networks will retain their composition and structure. When dispersal between habitat patches is low, all types of species interactions act as a strong determinant for whether species can colonize suitable habitats. This colonization resistance drives species turnover, which breaks apart current networks and leads to the formation of new networks. However, when dispersal rates are increased, colonists arrive in high abundance in habitats where they are well adapted, so interactions with resident species contribute less to colonization success. Dispersal ensures that species associations are maintained as they shift in space, so networks retain similar composition and structure. The crucial role of dispersal reinforces the need to manage habitat connectivity to sustain species and interaction diversity into the future.

Ecological networks characterize the diversity of species and their interactions 1 . The structure of ecological networks is being transformed by species extinctions and invasions driven by global environmental change 2,3 . The effects of altered network structure on the functioning and stability of ecosystems is now well documented 4,​5,​6 , but little is known about how networks will reorganize in the future. Will ecological networks remain intact, collapse to simpler structures or reassemble with little similarity to those we see today?

Ecological networks reorganize when interactions between species are lost or when new interactions are formed 7 . Interactions are lost through extinctions or when previously interacting species no longer occupy the same habitats. Interactions are gained when species that were previously separated in space, shift to have overlapping ranges. In addition, changes in abundance can cause species interactions to be gained or lost without changes in co-occurrence 3,8,​9,​10 .

Species interactions are thought to cause ecological networks to reorganize when the environment changes, because they disrupt species sorting—whereby species shift their spatial distributions to track changes in environmental conditions 11,​12,​13 . Competition can impede species sorting by preventing species from successfully establishing in habitats where the local environment would otherwise be suitable 7,14,15 . Mutualist interactions may keep species together as they shift in space, but may also hinder range shifts, if the new habitat is unsuitable for one of the species 16,17 . In food webs, consumer distributions are limited by prey availability, while prey may be prevented from colonizing new patches that have abundant predators 16 . Yet, despite this knowledge, it is unclear how these effects will scale up to determine how entire ecological networks reorganize 3,8,10,11 .

We also expect network reorganization to depend on how species disperse between habitats. Dispersal is required for species sorting 12,15,16,18 , but it can also alter how species interact, because colonists interact with resident species 11,15 . Whether species can track environmental change through species sorting depends both on the distance and rate at which they disperse 19 . The degree to which competition can impede species sorting has been shown to depend on both of these aspects of dispersal 15,18,20 . Furthermore, interspecific differences in dispersal distance in competitive networks can break apart species interactions 18 . It is, however, not clear how changes in the overall rate of species dispersal will affect the degree to which species interactions cause the reorganization of more complex ecological networks. This knowledge is needed, because human land use is fragmenting landscapes, impeding the dispersal of organisms between habitats 21 .

We hypothesize that the rate of dispersal should govern how ecological networks reorganize under environmental change. We predict that the effect of species interactions on this reorganization should decrease as dispersal rates increase. We further predict that different types of species interactions (for example, competitive, facilitative, trophic) should all mediate network reorganization, but that this effect would be greatest for negative interactions (for example, competition, predation), because they repel interacting species, whereas facilitative interactions should keep species together as they shift in space 22 . Here, we test this hypothesis by combining biogeographic simulation models 15,18 with metacommunity network theory 23,​24,​25 . We show the conditions under which networks reorganize to retain their structure and composition as they shift in space.

Our simulation model consists of a metacommunity of 200 patches that spans a linear spatial environmental gradient (for example, temperature). The metacommunity is populated by 80 species and their distributions and abundances are determined by their environmental optima, their interspecific interactions and dispersal. We simulate temporal environmental change by gradually and evenly increasing the environmental value in all patches, while retaining the spatial environmental gradient (for example, regional warming). We chose a magnitude of environmental change that requires species to shift their ranges to persist. We contrast four scenarios where interspecific interactions were: (1) absent; (2) purely competitive; (3) mixed (competitive, facilitative, predator–prey); or (4) a food web with three trophic levels. In each scenario, we contrast the dynamics of the model over nine different average dispersal rates, spanning the range from 10−5 to 0.5. Individual species dispersal rates are drawn from a normal distribution around this average and they define the proportion of each population that disperses at each time step. We assume that the proportion of dispersers arriving in each patch decreases exponentially with the distance from the originating patch, but that the rate of exponential decay varies between species. For analysis, we define the ecological networks as the species that are present in a habitat patch and the interspecific interactions that link them 9 . Links are directed and weighted by the abundance of species i multiplied by the per capita effect of species i on species k. To analyse network change in the no-interaction scenario, we construct networks by assuming that all species have identical per capita effects on all other species, so that link weights are based only on the relative abundances of species in the community.

We measured change in two aspects of network reorganization—compositional change and structural change. Compositional change was quantified as network link dissimilarity 9 , which is the minimum extent to which the post-environmental-change networks differed from any pre-environmental-change network, regardless of their location in the metacommunity. Structural change quantifies the degree to which the structure of the networks change through time as captured by a range of metrics commonly used to quantify network structure (species number, link density, compartmentalization, average compartment throughflow, average link weight and trophic levels 26 ).

## Results and discussion

We find that all types of species interactions lead to network reorganization, but the degree to which this occurs depends on the average rate of dispersal (Figs 1, 2a). Without species interactions (Fig. 2a), there is negligible network reorganization, except when dispersal is so limiting that new populations cannot be established. However, even very low dispersal (0.0005) is enough to ensure that non-interacting ecological networks remain intact, as their component species track their environmental niches together.

When species interact, much higher rates of dispersal are required to keep ecological networks intact as the environment changes (Fig. 2a). Low dispersal rates (for example, 0.0005), that are sufficient for non-interacting networks to remain intact, are not sufficient for interacting networks, which results in considerable reorganization (approximately 75% for food-web networks). However, as dispersal is increased, this reorganization decreases, so that with an average of 10% dispersal there is less than 10% network reorganization in each of the interaction network types. Furthermore, with high dispersal, reorganization of the interacting networks is only slightly higher than in the non-interacting networks, indicating that the effect of species interactions on network reorganization is highly dependent on the average rate of species dispersal.

The effect of dispersal on network reorganization occurs, because dispersal mediates the degree to which species interactions acts as a filter for determining whether species can colonize a new habitat with favourable abiotic conditions (Supplementary Fig. 1). With low dispersal rates, species attempt to colonize new habitats with only a few individuals and their colonization success is greatly determined by how they interact with the resident community, even if they are well-suited to the local conditions. With higher dispersal rates, colonist numbers are larger, so their impact on resident species is greater and they are better able to overcome the resistance of the established community. High dispersal rates ensure that there is low interspecific variation in the rate at which species shift their ranges (Fig. 2b), so networks remain intact as they shift in space. By contrast, with low dispersal there is greater interspecific variation in range shift rates and networks experience high compositional turnover. This overall effect of average dispersal rate on network reorganization occurs despite interspecific differences in dispersal rates and kernels; increasing these differences should lead to greater network reorganization 18 . However, our results clearly demonstrate the importance of maintaining high rates of species dispersal to keep ecological networks intact in changing environments.

The relationship between compositional turnover and dispersal is consistent for all networks, although the amount of reorganization differs depending on the types of interactions that comprise the ecological networks (Figs 1, 2a). Competitive networks experience more compositional turnover than those that include mutualisms, because positive interactions facilitate the colonization of new habitats and therefore are more easily maintained during range shifts 27 . In food webs, the degree of compositional turnover depends on the trophic level of the species that form the interactions. In particular, predatory interactions experience the highest turnover (Fig. 2c), because predators are disproportionately lost from the networks as the environment changes (Fig. 3c). Predators are only able to track their environmental niches when their prey is in sufficient abundance. With low dispersal predators go extinct, because they are unable to keep pace with the changing environment; predators are left stranded outside their environmental niches. When dispersal is too high, excessive emigration reduces population sizes and predators cannot persist, even in stable environments. Therefore, the range of dispersal rates that allows species to persist becomes narrower as trophic level increases. Top predators are known to be especially vulnerable to environmental change 28,29 and our results support this.

Change in link composition occurs through the loss and gain of interactions, although losses are more prevalent than gains (Fig. 3). Interaction gains and losses occur when the composition of the networks changes, as well as when shifting abundances alter which interactions are realized 9 . Losses decrease as dispersal increases, as is evident in the maintenance of the distribution of realized interaction strengths with high dispersal (Supplementary Fig. 2); at low dispersal rates, weak interactions (that is, involving rare species) are disproportionately lost. Gains occur when dispersal is not limiting and are most common in food-web and mixed-interaction communities. In food webs, gains occur for plants under low dispersal (Fig. 3c) when higher trophic levels are lost, because species are able to expand their ranges to environments where they were previously excluded by herbivory 30,31 . However, higher dispersal results in gains for herbivores and carnivores (Fig. 3c). This occurs because these dispersal rates allow more species to persist, and those that do, take advantage of the loss of those that do not, and so expand their ranges into new environments.

We also find that the structural properties of the networks are best maintained when dispersal rates are high (Fig. 4). Spatial differences in link density and the other measured network properties are maintained as the networks shift in space (Fig. 5 and Supplementary Figs 3–6). With low dispersal, these network properties and their spatial differences erode as the networks reorganize, but increasing the dispersal rate maintains these properties. This includes properties that reflect the diversity of species and interactions in the network (number of species, link density), as well as compartmentalization, average compartment throughflow, average link weight and trophic levels, which reflect network structure. Preserving these network properties is desirable, because they are considered important for the stability and functioning of ecosystems 26,32 . In addition, high dispersal also minimizes the change in network structure that occurs within each habitat patch, despite compositional turnover (Supplementary Fig. 7). This is because the greatest species diversity is maintained when dispersal is high; the networks remain complex, even though their composition has changed.

## Conclusions

In order to forecast the change in biodiversity and functioning of future ecosystems, we must consider entire species networks 33,34 . Despite the complex ways that species interactions will affect the response of communities to environmental change, we find that changes in dispersal rate lead to surprisingly consistent patterns of reorganization across different types of networks. Although predicting how ecological networks will reorganize during environment change remains a considerable challenge 33 , our results show that dispersal determines the degree to which future networks resemble those we see today. In particular, when dispersal rates are high, networks reorganize in a way that preserves current species associations and network structural properties. What constitutes high dispersal will depend on the species of interest. However, it should correspond to those rates of dispersal that ensure that species are present in habitats that are suitable for growth and that allow them to shift their distributions in response to environmental change 19 . Unfortunately, landscapes around the globe are increasingly fragmented by human land use, and this is likely to be impeding species dispersal 21 . Our results suggest that the preservation and restoration of habitat connectivity 35,36 with protected area networks 37,38 may allow for resilient and predictable reorganization of communities as the environment changes.

## Methods

### Metacommunity model

Community dynamics were simulated in R (version 3.2.2) 39 using modified Lotka–Volterra equations 25 : $(1) X i j ( t + 1 ) = X i j ( t ) exp [ C i + ∑ k = 1 S B i k X k j ( t ) + A i j ( t ) ] + I i j ( t ) − X i j ( t ) a i$ where Xij(t) is the abundance of species i in patch j at time t. Ci is its intrinsic rate of increase. Bik is the per capita effect of species k on species i. Aij(t) is the effect of the environment in patch j on species i at time t. Iij(t) is the abundance of species i immigrating to patch j at time t. ai is the proportion of the population of species i that disperses at each time step. The metacommunity consists of S species.

Patches are equally spaced across a linear environmental gradient and species environmental optima Hi within each trophic level are equally distributed across the initial conditions. The effect of the environment in patch j at time t on species i follows a Gaussian function: $(2) A i j ( t ) = h − [ h exp ( − ( E j ( t ) − H i ) 2 2 σ 2 ) ]$ --> where h is a scaling parameter, Ej(t) is the environment in patch j at time t and σ is the standard deviation.

There are M patches in the metacommunity. The abundance of immigrants to patch j from all other patches is governed by: $(3) I i j ( t ) = ∑ l ≠ j M a i X i l ( t ) exp ( − L d j l )$ where djl is the geographic distance between patches j and l, and L is the strength of the exponential decrease in dispersal with distance. Individuals that disperse off either edge of the metacommunity are reflected back.

Interaction parameter values and community types were modified from ref. 25 . We fixed intraspecific interaction values across species to isolate the effects of interspecific interactions (−0.15 for predators, −0.2 for all other species). In the no-interactions community, all interspecific interactions were 0. In the competitive and arbitrary communities, negative and positive interactions were drawn from uniform distributions (−0.15–0) and (0–0.075), respectively. In the mixed communities, 65% of the interactions were competitive (−/−), 25% were predator–prey or parasitic (+/−) and 10% were mutualistic (+/+). In the food-web communities, interspecific interactions were drawn from uniform distributions between 0 and −0.1 (competition between plants), −0.3 (the effect of herbivores on plants), 0.1 (the effect of plants on herbivores), −0.1 (the effect of predators on herbivores) and 0.08 (the effect of herbivores on predators). This results in a food web with three trophic levels. Plants compete with each other to varying degrees, herbivores can feed on any plant, but the benefit that they receive varies across species, as does the effect of each herbivore population on each plant population. Likewise, predators can feed on any herbivore, but the benefit that they receive varies across species, as does the effect of each predator population on each herbivore population. All interaction values were scaled by dividing by 0.33S. Although the per capita interaction strengths are drawn from uniform distributions, multiplying them by the species abundances in the local patches results in a distribution of realized interaction strengths with a few strong and many weak interactions (Supplementary Fig. 2). This matches the general patterns of interaction strength distributions that have been observed in natural ecosystems 40 .

The rate of exponential decay in dispersal distance L for each species i was drawn from a normal distribution. The mean for this distribution was 0.3 (plants), 0.2 (herbivores) and 0.1 (predators), so that dispersal distances increased with trophic level 21 . The σ of this distribution was equal to 0.25× mean, so that variation scaled with the mean.

### Simulations

We simulated metacommunities with M = 200 patches and S = 80 species with the following parameters: Xij(t = 1) = 10, Ci = 0.05, h = 300, σ = 50 and d1,200 = 200. This size of metacommunity was used to ensure that edge effects were not prevalent. Initial abundances, Xij(t = 1), and growth rates, Ci, were based on those used previously 25 . The number of species and the parameters that govern their response to the environment, h and σ, were chosen to ensure that species were limited to a fraction of the metacommunity and that their ranges overlapped enough to ensure local diversity of 10–35 species. We chose to use a distance of one between each patch. Simulations ran for 7,000 time steps. The initial environment spanned a linear gradient across the region from E1 = 1 to E200 = 80. This range of environmental values was chosen to ensure that species distributions were spread across the metacommunity, with overlap. The environment remained constant for the first 2,000 time steps to allow the communities to reach equilibrium. The environmental value, across the region, was then steadily increased by 20 over the next 3,000 time steps to simulate environmental change. This increase in environmental value was chosen to ensure that species were forced to shift their distributions in order to persist in the metacommunity. The environment was held constant for the final 2,000 time steps to allow the communities to reach equilibrium again.

We contrasted nine mean dispersal rates ( $a ¯$ ) from 0.0001 to 0.5 that specify the proportion of the population that moves in each time step. The individual dispersal rate a of each species i was drawn from a normal distribution with a mean of $a ¯$ and σ =  $a ¯ × 0.25$ , so that variation in dispersal rate scaled with $a ¯$ . This was replicated 100 times for each community type, each time with new randomly generated interactions, in order to estimate mean values and variation in our response variables at each dispersal rate.

### Response variables and analysis

All response variables were based on the comparison of the final network in patches 101 to 150 with the pre-change network (all patches). The final environment in these 50 patches corresponded to the pre-change environment in patches 51 to 100. We restricted our analysis to these patches to ensure that our results were not affected by edge effects in the metacommunity. Nj(t) is the network present in patch j at time t. The species that are present form the nodes of the network and the links are formed by the interspecific interactions. Link weights are given as the realized interaction strengths in patch j at time t. In order to analyse network change in the communities without interspecific interactions, we assigned an equal interaction strength B ik of one to all possible pairwise interactions. This produced a network containing all species present at time t, with links from the most abundant species to all others.

We calculated network compositional turnover as the mean network dissimilarity between each final network and its most similar pre-change network. Network dissimilarity was calculated as the Bray–Curtis dissimilarity of the weighted species interaction networks, using the betalink R package 9 : $(4) b n n ′ = ∑ k S 2 | w n k − w n ′ k | ∑ k S 2 w n k + w n ′ k$ where n and nʹ are two different networks and wnk is the weight of interaction k in network n.

In the food-web communities, we also quantified network dissimilarity of the networks formed by just plant competition, herbivory or predation, by analysing subsets of the interaction web that included the relevant nodes and links.

We quantified interaction losses and gains using the betalink R package 9 : $(5) Gains = a a + b + c$ $(6) Losses = b a + b + c$ where a is the number of interactions that is present in the initial network, but not the final network, b is the number of interactions that is present in the final network, but not in the initial network, and c is the number of interactions that is present in both networks 41 .

Range-shift rate variation was calculated as the interspecific σ of the mean number of time steps between successful colonisations of new patches at the leading edge of the range shift.

We calculated change in network structure by contrasting the final weighted species interaction network with: (1) the pre-change network with the greatest compositional similarity (as identified in the compositional analysis); and (2) the pre-change network in the same patch. We measured five network properties that are thought to be important for the stability and functioning of ecosystems 26 : the number of nodes (species richness), link density, network, network compartmentalization, and average compartment throughflow, average link weight, as well as the number of trophic levels in the food-web communities. Network properties were calculated using the NetIndices package in R 42 . Network change was calculated as the property of the final network (t = 7,000), divided by its value in the pre-change network (t = 2,000).

### Code availability

All code for the simulations and figures is available on GitHub (https://github.com/plthompson/RangeShifts).

### Data availability

All data and analyses used for this manuscript can be reproduced using this R code.

## Additional information

How to cite this article: Thompson, P. L. & Gonzalez, A. Dispersal governs the reorganization of ecological networks under environmental change. Nat. Ecol. Evol. 1, 0162 (2017).

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

We thank M. O’Connor, B. Beisner, G. Fussmann, E. Pedersen, A. Ives and members of the Gonzalez lab for assistance and valuable feedback. P.L.T. is supported by NSERC, Vineberg and Killam fellowships. A.G. is supported by the Canada Research Chair program, Killam Fellowship, the Liber Ero Chair in Conservation Biology and NSERC.

## Author notes

• Patrick L. Thompson

Present address: Department of Zoology, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada

## Affiliations

1. ### Department of Biology, McGill University, Montreal, Quebec H3A 1B1, Canada.

• Patrick L. Thompson
•  & Andrew Gonzalez

## Authors

### Contributions

P.L.T. and A.G. designed the study. P.L.T. wrote the code and performed the simulations. P.L.T. wrote the first draft of the manuscript and both authors contributed substantially to revisions.

### Competing interests

The authors declare no competing financial interests.

## Corresponding author

Correspondence to Patrick L. Thompson.

## PDF files

1. 1.

### Supplementary Information

Supplementary Figures 1–8.