Food web persistence in fragmented landscapes

Abstract

Habitat destruction, characterized by patch loss and fragmentation, is a key driver of biodiversity loss. There has been some progress in the theory of spatial food webs; however, to date, practically nothing is known about how patch configurational fragmentation influences multi-trophic food web dynamics. We develop a spatially extended patch-dynamic model for different food webs by linking patch connectivity with trophic-dependent dispersal (i.e. higher trophic levels displaying longer-range dispersal). Using this model, we find that species display different sensitivities to patch loss and fragmentation, depending on their trophic position and the overall food web structure. Relative to other food webs, omnivory structure significantly increases system robustness to habitat destruction, as feeding on different trophic levels increases the omnivore's persistence. Additionally, in food webs with a dispersal–competition trade-off between species, intermediate levels of habitat destruction can enhance biodiversity by creating refuges for the weaker competitor. This demonstrates that maximizing patch connectivity is not always effective for biodiversity maintenance, as in food webs containing indirect competition, doing so may lead to further species loss.

1. Introduction

Ecological communities across the world are under threat from ongoing habitat destruction, a leading driver of biodiversity loss [1]. Resulting from land use change, pollution, over-exploitation and climate change, habitat destruction can be characterized into two components: patch loss and patch fragmentation [2]. The first, patch loss, is simply a decrease in the total habitable area, which naturally reduces population sizes and thus increases the probability of species extinction. The latter, patch fragmentation, is the division of the habitable area into disconnected or poorly connected subpatches [3], which is also known to increase species extinction risk, as the resulting subpatches are smaller and the subpopulations inhabiting them are more isolated [2–5]. Drivers of patch fragmentation also include natural barriers (e.g. rivers and deserts) as well as anthropogenic barriers (e.g. roads, dams and fences) [6–8].

While it is clear that ecological communities are damaged by habitat destruction, its precise impact on a community is much harder to predict. There has been extensive research, encompassing both empirical and theoretical studies, into the separate effects of patch loss and fragmentation [2–5,9,10], while studies on their interactive effects are relatively rare. Additionally, it is readily apparent that the effects of fragmentation on a given species strongly depend on its dispersal ability [2,11–16]. In particular, species with greater dispersal capability are less affected by patch fragmentation, as greater dispersal range allows wider barriers to be bypassed, directly counteracting the effects of fragmentation [17]. Furthermore, the interactions between species in a given community can be a key determinant for the effects of habitat destruction [1,18–22]. It has often been found that species at higher trophic levels are the first to go extinct through habitat loss [23–26], in accordance with the trophic rank hypothesis [27]. But omnivorous species do not necessarily follow this paradigm [28,29], and indirect interactions between species in lower trophic levels, such as exploitative or apparent competition, may also modify the sensitivity of their predators to habitat destruction [29–32].

To get insights into trophically linked communities in fragmented landscapes, further theoretical study should address all of these factors: patch loss and fragmentation, variation in species dispersal characteristics, and the trophic structure. Pillai et al. [31] developed a modelling framework for complex food web structures to describe the patch dynamics of the various trophic links instead of individual species. However, their framework is spatially implicit, in which any species can access any habitat patch with prey species. Habitat destruction creates spatial fragmented landscapes for which this spatially implicit framework is insufficient. Hiebeler [11] has already characterized such landscapes in terms of the densities of two habitat types (suitable and unsuitable) and their clumping degrees, thus allowing the effects of habitat loss and habitat fragmentation to be investigated separately by using a pair approximation (PA) approach [33–37]. In addition, Liao et al. [12,13,38] used this approach to explore how a species's dispersal capability affects its survival in landscapes subject to habitat destruction. Thus, there exist modelling techniques to fully describe the effects of landscape fragmentation on complex trophically linked communities, yet very few studies have done so to date.

In this study, we develop a spatially extended patch-dynamic model for different food webs in fragmented landscapes, based on the existing modelling frameworks of Pillai et al. [31]. As it is not feasible to consider the full diversity of possible food web structure, we restrict our attention to four common trophic modules consisting of three species: a simple food chain, omnivory, exploitative competition and apparent competition (figure 1). These typical modules describe the most important interaction types among species and form a basis for studying more complex food webs. In addition, we assign species dispersal ranges to reflect the common observation that a species's dispersal range increases with its trophic level [39–42]. Using this model, we first investigate how patch loss and fragmentation separately and interactively affect the persistence of species embedded in each of these trophic structures, and then explore whether species feeding preference/pressure can modify the effects of landscape fragmentation on community patterns.

Figure 1.

Four types of food web structures: (a) a simple food chain, (b) an omnivory food web, (c) exploitative competition and (d) apparent competition (arrow represents predation and dotted line represents competition). Each food web consists of three interacting species but with different dispersal traits: species 1 with neighbour dispersal, species 2 having random dispersal within habitat fragments and species 3 with global dispersal.

2. Material and methods

(a). Landscape structure

We model the landscape as an infinite lattice of cells (i.e. sites), each representing a patch that can be either empty or occupied by a specific set of trophically linked species. To introduce habitat destruction, we assume the landscape consists of two types of habitat patch: suitable (s) and unsuitable (u), where only s-patches (patch availability) can permit species colonization, while u-patches (patch loss) are unsuitable for any species establishment (s + u = 1). According to Hiebeler [11], the clustering degree of a given patch (e.g. s) can be characterized by the local density q_s/s (so-called patch connectivity), representing the conditional probability that the neighbour of a randomly chosen s-patch is also an s-patch, with q_s/s = ρ_ss/ρ_s. The pair density ρ_ss denotes the probability that a randomly chosen pair of neighbouring patches are both s-patches. Thus, the fragmentation degree of s-patches is inversely related to the clustering degree, defined as 1−q_s/s. According to the orthogonal neighbouring correlation method for landscape generation (using von Neumann neighbourhood; see details in [11,43]), we have

2.1

In particular, the suitable patches are randomly distributed at s = q_s/s.

(b). Coupling dispersal range to trophic level

We consider four trophic modules containing three species (species 1, 2 and 3; illustrated in figure 1): a simple food chain (basal species 1 → intermediate consumer 2 → top predator 3), a food web with an omnivorous top predator (omnivory), two competing species feeding on one prey species (exploitative competition) and one species feeding on two competing prey species (apparent competition). To reflect the fact that species dispersal range increases with trophic level/body size (as commonly observed in [39–42]), we assign each species a different dispersal mode: (i) species 1 can only colonize the neighbouring s-patches (neighbour dispersal; using von Neumann neighbourhood with z = 4); (ii) species 2 has uniform probability to colonize any s-patch within a habitat fragment (so-called patch cluster that consists of a group of connected patches; within-fragment dispersal), thus species 2's dispersal range is highly correlated with patch connectivity; (iii) species 3 has uniform probability to colonize any s-patch in the landscape (global dispersal). As such, the u-patches as barriers (e.g. rivers, roads, dams and fences) can only limit the dispersal of species 1 and 2, while the spread of species 3 is not affected. Therefore, we can describe the dynamics of: (i) species 1 with a PA model, which has already proven qualitatively useful in characterizing spatial correlation between neighbours in lattice-structured landscapes [11–13,33–38,43–47]; (ii) species 2 with a modified mean-field approximation (MFA) incorporating patch clustering degree q_s/s (as demonstrated in [38]); and (iii) species 3 with an MFA model [31].

Following Liao et al. [38], we can describe the patch dynamics of a simple food chain subject to the colonization–extinction–predation processes (models for other trophic modules shown in the electronic supplementary material, appendix A).

2.2

2.3

2.4

where all parameters are interpreted in table 1 (see details in [38]). Note that this model mainly focuses on describing the patch occupancy of trophic links or subcommunities (i.e. 1, 1 → 2 or 1 → 2 → 3) rather than those of individual species [31].

Table 1.

Parameter interpretation.

parameter	interpretation
u	fraction of unsuitable patches (habitat patch loss)
s	fraction of suitable patches (patch availability)
ci	colonization rate of species i
ei	intrinsic extinction rate of species i
cji	colonization rate of species j when feeding on prey species i
eji	intrinsic extinction rate of species j when feeding on prey species i
μji	the top-down extinction rate of species i eaten by species j
ρi	global patch occupancy of species i (i = 1, 2, 3)
ρ(i,j)	patch occupancy by the trophic link i → j, with ‘(i, j)’ indicating species j feeding on species i within a local patch
ρi,j	probability of a randomly chosen pair of neighbouring patches that one is i and another is j (i.e. pair density; i,j ∈ {1, 2, 3, u, s})
qs/s	clustering degree of suitable patches (i.e. patch connectivity), indirectly indicating mean patch cluster size and habitat fragmentation
qi/j	conditional probability that the neighbour of a j-patch is an i-patch (i.e. local density; i,j ∈ {1, 2, 3, u, s})

Here, we emphasize that: (i) species 1 is restricted to colonizing its adjacent s-patches, represented in equation (2.2) by taking the pair density of neighbouring patches (1–s) available for colonization equal to ρ_1s = (ρ₁ − ρ_1u − ρ₁₁), as there are three possible neighbour states for an occupied 1-patch: 1, u or s. In order to construct a closed system, we further derive the dynamics of ρ₁₁ and ρ_1u as shown in equations (B5–B6) in the electronic supplementary material, appendix B. (ii) In equation (2.3) for 1 → 2 links, we multiply the colonization term by the patch clustering coefficient q_s/s to estimate the limited dispersal of species 2, which has proven effective in spatially correlated landscapes [38]. The coefficient q_s/s can be regarded as a measure of the average size of habitat fragment (i.e. an area of connected s-patches) [12,13,33,34]. Thus, our modified term can be interpreted as allowing species 2 to disperse only within habitat fragments. (iii) Equation (2.4) for 2 → 3 links is unmodified from the framework of Pillai et al. [31], as species 3 disperses globally.

(c). Numerical simulations

Using this spatially extended model, we first investigate how patch loss and fragmentation separately affect species persistence in trophically linked communities. In these food webs where species compete, we introduce a trade-off between competition and dispersal range (as commonly used in ecological models to analyse species coexistence [29,32]); hence the species with a greater dispersal range is a poorer competitor and vice versa (scenarios with no competition–dispersal trade-off shown in electronic supplementary material, figures S5 and S6 in appendix D). When species 3 can feed on both species 1 and 2, we assume species 3 prefers to consume species 2 if both prey species are present in a local patch. We quantify this preference by comparing the intrinsic extinction rate of species 3 when preying on species 1 or 2, ψ = e₃₁/e₃₂ ≥ 1 (e₃₁ ≥ e₃₂; table 1). Additionally, when species 2 and 3 compete for feeding on the same prey species 1, species 3 is assumed to require a larger nutrient input than species 2, reflecting the body size gradient that is commonly observed in food webs [39–42,48]. To represent this, we assume there is a higher feeding pressure on species 1 when consumed by species 3 than by species 2, quantified by comparing the top-down extinction rate of species 1 in such links ω = μ₃₁/μ₂₁ ≥ 1 (μ₃₁ ≥ μ₂₁). Thus, we further consider how species 3's feeding preference, ψ, and the feeding pressure on species 1, ω, modify the effects of habitat destruction on spatial food web dynamics.

Here, we use numerical methods to derive the non-trivial stable equilibrium states for system simulations, therefore determining which species can be expected to survive and which to go extinct. Note that our results are qualitatively robust for a broad range of parameter combinations (electronic supplementary material, figures S1–S14 in appendices C–F) and that, as such, we use symmetrical parameter combinations as a representative reference parameter set throughout.

3. Results

(a). Effects of patch availability and connectivity on species persistence in food webs

We find that species' responses to patch availability and connectivity depend on their trophic position and the food web structure (figure 2). In simple food chains (figure 2a), increasing patch availability or connectivity increases species persistence and thus system robustness (i.e. higher patch occupancy; electronic supplementary material, figure S1 in appendix C). Species at higher trophic levels display higher sensitivity to patch loss and fragmentation, which go extinct first when patch availability and connectivity decrease due to trophic cascading effect.

Figure 2.

Interactive effects of patch availability and patch connectivity on species regional coexistence in different food webs, simultaneously considering species dispersal (1, neighbour dispersal; 2, within-fragment dispersal; 3, global dispersal). Four food web structures are included: (a) a simple food chain, (b) omnivory, (c) exploitative competition and (d) apparent competition. Invalid region: see equation (2.1). Parameter values: species colonization rate c_i = c_ji = 1, intrinsic extinction rate e_i = e₃₂ = 0.05 and species feeding preference cost ψ = e₃₁/e₃₂ = 3, top-down extinction rate μ_ji = 0.025 (i,j = 1,2,3).

Similarly, in the food web with an omnivorous top predator (figure 2b), all species can persist at high levels of patch availability and connectivity. However, in contrast with the simple food chain, as patch connectivity decreases, species 2 becomes extinct before species 3. In this case, both species 2 and 3 can feed directly on species 1 and thus have similar vulnerability to trophic cascading effects (bottom-up control). Yet the dispersal superiority of species 3 allows it to survive in more fragmented landscapes where species 2 with limited dispersal is unable to persist. Thus, the maximum patch occupancy of 1 → 3 links occurs at intermediate patch availability and connectivity, more precisely along a boundary where species 2 just goes extinct (electronic supplementary material, figure S2 in appendix C). In highly connected landscapes, the dispersal advantage of species 3 diminishes, so species extinctions are once again predicted by the trophic rank hypothesis (that species at higher trophic levels go extinct sooner), as observed in simple food chains.

Unlike the food webs above, when species 2 and 3 compete for the same prey species 1 (species 3 with a greater dispersal range is a poorer competitor), species 3 becomes extinct at high levels of patch availability and connectivity (figure 2c). In such situations, species 3 has no dispersal advantage over species 2, but the competitive disadvantage of species 3 leads to its extinction. At intermediate patch connectivity, all species can survive as species 3's superior dispersal allows it to find patches where the dispersal-limited species 2 cannot access. Further decreasing patch connectivity causes species 2 to go extinct before species 3, as in omnivory food webs. Again, the patch occupancy of the 1 → 3 link (in this case equivalent to the patch occupancy of species 3) peaks at the extinction threshold of species 2 (electronic supplementary material, figure S3 in appendix C).

In the food web with apparent competition between species 1 and 2, species 1 outcompetes species 2 in most landscape types because of its competitive superiority (figure 2d). Species 2 is able to survive only in a relatively small region of the landscape space characterized by low connectivity (around q_s/s = 0.2) and intermediate patch availability (around s = 0.5) (electronic supplementary material, figure S4 in appendix C). Species 3 persists in landscapes with sufficiently high habitat availability as it can easily switch preys between species 1 and 2, again reflecting its sensitivity to a trophic cascade (bottom-up control).

Comparing system robustness with habitat destruction across these trophic structures, we find that the omnivory food web allows the complete community to survive on the widest range of landscape types. This range decreases for the simple food chain and the food web with exploitative competition. The food web with apparent competition has the smallest region where all species can survive.

(b). Species feeding preference/pressure modifying community patterns in fragmented landscapes

While increasing species feeding preference (ψ = e₃₁/e₃₂ > 1 in both omnivory and apparent competition) or feeding pressure (ω = μ₃₁/μ₂₁ > 1 in both omnivory and exploitative competition) slightly increases the extinction risk of species 2 (despite the fact that species 2 is not directly affected by either of changes), it greatly accelerates the extinction of species 3 following habitat destruction (figures 3 and 4). This is explained by the fact that the extinction of species 1 can cascade and cause the extinction of species 3. However, these negative effects of increasing feeding preference or pressure are reduced when species 3 is an omnivore, as it feeds primarily on species 2 rather than species 1 at low levels of habitat destruction. In the food webs with exploitative or apparent competition, we do not observe this moderating effect when increasing feeding pressure or preference, respectively. In the case of exploitative competition, this is due to the fact that species 3 must consume species 1 and consequently increasing feeding pressure always increases species 3's sensitivity to the trophic cascade (bottom-up control), leading to a significant shrink in its survival region of landscape space (figure 4d). For apparent competition, the mechanism is similar: species 1 outcompeting species 2 in the majority of landscapes results in species 3 only feeding on prey species 1 (figure 3d).

Figure 3.

Effect of variation in species feeding preference cost (ψ = e₃₁/e₃₂ = 1, 3, 5, 7 at fixed e₃₂ = 0.05) on species extinction risk in omnivory versus apparent competition, simultaneously by varying both patch availability and patch connectivity. Again, species dispersal ranges: 1, neighbour dispersal; 2, within-fragment dispersal; 3, global dispersal. Invalid region: see equation (2.1). Other parameter values seen in figure 2.

Figure 4.

Effect of variation in species top-down extinction rate (ω = μ₃₁/μ₂₁ = 1, 3, 5, 7, 9 at fixed μ₂₁ = 0.025) on species persistence in omnivory versus exploitative competition, while again varying both patch availability and connectivity. Species dispersal ranges: 1, neighbour dispersal; 2, within-fragment dispersal; 3, global dispersal. Other parameter values: figure 2. Invalid region seen in equation (2.1).

4. Discussion

Traditional metacommunity theory for food webs mostly considers models of the relative occurrence of species within patches across a landscape (i.e. spatially implicit patch models) while ignoring the details of local dispersal and patch connectivity. Here, we propose a spatially extended patch-dynamic model for food webs by incorporating patch connectivity with trophic-dependent dispersal (i.e. species at higher trophic levels displaying longer-range dispersal [39–42]). Our model provides a new approach to study trophic networks in space. Using this model, we demonstrate that dispersal across space can play a critical role in maintaining trophic complexity. For example, the dispersal–competition trade-off allows the competing species to coexist on the regional scale (despite competitive exclusion on the local scale) in fragmented landscapes (figure 2c,d).

Ignoring trophic interactions, previous metapopulation models predicted that species with poor dispersal ability are more likely to become extinct in fragmented landscapes [5,12,13,49]. In our model, however, incorporating trophic interaction into the metacommunity system may reverse this prediction, resulting in different species sensitivities to habitat destruction (figure 2). In a simple food chain, species at higher trophic levels are found to be more vulnerable to patch loss and fragmentation despite their dispersal superiority (figure 2a), in accordance with the trophic rank hypothesis (a trophic cascade [27,50–52]). In the omnivory structure, however, the intermediate consumer with limited dispersal has greatest sensitivity to patch fragmentation, while the omnivorous top predator with dispersal superiority is able to persist in more fragmented landscapes by switching feeding on the basal species. But in highly connected landscapes, the intermediate consumer has very similar dispersal abilities to the top predator; consequently, we observe a return to the typical paradigm where the top predator is most sensitive to habitat loss. Interestingly, in the exploitative competition, species 2 monotonously decreases with habitat destruction, whereas species 3 displays diverse (positive as well as negative) responses. In particular, species 3 does not survive in highly connected landscapes due to competitive exclusion; instead, it can persist at intermediate patch loss and fragmentation because of a dispersal–competition trade-off. In the apparent competition, species 2 is competitively excluded by species 1 in most landscapes types, resulting in a bi-trophic system where species 3 shows more sensitivity to habitat destruction than species 1. In summary, the sensitivity of species to habitat fragmentation is not always monotonic with its dispersal ability [16], but instead is a complex function of species dispersal and interactions (e.g. competition and predation) with other species in the community.

By extension, our results suggest that system robustness, defined as the ability of a trophic community to tolerate habitat destruction without suffering species extinctions, depends strongly on the trophic structure of that community. As we would expect, competition between species significantly reduces robustness of the overall system, because it prevents all species from surviving on the same patch. By contrast, increased diet breadth for higher-trophic-level species (e.g. the module with an omnivorous top predator) significantly increases system robustness, as the typically more vulnerable species is allowed to survive by switching their feeding behaviour (adaptive feeding behaviour). This indicates that the omnivore can modify its diet dependent on prey availability, either by switching prey or by adjusting the proportion of each in a mixed diet in response to patch fragmentation [53]. Essentially, feeding on different trophic levels (omnivory) increases the number of available habitat patches accessible to the omnivorous top predator, thus offering more opportunities for its survival [29,32].

In the food webs with exploitative or apparent competition, we find that intermediate landscape fragmentation maximizes species diversity, while low or high fragmentation lead to the loss of one or more species (figure 2c,d). The peak observed in species richness at intermediate patch fragmentation represents a compromise between competition and dispersal mediated by patch fragmentation. In particular, when species compete for the same resource, high levels of habitat fragmentation severely limit the colonization opportunities (and therefore patch occupancy) of poor dispersers, allowing the inferior competitor with longer-range dispersal to survive on the landscape. By contrast, in highly connected landscapes, even species with short-range dispersal are able to access to most of the available habitat as such, the poor competitor is driven to extinction. If this trade-off holds in nature, moderate patch fragmentation could promote the survival of long-range dispersers (e.g. increased patch occupancy of species 3 in electronic supplementary material, figure S3). This suggests habitat heterogeneity as a critical factor for biodiversity maintenance, as it can provide refuges for the poor competitor (via long-range dispersal) that the strong competitor with dispersal limitation is unable to access (i.e. a competition–dispersal trade-off, commonly used in traditional metapopulation models [29,32,54,55]).

This is one example of a more general paradigm that landscape boundaries promote biodiversity, which has been observed frequently on the global scale [56–58]. An obvious example is the loss of biodiversity in Australia and the south Pacific that followed colonization from Europe due, in part, to the introduction of superior competitors from that continent [59,60]. Our results show that this paradigm extends to the smaller scale of an individual landscape, and thus increasing patch connectivity is not always the optimal strategy for biodiversity conservation. Indeed, it may result in further species loss. This refutes previous suggestions that maximizing the connectivity of good-quality habitat patches is always an effective way to promote species diversity [4,5,9,61,62]. Instead, landscape fragmentation may, in some cases, lead to increases in species richness, especially at modest levels, despite ultimately causing the collapse of the food web at more extreme levels (as shown by previous spatially implicit modelling studies [29,32]).

In our model, we have made two simplifying assumptions. First, we only considered three ideal types of dispersal scaling (i.e. neighbour dispersal, dispersal within fragments and global dispersal), with a higher trophic level displaying longer-range dispersal (as commonly observed in [39–42]). In such case, species dispersal ranges are essentially categorical, which is relatively restrictive as species in nature show a broad range of movement behaviours [42,63–65]. Such categorical description can be naturally linked to the effects of fragment size and patch connectivity, but it does eliminate the effect of distance between fragments [2–5,42]. Thus, this omission could be further explored by comparing our predictions with those models using more realistic dispersal ranges. A second simplification used in this model is the division of habitat into suitable and unsuitable habitats. In fact, real landscapes rarely consist of neatly divided patches of ‘habitat’ and ‘non-habitat’ [9,13]; instead habitat degradation coincides with reduction in habitat quality, so that most landscapes display at least some level of habitat variegation (i.e. varying suitability for species). To account for this, future study could include the range of possible habitat types, and apply more complex metrics to characterize the overall spatial landscape structure.

5. Conclusion

We develop a spatially extended patch-dynamic model to include spatial heterogeneity in order to investigate how trophic communities, characterized by different food webs, differ in their responses to habitat destruction. Each module produces unique species survival patterns in fragmented landscapes. As such, we suggest that, in conservation efforts, the community structure to be preserved must be considered in combination with habitat configurational fragmentation [10,14–16,62,66]. In particular, we find that, in food webs with a dispersal–competition trade-off between species, the greatest species diversity is achieved at intermediate levels of habitat destruction. Thus, the common recommendation to mitigate negative impacts of landscape fragmentation on biodiversity by increasing habitat connectivity [61,67] could, in fact, be detrimental to some communities. This calls for particular caution when designing conservation strategies for biodiversity maintenance in trophically linked communities, as species loss resulting from habitat management will simultaneously influence multiple species across trophic levels, possibly resulting in the collapse of the entire community. Our model further demonstrates that differential sensitivities to patch loss and fragmentation are closely related to species traits (e.g. dispersal, competition and trophic position), thus identification of these traits from empirical data would contribute to the setting of conservation priorities in applied ecology. Experimental tests of these predictions could be performed in natural or laboratory-based model systems (e.g. microcosms and field observations) that allow the direct manipulation of metacommunity size and patch connectivity [14,15,66,68]. Overall, our extended modelling framework offers a promising way to advance the spatial food web theory in fragmented landscapes and provides new insights into biodiversity conservation.

Data accessibility

This article has no additional data.

Authors' contributions

J.L. conceived the study and wrote the manuscript; J.L. and D.B. performed the analysis and discussed the results; D.B. and B.B. improved the manuscript.

Competing interests

We declare we have no competing interests.

Funding

This study was supported by the DFG through grant FOR 1748, the Opening Fund of Key Laboratory of Poyang Lake Wetland and Watershed Research (Jiangxi Normal University), Ministry of Education (no. PK2015004 and TK2016002), Jiangxi Provincial Education Department (no. GJJ160274) and the Doctoral Scientific Research Foundation of Jiangxi Normal University (no. 12017778).