Structural Dynamics and Robustness of Food Webs

Food web structure plays an important role when determining robustness to cascading secondary extinctions. However, existing food web models do not take into account likely changes in trophic interactions (“rewiring”) following species loss. We investigated structural dynamics in 12 empirically documented food webs by simulating primary species loss using three realistic removal criteria, and measured robustness in terms of subsequent secondary extinctions. In our model, novel trophic interactions can be established between predators and food items not previously consumed following the loss of competing predator species.

By considering the increase in robustness conferred through rewiring, we identify a new category of species—overlap species—which promote robustness as shown by comparing simulations incorporating structural dynamics to those with static topologies. The fraction of overlap species in a food web is highly correlated with this increase in robustness; whereas species richness and connectance are uncorrelated with increased robustness. Our findings underline the importance of compensatory mechanisms that may buffer ecosystems against environmental change, and highlight the likely role of particular species that are expected to facilitate this buffering.


Human-induced changes to the global environment driven by climate change, pollution, and habitat destruction are expected to cause widespread extinctions of populations and species globally (e.g., Brook et al. 2003). The robustness of ecological communities to such changes has been the subject of numerous empirical and theoretical studies (e.g., Shin et al. 2004; Dobson et al. 2006; Saavedra et al. 2008), revealing that the loss of individual species can lead to cascading secondary extinctions (Ebenman et al. 2004).

A particular focus has been on food webs (networks representing biomass flow through ecosystems), and the relationship between their structure and robustness to species loss (Dunne et al. 2002, 2004; Dunne & Williams 2009). Enhanced ecological realism has been incorporated into food web analyses by employing plausible extinction sequences (Srinivasan et al. 2007) and by incorporating the effect of human-mediated disturbances (Coll et al. 2008). However, existing models remain inherently static in their description of food web response to species loss. This reflects available empirical data which mostly represent food webs either as a snapshot in time (Thompson & Townsend 2005) or aggregated over time (Martinez 1991).

Recent work has sought to analyse the interplay of structure and dynamics in food webs (Pascual & Dunne 2006). One approach has been the combination of food-web topologies with bioenergetic and population dynamic models that represent predator-prey interactions by a system of nonlinear differential equations. Such investigations have, for example, considered the effects of single species removal in reconstructed “fossil” food webs (Roopnarine et al. 2007) and synthetic topologies generated by the niche model (Berlow et al. 2009). Some studies have begun to incorporate adaptive foraging (Brose et al. 2003; Kondoh 2003, 2006; GarciaDomingo & Salda˜na 2007), by which consumer species maximize the energy gain per unit foraging effort by behavioural shifts in prey selection.

Foraging theory has also been used to predict species interactions and resulting food web structure (Petchey et al. 2008). The consequences of species loss have also been modelled in food webs where predators preferentially consume competitively dominant prey species and thus prevent the competitive exclusion of many other subordinate competitors (Brose et al. 2005). Nevertheless, in each of these approaches the underlying trophic structure remains essentially static through time. A general framework for considering the structural dynamics of food webs would increase the realism of theoretical models in accordance with the observation that species are able to adjust their feeding behaviour in response to changing environments.

The diet of a consumer is to a large extent constrained by its phylogenetic history, morphology, and body size (Cousins 1985; Ives & Godfray 2006; Bersier & Kehrli 2008). However, individuals of many species will respond to altered biotic and abiotic conditions by incorporating into their diets items not previously consumed. Such flexibility is widely expected given that the fundamental niche (Hutchinson 1957) of most species is likely to be much wider than the realized niche that will be measured empirically: where competition for prey items is relaxed or removed, “novel” resource species will be exploited.

For example, zooplankton alter patterns of resource intake depending on the abundance and variety of prey (Gentleman et al. 2003); food selection by an omnivorous thrip (Frankliniella occidentalis) varies depending on host-plant quality and prey availability (Agrawal et al. 1999); and Chaoborus larvae show reduced prey selectivity when prey abundance is low and larvae are hungry (Pastorok 1980). Thus, the high abundance of a common prey may mask the ability of predators to consume other, less abundant prey which will become a viable source of nutrition if typical prey resources are depleted or lost (Pimm 1991).

Motivated by such examples of species’ ability to alter their feeding patterns in response to the abundance of actual and potential prey species, we explore the consequences of incorporating predator-prey “rewiring” (predators switching to food items not previously consumed) into simulation-based analyses of structural food-web robustness. We extend static models of food webs by introducing trophic interactions that can respond to the loss of species from an ecosystem—structural dynamics—and quantify the resulting robustness to secondary extinctions.

Our results allow the identification of a new category of species, which we call “overlap species”, which promote robustness as shown by comparing simulations incorporating structural dynamics to those with static topologies. Following removal of a competing predator in our model, overlap species indicate other predators that can establish novel trophic interactions (i.e., “rewire”) to the removed predator’s former prey. Our results suggest the importance of compensatory mechanisms— and particular species—that may enhance food web robustness in the face of environmental change.

2.2 Materials and Methods

We analysed 12 of the best-characterized food webs available, some of which have been previously studied for their robustness to simulated primary species loss. The focal food webs represent a wide range of species numbers, linkage densities, taxa, habitat types, and methodologies (Table 2.1; Dunne et al. 2002; references in Allesina & Pascual 2009). We studied trophic species versions of the 12 food webs. The use of trophic species (hereafter referred to as species), that is, groups of taxa that share the same set of predators and prey (Briand & Cohen 1984), is a widely accepted convention in structural food-web studies that reduces methodological biases related to uneven resolution of taxa within and among food webs (Williams & Martinez 2000).

For each food web, we simulated species loss by sequentially removing either (1) randomly chosen species; (2) the least connected species preferentially; or (3) species at high trophic level preferentially; for each criterion, 1000 deletion sequences were simulated for each food web. For criterion (2), removal of the least connected species, total trophic connections (“degree”) was calculated for each species for both predator and prey links; the probability of a species, i, being chosen for removal was

pi = (ki) ?1 P (kj ) ?1 , (2.1)

where ki is the degree of species i and the summation runs over all species in the food web. For criterion (3), the probability of a species, i, being chosen

Structural properties of food webs and simulation results

for removal was

pi = T Li P T Lj , (2.2)

where T Li is the trophic level of species i and the summation runs over all species present in the food web. We use the longest-chain definition of trophic level, which is calculated as one plus the longest trophic chain from the consumer to a basal species, as this gives the greatest scope for rewiring (given our constraint on trophic level feeding; see below). Our qualitative results are robust to other definitions of trophic level including the shortestchain, prey-averaged (Levine 1980), and short-weighted algorithms (Williams & Martinez 2004) (data not shown). Criteria (2) and (3) reflect the increased vulnerability of specialists and species at higher trophic levels, respectively, to environmental perturbations such as habitat fragmentation (Raffaelli 2004). In food webs with only one or two basal species and where one of those basal species is classified as detritus, we set the detritus “species” as the last to be removed in the extinction sequence (Fath et al. 2007).

Following the removal of a species from a food web, previous studies (e.g., Dunne et al. 2002) remove all trophic links associated with that species. In our predator-prey rewiring model, some of the removed species’ prey links may be rewired to new predators if biologically plausible. This is motivated by the likelihood that a species losing a predator species becomes more available to other predator species, for example, because of reduced competition. The plausible set of new predators for a given species is determined by the rewiring graph (Figure 2.1a–c). For each food web, we first obtained the

The predator-prey rewiring model uses a rewiring graph which indicates biologically plausible trophic rewirings and is derived from a food web

predator-overlap graph (also referred to as the resource graph) (Cohen 1978). In the predator-overlap graph, species are joined by an undirected link if they share a common predator. The rewiring graph is obtained from the predatoroverlap graph and contains directed links. A link i ? j indicates that, in addition to the shared predators, species i has at least one predator that does not prey on species j, and those predators are at higher trophic level than species j. In the predator-prey rewiring model, following the removal of a species, each of the removed species’ prey links is considered for rewiring (Figure 2.1d,e). For the remaining prey species, we obtain a set of potential predators from the directed nearest neighbours in the rewiring graph. A new predator is selected randomly from the set of potential predators and the trophic link is rewired accordingly; if no potential predators are available then the trophic link is removed.

Rewiring can dynamically alter the structure of the rewiring graph, thereby presenting additional possibilities for rewiring following further species removals (Figure 2.1f); this process ensures that the most plausible rewirings are implemented first. Once each of the removed species’ prey links has been considered for rewiring, another species is selected for removal and the process repeats. Because of its basis in the predator-overlap graph, the rewiring graph indicates the most plausible rewirings. There are a number of interpretations for these “new” trophic interactions: (1) they are unobserved in the empirical data yet are still biologically plausible; (2) they are unobserved in the empirical data as they are not biologically plausible; (3) they are observable yet are not sufficiently frequent to have been included in the documented food web; (4) they are observable but have been missed in the collation of the food web because of 33 practical limitations (Martinez et al. 1999). Because modern food webs are sampled in the field extensively over time and space, it is likely that the links included in the food webs already reflect many of the observable, short-term, predator-prey switches.

However, these data cannot account for trophic links that may emerge when the food web is subject to severe perturbations: we simulate species removal until no species remain. This also makes it difficult to determine, without detailed individual examination, whether a suggested trophic rewiring that is unobserved in the empirical data should be classified as biologically plausible, category (1), or not, category (2). Our approach to rewiring may be considered conservative since we required that new predators are at higher trophic level than the prey species, as observed empirically for free-living prey (Woodward et al. 2005). Having obtained the rewiring graph for a food web, we define overlap species systematically. An overlap species is a species in the rewiring graph that has at least one directed link pointing from it to another species in the rewiring graph: it has out-degree > 0 (Figure 2.1c).

However, we do not denote species involved in trophic looping (where a trophic chain closes on itself, and excluding cannibalism) as overlap species unless there are distinct top predators in the food web. This is due to the way in which we have designated all species involved in trophic looping as being at the highest, chain, trophic level of the food web, whilst forbidding rewiring to take place between species at the same, nominal, trophic level. We stress that this reflects an algorithmic choice of the model and does not constitute a comment on any underlying ecological process.

We examined the impact of species loss on food web stability by considering the number of potential secondary extinctions that may result. A secondary extinction occurs when a non-basal species loses all of its prey items, and also when a cannibalistic species loses all of its prey items except itself. Following previous studies (Dunne et al. 2002), “robustness” of food webs to species loss was quantified as the fraction of species that had to be removed for all species to go extinct. The maximum possible robustness is 1 and the minimum is 1/S, where S, the species richness, is the initial number of (trophic) species in the food web. Values for the robustness were obtained both with and without predator-prey rewiring.

To compare the effect of rewiring between food webs, we calculate the proportional change in robustness: (Rr ? R0)/(1 ? R0); where Rr is the robustness including rewiring, and R0 is the robustness excluding rewiring. Although this expression allows for negative values, rewiring of the kind represented here is highly unlikely to reduce the robustness of the food web. We refer to positive values as a proportional increase in robustness. The maximum possible proportional increase in robustness is 1 and the minimum is 0. We averaged the proportional increase in robustness for the three removal criteria in order to have one representative value for each food web. We examined correlations between the proportional increase in robustness and three food-web measures: species richness (S); connectance (C), the fraction of all possible trophic links, L, including cannibalism that are realised (L/S2 ); and the initial fraction of overlap species in the food web (P).

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