Does evolution design robust food webs?

Abstract

Theoretical works that use a dynamical approach to study the ability of ecological communities to resist perturbations are largely based on randomly generated ecosystem structures. By contrast, we ask here whether the evolutionary history of food webs matters for their robustness. Using a community evolution model, we first generate trophic networks by varying the level of energy supply (richness) of the environment in which species adapt and diversify. After placing our simulation outputs in perspective with present-day food webs empirical data, we highlight the complex, structuring role of this environmental condition during the evolutionary setting up of trophic networks. We then assess the robustness of food webs by studying their short-term ecological responses to swift changes in their customary environmental richness. We reveal that the past conditions have a crucial effect on the robustness of current food webs. Moreover, directly focusing on connectance of evolved food webs, it turns out that the most connected ones appear to be the least robust to sharp depletion in the environmental energy supply. Finally, we appraise the ‘adaptation’ of food webs themselves: generally poor, except in relation to a diversity of flux property.

1. Introduction

Understanding and linking both the structure and functioning of ecosystems has been addressed as one of the major issues in ecology, particularly owing to increasing pressures on biodiversity [1]. The large diversity/complexity-stability debate (see [2], for a recent review), rooted in this issue, has been approached from different perspectives. Studying food webs—the representation of who eats whom in ecosystems—constituted a first one. While pioneer food web models (e.g. [3]) were able to produce satisfactory food web structures (in the light of their properties), they are not suited to explain how these properties emerge. Moreover, they do not provide a quantification of interaction strengths, prerequisite for a population dynamics model of interacting species.

The last two decades have seen the development of community evolution models that came to address these limitations (e.g. [4–6]). They consist of embedding an explicit demographic model in the main evolutionary model. In those models, species are characterized by some traits, which drive the demography of the whole interacting community on a fast time scale. On a longer time scale, these traits evolve according to the selection pressures exerted on each of them. New species are introduced randomly, ultimately leading to the emergence of communities. The diversity and structure of the resulting food webs are hence emergent properties. The model developed by Loeuille & Loreau [4] has the advantage of being relatively simple as it implies only one characterizing trait per species, the maturity body size. However, these networks, because species share the same foraging characteristics (prey size distance and feeding specialization level), always emerge with rather uniform structures [7]. Subsequently, several studies have built upon the pioneer work of [4] (see [8], for a recent review), and in particular have attempted to also consider the evolution of these foraging traits, intending to reproduce a more realistic variety of feeding strategies and hence of food web structures.

Structural properties such as food chain length, connectance or even simpler, species diversity has been shown to vary along environmental gradients [9], for example, in lakes [10,11] , streams [12] or high latitude marine ecosystems [13]. Some research using community evolution models has also discussed the effects of parameters controlling global-scale processes (e.g. environmental richness, temperature) on the emergent structures of food webs [14–16]. Nevertheless, none of them belong to the aforementioned studies that allow diversification of feeding strategies.

Many studies, motivated by the observations of increasing rates of species loss [17], have tried to relate the structure of food webs to their fragility, for example, by studying secondary extinctions driven by primary extinctions [18–20]. Although some of these studies use quantitative population dynamics models to study the effects of perturbations, they almost always rely on network structures generated by algorithmic methods, ignoring the evolutionary history of food webs. Besides, an increasing number of studies are focusing on how evolutionary processes affect the dynamics and stability of communities [21–23]. However, evolution is generally taken into account only as a component of community response after a perturbation occurs. While this role of evolution in the long term response is significant, its role in the way it has shaped in the past a current system before the occurrence of the perturbation may be as important.

With the concern of focusing on this upstream role (does evolution design robust food webs?), we have developed a community evolution model describing the genesis of food webs. Using a unified framework, we proceed in two stages. We first ask how we could explain the diversity of actual trophic structures (provided by empirical data) from a straightforward hypothesis on their evolutionary history: the variations in a single control parameter determining the environmental richness during evolution. We then more precisely relate the value of this environmental richness parameter to characteristic properties of simulated food web structures. In a second part, we ask if evolution, through different conditions, may have provided specific properties to food webs, granting them a given robustness. We focus on the connectance-robustness debate. Finally, we also briefly address the ‘adaptive status’ of food webs by setting up a virtual common garden experiment. We ask whether evolutionary processes could optimize some properties of trophic networks.

2. Method

(a). Model

The model is derived from Loeuille & Loreau’s work [4] (LL in the following), with modifications in both the ecological assumptions and the methods used.

In addition to the solely evolving body size trait in LL, we consider the evolution of two other adapting traits for the feeding kernel: its width (see also [24] for related work) and the preferred prey body size.

For a species i in a community, we denote x_i its typical (average, maturity) body size. Feeding kernel is Gaussian-shaped. Its width is defined by s_i, i.e. the degree of generalism of the consumer it characterizes. It is centred on the optimal prey body size $x_{{\mathrm{opt}}_i}$.

Thus interactions in the trophic network are not set a priori but emerge from the relative body sizes of every species pair in the community, combined with their feeding kernels.

For convenience, we denote ${\overrightarrow{\phi }}_i=(x_i,s_i,x_{{\mathrm{opt}}_i})\in {\mathbb{R}}^3$ the trait vector, thus the phenotype of species i. Following this notation, the feeding kernel of species i is denoted γ(x, ${\overrightarrow{\mathit{\phi }}}_i$) where x is the body size of a prey. N_i(t) denotes the biomass of species i at time t.

A generic ordinary differential equation describes the population dynamics of n interacting species, and an additional equation describes the dynamics of a basal resource on which some species feed:

$$\{\begin{array}{c}⋮\hspace{0.17em}\\ \frac{\text{d}{N}_i}{\text{d}t}=N_i(\underset{\begin{array}{rl}& \mathrm{basal}\hspace{0.17em}\mathrm{resource}\hspace{0.17em}\mathrm{consumption}\\ & \hspace{0.17em}\end{array}}{\underbrace{\hspace{0.17em}{f}_P{F}_P(\overrightarrow{{\phi }_i},\mathbf{\Phi },\mathit{N})}}+\underset{\mathrm{species}\hspace{0.17em}\mathrm{consumption}}{\underbrace{\hspace{0.17em}{f}_C{F}_C(\overrightarrow{{\phi }_i},\mathbf{\Phi },\mathit{N})}}\hspace{0.17em}\\ -\underset{\mathrm{mortality}}{\underbrace{m(\overrightarrow{{\phi }_i})}}-\underset{\mathrm{competition}}{\underbrace{C(x_i,\mathbf{\Phi },\mathit{N})}}-\underset{\begin{array}{rl}& \mathrm{mortality}\hspace{0.17em}\mathrm{from}\hspace{0.17em}\mathrm{predation}\\ & \hspace{0.17em}\hspace{0.17em}\end{array}}{\underbrace{{\mu }_P(x_i,\mathbf{\Phi },\mathit{N})}})\\ ⋮\hspace{0.17em}\\ \frac{\text{d}{N}_0}{\text{d}t}=\underset{\mathrm{supply}\hspace{0.17em}\mathrm{level}}{\underbrace{I}}-\underset{\mathrm{output}\hspace{0.17em}\mathrm{rate}}{\underbrace{e}}{N}_0-\underset{\mathrm{species}\hspace{0.17em}\mathrm{consumption}}{\underbrace{{\mu }_P(0,\mathbf{\Phi },\mathit{N})N_0}}\hspace{0.17em}\end{array}$$ 2.1

where vectors $N(t)$ and $\mathbf{\Phi }$ bookkeep respectively the n community species biomasses (N₀(t) denotes the biomass of the basal resource) and 3-components traits. For each species i, we let x_i, s_i, and $x_{{\mathrm{opt}}_i}$ be adaptive traits that undergo evolution.

As in the LL model, selection on the maturity body size of a species (x) is based on a balance between optimal foraging behaviour [25], competition, and metabolic rates allometric relationships [26]. In the LL model, structure directly associates a consumer body size x with the prey size it can feed on, and as a consequence x is naturally constrained by prey availability. The additional flexibility of our model (a consequence of the evolution of the relative value of x_opt compared to x) removes this constraint on x. It begets the necessity for additionally taking into account physiological costs on oversized species [27].

Concerning the trait s, we considered a trade-off where a high value of s allows a predator to feed on a wide range of prey sizes (generalist strategy) but increases the prey handling time in its functional response and consequently decreases its maximal predation rate. By contrast, species with low s are limited to a small set of prey size but can handle them more efficiently owing to their specialist strategy. Here we echo [5] but with the trade-off between generalism and efficiency expressed differently. Furthermore, in our model, overspecialization through co-evolution does occur so that we had to take into account an additional intrinsic cost it shall entail (owing to, e.g. physiological or developmental constraints, or diet-specific costs [28]). Figure 1a,b synthesizes how trophic links are drawn (a) and the selective pressures on the feeding kernel and body size arising from the demographic model (b).

Figure 1.

(a) Trophic links set up from feeding kernels and organisms body sizes; (b) main evolutionary pressures on each adaptive trait. Ellipse: intrinsic pressure; rectangles: interaction mediated pressures; (c) explanatory scheme of the network emergence methods and of the disturbance experiment. The first step consists of setting up the model for different environmental richness values I (column I). We show here two contrasted example values: poor and rich environmental conditions. The second stage (column II) consists of simulating the eco-evolutionary model under these environmental conditions. Trophic networks emerge from successive diversifications. Coloured curves (here body size) correspond to carnivore species, i.e. which do no feed on the basal resource. Timescale on the left hand-side of the graphs is zoomed out in order to visualize food web diversification and then accelerated on the second half to reach evolutionary stabilization. From this final state, evolved food webs (column III) are analysed for different emerging properties. Discs colour code roughly indicates trophic position of species. Then (column IV), they are confronted with changes in environmental richness, what impact populations on a short time scale, potentially inducing species extinctions (black-filled circles). (Online version in colour.)

Adaptive dynamics theoretical framework [29–31] provides a very powerful toolbox that allows us to model and simulate efficiently the coevolution of such adaptive traits on the evolutionary time scale. Based on hypothesis at the individual stochastic processes level in a population (selection, mutations), adaptive dynamics infers the canonical equation, an ordinary differential equation for the mean value of an adaptive trait. The canonical equation is easily extended to several coevolving species in a community and to several traits for each species [30]:

$$\frac{\text{d}{x}_i}{\text{d}\tau }=k_x{\hat{N}}_i(\mathbf{\Phi })\frac{\mathrm{\partial }f}{\mathrm{\partial }{x}_{\mathrm{mut}}}({\overrightarrow{\phi }}_{\mathrm{mut}}=\overrightarrow{{\mathit{\phi }}_i},\mathbf{\Phi }),$$ 2.2

where τ is the evolution time, k_x, k_s and k_d are mutation-related constants, ${\hat{N}}_i(\mathbf{\Phi })$ the vector of equilibrium values of population biomass, determined by the traits vector $\mathbf{\Phi }$. Finally, $f({\overrightarrow{\phi }}_{\mathrm{mut}},\mathbf{\Phi })$ is the invasion fitness, key element of adaptive dynamics, which allows us to assess the invasion success of a mutant in a resident population. Two similar additional equations complete the description of the co-evolution dynamics for traits s_i and $x_{{\mathrm{opt}}_i}$. Here, we simply assumed that within a species, the three traits are not linked, which means that the mutations occur independently for the three traits. This system of 3n ordinary differential equations drives the coevolution of the n interacting species in the community. See the electronic supplementary material, S1 for further details.

(b). Network emergence

We start with an initial single species (n = 1) for which we derive and integrate the canonical equations (2.2), describing the evolutionary dynamics of its three characteristic traits. Trait values therefore change continuously. We stop integration upon two possible events:

• (i)extinction: traits in the population coevolve to a point where one of the species (demographic equilibrium) population size vanishes. We remove this species from the community; and
• (ii)speciation: one of the species undergoes evolutionary branching (detected with adaptive dynamics tools, see details in the electronic supplementary material, S1).

We then rewrite (2.2) following the updated number of species (n + 1 or n − 1). We iterate the process until a chosen final evolutionary duration time is passed. A typical simulation is given by figure 1c, panel II).

At each (evolutionary) time step, we checked that equation (2.1) leads to a stable ecological equilibrium (see the electronic supplementary material, figure S2), which is a prerequisite for the adaptive dynamics standard toolbox. Electronic supplementary material, S1 provides advantages of such methods for network emergence compared to what has been typically used.

(c). Analysis of food webs

(i). Environmental richness

We decided to focus our analysis on the parameter I, the influx of basal resource N₀ in the trophic community. In LL, the basal resource referred to a (limiting) nutrient biomass. However, to grant a more general application scope to our model, we broaden the possible interpretation of N₀ to include available products of primary production (and indeed, we chose in this study to model the entry of the system at the primary production level, see the electronic supplementary material, S1). In general terms, I represents the energy supply of our trophic networks. In the following, for language convenience, we chose to refer to it as environmental richness, where a high (low) parameter value indicates large (poor) amounts of energy in the trophic network (e.g. estuary/oligotrophic waters).

(ii). Simulated versus empirical food webs

For each value of I in a log scaled range of 1000 values from 0.1 to 350, we started from a single species, which traits (x_ini, s_ini, $x_{{\mathrm{opt}}_{\mathrm{ini}}}$) were randomly chosen. We let evolution generate through our algorithm a diversified food web (see the electronic supplementary material, S1 for further details).

In parallel, we also compiled data from 213 natural food webs from the ECOWEB database [32], and determine their structural properties (see above). We also compiled data from another large database of ecological networks [33], on which species size distributions are available. It allowed us to compare, for example, the distributions of predator prey mass ratios of this database with our simulations (electronic supplementary material, figure S5).

(iii). Descriptors

We analysed both evolved and empirical trophic networks for a series of descriptors (see the electronic supplementary material, S1 for details): the species diversity S (final number of species), the connectance (L/S(S + 1), where L is the number of realized links), the maximum trophic level (see [14]), functional diversity indices for species attributes x, s and x_opt (simplifying FDvar of [34]), and the diversity of trophic fluxes, or entropy [35–37].

(d). Disturbance experiment

(i). Basic procedure

Food webs are exposed to new environmental conditions (I = I_perturb.), different from those they experienced during their evolution (I = I_evol.). We then measure the immediate demographic response through system (2.1): species stabilize, on the demographic timescale, to some modified abundance equilibrium values (figure 1c; electronic supplementary material, figure S4).

We can, therefore, estimate how evolved food webs respond for various, new conditions, in terms of several food web properties changes. Perturbation-mediated extinctions are recorded when some of these new abundances fall below a threshold value. The relative species loss is thus the number of these recorded extinctions, divided by the pre-disturbance number of species. It allows us to define the robustness of a given food web as the disturbance level beyond which the relative species loss exceeds 0.5 (meaning that the food web loses half of its original species diversity).

Besides, both as a secondary consequence of these species loss and because of overall changes in abundances, all other properties of food webs (see previous ‘descriptors’ section) are likely to be impacted as well. For instance, we can calculate the change of the maximum trophic level among species in the network, which can be downwards (e.g. loss of the highest trophic level species), but also upwards (rebalancing of the diet of these species).

For each of the 1000 mature food webs (I = I_evol. ∈ [0.1, 350], previous section), we confront them to 1000 new richness levels (I = I_perturb.) from the same range. We hence get a 1000 × 1000 treatment.

(ii). Connectance-robustness debate

It is difficult to determine a posteriori the environmental richness of past evolutionary times in the field. We thus found it necessary to try to directly link observable properties of contemporary evolved food webs to their robustness, bypassing the knowledge of the past environmental conditions. It motivated our second approach, in which for a given perturbation level, we chose to relate the connectance of a mature evolved food web to its relative species loss. As the connectance is an emergent property and not a control parameter, it provides irregular values as a predictor variable for the relative species loss. Computation of the average prediction value, as well as the associated local variance, was performed through a moving Gaussian smoothing kernel (see details in the electronic supplementary material, S6).

In this experiment, we reduced the richness level of each of the 1000 evolved food webs by a multiplicative factor: I_perturb./I_evol., in the range of values from 1 (no change) to 0.2 (reduction by a factor 5).

(iii). (Virtual) common garden experiment

Lastly, we are interested in the comparisons of pairs of trophic networks. The ‘native’ food web has evolved for a first given value of environmental richness and continued to face the same condition (I_evol. = I₀, no perturbation). By contrast, the ‘exogenous’ one, has evolved for another value of the energy input level, but then undergoes the first environmental richness as a perturbation (I_perturb. = I₀, I_evol. ≠ I₀). We compute, for each pair of networks, the comparative species loss, corresponding to the difference between the number of species of the exogenous food web minus the number of species of the native one. Similarly, we computed the comparative entropy loss.

3. Analysis of food webs

In this section, we compare the structural properties of our simulated evolved food webs with empirical data and discuss their variations along the spectrum of contrasted environmental richness values we sampled to generate them.

Theoretical networks are confronted with the empirical food webs of the ECOWEB’s database in the light of several properties (figure 2). While they were generated by only varying a single control parameter, the relationships between emerging properties of evolved food webs are not curvilinear, the dot clouds spreading over a two-dimensional region. Even if natural data usually better fill the range of variation for some properties, we were able to reproduce an appreciable part of the diversity of trophic structures observed in the field. It thus suggests that a limited number of factors could explain this diversity.

Figure 2.

(a) The fraction of possible links between species that are realized. (b) Maximum trophic level recorded in each trophic network. (c) Percentage of species feeding on the basal resource. (d) Percentage of species that are not consumed. Parameters, except I, are fixed and take the following values: α₀ = 0.5, σ_compet = 0.4, h₀ = 0.5, h₁ = 0.05, γ₀ = 1, m₀ = 0.1, x_max = 15, s₀ = 0.1, f_p = 0.85, f_c = 0.45. (Online version in colour.)

Empirical observations and theoretical data show similar general relation trends. However, we have not done further precise statistical tests here because it does not make much sense for several reasons. First, mere data fitting may generally be a poor test of model performance in ecology [38]. Second, we cannot readily link our species and their traits with these sets of empirical data as the authors do not report body sizes and often pool several species in the same node. Finally, in empirical food webs, data are all the same compiled over a wide range of environmental conditions, and for varied components of them. It thus makes it difficult to directly compare the variations of their characteristic properties with a single environmental determinant as the basal input level on which we focused.

Figure 3 shows in more detail the variations in selected properties of emerging food webs against the spectrum of contrasted environmental richness we considered. We chose to emphasize species diversity, connectance and trophic level as they may be the most directly comparable properties with empirical data. Nevertheless, we also present variations of functional diversity indices for the adapting traits of species in the networks.

Figure 3.

Upper panel: normalized emergent properties against the evolutionary environmental richness I (blue, species diversity; red, connectance; yellow, maximum trophic level); lower panel: normalized functional diversity indices against the evolutionary environmental richness I. Functional diversity is computed for (blue) body size, (red) degree of generalism, and (yellow) optimal prey body size. (Online version in colour.)

The first striking result is that these index curves shape differently. Species diversity increases with environmental richness, as does logically the functional diversity index on maturity body size x. Connectance and maximum trophic level first increase with the control parameter I but then decrease when I reaches higher values. While the values of I that maximize connectance are low to intermediate, those maximizing the maximum trophic level are distinctly higher. The functional diversity indices on both generalism level s and preferred prey body size x_opt are also maximized for distinct values of environmental richness.

Interestingly, our set-up makes it possible to focus on the potential key role of our control parameter in the resulting emergent structure of food webs. In particular, three highlighted properties cannot be maximized at the same time, because they are maximized for trophic networks evolved with three different environmental richness values. Highest species diversity does not necessarily imply the highest trophic complexities. This last point was previously highlighted in [14]. However, the control parameters used in this study to produce the different levels of diversity are replaced in our case by our additional evolving traits s and x_opt. We can discuss why maximum trophic levels or highest connectance values can be highlighted for different, not maximal values of environmental richness by examining more closely the structure of evolved food webs and the characteristics of species present in the networks (electronic supplementary material, figure S6).

For very low values of this parameter, all species feed on the basal resource (herbivores/primary consumers), and hence no real trophic structure emerges. For higher values of environmental richness, when first secondary consumers appear (generalists), species diversity is still relatively low, which explains why these newly appeared trophic links increase connectance so much (statistical effect). From then on, species number increases faster than new trophic links develop, so that connectance evolves on a downward trend. In parallel, if we distinguish in trophic communities carnivorous species from primary consumers when general species diversity increases with environmental richness, one can observe that the number of carnivorous species rapidly saturates. By contrast, the number of primary consumer species keeps growing. Hence, once passed an optimal environmental condition for which food webs show the most complex structure with high trophic levels, the proportion of primary consumers in the network statistically increases. For high-level predators, that are very often omnivorous generalists, the distribution of prey in their diet reflects that of the community: it is turned towards a higher proportion of low trophic level primary consumers. Higher trophic level prey are somehow diluted, and the mean trophic level of prey in the diet is then lowered and entails a decrease in the aggregated highest predator trophic level.

(a). Discussion

Previous studies have also investigated the role of environmental attributes on food web structure, and especially on food chain length. Three hypotheses have been formulated [10], namely the productivity hypothesis, the ecosystem size hypothesis, and the combined productive-space hypothesis. While this pioneering study showed a strong inclination for the ecosystem size hypothesis, other studies have shown results in favour of the other two [11,39,40].

Our result on the complex structuring role of environmental richness can give support to this productivity hypothesis. An advantage of our study is that we could isolate the effects of this structuring factor and test variations on a wide range of theoretical values. To illustrate this, we can compare our results with a recent study that looked at structural variations in marine communities at high latitudes along an environmental productivity gradient [13]. Like them, we find the lowest connectance values for low environmental productivity, and higher connectance values (or higher trophic levels) for high productivity values. However, in our case, the trophic complexity (connectance or functional diversity) of evolved food webs, after a first increase to some maximum value, then begins to decrease again for high environmental productivity. It underlines the fact that relationships between global scale parameters and network structure are not always straightforward and monotonous, and could give cues of why whichever simple hypothesis may be verified in some situations but defaulted in others. We note that our results are robust to significant changes in model assumptions (see the electronic supplementary material, S5 and figure S5).

4. Disturbance experiment

In this section, our goal is to show if/how evolution has led food webs, depending on the environmental conditions, to develop some specific properties conferring them a given robustness. We discuss the mechanisms at work behind our results. We then question the ‘adaptive status’ of trophic networks, and finally ask whether evolutionary processes maximize some of their properties by setting up a common garden experiment.

Relative species loss for all 1000 × 1000 treatment configurations are shown in figure 4a. It highlights three main outcomes. First, food webs appear to be quite robust to moderate environmental changes (small variations around the default energy supply level I, i.e. on either side of the white diagonal): no catastrophic collapses, low relative species losses. Second, evolved food webs appear to be much more sensitive to decreases of the environmental richness (depletion) than to increases (enrichment). Lastly, we found that food webs which have evolved in poor environments are less robust (more relative species losses) to environmental depletion than networks that have evolved in a richer one.

Figure 4.

Short-term, ecological responses of food webs when they are subjected to new environmental conditions different from their evolutionary environment. Panels (a,d) present, respectively, the relative species losses and the gains/losses of maximum trophic level observed. Red arrows on (a) show the reduction factor needed to reduce the number of species by half, for two contrasted I_evol. Panels (b,c) show the relative species losses when the productivity of the basal food web resource is depleted by a certain percentage. Food webs are sorted by connectance (b) or maximum trophic level (c), and values are smoothed by a Gaussian kernel. Panels (e,f) show, respectively, the comparative losses of species diversity and entropy (diversity of flows) of evolved trophic networks. Comparative loss refers to the difference between the new property value of a food web for a given, new, environmental richness, and the value of the same property for the ‘native’ food web that has evolved in this later environmental richness. (Online version in colour.)

Now, by directly linking the relative species loss to the emerged connectance of evolved food webs (figure 4b), we focused on environment depletion. We observed that trophic networks characterized by low connectance values appear to be more robust to a decrease in their energy supply level. By contrast, the most connected of our evolved food webs lose about half of their species for a halving of the environmental richness. However, examining the variance of the relative species loss data (electronic supplementary material, figure S7), we observe high values for low connected food webs experiencing strong environmental depletion (bottom-left corner). It means that behind the average value is hidden a significant diversity of food webs responses to perturbation (see the electronic supplementary material, figure S7 for details). Away from these connectance values, food webs respond more consistently to perturbations.

We performed the same analysis for maximum trophic levels. We observed that food webs characterized by high trophic levels appear to be more robust to environmental depletion than networks characterized by lower values (figure 4c).

One could ask about the mechanisms behind these results. We showed that species characterized by highest trophic levels, i.e. secondary consumers or top predators, were more prone to go extinct following a depletion of the environmental richness (electronic supplementary material, figure S9). It may thus sound counterintuitive that food webs which reach the highest trophic level (overall, they also contain the highest proportion of carnivorous species, see the electronic supplementary material, figure S6) are the most robust ones. We propose an explanation based on an analogy with a simple 2-species predator–prey system (see the electronic supplementary material, S4, figure S10). We conclude that in low-connectance, high maximum trophic level networks, the numerous high-level predators are best ‘settled’ and less prone to extinction than the few high trophic level predators in higher-connected, lower maximum trophic level networks.

We have looked so far to impacts of perturbation through (downward) changes in one specific property: species diversity. Results on maximum trophic level gains/losses show us some intriguing results (figure 4d). It appears that all food webs increase their maximum trophic level when they are confronted with a new, intermediate value of environmental richness, regardless of their evolutionary conditions (positive values for I_perturb. ≃ 10¹). It shows that evolutionary history does not always shape food webs in a way that their functioning, at least for some characteristics (here maximum trophic level), be maximized for the environmental conditions that have accompanied their evolutionary emergence.

Undoubtedly, a food web is not an adaptive unit that directly undergoes natural selection, and we do not have any mechanistic way to determine how the concept of individual fitness could transfer to a whole community. Still, we wanted to push this analogy and assess whether trophic networks could be designed by coevolution so that they would particularly fit their environment for some property related to their functioning that could de facto be a proxy for a ‘food web fitness’ measurement. With that goal, we observed our setting as a (virtual) common garden experiment (see Methods).

Comparative species loss of the ‘exogenous’ food web compared to the ‘native’ food web are shown in figure 4e.

The striking result is that, concerning species diversity, food webs that emerged for low to intermediate environmental richness values are not especially best ‘adapted’ to their environment. Indeed, most of the trophic networks that evolved in a richer milieu keep a higher number of species when they undergo even severe environmental depletion, compared to food webs evolved from the beginning in these poor environmental conditions (red area under the diagonal). Not shown results for other properties (e.g. connectance, trophic level) highlight similar trends.

However, when looking at properties derived from information theory [41] (see Methods), we found that evolution seems to maximize the diversity of fluxes of energy between trophic levels (see the electronic supplementary material, S1). For most evolved food webs, any disruption of environmental richness from customary conditions induces values of these properties that are lower than those that characterize food webs that have evolved in these environments (figure 4f).

(a). Discussion

Both topological and dynamical studies have questioned the relationship between the structure and the robustness of food webs by studying their responses to species loss [18,19,42]. Dynamical approaches can answer some of the weaknesses of topological approaches (e.g. misleading picture of potential secondary extinctions). However, most of these dynamical approaches are based on generalized Lotka–Volterra models, ignoring the evolutionary history of the communities generated. We first depart from these studies by explicitly taking into account this evolutionary history to produce the various structures of obtained food webs, thus incorporating in our assumptions the processes that designed the empirical trophic networks.

The second type of divergence concerns the type of disturbance. Former studies were conducted through the analysis of secondary extinctions following the initial loss of one or more species. Primary species losses were discussed as being the result of several disturbance factors, that however, usually stay out of the scope of the studies. Even if the results may vary depending on how the species are primarily removed (e.g. [43]), one of the major findings of these investigations is that food webs characterized by high connectance values appear to be the most robust.

Here we have a different approach. When primary extinctions are proximate causes for secondary extinctions, explicitly taking into account changes in environmental conditions is like considering distal causes for these extinctions. Hence, we do not decide a priori which species potentially disappear, but we estimate it a posteriori from the new environmental parameter value along with the population dynamics model.

Therefore, because we obtained opposite results with both the different selected dataset and methodology, we do not contradict the current paradigm around the connectance-robustness debate. Instead, we provide additional elements of understanding and underline the precaution of attributing too straightforwardly a high robustness to highly connected food webs if the environment is to undergo depletion disturbances. As pointed out by Donohue et al. [44], it is not surprising that different natures of perturbations entail diverging stability responses of communities. However, while these studies focused on the effect of primary extinctions as the perturbation mechanism, they also differ from our approach by not taking into account the evolutionary history of trophic networks. It would therefore be interesting to explore the effects of other types of perturbations, but in the context of our evolved networks, to assess which difference in the model hypothesis (evolved food webs dataset or perturbation type) is the most responsible for diverging results.

Our results are also in line with the fact that the relationship between connectance and robustness in food webs, or complex networks in general, can be thought of in ‘two ways’ [45]. On the one hand, the propagation of an explicit disturbance may be favoured in a highly connected network because of its lower compartmentalization [45,46]. However, on the other hand, such a highly connected structure may be less prone to getting fragmented, consequently to species removal perturbations (primary extinctions) [18,19]. We also highlight that food webs with a similar level of connectance may respond very differently to perturbations so that the average response may not always be very informative. This final result is very sensitive on the dataset used, and we commonly recommend taking precautions.

We chose here to focus on the short-term, demographic only, responses, with no post-perturbation evolution taken into account. We are nevertheless aware that a growing field in ‘eco-evolution’ shows interest in rapid evolution and the intermingled timescales of demography and evolutionary adaptation [47]. It will be a natural development of this study to also consider evolutionary processes in response to perturbation.

We finally note that our results were robust to both changes in model assumptions as well as in the procedure to produce the set of simulated food webs (see, respectively, electronic supplementary material, figures S13 and S8).

The fact that ecosystems may develop or evolve by maximizing some of their properties is a long, contentious debate in ecology [38]. The approach discussed here allows us to question the level of adaptation of a food web to its evolutionary environment by comparing it to other food webs subjected to this environment without an adaptation period. It provides a complementary point of view to the extent to which evolution leads an entity, here, in this case, a food web, to develop optimal properties. Considering food webs as super-organisms is a concept widely discussed in the evolutionary and ecological literature [38,48]. Loreau [38] argues that while near optimization of ecosystems properties is conceivable (with constraints on strengths and directions of individual and group selections), there is no reasons to believe that it will be generally achieved, and that there is no objective criterion to forecast it. Here we present contrasting results. In contrary to what usually cross-transplantation experiments on real organisms show (e.g. [49]), food webs do not appear to be particularly ‘adapted’ to the environment in which they evolve in, for the most characterizing properties we checked. A property related to diversity and organization of trophic fluxes appears to be the only candidate of evolution-optimized property of food webs.

Data accessibility

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Authors' contributions

B.G. and M.G. designed the model, performed the study and analysed the results. All authors contributed to the writing of the manuscript.

Competing interests

We declare we have no competing interests.

Funding

The PhD scholarship of B.G. was funded by a PhD contract of the Doctoral School ED251 at Aix-Marseille University.