Evolutionary food web models: effects of an additional resource

Abstract

Many empirical food webs contain multiple resources, which can lead to the emergence of sub-communities—partitions—in a food web that are weakly connected with each other. These partitions interact and affect the complete food web. However, the fact that food webs can contain multiple resources is often neglected when describing food web assembly theoretically, by considering only a single resource. We present an allometric, evolutionary food web model and include two resources of different sizes. Simulations show that an additional resource can lead to the emergence of partitions, i.e. groups of species that specialise on different resources. For certain arrangements of these partitions, the interactions between them alter the food web properties. First, these interactions increase the variety of emerging network structures, since hierarchical bodysize relationships are weakened. Therefore, they could play an important role in explaining the variety of food web structures that is observed in empirical data. Second, interacting partitions can destabilise the population dynamics by introducing indirect interactions with a certain strength between predator and prey species, leading to biomass oscillations and evolutionary intermittence.

Appendix

Fig. 5

Biomass evolution of the food webs shown in Fig. 1a (upper row) and d (bottom row). In the upper row, both resources have identical sizes $z_{R_{1}}{=}~z_{R_{2}}{=}~0$. The resources in the bottom row have a size distance of d ($z_{R_{1}}{=}0$ and $z_{R_{2}}{=}~d$). a, c Biomasses of both resources. Note that the curves in a overlap since both resources have identical sizes. b, d Biomasses of representative morphs of different trophic level. All biomasses of the resources and morphs reach a static fixed point. Small fluctuations are caused by evolutionary modification of the food web

Fig. 6

Network time series and food web structure for a second resource of size $z_{R_{2}}\!=6\,=\,3d$: time-averaged biomass-bodysize histogram (left), temporal evolution of bodysizes contained in the system (middle), and resulting network structure (right). The food web reaches an evolutionarily static state with two disconnected partitions each of which is based on one specific resource. The lower partition has a maximal trophic level of three, while the other has a maximal trophic level of four. Both exhibit the classical network structure, but with distinct bodysize compartments

Fig. 7

Sketch of the influence of feeding interactions between morphs. The initial motifs considered (time t ₀) are a predator (grey) and prey (blue) pair (top panel), and a triangle motif that contains an additional morph (red) (bottom panel). In both motifs, the influence of the increase/decrease of the biomass of the prey/predator on the other morphs’ biomasses is illustrated. The biomass of one of them is fixed to a higher/lower value (t ₁, underlaid in grey) and the reaction of the other morphs (t ₂) is sketched. The biomasses are indicated by the size of the nodes. Top In a food chain, the biomass of the predator is proportional to the prey’s biomass, while the prey’s biomass is inversely proportional to the predators biomass. Bottom Due to the additional morph, the biomass relationships are changed. For instance, the decrease in the prey’s biomass still leads to an decrease of the predator’s biomass, but due to the additional morph the decrease of the predator’s biomass is buffered: the predator can consume the red morph. Similar effects can be seen for a change in the predator’s biomass. If it decreases the prey’s biomass does not increase linearly, since the red morph also increases in biomass and so does its consumption of the prey. Therefore, the prey’s biomass only increases slightly. The additional morph therefore induces a phase shift between prey and predator