Size-based predictions of food web patterns

Abstract

We employ size-based theoretical arguments to derive simple analytic predictions of ecological patterns and properties of natural communities: size-spectrum exponent, maximum trophic level, and susceptibility to invasive species. The predictions are brought about by assuming that an infinite number of species are continuously distributed on a size–trait axis. It is, however, an open question whether such predictions are valid for a food web with a finite number of species embedded in a network structure. We address this question by comparing the size-based predictions to results from dynamic food web simulations with varying species richness. To this end, we develop a new size- and trait-based food web model that can be simplified into an analytically solvable size-based model. We confirm existing solutions for the size distribution and derive novel predictions for maximum trophic level and invasion resistance. Our results show that the predicted size-spectrum exponent is borne out in the simulated food webs even with few species, albeit with a systematic bias. The predicted maximum trophic level turns out to be an upper limit since simulated food webs may have a lower number of trophic levels, especially for low species richness, due to structural constraints. The size-based model possesses an evolutionary stable state and is therefore un-invadable. In contrast, the food web simulations show that all communities, irrespective of number of species, are equally open to invasions. We use these results to discuss the validity of size-based predictions in the light of the structural constraints imposed by food webs.

Appendix: Assembly algorithm

The assembly algorithm is a replicate of that by Hartvig (2011), but presented below for completeness.

Model communities are formed using sequential assembly by introducing one new species at a time in low density ($10^{-10}$ g/vol) (Post and Pimm 1983; Drake 1990; Law 1999) from a species pool. If invasion fitness is positive, then the system is stimulated till it reaches steady state which can be a fixed point, periodic, or even chaotic, detected using heuristic algorithm. Fitness is measured using the per capita population growth rate (i.e., the evaluation of the right-hand side of Eq. (5)). A species is assumed to be in steady state if its absolute fitness is smaller than $1/1{,}000$ year⁻¹. During simulation, species are removed if they are going to extinction, defined as (1) population biomass falls below the extinction threshold $10^{-20}$ g/vol; (2) fitness is smaller than $-1/250$ year⁻¹, while the biomass is below $10^{-5}$ g/vol; or (3) fitness is smaller than $-1/1{,}000$ year⁻¹, while the biomass is below $10^{-10}$ g/vol. The assembly proceeds to a new invader if the introduced invader has negative invasion fitness, or if the augmented community (resident community plus invader) has reached equilibrium state.

In addition, the continuous species pool is discretized evenly in the x direction with a step size $\delta \log w = 0.1$. Results appear independent of the choice of discretization.