A fish tank model for assembling food webs

Abstract

In the past two decades, several models for food webs have been proposed. Those models provide possible explanations on how the food webs we observe today arrive at their respective network structure. Those well established models almost all rely on two common parameters, the numbers of species and trophic links, as well as assuming that species are ranked in some hierarchical order or ecological dimensions. Under those model assumptions species are then allowed to interact with each other depending on their relative positions in relevant ecological dimensions, resulting in simulated food webs that can capture the characteristics of their real-life counterparts. In this paper, we propose a simple model for food webs following biological intuitions. Our model differs from others in that we do not have the prior assumption of species being ordered in any ecological dimensions, and we do not assume a particular number of trophic links. Our model here takes two basic parameters, the number of species and the number of resources, and allows the random encounter between species and resources, and as a result forming trophic interactions. One critical assumption in this model is that after a species obtains resources, it will then become new resources for other species to utilise. In essence, the model here constructs food webs by passing resources among different species. Our model predicts the maximum number of trophic links of a food web when given the number of species, and shows that connectance is a non-linear decreasing function of species number. Furthermore, this simple model also demonstrates that the number of trophic levels tends to decrease when resource number is larger, echoing empirical studies from the literature. We further modified our simple model to fit a particular food web data and suggest the possible mechanism underlying the growth of the empirical food web. Lastly, we assessed the performance of our model by fitting it to a wide range of real food webs and compared the result with those derived from other models.