Modeling Food Webs: Exploring Unexplained Structure Using Latent Traits

Abstract

Several stochastic models have tried to capture the architecture of food webs. This approach is interesting, but it is limited by the fact that different assumptions can yield similar results. To overcome this limitation, we develop a purely statistical approach. Body size in terms of an optimal ratio between prey and predator is used as explanatory variable. In 12 observed food webs, this model predicts, on average, 20% of interactions. To analyze the unexplained part, we introduce a latent term: each species is described by two latent traits, foraging and vulnerability, that represent nonmeasured characteristics of species once the optimal body size has been accounted for. The model now correctly predicts an average of 73% of links. The key features of our approach are that latent traits quantify the structure that is left unexplained by the explanatory variable and that this quantification allows a test of whether independent biological information, such as microhabitat use, camouflage, or phy-logeny, explains this structure. We illustrate this method with phylogeny and find that it is linked to one or both latent traits in nine of 12 food webs. Our approach opens the door to the formulation of more complex models that can be applied to any kind of biological network. abstract: Several stochastic models have tried to capture the architecture of food webs. This approach is interesting, but it is limited by the fact that different assumptions can yield similar results. To overcome this limitation, we develop a purely statistical approach. Body size in terms of an optimal ratio between prey and predator is used as explanatory variable. In 12 observed food webs, this model predicts, on average, 20% of interactions. To analyze the unexplained part, we introduce a latent term: each species is described by two latent traits, foraging and vulnerability, that represent nonmeasured characteristics of species once the optimal body size has been accounted for. The model now correctly predicts an average of 73% of links. The key features of our approach are that latent traits quantify the structure that is left unexplained by the explanatory variable and that this quantification allows a test of whether independent biological information, such as microhabitat use, camouflage, or phylogeny, explains this structure. We illustrate this method with phylogeny and find that it is linked to one or both latent traits in nine of 12 food webs. Our approach opens the door to the formulation of more complex models that can be applied to any kind of biological network.

Matching–centrality decomposition and the forecasting of new links in networks

“…Specifically, the decomposition is implemented at the node level, with each node characterized by latent traits of matching and centrality. Latent traits are variables whose values are unknown a priori, but can be estimated a posteriori from the network adjacency matrix itself [19,20]. The model, called the matching-centrality model, is implemented in such a way that the closer the matching traits of two nodes, the greater the probability that they are linked, and the higher the centrality trait of a node, the greater the probability that this node makes links.…”

Trait- and size-based descriptions of trophic links in freshwater food webs: current status and perspectives

“…Even if we could define a single abstract feeding niche to characterize trophic links in a food web, body size may not correlate strongly with the niche parameters (Williams et al, 2010). Moreover, multidimensional niches requiring additional traits can describe the topology of empirical food webs with higher likelihood than one-dimensional niche models, including those based on body size (Alessina et al, 2008;Rohr et al, 2010;Williams and Purves, 2011;Eklöf et al, 2013). In less abstract terms, the presence and strengths of trophic links are affected by temperature (Henri et al, 2012;Rall et al, 2012), species identity (Nakazawa et al, 2011, Gilljam et al, 2011Rall et al, 2011), evolutionary history (Bersier and Kehrli, 2008), and predator and prey traits more mechanistically tied to the predation process (Winemiller, 1991;Wirtz, 2012;Klecka and Boukal, 2013).…”

Structural Network Properties of Niche-Overlap Graphs

“…Williams et al elaborated the probabilistic niche model that reveals the niche structure and the role of body size in foodwebs [13]. Rohr et al developed a model to capture the architecture of food-webs to uncover the major factors underlying food-web organization [14]. Thierry et al analysed the consequences of the body mass distribution for food web topology [15].…”