Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces |
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Authors: | Åke Brännström Linus Carlsson Axel G. Rossberg |
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Affiliation: | 1.Department of Mathematics and Mathematical Statistics,Ume? University,Ume?,Sweden;2.School of Biological Sciences,Queen’s University Belfast,Belfast,UK;3.Evolution and Ecology Program,International Institute for Applied Systems Analysis (IIASA),Laxenburg,Austria |
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Abstract: | Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically. |
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