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Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces
Åke Brännström1, Linus Carlsson, Axel G Rossberg
1Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden. ake.brannstrom@math.umu.se
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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