title: Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces.
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.
authors.affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden. ake.brannstrom@math.umu.se
authors.forename: Åke
authors.initials: Å
authors.lastname: Brännström
authors.forename: Linus
authors.initials: L
authors.lastname: Carlsson
authors.forename: Axel G
authors.initials: AG
authors.lastname: Rossberg
mesh_terms: D000818:Animals; D017753:Ecosystem; D020387:Food Chain; D008954:Models, Biological