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Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
School of Biological Sciences, Queen’s University Belfast, Belfast, BT9 7BL UK.
2011 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 3, 575-592 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springerlink , 2011. Vol. 63, no 3, 575-592 p.
Keyword [en]
Food web, Intervality, Ultrametric, Consecutive ones property, COP, Ornstein–Uhlenbeck process, Branching process, Ecological model
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-50108DOI: 10.1007/s00285-010-0383-3OAI: oai:DiVA.org:umu-50108DiVA: diva2:459594
Available from: 2011-11-26 Created: 2011-11-26 Last updated: 2017-12-08Bibliographically approved

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