Brännström Åke, Carlsson Linus, Rossberg Axel G
Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden.
J Math Biol. 2011 Sep;63(3):575-92. doi: 10.1007/s00285-010-0383-3. Epub 2010 Nov 16.
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.
食物网代表了生态系统中的营养（摄食）相互作用。自20世纪70年代末以来，人们已经认识到食物网与区间图有着惊人的密切关系。对食物网区间性的一种解释是，营养生态位空间是低维的，这意味着一个物种的营养特征可以由一个或至多几个数量性状来表示。在一篇配套论文中，我们通过模拟一个最小食物网模型证明，当生态位空间是高维时，食物网也有望是区间的。在这里，我们通过证明高维生态位空间中食物网区间性的一组严格条件，来刻画这一现象背后的基本机制。我们的结果适用于一大类食物网模型，包括之前通过数值研究的特殊情况。
