<preprint> Part-whole relations between food webs

Dear Colleagues,

this message is really about food webs.

Please have a look at my manuscript

       Part-Whole Relations Between Food Webs and the Validity of
       Local Food-Web Descriptions

recently accepted for Ecological Complexity.  It gives formulae
relating the topology of large food webs to the topology of random
sub-samples thereof of arbitrary size, and argues that, since such
relations exist, food webs sampled at different scales contain, as far
as topology is concerned, similar information.  And no, the question
how L scales with S is explicitly excluded :) .

Your comments are welcome!

Axel Rossberg

URL: http://axel.rossberg.net/paper/Rossberg2007a.pdf

Abstract:

This work analyzes the relationship between large food webs describing
potential feeding relations between species and smaller sub-webs
thereof describing relations actually realized in local communities of
various sizes. Special attention is given to the relationships between
patterns of phylogenetic correlations encountered in large webs and
sub-webs. Based on the current theory of food-web topology as
implemented in the matching model, it is shown that food webs are
scale invariant in the following sense: given a large web described by
the model, a smaller, randomly sampled sub-web thereof is described by
the model as well. A stochastic analysis of model steady states
reveals that such a change in scale goes along with a renormalization
of model parameters. Explicit formulae for the re-normalized
parameters are derived. Thus, the topology of food webs at all scales
follows the same patterns, and these can be revealed by data and
models referring to the local scale alone. As a by-product of the
theory, a fast algorithm is derived which yields sample food webs from
the exact steady state of the matching model for a high-dimensional
trophic niche space in finite time.