Stability in large webs

Allesina & Tang (2012 Nature): An extension of analytic, Wigner semicircle theorem-like, stability criteria to predator-prey, competition and mutualism cases. Finds predator-prey interactions permit stability in networks as large and complex as real ones. Hierarchy is: competition-mutualism mixture, random, predator-prey. Finds that stability is less likely when both predator-prey networks and mutualistic networks are given more realistic structure (i.e. niche-model structure and nestedness respectively). Continue reading Stability in large webs

Link distribution in static community models like the niche model

I was recently reading a 2006 review of food web structure by Jennifer Dunne, which includes a very thorough discussion of static community models like the niche model (Williams & Martinez 2000, Nature), and I was struck again by how unclear it is – to me, anyway – what exactly it is that these static models represent. There’s no doubt that they do an excellent … Continue reading Link distribution in static community models like the niche model

Pretty food web graphs

When analysing output from the Webworld food web assembly algorithm (Drossel et al. 2001, J. Theor. Biol.), I often need a good way to quickly summarise the key properties of a web. In a recent project, I created a version of Webworld in which species could invade from outside the web (randomly generated species traits, as opposed to traits derived through mutation of a native … Continue reading Pretty food web graphs

The change in the distance from the convex hull to the internal equilibrium during assembly

Law & Morton (unpub.) found that the distance between the interior equilibrium and the convex hull, measured as mean , increased as a permanent food web assembly progressed. I did a small set of assembly runs to test the robustness of this result, and to discover what causes to increase. An introduction to permanence and example of how it is calculated can be found in … Continue reading The change in the distance from the convex hull to the internal equilibrium during assembly

Permanence and the distance from the convex hull to the interior equilibrium

Background To use permanence, Lotka-Volterra dynamics have to be assumed, because it is only in this case that a sufficient condition for permanence is known: Such a dynamical system is permanent if two conditions hold (Hofbauer and Sigmund 1988, The theory of evolution and dynamical systems p. 98). (1) It is dissipative; this is true for Lotka-Volterra systems where all the basal species are self-limiting … Continue reading Permanence and the distance from the convex hull to the interior equilibrium

An example linear programming problem in Octave

Tools for solving linear programming problems are useful to me because the necessary condition for permanence in a Lotka-Volterra system can be reduced to a linear programming problem (Jansen 1987, J. Math. Biol.; Law & Morton 1996, Ecology). Below, I’ve adapted an example from Tommi Sotinen’s ORMS 1020 lecture notes (p. 24-38) to demonstrate how to solve a linear programming problem in Octave. —– Giapetto’s … Continue reading An example linear programming problem in Octave