# Food web assembly algorithms

A food web assembly algorithm is a series of repeating steps by which a model food web can be created. Starting with one or a few species, new species are permitted to invade at each time step, and are lost at each time step, according to some prespecified rules. There is already a large body of food web assembly literature (Tregonning & Roberts 1979, Post … Continue reading Food web assembly algorithms

# 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: $\dot{x}_{i} = x_i \cdot f_i(x) = x_i \cdot (r_i + (A \cdot x)_i) \quad \forall i = 1, \ldots, n.$ Such a dynamical system is permanent if two conditions hold (Hofbauer and Sigmund 1988, The theory of evolution … 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