Generalized Lotka Volterra Communities

Generalized Lotka-Volterra communities are toy models for which it is very easy to calculate the invasion fitness for new potential community members. Although these models are biologically rather unrealistic, their easy accessibility makes them ideally suited for the initial exploration of ideas, and the construction of examples or counterexamples. In continuous time, for i = 1,..., k, dn(X, dt

b(X,) - £ c(X,, Xy) e(Xy, n(Xy), E, ) (t) j=i X n(X,■ )(t)

with Ej consisting of some additional environmental variables, like the weather, various weighted sums of the »(X,), etc., and e some recipe that when fed with a trait vector X and scalar and vectorial time functions » and Ej produces a scalar time function e (X, », Ej). Similarly, in discrete time, n(X, )(t-

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