Dynamically evolved community size and stability of random Lotka-Volterra ecosystems

We use generating functionals to derive effective dynamics for Lotka-Volterra systems with random interaction coefficients. From this effective process we study the stability and size of the resulting species communities. The size of the ecosystem is not set from the beginning. Instead, we start from a set of possible species, which may undergo extinction. How many species survive depends on the properties of the interaction matrix; the size of the resulting food web at stationarity is a property of the system itself in our model, and not a control parameter as in most studies based on random matrix theory. We find that prey-predator relations enhance stability, and that variability of species interactions promotes instability. Complexity of inter-species couplings leads to reduced sizes of ecological communities. Dynamically evolved community size and stability are hence positively correlated.