Feasibility of sparse large Lotka-Volterra ecosystems

Understand

Consider a large ecosystem (foodweb) with n species, where the abundances follow a Lotka-Volterra system of coupled differential equations.

• We assume that each species interacts with d other species and that their interaction coefficients are independent random variables.
• This parameter d reflects the connectance of the foodweb and the sparsity of its interactions especially if d is much smaller that n.
• We address the question of feasibility of the foodweb, that is the existence of an equilibrium solution of the Lotka-Volterra system with no vanishing species.