Stability analysis in the Lotka-Volterra model Species 2 extinct at equilibrium and species 1 at K 1 . Both of these eigenvalues must be less than one for the equilibrium to be stable. Stability analysis in the Lotka-Volterra model Species 1 extinct at equilibrium and species 2 at K 2 . Both of these eigenvalues must be less than one for the equilibrium to be stable. Both species present at equilibrium.
Strong competition prevents two species from stably co-existing.
Under these conditions, is positive and less than one in magnitude. Weak competition allows two species to co-exist, but only if their growth rates are positive and less than two. We will talk about how these conditions were obtained and also how to analyse the model when r 1 does not equal r 2 in class. A simple graphical analysis is often made of the Lotka-Volterra model, but this method is less exact than a local stability analysis. In the graphical analysis, N 2 is plotted against N 1 .