Competition and MacArthur Model of resource

Now I m studying the competition models like MacArthur Model for resource subdivision ( COMPETITION Keddy 2001 Kluwer). He explored the possible mechanisms underlying the aij of the Lotka-Volterra equations, and the implications of these for the way in which organisms might subdivide the resources available to them. The problem is the realistic measured of competition matrix. MacArthur model is mostly based on statistical properties of Normal distribution.