Fitness optimization and evolution of permanent replicator systems

Food webs and the principle of evolutionary adaptation

“…In this work the functional S p (u) was maximized for the predator-prey model for the given constant T and given initial conditions, which poses some computational difficulties. In the present text we solve the same problem using an additional hypothesis of time separation in our model, similar to what was done for certain classes of replicator equations in [2,6,10]. This hypothesis allows a significant simplification in solving problem (1.3).…”

“…In [2] it was suggested to look at the replicator equation from an evolutionary prospective, allowing for the changes of the parameters within the same system realization; the basic assumption was the separation of the time scales whereas during the fast time dynamics the system settles at an asymptotic regime, and during the slow time dynamics the system is allowed to change its parameter values according to some prescribed evolutionary principle (usually the fitness maximization). This approach was further extended and illustrated by other examples of replicator equations in [6] and [10]. The Lotka-Volterra equations, being a close relative to the replicator equation, are equally well suited for this approach of evolutionary adaptation, and in the present text we show how to implement it using a specific example of the Lotka-Volterra equations -the so-called food chains and food webs (e.g., [5]).…”