ABSTRACT
The increase in mean fitness is a result referred to as Fisher's Fundamental Theorem of Natural Selection [16]. The mean fitness acts as a Lyapunov function for system (1) so that it can be shown the allele frequency Pt converges to a fixed point [9, 16]. The value to which Pt converges, however, depends on the fitness matrix and the initial values. For k = 2 alleles, there are at most three fixed points for model (2) provided Wi; :F c=constant for all ij. They are (1,0)T, (0, 1)T, and {p, 1-p)T, where
p = Wu - W12 + W22 - W12 • The asymptotic behavior in this case is straightforward and is summarized in the next lemma.
