  We study the limit distribution of the largest fitness for two models of
weakly correlated and identically distributed random fitnesses. The correlated
fitness is given by a linear combination of a fixed number of independent
random variables drawn from a common parent distribution. We find that for
certain class of parent distributions, the extreme value distribution for
correlated random variables can be related either to one of the known limit
laws for independent variables or the parent distribution itself. For other
cases, new limiting distributions appear. The conditions under which these
results hold are identified.
