The analysis
of the two locus model shows that alleles with a positive effect on
can only be selected if the advantage gained by this effect is
not outweighed by the selection against the pleiotropic effects. The
ratio of directional to stabilizing selection determines whether the
population is invadable by a mutation with pleiotropic effects. In this section we examine the
invadability problem for the four locus case. The population is not
invadable if the fixed point 
is locally stable and
invadable if F1 is unstable.
The fixed point F1 is stable
if the following conditions are satisfied:
Thus, for each combination of loci with opposite pleiotropic effects, the same conditions for local stability have to be fulfilled as for the two locus model (conditions (16), (17), (18) and (19)). In addition there are two other conditions which take into account the possibility of `cooperation' (as defined above) between the loci, which implies that the fixed point F1 can become unstable even if the criterion for the stability of each two locus system is fulfilled.