of individuals of each species per unit time. Since µ multiplies k, there is no loss of generality in assuming the ratio of µ and d to be as µ and d tend to 0.

The inequalities in (14) are useful in guiding our choice of parameters in the discrete coevolutionary model such that non-fluctuating patterns form. We emphasize that we are looking at the development of non-fluctuating heterogeneous spatial patterns due only to linear effects. It may be shown that one implication of (14) is that k1 and k3 must have opposite sign. Thus, referring to (6), we find that matching homozygotes must be helpful to homozygotes in one species and harmful in the other species if spatiallyheterogeneous patterns are to form and be fixed.