CYTONUCLEAR THEORY FOR HAPLODIPLOID SPECIES AND X-LINKED GENES - II -STEPPING-STONE MODELS OF GENE FLOW AND APPLICATION TO A FIRE ANT HYBRID ZONE

We develop cytonuclear, hybrid zone models for haplodiploid species or X-linked genes in diploid species using a stepping-stone framework of migration, in which migration rates vary with both direction and sex. The equilibrium dines for the allele frequencies, cytonuclear disequi libria, and frequencies of pure parental types are examined for specie s with diagnostic markers, under four important migration schemes: uni form migration of both sexes in both directions, greater migration of both sexes from one direction, greater migration of females, and great er migration of males. Of the three cytonuclear variables examined, th e allele frequency dines are the most informative in differentiating a mong the various migration patterns. The cytonuclear disequilibria and the frequency of the pure parental types tend to be useful only in re vealing directional asymmetries in migration. The extent of hybrid zon e subdivision has quantitative but not qualitative effects on the dist ribution of cytonuclear variables, in that the allele frequency dines become more gradual, the cytonuclear disequilibria decrease in magnitu de, and the frequencies of pure parentals decline with increasing subp opulation number. Also, the only major difference between the X-linked and haplodiploid frameworks is that a higher frequency of pure parent als is found when considering haplodiploids, in which male production does not require mating. The final important theoretical result is tha t censusing after migration yields greater disequilibria and parental frequencies than censusing after mating. We analyzed cytonuclear data from two transects from a naturally occurring hybrid zone between two haplodiploid fire ant species, Solenopsis invicta and S. richteri, usi ng our stepping-stone framework. The frequency of S. invicta mtDNA exc eeds the frequency of the S. invicta nuclear markers through much of t his hybrid zone, indicating that sex differences in migration or selec tion may be occurring. Maximum-likelihood estimates for the migration rates are very high, due to an unexpectedly large number of pure paren tal types in the hybrid zone, and differ substantially between the two transects. Overall, our model does not provide a good fit, in part be cause the S, invicta-S. richteri hybrid zone has not yet reached equil ibrium.