Effects of Wolbachia on genetic divergence between populations: Mainland-island model

Integrative and Comparative Biology, Apr 2002 by Telschow, Arndt, Hammerstein, Peter, Werren, John H

m = proportion of the island population that are migrants from the mainland, defined each generation at the time of migration.

s = selective advantage of the G allele on the island (fitness of G individuals is 1 s, that of g individuals 1).

Maintenance of divergence model

First, we investigated the effect of Wolbachia on Maintenance of Divergence between the island and mainland populations. This involved a starting situation in which complete lack of gene flow between island and mainland had already led to allopatric divergence with fixation of G on the island and g on the mainland. We investigated the population genetics of the G allele on the island population after introduction of migration from the mainland (m proportion migrants per generation). In this model, either a single strain of Wolbachia was present at the initial island equilibrium (case A) or we had initially two different strains on mainland and island (case A B).

We examined the model (2)-(4) for a set of parameter values that seemed biologically realistic. Since most Wolbachia have rather high probabilities of being passed on from a female to her eggs, transmission rates of t = 0.99 and t = 0.90 were used for both Wolbachia types. CI levels are more variable, and range from very low in Drosophila melanogaster to complete incompatibility in Nasonia vitripennis (Hoffman and Turelli, 1997; Breeuwer and Werren, 1990). CI levels of l = 0.99, l = 0.90, l = 0.80 and l = 0.50 were examined, since these encompass the range from nearly complete CI to rather weak CI. Very weak CI, as in D. melanogaster, can also effect the divergence between the populations, but the effects are much less pronounced and therefore not discussed in the paper.

Stability of the CI system. We first investigated the stability of the CI system. By this we mean whether the Wolbachia A infection is maintained on the island population despite migration from the mainland. In general we found that the island Wolbachia type remained at relatively high frequency across the range of migration rates until the migration rate approached a "threshold," above which the Wolbachia A went to extinction. Additionally we found that selection at the G-g locus stabilized the CI system at higher migration rates than when there was no selection at this locus. Figure 3 shows the equilibrium frequencies of Wolbachia A and the G allele as a function of migration for fixed selection coefficient and Cl-level. Figure 3a, b compares case 0 (No Wolbachia) to case A (unidirectional CI) and to case A B (bidirectional CI) whereas Figure 3c, d shows the corresponding cytotype frequencies. The island Wolbachia can be maintained at relatively high migration rates. At low-tomoderate migration rates (e.g., 0

Also shown in Figure 3 are the equilibrium frequencies of G in the two populations for different migration rates and CI levels (but a fixed selection coefficient s = 0.01 or s = 0.1). As can be seen, the presence of uni- or bidirectional CI increases genetic divergence between the two populations at the selected locus, over a broad range of migration rates. This can be interpreted as a reduction of the effective migration rate caused by Wolbachia. When both Wolbachia have a CI level of l = 0.9, presence of Wolbachia A and B increases G allele frequency on the island from zero to 26% (for s = 0.01) or 91 % (for s = 0.1), even when migration rates are as high as 10% per generation. Figure 4 shows that the threshold migration rate (i.e., the migration rate that causes collapse of Wolbachia A type) depends, to a good approximation, linearly on the selection coefficient s. For instance, if both CI levels are l = 0.9 and t = 0.99, the threshold migration rate is approximately 0.19 0.15s (Fig. 4a). Both the slope and constant are high if CT level is high. The threshold migration rate is higher for the unidirectional case A compared to case A B. Threshold migration rates for lower transmission rate of t = 0.9 are shown in Figure 4b. As can be seen, lower transmission rate has only a small effect in case A B, but results in a significant reduction of threshold migration rates in case A.