Our model demonstrates that an incompatibility system completely linked with a sex determination locus causes a frequency-dependent selection, and can therefore favour rare alleles through male function. Thus, it may induce the spread of the female-sterility allele (rare) within a hermaphroditic population. Contrary to the results predicted by Lloyd (1975) and Charlesworth & Charlesworth (1978), this model can explain male frequencies greater than 0.5 in a functionally androdioecious species. However, the equilibrium frequency of male phenotypes is highly dependent on three key parameters: the dominance of female-sterility at the sex locus, the number of alleles at the self-incompatibility locus, and the fitness advantage of the male morph.
In our dominant model, all Am alleles are found in S1Am haplotypes, which is expected if the female-sterility mutation arises only once, and the S1 allele is associated only with Am: the S1Ah haplotype does not exist. Two explanations would lead to this case. In the first explanation, when the female-sterility mutation first appears, S1 alleles are as common as any other S allele, and associated with the Ah allele in hermaphrodites. However, even if the S1Ah haplotype is initially quite common, there is a selective process that reduces its frequency. As the S1Am male haplotype becomes common, as a result of the male advantage coupled with the compatibility advantage, the S1 allele will be at a disadvantage in hermaphrodites. Through this selective process, S1Am frequency increases and the S1Ah haplotype, although not completely eliminated at equilibrium (result not shown), may be eliminated in small populations by random drift, so that S1 remains only in the S1Am haplotype. In the second explanation, when the female-sterility mutation first appears, this new allele, Am, has a pleiotropic effect on the self-incompatibility locus, which creates a new S-allele called S1. This S1 allele is then only associated with Am.
We chose to model a GSI rather than a sporophytic self-incompatibility for several reasons. First, GSI is more widespread than SSI in angiosperms (Charlesworth, 1985). Secondly, GSI is simpler to implement and thus ideal for an initial approach. Thirdly, GSI is the only system in which maleness can be associated with a single S-allele. In the SSI case, the female-sterile haplotype would never benefit from an absolute cross-compatibility advantage.
In our study, the results of models are highly dependent on the dominance relation at the sex locus. If female-sterility is dominant, a high frequency of males (>50%) can be maintained within populations even when their advantage in fitness is low (K ≤ 2), as long as the number of S-alleles is also low (n < 6) (Fig. 1). On the other hand, if female-sterility is recessive, equilibrium male frequency is smaller than or equal to 0.5 (Fig. 2). When female-sterility is dominant, only one SI allele is associated with female-sterility (S1Am) and it is exclusively paternally inherited. This haplotype is more frequently transmitted than others because it benefits from (i) a cross-compatibility advantage resulting from the allele S1 [males are always compatible (fully or half-compatible) with all hermaphroditic genotypes]; (ii) a male-biased paternal sex ratio resulting from a greater cross-compatibility of male-determining alleles; and (iii) a male fitness advantage (K). The first two phenomena are a result of the fact that males can interact with n − 1 partners (different genotypes), whereas hermaphrodites have only n − 2 possible partners. Consequently, a small n causes a higher male advantage than a large n, and the former situation should be encountered more frequently in small, recently founded populations (colonization event). However, as the number of SI alleles (n) increases, incompatibility among hermaphrodites decreases and the male cross-compatibility advantage becomes negligible. This can occur through mutation or, more probably, migration from other populations, especially in wind-pollinated species such as Phillyrea, Fraxinus, and Mercurialis. Consequently, when n is high, the difference in fitness between males and hermaphrodites depends only on their relative advantage in male fitness, and the equilibrium male frequency matches the results of the compensation model.
If female-sterility is recessive (see Appendix), the two male haplotypes (S1Am and S2Am) can be found in a heterozygous state in hermaphroditic individuals so that no haplotype is exclusively associated with males and paternally inherited. Consequently, males benefit from only a weak cross-compatibility advantage. Paradoxically, we find that the male advantage in fitness (K) favours the frequency of hermaphrodites: as K increases, the frequency of S1Am and S2Am haplotypes increases in the pollen pool, and providing that n is large enough, more hermaphrodite phenotypes (heterozygotes for S1Am or S2Am haplotypes) will be produced than male phenotypes. Consequently, when female-sterility is recessive, the equilibrium male frequency is even smaller than in the compensation model for large values of n and K (Fig. 2). The genetics of sex determination has been studied in only two species; female-sterility is dominant in one species (Pannell, 1997b) and recessive in the other (Wolf et al., 1997). Therefore, it is not possible to draw any conclusion about the dominance of female-sterility.
The number of S-alleles (n) that are maintained at mutation–selection equilibrium within a finite population depends on population size N in a gametophytic self-incompatibility system (Wright, 1939; Vekemans & Slatkin, 1994; Schierup, 1998; Vekemans et al., 1998), and may be less than six when N < 50 (Vekemans & Slatkin, 1994; Schierup, 1998). This small value of n above which a high frequency of males cannot be maintained in our dominant model is thus plausible in small populations.
The linkage between the two loci is a key assumption in our model. Indeed, if the linkage between self-incompatibility and sex determination is not complete, our results coincide with those of the compensation model (results not shown). However, the recombinant haplotype for the S-allele originally associated with female-fertility (S1Ah in the dominant model), will have a higher probability of being lost by drift than the nonrecombinant male haplotype (S1Am), provided that n is small enough (see above discussion).
The male haplotype (S1Am) can be regarded as a selfish gene, which favours its own transmission to the detriment of the others. Indeed, this exclusively paternally inherited haplotype not only suppresses the female function, but also biases the sex ratio of its own offspring and thus acts as a sex-ratio distorter. Selection acts on the haplotype as a whole, and so recombination between the two loci might be selected against. Such selfish haplotypes, implying two loci that never recombine (carried in an inversion loop, for example), have already been described (e.g. sex-ratio distorters; see review in Werren & Beukeboom, 1998).
In this study, we have modelled the evolution of male frequency considering that androdioecy evolves from hermaphroditism, as in all previous theoretical studies (Lloyd’s (1975), Charlesworth & Charlesworth’s (1978) phenotypic models as well as Pannell’s (1997a) metapopulation genetic model). However, the only clear data favour androdioecy as a reversion from dioecy (Mercurialis annua, Pannell, 1997d). Because experimental data are so scarce, we still cannot reject the hypothesis of an evolution from hermaphrodism. Moreover, in the case of Phillyrea angustifolia, even if phylogenetic data (Wallander & Albert 2000) do not provide a sufficient resolution to determine whether androdioecy evolved from dioecy or hermaphrodism, the presence of a relict pistil in male flowers, as the only significant morphological difference between male and hermaphrodite flowers (Lepart & Dommée, 1992), strongly suggests that androdioecy has evolved from an hermaphrodite ancestor.
In conclusion, a gametophytic self-incompatibility system linked to a nuclear sex determinism, by causing a frequency-dependent selection, may explain the high frequencies of males recently reported in some androdioecious species (these include the functional androdioecious species P. angustifolia (Vassiliadis, 1999) and in two other potentially androdioecious species, Fraxinus lanuginosa (10–49.7% males in populations) (Ishida & Hiura, 1998) and Fraxinus ornus (50% males in populations) (Dommée et al., 1999), for which the pollen of hermaphrodites has been proven potentially fertile). The conditions required by the model to explain the maintenance of high male frequency within a hermaphroditic population are dominance of female-sterility (Am > Ah) with a complete linkage between Am and S1 alleles, and a few S-alleles. Controlled crosses can easily test both predictions of this model.
Datisca glomerata (C. Presl) Baill.
|Source||Large Mammals||Small Mammals||Water Birds||Terrestrial Birds|
|Source||Large Mammals||Small Mammals||Water Birds||Terrestrial Birds|