m.r.Life ι**=7/3ψ

Mating systems and sex ratios

Density dependent interactive competition can select the mating structure of Fisherian sex ratios

The diploid genome is the perfect heritable code for equal genetic sharing in a sexually reproducing pair, and the male-haploid female-diploid genome for female biased sharing in eusocials with no pair bond. But the evolution of sexual systems in natural populations is more like a continuum where the energetic fitness component of the male is not either exactly as important as that of the female, or basically zero. The evolution of intermediate sexual systems do generally not include an integer number of males per females, and the ploidy level is then too rigid to act - in itself - as the complete heritable code for the sexual system.

This is e.g. illustrated by the optimal sex ratio of the reproducing unit

(φ / θ)** = ψ ι**

as it is selected by density dependent competitive interactions in populations with no offspring workers [φ is the proportion of males; θ the proportion of females; ψ the cost gradient of interference; and ι** the level of interference; Witting, 1997, 2002]. The diploid case with an even sex ratio and equal sharing is the strict equilibrium only in populations with stable net energy and an attracting resource bias exponent of unity [ ψι** = 1 ]. Populations with increasing net energy and a resource bias above unity are instead selecting for a male biased in the sex ratios and gene sharing, and populations with a declining net energy and a resource bias that is smaller than unity are selecting for female biased sex ratios and gene sharing. Yet, the diploid genome with fair inheritance is a rather rigid code that is not easily adjusted on a continuum with changes in the optimal sharing of the offspring genome between the parents.

A diploid selection solution, however, is obtainable if we integrate the selection of density dependent competitive interactions with the Fisherian sex ratio theory. This theory takes a ploidy level and a mating pattern for granted, and it is then calculating the optimal sex ratio from the frequency dependent fitness advantages of parents that produce offspring in a different sex ratio than the average sex ratio in the population. The original case with random mating and a diploid genome that was considered by Fisher (1930) is illustrated in Fig. 1. It illustrates that an even sex ratio is the optimum, because the rare sex has an advantage in sexual reproduction over the common sex so that the relative fitness of the two sexes is the same only when the sex ratio is even.

Fig. 1 The fitness of two variants with respectively an even and a female biased sex ratio, assuming that mating is random and that the two variants are equally abundant. The circles represent females, the squares males, and the lines indicate the transfer of genes with the open square indicating random mating. The fitness (F) of a gene is given as the average number of copies of that gene in the grand-offspring. The variant with the even sex ratio has the highest fitness, even though the intrinsic growth rate in terms of individuals is highest in the lineage with a female biased sex ratio. From Witting (1997).

Where random mating is selecting for an even sex ratio, local mating is selecting for a female biased sex ratio (Hamilton, 1967). Local mating occurs when individuals mate with a relatively permanent set of neighbours that are more closely related to one another than the average relatedness in the population. The sons of a single female will then compete with one another for a limited number of matings, and it will pay to invest less in sons because the more sons a female produces the fewer matings each of them will get. If this local mating occurs within groups that are founded by s females, it follows (Hamilton, 1967; Witting, 1997) that the attracting Fisherian sex ratio

(φ / θ)** = (s - 1) / (s + 1)

is zero at the lower limit where mating occurs between sons and daughters [ s = 1 ], and even when mating is random [ s → ∞ ].

With the Fisherian sex ratio being a partial equilibrium that is dependent upon the ploidy level and the degree of local mating we may, for a given ploidy level, consider selection across the set of local mating patterns that defines a Fisherian sex ratio between zero and one. This is illustrated in Fig. 2, where the two-fold cost of the male is selecting for local mating and a strongly female biased sex ratio.

Fig. 2 The fitness of two variants with respectively an even and a female biased sex ratio, when mating is local. The fitness (F) of a gene is given as the average number of copies of that gene in the grand-offspring. With local mating it is the female biased variant that is most fit because it has the highest intrinsic growth rate. From Witting (1997).

This prediction, of no males and no sexual reproduction, is in agreement with Malthusian Relativity that predicts asexual reproduction in populations of self-replicating cells with a week or absent resource bias from interactive competition. In multicellular animals with interactive competition we predict instead sexual reproduction with some males, and when the Fisherian sex ratio is combined with the sex ratio of Malthusian Relativity we find that the density dependent interactive competition is selecting the degree of local mating

s** = (ψ ι** + 1) / (1 - ψ ι**)

to make the equilibrium sex ratio match the ploidy level of the genome.


Fig. 3 Left: The degree of local mating, given as the number of foundresses, plotted as a function of the proportion of males in haplodiploids. The curve represents the theoretical prediction, and the diamonds are Werren’s (1983) data on the parasitic wasp Nasonia vitripennis. From Witting (1997). Right: The sex ratio in new-born spotted hyena against clan size. Data from Holekamp and Smale (1995); figure from Witting (1997).

Fisherian sex ratio theory is one of the most successful theories of natural selection when it comes to producing contingent evolutionary explanations that are confirmed by data (e.g., Fisher, 1930; Hamilton, 1967; Trivers and Hare, 1976; Hardy, 2002). But the theory cannot stand alone when it comes to long-term evolution, where it predicts sex ratios at the female biased limit with no males.

Selection by interference competition provides a sufficient theory for the long-term evolution of non-trivial sex ratios, and the result that the degree of local mating can be predicted from the proportion of males (Fig. 3, left; Witting, 1997) is confirmed by data from Werren (1983).

Other data that indicate that interference competition is an important factor for the evolution of sex ratios includes more general patterns. Other things being equal, low-energy species should be more likely to be situated below the competitive interaction fix-point of a stable body mass than high-energy organisms, while high-energy organisms should be more likely above the fix-point than low-energy organisms. This agrees with the general trend that female biased sex ratios are common in insects and poikilotherm vertebrates, while male biased sex ratios tend to be more common among birds and mammals (Charnov, 1982; Wrensch and Ebbert, 1993).

Positive correlations between the population abundance and the proportion of males have also been found in several species. This is illustrated in Fig. 3 (right) for the spotted hyena (Holekamp and Smale, 1995), and reported also for white-tailed deer (McCullough, 1979) and northern elephant seals (Le Boeuf and Briggs, 1977). For small rodents with cyclic dynamics, Naumov et al. (1969) found that the percentage of males increases when the abundance is high, while females predominate during the low phase of the cycle.

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