Local mate competition with lethal male combat: effects of competitive asymmetry and information availability on a sex ratio game

Abstract

We constructed a sex allocation model for local mate competition considering the asymmetry of competitive abilities among sons. This model assumes two females of a parasitoid wasp oviposit on the same host in sequential order. The evolutionarily stable strategy will be in either Stackelberg or Nash equilibrium, depending on whether the females can recognize their opponent's sex ratio or not, respectively. The Nash equilibrium predicts the second female produce more males than the first. If the second female is able to know and respond to the strategy of the first (a Stackelberg equilibrium), the first will decide an optimal sex ratio assuming that the second reply to it. Under such an assumption, our model predicts that not producing sons is adaptive for the second female when the sons she produces have low competitive ability. Males of parasitoid wasps Melittobia spp. are engaged in lethal male-male combat, indicating large asymmetry in mating success among sons. If females have the ability to recognize their opponent's sex ratio, our model suggests that the severe lethal male-male combat may be one factor explaining their extremely female-biased sex ratio that is unexplainable by pre-existent models.

Evolution of the scale and manner of brother competition in pollinating fig wasps

“…The relative synchronicity of the females' egg laying in each fig and eclosure of offspring also invalidates the appropriateness of these theories. In any case, these models predict lower sex ratios when fighting occurs, not higher (Abe et al 2003a). On the other hand, the effects of sex ratios on male mating strategies are well appreciated (Shuster & Wade 2003;Kokko & Jennions 2008).…”

“…In contrast, we calculated relatedness with data independent of the sex ratios, namely the number of foundresses. Abe et al (2003a) have suggested that fatal fighting can result in the production of very female-biased sex ratios. Their model critically depends on the fatality of fights and on the asymmetric fighting ability of sons resulting from eclosion order (Abe et al 2003b).…”

Sex ratio elasticity influences the selection of sex ratio strategy

“…There are three sex ratio strategies (SRS) in nature-male-biased sex ratio, female-biased 2 sex ratio and, equal sex ratio depending on the proportion of male offspring being greater 3 than, less than, or equal to ½. The problem was already noted in Darwin's (1859) "Origin 4 of Species," and it was R. A.…”

“…1 Applying Equation (4) to Equation (3), we obtain the following ESS sex ratio as 2 , means the sensitive degree of the male survival rate to sex ratio is greater than that of 8 female, from Equation (6), we have as an ESS sex ratio, i.e., the female-biased 9 sex ratio is an ESS ( Figure 1A, blue line); ii) If , which means the sensitive 10 degree of the male survival rate to sex ratio is equal to that of female, from Equation (6), 11 we have as an ESS sex ratio, i.e., the unbiased sex ratio is an ESS (see the red 12 star point of the Figure 1A and 1B); iii) If , which means the sensitive degree of 13 the male survival rate to sex ratio is less than the female, from Equation (6), we have 14 as an ESS sex ratio, i.e., the male-biased sex ratio is an ESS ( Figure 1B (ii) If , that is, the male survival rate is unitary elastic, then 24 1) When (the female survival rate is inelastic), i.e, , which means ESS (Figure 2A, magenta line); 1 2) When (the male survival rate is unitary elastic), i.e., which 2 means the sensitive degree of the male survival rate to sex ratio is equal to that of female, 3 from Equation (6), we have as an ESS sex ratio, i.e., the unbiased sex ratio is an 4 ESS (see the red star point of the Figure 2A and 2B); 5 3) When (the female survival rate is elastic), i.e., , which means 6 the sensitive degree of the male survival rate to sex ratio is less than the female, from 7…”

“…Here, let's use the price elasticity 2 of demand to illustrate this concept used in economics (Taylor and Weerapana 2011). 3 Price elasticity of demand is a measure used to show the responsiveness, or elasticity, of 4 the quantity demanded of a good or service to a change in its price. More precisely, it gives 5 the percentage change in quantity demanded in response to a one percent change in price 6 (holding constant all the other determinants of demand, such as income.…”