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Runaway Sexual Selection When Female Preferences Are Directly Selected

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Runaway Sexual Selection When Female Preferences Are Directly Selected Evolution, 54(6), 2000, pp. 1862±1869 RUNAWAY SEXUAL SELECTION WHEN FEMALE PREFERENCES ARE DIRECTLY SELECTED DAVID W. HALL,1 MARK KIRKPATRICK, AND BRIAN WEST Section of Integrative Biology C0930, University of Texas, Austin, Texas 78712 1E-mail: [email protected] Abstract. We introduce models for the runaway coevolution of female mating preferences and male display traits. The models generalize earlier results by allowing for direct natural selection on the preference, arbitrary forms of mate choice, and fairly general assumptions about the underlying genetics. Results show that a runaway is less likely when there is direct selection on the preference, but that it is still possible if there is a suf®ciently large phenotypic correlation between the female's preference and the male's trait among mated pairs. Comparison of three preference functions introduced by Lande (1981) shows that open-ended preferences are particularly prone to a runaway, and that absolute preferences require very large differences between females in their preferences. We analyze the causes of the runaway seen in a model developed by Iwasa and Pomiankowski (1995). Key words. Mating preferences, runaway, sexual selection. Received December 31, 1999. Accepted June 29, 2000. Why have females of some species evolved mating pref- selection acting on the pleiotropic effects of genes that affect erences for males with extreme secondary sexual traits? A mating preferences will also cause those genes to fall under mechanism that has been widely discussed was proposed by direct selection (Kirkpatrick 1982; 1985). Male parental care Fisher (1958, p. 152) in a famous but obscure passage. In generates direct selection on preferences because a female's modern terms, Fisher suggested that male display traits and mate choice affects her fecundity. Search costs may also lead female preferences will naturally become genetically corre- to direct selection on preference (Kirkpatrick 1985; Pomian- lated. As a result, further exaggeration of the male trait caused kowski 1987). These considerations have led to the sugges- by sexual selection will cause the preference itself to become tion that some kind of direct selection may be acting on more exaggerated as a correlated selection response. Because virtually all preference genes (Kirkpatrick and Ryan 1991; more exaggerated preferences in turn cause stronger sexual Ryan 1997). selection on the male trait, the preference and trait could Despite the large amount of work that has been done on coevolve in an explosive ``runaway process.'' Fisher's verbal the runaway process and on direct selection of preference logic was veri®ed much later by genetic models (O'Donald genes, we do not know how the two mechanisms interact. 1980; Lande 1981; Kirkpatrick 1982). We do know that if direct natural selection favors a particular Theoretical work since Fisher has revealed two key points value of the preference, then there is an equilibrium in which that he did not discuss (reviewed in Kirkpatrick and Ryan the preference lies at its favored value. At this equilibrium, 1991; Andersson 1994). The ®rst regards the outcome of the the male trait takes a value that is a compromise between the coevolution between the preference and male trait. Genetic forces of natural and sexual selection acting on the male trait models show that one possibility is that they will arrive at a (Lande 1981, eq. (10); Kirkpatrick 1985, eq. (12)). But is stable equilibrium point. However, if the genetic covariance this equilibrium always stable, or can an unstable runaway between the preference and trait is large enough, the equi- ensue if the genetic covariance becomes suf®ciently large? librium becomes unstable. In a landmark paper, Lande (1981) Intuitively, we might suspect that direct selection on the pref- discovered that in such a case, a rapid burst of evolution will erence will make the equilibrium more stable and therefore follow in which the trait and preference evolve at an expo- make a runaway less likely. That conclusion has not, how- nentially increasing rate until genetic variation is exhausted ever, been studied with a genetic model. or the intensity of natural selection becomes very severe. Another reason for revisiting the runaway is to learn more Lande identi®ed this unstable outcome with what Fisher de- about the conditions under which it will occur even when scribed verbally as the runaway process. Others have used there is no direct selection on the preference. Lande's (1981) runaway to indicate whether evolution of the male trait leads conclusions were developed in two stages. The ®rst assumes to exaggerated female preference at equilibrium, regardless that females choose males using one of three preference rules, of the equilibrium's stability, whereas Fisher did not make and that the additive genetic and phenotypic values for the that distinction. Generally, however, the term runaway now preference and trait are normally distributed. He then found refers to the outcome discovered by Lande in which a pop- the conditions for a runaway given known values for the ulation evolves rapidly away from an unstable equilibrium. genetic variances and covariance. A question we consider A second development since Fisher is the appreciation of here is when will a runaway occur if the characters are not other processes that can establish extreme mating preferenc- normally distributed and females choose their mates by any es. One important mechanism is natural selection acting di- kind of process. In the second stage of Lande's analysis, he rectly on the genes underlying a preference (Lande 1981; made detailed assumptions about the genes underlying the Kirkpatrick 1982; Bulmer 1989). Direct selection on pref- preference and trait. With those, he found that a runaway erence genes happens for many reasons. For example, natural occurs when mutation rates at the preference loci are suf®- 1862 q 2000 The Society for the Study of Evolution. All rights reserved. RUNAWAY WITH DIRECT SELECTION 1863 ciently large. The genetic assumptions used in this second genetic covariance as a known quantity; later in the paper phase of the analysis, however, have been criticized as bi- we will calculate its size. ologically unrealistic (Turelli 1988). This paper investigates When the population is near an equilibrium, the forces of when a runaway is possible under more general and perhaps directional selection acting on the male trait and female pref- realistic assumptions about the genetics. erence are weak. In that case, the changes in their means We begin by developing a model of the runaway that allows caused by one generation of selection are for direct selection on the preference and that makes fairly 11 general genetical and behavioral assumptions. Following D¯¯t 5 Gttb (t, pÅ) 1 G tppb (pÅ), (1a) 22 Lande's approach, this section assumes that the critical ge- netic covariance between the preference and trait has a known 11 DpÅ 5 G b (pÅ) 1 G b (¯t, pÅ). (1b) value. Analysis shows that direct selection of preference 22pp tpt genes does indeed stabilize the equilibrium, but that a run- Here G and G are the additive genetic variances and and away can still occur if the genetic covariance is big enough. t p bt b are the directional selection gradients for the male trait Next, we use recent theoretical results that allow the genetic p and female preference, respectively. The bs represent the covariance to be calculated to determine when the runaway selective force restoring the population to the equilibrium, will occur under a broad range of mating behaviors. We then and are de®ned as the regression of lifetime relative ®tness return to the three preference rules introduced by Lande regressed onto the character value (see Lande and Arnold (1981) to ®nd when a runaway will occur under those con- 1983). At equilibrium the bs are equal to zero (assuming the ditions when there is direct selection on the preference. The preference and trait are not perfectly correlated). The selec- analytic results are checked by simulations. Finally, we use tion gradient on the male trait is a function of the mean these results to study the runaway in a model of cycling preference pÅ as well as the mean trait Åt because male ®tness sexual selection introduced by Iwasa and Pomiankowski depends in part on sexual selection caused by the preference. (1995). The factors of 1/2 are present due to the sex-limited expres- sion of both characters. THE MODEL Equations (1) hold for any intensity of selection if the additive genetic values for the trait and preference are nor- Consider a species with two sex-limited characters, a male mally distributed in the population. They hold much more trait with mean Åt and a female preference with mean pÅ. The generally, however, as long as directional selection is weak female preference can be any character that in¯uences her and the genes affecting the characters have additive effects choice of mate. We make no assumptions about how mate (T. Johnson and M. Kirkpatrick, unpubl. data). Because we choice works or what the mating system is, only that pairing are interested in how the population evolves near an equi- is controlled by the females. Females that differ in their pref- librium, directional selection is necessarily weak and so the erence differ in the likelihood that they will mate with a male following results apply whenever the more general genetic with a given trait value. Thus, for our purposes a ``prefer- assumptions outlined above are met. Without losing any gen- ence'' is any phenotype expressed by females that affects the erality, it is convenient to choose a scale of measurement probabilities that they will mate with different types of males. that sets the equilibrium values of the male trait and female Direct selection on preference genes causes a female's pref- preference equal to zero.
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