Proc. NatL Acad. Sci. USA Vol. 78, No. 6, pp. 3721-3725, June 1981 Evolution Models of speciation by sexual selection on polygenic traits (mating preferences/sexual dimorphism/genetic correlation/runaway process) RUSSELL LANDE Department of Biophysics and Theoretical Biology, University of Chicago, Chicago, Illinois 60637 Communicated by James F. Crow, February 10, 1981 ABSTRACT Thejoint evolution offemale mating preferences a male trait and female preferences for it both increase geo- and secondary sexual characters of males is modeled for polyga- metrically or exponentially with time until finally checked by mous species in which males provide only genetic material to the severe counterselection. This genetic mechanism could rapidly next generation and females have many potential mates to choose create a new species by sexual isolation and phenotypic diver- among. Despite stabilizing natural selection on males, various gence of a population from its closest relatives. It also could types of mating preferences may create a runaway process in reinforce or accelerate other modes of speciation. which the outcome of phenotypic evolution depends critically on O'Donald (10) confirmed the basic of the genetic variation parameters and initial conditions of a pop- numerically operation ulation. Even in the absence ofgenetic instability, rapid evolution Fisher's runaway process, using two-locus models, in which one can result from an interaction ofnatural and sexual selection with locus with two alleles codes for variation in males and one di- random genetic drift along lines of equilibria. The models eluci- or triallelic locus influences female mating preferences. He date genetic mechanisms that can initiate or contribute to rapid found that the rate and extent of evolution is enhanced when speciation by sexual isolation and divergence of secondary sexual the most preferred genotype at the male character locus is re- characters. cessive and that linkage can influence the dynamics. However, such models greatly restrict the evolution ofa trait, which must The distinction between natural and sexual selection drawn by cease with the fixation of an allele at the corresponding locus. Darwin (1) is that natural selection arises from variance in in- For quantitative characters, it is generally more realistic to em- dividual survival (and fecundity), whereas sexual selection re- ploy a polygenic model (11, 12) and to allowfor the maintenance sults from variance in mating success. Dimorphism ofsecondary of genetic variability by mutation and recombination (13, 14). sexual characters in higher animals is caused by two major fac- Female mating preferences have been demonstrated in a tors: combat or competition between individuals of one sex variety of arthropods and vertebrates (7-9, 12), indicating that (usually males) for mates and mating preferences exerted by the there is (or was) some genetic variation for them. A complete opposite sex (females) (1). The fitness of a trait with respect to set of mating preference functions, which would specify for mating success can override its value for survival, creating a kind every female phenotype the sexual preference for each male of maladaptive evolution that may contribute to the extinction phenotype, has not been measured for any population. Al- of a population (2-6). In contrast to intermale competition, though for most species it may be difficult or impossible to ob- which entails an obvious advantage of mating success for the tain, such information is necessary to determine the course of winners, Darwin was unable to explain why in many species evolution of male secondary sexual characters and female mat- with polygamous systems of mating (where males are promis- ing preferences. To clarify Fisher's mechanism for rapid spe- cuous and invest little or nothing but gametes in their offspring) ciation by sexual selection, I analyze here the joint evolution females should prefer mates with extreme characters that are ofmale secondary sexual characters and different types offemale apparently useless or deleterious for survival, such as the ex- mating preferences which have been discussed, often incor- travagant plumage of some male birds and the exaggerated rectly, in the literature on sexual selection. horns and tusks of certain male mammals (1, 7-9). Fisher (2, 3) suggested an ingenious solution to Darwin's QUANTITATIVE GENETIC MODELS problem by outlining a genetic mechanism for the joint evo- lution offemale mating preferences and secondary sexual char- Evolution of the Mean Phenotypes. Consider for simplicity acters of males. An essential feature of this mechanism is the two sex-limited quantitative traits: a male character, z, and a genetic correlation between the sexes; that is, the extent to female mating preference, y, each influenced by multiple au- which variations in male and female traits are influenced by the tosomal genes and subject to environmental effects. On an ap- same genes or segregating factors. Even if the genes affecting propriate scale ofmeasurement, both traits are assumed to have these characters are not mutually pleiotropic, a positive cor- normal distributions, p(z) and q(y), with means i and g and phe- relation between them will nevertheless arise in the population notypic variances o2 and A. For continuously varying charac- because of assortative mating created by genetic variance in ters, a logarithmic scale of measurement often renders the dis- mating preferences (where the more discriminating females tributions approximately normal with variances roughly mate with the more extreme males). The evolution of mating independent ofthe mean values (11). The additive genetic var- preferences may be self-reinforcing because, once started, fe- iances of the male and female traits are denoted as G and H, males are selecting not only for more extreme males but also and the additive genetic covariance between them, B, is due indirectly, through the genetic correlation, for a higher inten- to pleiotropy and nonrandom associations ofalleles at different sity of mating preferences. Fisher (3) stated that the result of loci. In a population ofautosomal genotypes, B is the covariance this positive feedback could be a "runaway process," in which of additive genetic effects when in males with those when in females. These genetic variation parameters ofa population can The publication costs ofthis article were defrayed in part by page charge be estimated from phenotypic correlations between relatives payment. This article must therefore be hereby marked "advertise- or from artificial selection experiments (11, 12). ment" in accordance with 18 U. S. C. §1734 solely to indicate this fact. It is assumed that in each generation every female is insem- 3721 Downloaded by guest on September 30, 2021 3722 Evolution: Lande Proc. Natl. Acad. Sci. USA 78 (1981) inated and that males do not help raise offspring or protect or to the fingers (15). It seems likely that in many higher animals, provision their mate(s); hence, the expected number ofprogeny as in man, both sensory perceptions and emotional reactions of from a given female is independent ofher mate choice. In any an individual often scale as power functions ofquantities related particular generation, female mating preferences do not change to secondary sexual characters and mating displays. Such a the mean fitness in a population but act only to redistribute fit- mechanism may underlie the responses of many animals to su- ness among the different male phenotypes. Thus, there is no pernormal stimuli (16). Thus, suppose that a quantitative char- selection directly on female mating preferences, which evolve acter of males, 4, produces a perception and associated sexual only as a correlated response to selection on males. The direct preference, 4i, in a given female proportional to k, where y is response to one generation of selection on males and the cor- a constant pertaining to the particular female. Ifthe male char- related response in female mating preferences are acter is analyzed on a logarithmic scale, z = lno, as is often appropriate for statistical purposes, the psychophysical pref- E= '/2GS/cr Ay= 112BSIo', [1] erences of a given female can be written as in which S is the selection differential on males, the difference oc eYZ. [8a] between selected and unselected adults, and the factors of 1/2 qzizly) account for the sex-limited expression of both traits (6, 11). Individual females are assumed to differ in the degree of dis- Natural selection on males is assumed to act through differ- crimination in mate choice, y. ential viability, followed by sexual selection through differential Animal perceptions ofsome sensory modalities, such as color mating success. Writing the viability of males with phenotype or the pitch of a sound, and matching constraints between the z as w*(z), the distribution ofmale phenotypes after natural se- sexes may result in unimodal preferences. Such preferences lection is could be either an absolute intrinsic property ofeach female or could be relative and scaled to the distribution of male phe- p*(z) = w*(z)p(z)/fw*(z)p(z)dz. [2] notypes in a population. Females who prefer most a particular value of a male char- Weak natural selection toward an optimal male phenotype, 6, acter, regardless of its distribution in the population, are de- can be approximated by a Gaussian function, scribed by absolute preferences. An important class ofabsolute w*(z) = e-(z - 0)2/2w2 [3a] "preference" occurs where homologous or complementary characters of the sexes are under a matching constraint that in which w indicates the range of male phenotypes around the determines the probability of successful mating. In many spe- optimum with high viability. After natural selection alone, the cies, male and female morphology and sexual behaviors are distribution of male phenotypes is normal with mean and mutually constrained in some way. A simple form of absolute variance preference is that for a given female the most preferred male ± z* = (zFW2 + 6o2)/(W2 + a,) [3b] phenotype is y with a tolerance of v or where the characters ofmates are somehow constrained to be within about ± vofeach (72* = W2a,2/(W2 + ag).