Xu and Servedio (PNAS 2026) used infinitesimal quantitative-genetic models to argue that the classical 'lek paradox' — the expectation that mate choice should deplete the additive genetic variation in male display traits that mate choice itself requires — rests on a false premise: variation in female preferences and male display traits can instead mutually exaggerate each other. The authors themselves frame this result as a 'proof of concept' obtained under restrictive assumptions, leaving open whether it survives relaxation of those assumptions and whether it operates in nature. This problem asks for a completion of that program: establish, theoretically and empirically, when mate choice depletes versus exaggerates additive genetic variance in display traits and preferences — specifically beyond the infinitesimal (many small-effect loci) genetic architecture, beyond psychophysical preference functions, with linkage or pleiotropy between trait and preference loci, with environmental variance, and via direct empirical tests correlating measured preference functions and selection strengths with additive genetic variances rather than heritabilities. The components above remain unaddressed in the published literature to date.

Background

In species with female mate choice, females are assumed to gain indirect (genetic) benefits from choosing particular males, which requires substantial additive genetic variance (the component of trait variation transmitted from parents to offspring, distinct from heritability, which is the fraction of phenotypic variance that is genetic) in male display traits or overall quality. A long-standing worry — the 'lek paradox', named after lekking species in which males display at communal arenas and offer females no direct resources — is that sexual selection itself should erode this variance: if females consistently prefer the same extreme males, the loci underlying display traits should be driven toward fixation, eventually leaving nothing to choose among, yet in nature sexually selected traits often show more, not less, genetic variation than other traits (Taylor and Williams 1982; Reynolds and Gross 1990; Pomiankowski and Møller 1995). Classical rescue proposals include 'genic capture' — the idea that display traits depend on overall condition, which is affected by so many loci that mutation continuously restores variation (Rowe and Houle 1996) — and related condition-dependence and physiological routes, whose sufficiency remains empirically contested.

The theoretical backdrop is quantitative-genetic models of preference–trait coevolution: Lande (1981) formalized Fisher's runaway process, in which a genetic correlation between a female preference and the male trait it favors causes both to escalate, and distinguished absolute preferences (each female prefers a specific male trait value) from relative preferences. Preference functions describe how a female's mating propensity depends on the male trait; an 'open-ended' preference never saturates with increasing trait value, and a 'psychophysical' preference is a specific open-ended form in which mating propensity depends only on the scaled difference between the male trait and the female's preferred value. Xu and Servedio (2026, previously bioRxiv 2024) re-examined the depletion assumption using the infinitesimal model of quantitative genetics — the approximation that offspring breeding values are normally distributed around the mid-parent value with a segregation variance (the within-family genetic variance generated by Mendelian segregation) that is independent of the parents' genotypes (Barton, Etheridge and Véber 2017), which holds when traits are controlled by many loci of small effect. Partitioning the one-generation change in genetic variance caused by mate choice, they showed that mate choice generates assortative pairing between males and females carrying similar display-trait genes, which increases between-family variance, so that under a broad range of conditions the equilibrium genetic variances of both the display trait and the preference exceed those under random mating — variance 'runaway' in place of variance depletion — provided preference variance is not too small and preferences not too weak, with effects strongest precisely in lek-like situations of strong mate discrimination at low cost. They also showed that a logistic (non-psychophysical) directional preference function can instead reduce trait variance, that their analytical treatment assumes no environmental variance, and that the analysis treats the trait–preference genetic correlation as arising solely through non-random mating (whereas empirical work documents physical linkage or pleiotropy — 'genetic coupling' — between signal and preference loci; Wiley et al. 2012; Xu and Shaw 2019; Ritchie and Butlin 2024).

Neighboring results sharpen why the remaining questions matter. Fry (2024) reformulated Fisher-runaway theory in terms of the heritability and phenotypic variance of realized mate choices and argued that a runaway requires mate choice to increase male-trait variance — a condition previously thought incompatible with strong directional preferences, which the Xu–Servedio result contests. DuVal et al. (2023) proposed 'Inferred Attractiveness', a learned-preference mechanism that likewise maintains trait variation over time. On the empirical side, the only broad comparative dataset (Prokuda and Roff 2014) measures heritabilities rather than additive genetic variances, and recent single-species quantitative-genetic work finds genic capture unlikely to maintain additive genetic variance in a wild lizard (Lindsay et al. 2023), so the classical rescue route remains unconfirmed and the mate-choice route untested.

Problem Statement

Establish when sexual selection through mate choice depletes versus exaggerates the additive genetic variance of male display traits and female preferences — completing, beyond the 'proof of concept' scope of Xu and Servedio (2026), the assessment of whether their variance-exaggeration resolution of the lek paradox holds in general and in nature. Concretely, determine each of the following, which together remove the source model's restrictive assumptions and test its predictions: (1) whether the mutual variance-exaggeration result survives genetic architectures other than the infinitesimal one — traits controlled by few loci of large effect, where offspring genotype distributions are non-normal and the within-family segregation variance depends on the mated pair (the published version's simulation of near-fixation loci began but did not complete this); (2) for which classes of preference functions — open-ended (with the psychophysical function as a special case), directional (including the logistic special case, which can instead produce variance reduction), stabilizing, and absolute versus relative — mate choice increases rather than reduces equilibrium trait variance, to be settled by a general treatment covering each of these families; (3) how physical linkage or pleiotropy between trait and preference loci — empirically documented as genetic coupling — quantitatively alters the variance dynamics, beyond the qualitative argument that results are conservative; (4) how environmental variance changes the one-generation and equilibrium results; and (5) whether the predicted association is empirically real: measure preference functions, preference strengths, and viability selection on preferences and display traits in natural or controlled populations, and test whether these correlate with direct estimates of additive genetic variance (not heritability) in sexually selected traits. These components serve the single objective of deciding whether the lek paradox is genuinely dissolved by mate-choice-driven variance exaggeration, which is settled once the depletion-versus-exaggeration boundary is established for each relaxation and at least a first empirical test of the predicted correlation structure has been performed.

References

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  2. Xu, K., & Servedio, M. R. (2024, revised 2025). When does sexual selection through mate choice deplete versus exaggerate genetic variation: is there a lek paradox? bioRxiv preprint (v1 2024-12-16, v2 2025-05-11). doi:10.1101/2024.12.10.627784, https://doi.org/10.1101/2024.12.10.627784
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