Condition-dependence, genotype-by-environment interactions and the lek paradox

The lek paradox states that maintaining genetic variation necessary for 'indirect benefit' models of female choice is difficult, and two interrelated solutions have been proposed. 'Genic capture' assumes condition-dependence of sexual traits, while genotype-by-environment interactions (GEIs) offer an additional way to maintain diversity. However, condition-dependence, particularly with GEIs, implies that environmental variation can blur the relationship between male displays and offspring fitness. These issues have been treated separately in the past. Here we combine them in a population genetic model, and show that predictions change not only in magnitude but also in direction when the timing of dispersal between environments relative to the life cycle is changed. GEIs can dramatically improve the evolution of costly female preferences, but also hamper it if much dispersal occurs between the life history stage where condition is determined and mating. This situation also arises if selection or mutation rates are too high. In general, our results highlight that when evaluating any mechanism promoted as a potential resolution of the lek paradox, it is not sufficient to focus on its effects on genetic variation. It also has to be assessed to what extent the proposed mechanism blurs the association between male attractiveness and offspring fitness; the net balance of these two effects can be positive or negative, and often strongly context-dependent.