Levels of Selection on Threshold Characters

Abstract

Threshold models are useful for understanding the evolution of dimorphic traits with polygenic bases. Selection for threshold characters on individuals is expected to be frequency dependent because of the peculiar way that selection views underlying genetic and environmental factors. Selection among individuals is inefficient because individual phenotypes fall into only two discrete categories that map imperfectly to the underlying genes. Incidence, however, can be continuously distributed among groups, making among-group selection relatively more efficient. Differently put, the group-mean phenotype can be a better predictor of an individual's genotype than that individual's own phenotype. Because evolution in group-structured populations is governed by the balance of selection within and between groups, we can expect threshold traits to evolve in fundamentally different ways when group mean fitness is a function of morph frequency. We extend the theory of selection on threshold traits to include group selection using contextual analysis. For the simple case of linear group-fitness functions, we show that the group-level component of selection, like the individual-level component, is frequency dependent. However, the conditions that determine which component dominates when levels of selection are in conflict (as described by Hamilton's rule) are not frequency dependent. Thus, enhanced group selection is not an inherent property of threshold characters. Nevertheless, we show that predicting the effects of multiple levels of selection on dimorphic traits requires special considerations of the threshold model.