Abstract
Regular environmental cycles such as day and night or the lunar cycle are ubiquitous and drive many biological processes. Many organisms have evolved endogenous time-keeping mechanisms to anticipate these cycles to accurately time their behavior or synchronize physiological processes. The evolution of such synchronization to environmental cycles and their variability is not very well understood. As an example, we use the marine insect
Clunio
(Diptera, Chironomidae), which synchronize adult emergence and reproduction with the lunar cycle, and show different emergence patterns across populations. We use a model constructed with replicator-mutator dynamics to provide a novel outlook at the evolution of these emergence patterns. In particular, we investigate the effect of two traits of individual phenotypic variability of emergence, the spread and shape, on population-wide emergence patterns. We find that the semilunar and lunar emergence patterns are alternatively stable and occur when the phenotypic distribution has a narrow and is roughly flat. Arrhythmic emergence occurs when the phenotypic distribution is wide and nearly flat. The semi-lunar pattern can only be observed when the parameter of rhythmicity is changed. With our model, we introduce the concepts of frequency-dependent selection and individual phenotypic variability into the theory of chronobiology, which gives us insights into the evolution of rhythmicity in these organisms.