A model for conditional male trimorphisms

Conditional dimorphisms are widespread in color, morphology, behavior, and life history. Such traits have been successfully modeled in game theory as conditional strategies, and in quantitative genetics as threshold traits. Conditional trimorphisms have recently been unveiled, and here we combine the rock-paper-scissors (RPS) model of game theory and the environmental threshold (ET) model of quantitative genetics to model trimorphisms that are environmentally induced and result from the expression of two thresholds. We investigated the tactic fitness structure for maintenance of alternative reproductive tactics in scarab dung beetles that constitute the first known examples of conditional male trimorphism. We parameterized a novel ternary fitness landscape that explains how conditional male trimorphism in these beetles can be maintained. We tracked changes in tactic frequencies in a wild population of Phanaeus triangularis and detected fitness intransitivity consistent with RPS dynamics. Quantitative predictions of our model compare favorably with corresponding observed parameters. The ternary landscape further reveals how geographic populations of these beetles can evolve between conditional trimorphism and dimorphism. The ternary model also suggests that polyphenic systems could potentially evolve between conditional and purely genetic mediation.