Modeling ephemeral mating encounters in insects: The emergence of mate-finding Allee effects and applications to theoretical models of sterile release

Abstract

Lack of successful mating encounters in two-sex insect populations is a mechanism that might trigger reproductive Allee effects. In this paper I examine a function that models ephemeral mating encounters through the expected density of pairs formed by individuals of both sexes at any time. When this function is incorporated in a general system of differential equations for a two-sex population the solutions exhibit the emergence of an Allee effect for low population densities. Compared with current conceptual models for mate-finding Allee effects, the proposed pairing function does not include a parameter that quantifies the Allee effect strength, a feature that might be useful when information to parameterize Allee effects is unavailable. The mating function is then used to numerically explore how mate-finding Allee effects are enhanced by the release of sterile males in theoretical models where (i) the initial sex ratio is skewed, (ii) sterile males are released in pulses and (iii) partial female remating is allowed.