Density-dependent prenatal androgen exposure as an endogenous mechanism for the generation of cycles in small mammal populations

Small mammal populations exhibit cyclic fluctuations in their population densities. Several hypotheses regarding the mechanisms underlying these population cycles have been advanced, but none has yet gained general approval. We propose here an endogenous mechanism based on the masculinization of female offspring in response to increased population levels. High population levels trigger the non-specific stress response resulting in high levels of circulating androgens in individuals of the population, including pregnant females. These androgens masculinize female offspring in utero, thereby reducing the reproductive capacity of the next generation and subsequently the population size. We have developed and analysed a mathematical model to investigate the possible role of prenatal androgen exposure in the generation of limit cycles. We find the locus of Hopf bifurcations for this model and show that limit cycles depend on three parameters: (1) the delay between birth and sexual maturation; (2) the slope of the function that relates average prenatal androgen exposure to total population density; and (3) the difference between the maximum birth rates of the low- and high-androgen exposed females. We derive the analytical form relating these parameters at the Hopf-bifurcation locus and discuss its biological ramifications. In brief, if each of these three parameters is sufficiently large, population cycles will result from the endogenous mechanism proposed.