| Abstract: | Mathematical models are developed in order to analyze whether or not social factors, such as, for example, the “social fence” (J. B. Hestbeck, 1982, Oikos 39, 157–163) will stabilize population density: the dynamic interaction between social factors and (dynamic) trophic factors is analyzed. It is concluded that social factors such as the “social fence” tend to stabilize population density; hence, if density cycles (as, e.g., seen in many microtine rodents) are observed in nature, it seems reasonable to conclude that density cycles are driven by, for example, trophic interactions and not by social factors. It is suggested that the “social fence” may explain why so many populations including several microtine populations have fairly stable densities despite the ever-existing destabilizing trophic interactions. Contrary to what is implied by J. B. Hestbeck (1983, “A Mathematical Model of Population Regulation in Cyclic Mammals,” Lecture notes in biomathematics, Vol. 52, Springer-Verlag, Berlin/New York), the analysis presented in this paper demonstrates that seasonal environmental changes are not essential for the generation of regular density cycles. Seasonal changes may, however, be necessary for generating a microtine-like density cycle. Empirical information on microtine rodents relating to the “social fence hypothesis” is discussed. |
