Competition Among Immatures Affects Their Adult Fertility: Population Dynamics

In part 1 we present data from a life history analysis of a discrete-generation laboratory population of Drosophila melanogaster. Two related density-dependent processes govern the population dynamics. (1) The egg-to-adult survival rate is a decreasing function of egg density; N = S(n), where N is adult density, n is egg density, and S'(n) < 0. (2) Because fertility depends on the egg (larval) density from which the females came, it is also a decreasing function of egg density; F(n) is eggs per female, and F'(n) < 0. The recursion function must be written in terms of eggs; thus, nt+1 = F(nt)1/2S(nt)nt. Three different functions are fitted by least squares to the F(n) data and to the S(n) data. Combining these functions according to equation (1) gives several different recursion functions that fit the data about equally well. Some of these functions result in limit cycles; there is one case of chaos. This case yields predictions of adult numbers, N, falling within the experimentally observed range. In part 2 we document the widespread occurrence of this delay effect of competition among immatures on their subsequent fertility, justifying the study of some of the theoretical consequences of equation (1). For a common class of survival functions, the adult-to-adult recursion is not defined, but rather there is a one-to-two mapping of the number of adults from one generation to the next, with the result that experiments or observations dealing with adult numbers could appear stochastic, obscuring the true dynamic behavior of the population. In part 2 we also reexamine the conclusions of some published experiments and observations that did not consider this delay effect. In particular, the data adduced as empirical evidence against the common occurrence of limit cycles or chaos do not necessarily warrant that conclusion.