Maternal effects mechanism of population cycling: a formidable competitor to the traditional predator-prey view

Abstract

In the language of mathematics, one needs minimally two interacting variables (two dimensions) to describe repeatable periodic behaviour, and in the language of density dependence, one needs delayed, not immediate, density dependence to produce cyclicity. Neither language specifies the causal mechanism. There are two major potential mechanisms: exogenous mechanisms involving species interactions as in predator-prey or host-parasite, and endogenous mechanisms such as maternal effects where population growth results from the cross-generational transmission of individual quality. The species interactions view stemming from a major observation of Elton and a simultaneous independent theory by Lotka and Volterra is currently dominant. Most ecologists, when faced with cyclic phenomena, automatically look for an interacting species one step below or above in a food chain in order to find an explanation. Maternal effects hypothesis, verbally suggested in the 1950s, had only found its theoretical implementation in the 1990 s. In a relatively short time, the degree of acceptance of this view grew to the level of a 'minority opinion' as evidenced by the widely used textbook of Begon et al. This short review attempts to describe the arguments for and against this internal two-dimensional approach.

Figure 1

Feedbacks between population growth and changes in individual quality implied in the maternal effects hypothesis. In contrast to traditional kinetic approaches in population ecology where $N_{t+1}/N_t=f(N_t)$, population abundance affects the growth rate through changes in individual quality, which in turn determines the abundance of offspring generation. These dependencies induce an inertial effect (equation (2.2)), whereby the current population growth rate depends on the growth rate at the previous generation $N_{t+1}/N_t=R_{\text{max}}\phi (N_t,(N_t/N_{t-1}))$. Cycles require two interacting variables; it is either two species or quantity and quality, as in the maternal effects case.