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Updated: Jun 24, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Maternal effects mechanism of population cycling: a formidable competitor to the traditional predator-prey view
Pablo Inchausti1, Lev R Ginzburg
1Centre d'Etudes Biologiques de Chizé (CNRS), 79360 Villiers-en-Bois, France.
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.
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