By T. Royama
A wisdom of animal inhabitants dynamics is key for the right kind administration of ordinary assets and the surroundings. This publication, now on hand in paperback, develops uncomplicated thoughts and a rigorous technique for the research of animal inhabitants dynamics to spot the underlying mechanisms.
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Extra info for Analytical Population Dynamics
As a result, the negative slope of a conditional reproduction curve for a small Z" would become steeper more quickly as X, increases, than it would for a large Z". Hence, the beech crop acts as a nonlinear perturbation (Fig. 13). 13 A nonlinear perturbation of a reproduction curve. The curvature of the reproduction curve changes as z" changes from ::'; to z~, causing the log equilibrium density to shift from X* to X***. Several more examples are conceivable. (1) A multivoltine parasitoid, which requires alternate hosts, may act as a nonlinear perturbation factor on a given host, if the parasitoid density is largely governed by the densities of other alternate hosts.
However, even in a stationary state, the population continues to fluctuate. In this sense, the stationary process is considered to be in a state of statistical equilibrium. Generally, the practical significance of the stationarity concept is the following. We usually have only one observed population series that is considered to be a realization of a given population process whose statistical properties are unknown - unless the series was generated by a known theoretical model. The ergodic theorem ensures that the statistical parameters (the mean, variance and covariances) of a stationary process can be consistently estimated by the corresponding sample parameters (time averages) calculated from a single realization of the time series of a sufficient length.
6 ECOLOGICAL MECHANISM UNDERLYING POPULATION REG ULA TION In deducing the statistical requirements for population persistence in the preceding sections, I have made no particular assumption as to the underlying mechanism. In other words, the requirement for regulation is a statistical stipulation with which every regulated population conforms, no matter what ecological mechanism underlies it. In this section, I shall discuss the ecological mechanism which ensures that the population process conforms with the statistical stipulation.