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Keywords:

  • Leslie matrix;
  • stationary age class distribution;
  • life history

Abstract

The influence of the various components of the life history on the stationary age class distribution of a population was studied by applying the Leslie matrix model and then considering the single age class frequencies as well as the average age and the cumulative age class distribution in the stationary state.

Since, for fixed survival probabilities, the effects of the (age specific) fecundities were shown to be already expressed by the (ultimate) growth rate, this investigation was concentrated on the influence of the survival probabilities and the growth rate. After having supplemented some useful details concerning the dependence of the growth rate on the life history and introduction of the shift concept as an interpretation of cumulative distributions, the mathematical results could be given a biologically intelligible meaning:

An increase in the growth rate for fixed survival probabilities is followed by a shift of all age class frequencies to earlier ages. Whereas age specific changes in fecundity do not result in age specific changes in the stationary age class distribution, increases in survival up to and including age k, say, do exhibit such changes in that they cause a shift of age class frequencies at least from those ages exceeding k to earlier ages.