Klasyczne modele pojedynczych populacji

Uchmański, Janusz

doi:0013-2969

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Title: Klasyczne modele pojedynczych populacji

Abstract:

The construction of single population models is justified when one wants to examine the inner mechanism responsible for density dynamics or population numbers. For one hundred years the logistic eąuation has been considered as the basie single population model. In the form used most freąuently in theoretical ecology it is restricted by some assumptions. Putting aside some of these assumptions allows to obtain models having various properties. The changing with time model parameters allow to examine the influence of variable environment on population dynamics. The introduction of time delay to model eąuations results in persistent oscillations of population density. The matrix model with a discret time step or a model with continuous time using particular difterential eąuations allow to describe a population, in which survival and offspring production depend on the age of individuals. One may reflect then on the constancy of population age structure. When looking carefully at population models with non-overlapping generations, which from the mathematical point of view are difference eąuations, one may observe that among Solutions of these eąuations there are oscillations with very long periods or infinite ones, i.e. total chaos. Finally, the ' stochastic models of single populations allow to ąuestion the probability of population extinction. The great possibilities of classic models of single populations may be breathtaking, but it has to be remembered that nonę of the assumptions within these models is true. Thus the methods through which these models found their place in the history of theoretical ecology may be even morę interesting.