About a model of biological population data collection: Can heteroscedasticity problem be solved or not?

In paper stochastic model with discrete time of migrations in finite part of plane is considered. It is assumed that migrations can be from every node of integer lattice to nearest nodes only, and these migrations depend on numbers of individuals in the respective nodes. Population size is assumed to be constant for every sequence of population size measurements. It is also assumed that there are two limits D1 and D2, D1, D1< D2, of local population size in node when respective node is attractable for migrants (Alley effect). If local population size is bigger than D2 node becomes unsuitable for migrants, and all individuals try to leave the respective node. After a certain number of time steps local population size is determined in randomly selected nodes (it looks like method of “throwing of frame” or “cutting of model trees” of entomological data collection but in considering situation it doesn’t lead to changing of conditions for population). Dependence of standard deviations of samples of various sizes on fixed values of population density are analyzed. In particular, it is shown that well-known problem of heteroscedasticity cannot be solved in principle for the situation when ecological model parameters must be estimated using empirical or experimental time series. Analysis of dependence of number of interactions of individuals per time step (average in time and space) on total population size allows pointing out new ways in modification of Verhulst model.

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