A dependence of the measure of stability, (a*)2, on the coefficient of correlation, p, is shown in Fig. 8.8. This figure illustrates one old ecological principle: physiologically close species, the reactions of them on the environmental perturbations being similar, cannot co-exist. This is a consequence of monotonous decrease of (a*)2 with the growth of p.

Finally, we would like to state the following. In experimental ecology we usually deal with the long time-series of observations of population sizes or biomasses of species belonging to one trophic level (for instance, various species of phytoplankton). Using these data we can estimate their statistical characteristics as their MMPs and the corresponding covariation matrix. Knowing these values we can estimate the measure of stability of such a type of community in the given environment. It is natural that all these estimations will be correct if the community is quasi-stationary.

8.8. Summary of the ecological important issues

Trophic chains are a simplification. Therefore Chapter 8 examines the thermodynamics of more complex systems: communities with competition between species. A Prigogine-like theorem can be applied again: the exergy of the community will be maximal. Furthermore, the resources in the environment tend to minimum indicating that the resources have a maximal utilisation. The system may play on r-strategists or on K-strategists to obtain these goals.

Moreover, communities of interacting populations evolve in such a manner that their MMPs always increase, attaining maximum at the stable structural equilibrium (this is the so-called Fisher principle after R. Fisher, who has proved the theorem). The Malthusian parameters are named the fitness of genetypes. The population with maximal fitness survives; the other populations are eliminated during the process of natural selection. It is shown that Fisher's theorem is equivalent to Prigogine's theorem in the thermodynamic theory of natural selection.

In conclusion, Prigogine's theorem also seems valid for communities and the general steady development towards a better fitness is consistent with Prigogine's theorem.

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Chapter 9

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