On the survival of populations in a heterogeneous and variable environment.

The survival time of small and isolated populations will often be relatively low, by which the survival of species living in such a way will depend on powers of dispersal sufficiently high to result in a rate of population foundings that about compensates the rate of population extinctions. The survival time of composite populations uninterruptedly inhabiting large and heterogeneous areas, highly depends on the extent to which the numbers fluctuate unequally in the different subpopulations. The importance of this spreading of the risk of extinction over differently fluctuating subpopulations is demonstrated by comparing over 19 years the fluctuation patterns of the composite populations of two carabid species, Pterostichus versicolor with unequally fluctuating subpopulations, and Calathus melanocephalus with subpopulations fluctuating in parallel, both uninterruptedly occupying the same large heath area. The conclusions from the field data are checked by simulating the fluctuation patterns of these populations, and thus directly estimating survival times. It thus appeared that the former species can be expected to survive more than ten times better than the latter (other things staying the same). These simulations could also be used to study the possible influence of various density restricting processes in populations already fluctuating according to some pattern. As could be expected, the survival time of a population, which shows a tendency towards an upward trend in numbers, will be favoured by some kind of density restriction, but the degree to which these restrictions are density-dependent appeared to be immaterial. Density reductions that are about adequate on the average need even not occur at high densities only, if only the chance of occurrence at very low densities is low. The density-level at which a population is generally fluctuating appeared to be less important for survival than the fluctuation pattern itself, except for very low density levels, of course. The different ways in which deterministic and stochastic processes may interact and thus determine the fluctuations of population numbers are discussed. It is concluded that some stochastic processes will operate everywhere and will thus necessarily result in density fluctuations; such an omnipresence is much less imperative, however, for density-dependent processes, by which population models should primarily be stochastic models. However, if density-dependent processes are added to model populations, that are already fluctuating stochastically the effects are taken up into the general, stochastic fluctuation pattern, without altering it fundamentally.