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By various observations on carabid populations the author attempts to give an impression of the quantitative occurrence of dispersal and of the relation between dispersal and the chance of founding populations (dispersal power). Pitfall-catches in the recently reclamed "Zuiderzee"-polder E-Flevoland demonstrate that within seven years individuals of a number of monomorphic macropterous and dimorphic species had founded populations there. From the very high frequency of full-winged individuals within the latter populations it follows that full-winged carabid individuals generally must have a much greater power of dispersal than flightless ones. Therefore, winged individuals of dimorphic species were about equally able to reach E-Flevoland as were those of monomorphic macropterous ones, whereas individuals of monomorphic brachypterous species obviously are seriously hampered. The early appearance of individuals of riparian species on the shores of an artificial lake in the dune area "Meijendel" suggests that particularly populations living in unstable environments extensively "invest" in dispersal. It appears, however, that an important "investment" in dispersal apparently is not restricted to species from unstable environments; at least some sparse populations living in more stable environments also "sacrifice" relatively great numbers of individuals for dispersal (Pterostichus strenuus). The hypothesis is proposed, that populations facing a high risk of extinction generally will have a sufficient chance of founding populations (high "turnover") when "investing" extensively in dispersal. Not only macropterous but - at least in some populations - also brachypterous individuals participate in migration, although in the populations studied the dispersal power of flightless individuals is found to be very small (Carabus problematicus). Under certain conditions the dispersal of full-winged individuals from wing-dimorphic populations may ultimately lead to a decrease or even a loss of dispersal power by a decrease of the frequency of macropterous individuals. It is assumed, however, that under certain natural conditions also brachypterous individuals may contribute to the spreading of risk within and between populations. The dispersal power of monomorphic macropterous, dimorphic and monomorphic brachypterous populations in a cultivated countryside like Drenthe is discussed. The connection between the dispersal power of different kinds of carabid populations and the resulting chance of survival under different conditions is discussed. Some suggestions for nature preservation management are given.

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.

Local numbers of ground beetle species of heathland appeared to be significantly associated with size of total area, whereas such relationships were not found for the total number of ground beetle species and eurytopic ground beetle species. Presence of species with low chances of immigration was highly associated with area. This is accordance with the "area per se" hypothesis for islands as far as extinction rates are concerned. The habitat diversity hypothesis and the random sampling hypothesis are of less importance for explaining this phenomenon. The importance of dispersal for presence and survival in fragmented habitats could be demonstrated. This result supports the founding hypothesis, under which founding of new populations is considered the main effect of dispersal. The frequency of heathland species with low powers of dispersal in habitats smaller than 10 ha was 76% lower on average than in areas larger than 100 ha. For heathland species with high powers of dispersal this frequency was only 22% lower on average. The period of isolation of the habitats studied, 26-113 years, appeared to be too long to persist for many populations of heathland species with low powers of dispersal.

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1. This paper discusses results of simulation studies with population models that were set up to illustrate the ideas about stabilization of population fluctuations and spreading of the risk of extinction expounded by den Boer (1968). In particular, the number of factors influencing net reproduction, the heterogeneity of the habitat and the possibility of a population's containing animals of different age classes were considered as possibly contributing to stabilization and to spreading of risk. 2. The model defined by equation (3.1.2), where r(t) denotes the net reproduction from t to t+1, f (t) denotes the value of the i-th environmental factor in year t, and where the other symbols denote positive constants, was simulated by choosing for the f(t) sequences of meteorological data from published tables. Such sequences may be serially correlated as well as correlated among themselves and using such real data was considered to be more realistic than working with sequences of independent random numbers, for example. Increasing the number k of factors turned out to stabilize fluctuations in the density. This fact could also be mathematically proved under not very restrictive assumptions. In a model where the logarithm of the net reproduction on the average is some-what greater than zero, and where "crashes" may occur at high densities, the population may persist for a very long time, even if the "size" of the crashes does not depend on density, and the times at which the crashes occur are chosen at random. 3. A model formulated in terms of matrices and vectors, in which a population was supposed to consist of 9 subpopulations and of several age classes was simulated. It was assumed that after a reproduction period the animals migrate between the subpopulations or emigrate from the whole population. It turned out that increasing the number of age classes may increase stability and that models where there is exchange of individuals between subpopulations by \ldmigration\rd are more stable than populations consisting of isolated subpopulations. Letting the exchange between subpopulations be \lddensity-dependent\rd had some stabilizing effect too, but not very conspicuously so.

Patterns of density fluctuations and survival times were estimated for the 64 most abundant carabid species, sampled continuously over 23 years with pitfalls in 89 sites in Drenthe (The Netherlands). I show that for most carabid populations density fluctuated between years, either randomly or between wider bounds than expected with random fluctuations. This was true for all groups, not just those occupying temporary habitats. I discuss the selective processes connected with dispersal (flight) abilities inside and outside populations of species occupying different kinds of habitat, and conclude that under natural conditions the powers of dispersal usually favour an optimal chance of survival of the species; this fits Wright's shifting balance model. Under cultivation, stable habitats have been drastically reduced and fragmented, so that local populations have become highly isolated and the risk of extinction is no longer spread over local groups. This has accelerated selection against dispersal features in isolated populations, so that species with low powers of dispersal apparently can no longer compensate for population extinctions by (re)foundings. Without adequate measures such species are doomed in these areas. Our work leads us to the conclusion that the current ideas on regulation of numbers and on group selection do not adequately describe the situation.