Stochastic population models: some concepts, definitions and results

Here we review the use of stochastic models in population biology. We provide precise definitions of demographic and environmental variance, and present a new concept of demographic covariance. We suggest that population fluctuations in many cases can be approximated by a diffusion process. Many interesting properties of the process can be expressed by the Green function, including the expected time to extinction which is of great interest in population viability analysis. We then apply this approach on density-dependent models without age structure and give a summary of some results obtained for age-structured models without density regulation. We suggest that these results may be very useful in practical management because they also give us the possibility of estimating the uncertainties in our estimates of for instance the probability of extinction of small populations. Their application will, however, depend on the availability of long-term data sets, where we can estimate the order of magnitude of essential parameters and evaluate their predictive power.