The spatio-temporal dynamics of a post-vaccination resurgence of rabies in foxes and emergency vaccination planning.

We used a simulation model to study the spatio-temporal dynamics of a potential rabies outbreak in an immunized fox population after the termination of a long-term, large-scale vaccination program with two campaigns per year one in spring and one in autumn. The 'worst-case' scenario of rabies resurgence occurs if rabies has persisted at a low prevalence despite control and has remained undetected by a customary surveillance program or if infected individuals invade to the control area. Even if the termination of a vaccination program entails such a risk of a subsequent new outbreak, prolonged vaccination of a wild host population is expensive and the declining cost-benefit ratio over time eventually makes it uneconomic. Based on the knowledge of the spatio-temporal dynamics of a potential new outbreak gained from our modelling study, we suggest "terminating but observing" to be an appropriate strategy. Simulating the decline of population immunity without revaccination, we found that a new outbreak of rabies should be detected by customary surveillance programs within two years after the termination of the control. The time until detection does not depend on whether vaccination was terminated within the fourth, fifth or sixth years of repeated biannual campaigns. But it is faster if the program was completed with an autumn campaign (because next-year dispersal then occurs after a noticeable decrease in population immunity). Finally, if a rabid fox is detected after terminating vaccination, we determine a rule for defining a circular hazard area based on the simulated spatial spread of rabies. The radius of this area should be increased with the time since the last vaccination campaign. The trade-off between the number of foxes potentially missed by the emergency treatment and the cost for the emergency measures in an enlarged hazard area was found.

Chance and risk of controlling rabies in large-scale and long-term immunized fox populations.

The large-scale immunization of European fox populations against rabies is currently under the microscope for reducing the considerable expenditure without putting public health at risk. Empirical knowledge is inadequate to interpret the lasting sporadic incidences and, therefore, to verify the final success of the immunization campaigns. By using a proven simulation model we show that rabies can persist on a very low level in the form of spatio-temporal moving infection clusters within a highly immunized fox population. We found further: (i) the existence of a threshold after which the chance of eradicating the disease by vaccination increases clearly, and (ii) that at least six years of 70% mean immunization rate are required to guarantee a likely success.

Reconciling classical and individual-based approaches in theoretical population ecology: a protocol for extracting population parameters from individual-based models.

The two main approaches in theoretical population ecology-the classical approach using differential equations and the approach using individual-based modeling-seem to be incompatible. Linked to these two approaches are two different timescales: population dynamics and behavior or physiology. Thus, the question of the relationship between classical and individual-based approaches is related to the question of the mutual relationship between processes on the population and the behavioral timescales. We present a simple protocol that allows the two different approaches to be reconciled by making explicit use of the fact that processes operating on two different timescales can be treated separately. Using an individual-based model of nomadic birds as an example, we extract the population growth rate by deactivating all demographic processes-in other words, the individuals behave but do not age, die, or reproduce. The growth rate closely matches the logistic growth rate for a wide range of parameters. The implications of this result and the conditions for applying the protocol to other individual-based models are discussed. Since in physics the technique of separating timescales is linked to some concepts of self-organization, we believe that the protocol will also help to develop concepts of self-organization in ecology.

Extinction risk in a temporally correlated fluctuating environment.

Usually extinction risk due to environmental stochasticity is estimated under the assumption of white environmental noise. This holds for a sufficiently short correlation time tauc of the fluctuations compared to the internal time scale of population growth r-1 (tauc/r-1<<1). Using a time-discrete simulation model we investigate when the white noise approximation is misleading. Environmental fluctuations are related to fluctuations of the birth and death rates of the species and the temporal correlation of these fluctuations (coloured noise) is described by a first-order autoregressive process. We found that extinction risk increases rapidly with correlation time tauc if the strength of noise is large. In this case the white noise approximation underestimates extinction risk essentially unless temporal correlation is very small (tauc/r-1<<0.1). Extinction risk increases only slowly with correlation time if the strength of noise is small. Then the white noise approximation may be used even for stronger temporal correlations (tauc/r-1>/=0.1). Thus, the estimation of extinction risk on the basis of white or coloured noise must be justified by time scale and strength of the fluctuations. Especially for species that are sensitive to environmental fluctuations the applicability of the white noise approximation should be carefully checked.

Pattern formation triggered by rare events: lessons from the spread of rabies.

Understanding of large-scale spatial pattern formation is a key to successful management in ecology and epidemiology. Neighbourhood interactions between local units are known to contribute to large-scale patterns, but how much do they contribute and what is the role of regional interactions caused by long-distance processes? How much long-distance dispersal do we need to explain the patterns that we observe in nature? There seems to be no way to answer these questions empirically. Therefore, we present a modelling approach that is a combination of a grid-based model describing local interactions and an individual-based model describing dispersal. Applying our approach to the spread of rabies, we show that in addition to local rabies dynamics, one long-distance infection per 14000 km2 per year is sufficient to reproduce the wave-like spread of this disease. We conclude that even rare ecological events that couple local dynamics on a regional scale may have profound impacts on large-scale patterns and, in turn, dynamics. Furthermore, the following results emerge: (i) Both neighbourhood infection and long-distance infection are needed to generate the wave-like dispersal pattern of rabies; (ii) randomly walking rabid foxes are not sufficient to generate the wave pattern; and (iii) on a scale of less than 100 km x 100 km, temporal oscillations emerge that are independent from long-distance dispersal.

Sociality in molerats : Metabolic scaling and the role of risk sensitivity.

The foraging behaviour and diets of the various bathyergid molerat species are reviewed briefly, and inferences are drawn concerning their dietary specialisation. A simple model has been constructed which investigates the risks of unproductive foraging by specialist feeders as a function of resource dispersion characteristics and group size. The model suggests that the principal benefit of group foraging is a reduction in foraging risk, rather than increased resource procurement per se. Meeting the energetic costs of non-workers in social groups necessitates a reduction of the total energetic expenditure of the colony. This is achieved by reducing body size, huddling in the nest, and scaling mass-specific resting metabolic rate virtually independent of mass.

A universal law of the characteristic return time near thresholds.

Dramatic changes at thresholds in multiple stable ecosystems may be irreversible if caused by man. The characteristic return time to an equilibrium increases when a threshold is approached. A universal law for this increase is found, which may be used to forecast the position of a threshold by extrapolation of empirical data. Harvesting experiments on populations are proposed that can be used to verify the method. Preliminary harvesting experiments on rotifer populations display a good agreement with the theory.

Population ecology of rotifers as a bioassay tool for ecotoxicological tests in aquatic environments.

The population dynamics of the monogonont rotifer Brachionus rubens were used under controlled experimental conditions as a sensitive bioassay for toxic substances in sublethal doses. Even slight reductions in organism fertility and life expectancy were reflected at the integrated level of population dynamics. Serving as bioindicators for the standard test are the population parameters "intrinsic rate of natural increase" (r), "carrying capacity" (k), "frequency" (f), and "pregnancy" of the density oscillations (p). The optimal spreading power (steepest slope of the response curves) lies at different concentration areas for each parameter, so that they can be used specifically in standard tests.