Spatial spread of Eurasian beavers in river networks: a comparison of range expansion rates.

1. Accurately measuring the rate of spread for expanding populations is important for reliably predicting their future spread, as well as for evaluating the effect of different conditions and management activities on that rate of spread. 2. Although a number of methods have been developed for such measurement, all these are designed only for one- or two-dimensional spread. Species dispersing along rivers, however, require specific methods due to the distinctly branching structure of river networks. 3. In this study, we analyse data regarding Eurasian beavers' modern recolonization of the Czech Republic. We developed a new methodology for quantifying spread of species dispersing along streams based on representation of the river network by means of a weighted graph. 4. We defined two different network-based spread rate measures, one estimating the rate of range expansion, with the range defined as the total length of occupied streams, and the second, named range diameter, quantifying the progress along one or several main streams. In addition, we estimated the population growth rates, and, dividing the population size by the range size, we measured the density of beaver records within their overall range. Using linear regression, we compared four beaver populations under different environmental conditions in terms of each of these measures. Finally, we discuss the differences between our method and the classical approaches. 5. Our method provided substantially higher spread rate values than did the classical methods. Both population growth and range expansion were found to follow logistic growth. In cases of there being no considerable barriers in dispersal routes, the rate of progress along main streams did not differ significantly among populations. In homogeneous environments, population densities remained relatively constant over time even though overall population sizes increased. This indicates that at large spatial scales, the population growth of beavers occurs through progressive space filling rather than increasing population density.