Patterns in spatial and temporal variation in population abundances of vertebrates

Abstract

In this thesis I investigate the heterogeneity of population abundance by using the Taylor’s power law relationship of mean and variance, in time and space.

Within the framework of stochastic population dynamics, the existence of a temporal Taylor’s power law were confirmed for a large number of British bird populations. Theoretical expectations predicted that environmental stochasticity would increase the slope of the mean-variance relationship while demographic stochasticity would reduce it. In addition, the slope should also be influenced by the strength of density dependence. Here, species specific slopes were mainly explained by the effect of life history variation on interspecific variation in demographic variance.

It is generally acknowledged that the spatial power law depend on scale, however, few studies have accounted for this. By using a model which incorporates both the local point process and spatial covariance of population densities, the variance was estimated as a function of area and parameters characterizing the underlying density process, thus generating a non-linear Taylor’s spatial scaling law. Using a novel method to estimate the underlying density field, the spatial aggregation pattern was investigated by the slope of the variance-area relationship in populations of birds and fish. For the bird species no effect of behavioural characteristics was found to influence interspecific differences in the spatial aggregation patterns. Instead, interspecific differences in overall abundance in the UK influenced the slopes, thus indicating a link between local processes and variation of abundance patterns at a regional level. For the fish species, interspecifc differences in the spatial aggregation of the distributions were related to behavioural differences. Consequently, the effect of sampling area on the spatial distribution may be predicted from basic behavioural characteristics.

The work of this thesis contributes to the ongoing discussion of Taylor’s power laws. It introduces framework to aid interpretation of future research, which is especially important in the context of other macroecologial pattern.