Taylor’s power law and fixed-precision sampling: application to abundance of fish sampled by gillnets in an African lake

Abstract

Taylor’s power law (TPL) describes the variance of population abundance as a power-law function of the mean abundance for a single or a group of species. Using consistently sampled long-term (1958–2001) multimesh capture data of Lake Kariba in Africa, we showed that TPL robustly described the relationship between the temporal mean and the temporal variance of the captured fish assemblage abundance (regardless of species), separately when abundance was measured by numbers of individuals and by aggregate weight. The strong correlation between the mean of abundance and the variance of abundance was not altered after adding other abiotic or biotic variables into the TPL model. We analytically connected the parameters of TPL when abundance was measured separately by the aggregate weight and by the aggregate number, using a weight–number scaling relationship. We utilized TPL to find the number of samples required for fixed-precision sampling and compared the number of samples when sampling was performed with a single gillnet mesh size and with multiple mesh sizes. These results facilitate optimizing the sampling design to estimate fish assemblage abundance with specified precision, as needed in stock management and conservation.