The relationships between abundance of animals and characteristics of habitats are important for theoretical and management reasons. However, data on populations and habitats frequently are unsuitable for model-based statistical analyses. The shape of the functional relation between abundance and habitat and the form of the error distribution are rarely known accurately, and noise in the data often is large relative to the signal. Kernel estimators, a type of nonparametric probability density estimation technique, can use available data to estimate the probability density function (pdf) of abundance, given specified habitat conditions. One nonparametric estimator, related to kernel estimators and based on the Cauchy distribution, is described in detail. It is applied to data from three studies of influences of habitat on populations: stream characteristics on salmon and trout biomasses, depth of the 2 °C isotherm on codtrap catches, and bottom temperature on capelin densities. Despite the differences among the data sets, the Cauchy kernel could be applied without modification in all cases. The pdf's of abundance were interpretable readily, captured dominant features of the biology of each species, and were suitable for management applications and for tests of hypotheses.
A Comparative Study of Various Probability Density Estimation Methods for Data Analysis