Statistical Detection of Density Dependence from a Series of Sequential Censuses

Abstract

The use of simple linear regression to estimate slopes of plots of N(t + 1) against N(t) as a test of density dependence has been criticized because such data violate the assumption of negligible measurement error in the independent variable and because they represent a time series rather than independent pairs of points. Of the several alternatives which have been suggested, ordinary and standard major axes and the coefficient of first-order autoregression behave in accordance with the logic of detecting density dependence in such plots. The power of the test of the slopes' being equal to 1 d epends on the magnitude of density-dependent and independent (random) influences and on the type of error, measurement or environmental. However, slopes of major axes appear to be unbiased estimators of the true slopes, when sequential population estimates include values sufficiently displaced from equilibrium conditions. If data follow a purely autoregressive process, density dependence can be detected without such displacement.