Estimation of Temporal Variability in Populations

Abstract

A common measure of the temporal variability of a population is the standard deviation of the logarithms of successive estimated population sizes, In(D-t). This measure overestimates true temporal variability (the standard deviation of the logarithms of true population density, In[Delta(t)]) because it is contaminated by spatial variance (variability among samples taken on the same date). The random error in D-t causes an overestimation of temporal variance, both directly and also indirectly, by causing ln(D-t) to underestimate ln(Delta(t)). Both problems are more severe if spatial variance is large or the sample size, on a date, is small. We develop an alternative estimator, which uses an estimate of spatial variance to correct for both problems. To evaluate it, we sampled from simulated populations with a wide range of clumping. The results show that the standard estimate can be badly biased. The new estimator is much better and is quite accurate over a broad range of conditions. Our results suggest a reanalysis of some ecological studies that have estimated temporal variability to attack theoretically important questions. In particular, the apparently greater average temporal variability of terrestrial arthropods compared with terrestrial vertebrates could be an artifact caused by the fact that, typically, clumping is weaker and density estimates are more accurate in vertebrates.