On the importance of sampling variance to investigations of temporal variation in animal population size

Abstract: Temporal variation in animal population size and the related concept of population stability are of substantial interest to animal ecologists (e.g., MacArthur 1955, Holling 1973). Empirical studies of variation in population size are not new (e.g., Watt 1964) but have become especially popular in recent years. Recent empirical work has included interesting research on the relationships between temporal variation in population size and such factors as extinction probability (Karr 1982, Pimm et al. 1988, Schoener and Spiller 1992, Tracy and George 1992), mean population density (Taylor and Woiwod 1980), latitude (Wolda 1978), human disturbance (Pechmann et al. 1991), body size (Gaston 1988, Gaston and Lawton 1988), food habits (Gaston and Lawton 1988, Redfearn and Pimm 1988), geographic range (Gaston 1988, Gaston and Lawton 1988), and taxonomy (Connell and Sousa 1983, Schoener 1985). However, estimation of temporal variation in population size is not a simple matter (Greenwood 1989, Mc Ardle 1989, McArdle et al. 1990). McArdle et al. (1990: 439) recently discussed "problems associated with the measurement and interpretation of population density variability that have confounded most, if not all, previous studies of the subject". These problems include "artefactual patterns" induced by commonly used transformations and misleading conclusions resulting from comparisons of populations sampled at different spatial and temporal scales. McArdle et al. (1990) also argued that the dependence of population variability on mean density should be considered in making comparisons of variability among species and populations. Recent contributions to the literature conclude with statements emphasizing the importance of properly estimating and comparing population variability and recommending additional statistical and biological work on the topic (McArdle et al. 1990, Schoener and Spiller 1992). Despite the fairly extensive literature on population variability and its estimation, there has been little discussion of the fact that virtually all of the empirical work has relied on estimates or indices to animal abundance (see McArdle and Gaston 1993). That is, estimates of population variability are not based on a time series of true population sizes measured without error, but on a series of estimates or indices (count statistics assumed to be related to population size by a proportionality constant, see Lancia et al. in press). Measures of population variability computed using point estimates of population size over time represent the sum of at least two conceptually distinct variance components. One component is temporal variation in actual population size and is relevant to interesting biological hypotheses. Another component is "sampling variation", defined here as the variation associated with the population estimation procedure. This component is sometimes called "error of estimation" and occurs whenever it is impossible to directly enumerate all individuals in the population. This component is not relevant to biological hypotheses and should not be included in measures of population variability computed for the purpose of addressing such hypotheses. We believe that the inclusion of this unwanted variance component in previous studies of population variability is at least as serious a problem as those associated with transformations and scale discussed by McArdle et al. (1990). For studies in which population size is estimated rather than indexed, it is usually possible to estimate the sampling variance of the population estimates. This component can then be subtracted from the total variance (e.g., based on point estimates) to estimate the variance component of interest. This basic approach has been used to estimate variance of survival probabilities among replicate groups of animals receiving different experimental