Introduction

Detection and estimation of density dependence is complicated because it usually operates with a time-lag due to intrinsic factors in individual development and life history (May 1973, 1981b; MacDonald 1978; Renshaw 1991; Nisbet 1997; Jensen 1999; Claessen et al. 2000) and extrinsic factors in an autocorrelated environment (Williams & Liebhold 1995; Berryman & Turchin 1997), including interspecific ecological interactions (Turchin 1990, 1995; Royama 1992; Turchin & Taylor 1992; Kaitala et al. 1997; Ripa et al. 1998; Hansen et al. 1999). The life history of a species may largely determine the relative importance of intrinsic and extrinsic factors in contributing to time-lags in population dynamics. For short-lived species with high population growth rates, such as some insects, ecological interactions may best explain time-lags longer than a generation (Turchin 1990, 1995; Royama 1992). For long-lived species with low population growth rates, such as many vertebrates, most time-lags may occur within a generation because of life history (Jensen 1999; Coulson et al. 2001; Thompson & Ollason 2001). Understanding density dependence has been impeded by the lack of a general quantitative definition that would allow comparisons among species with different life histories and forms of density dependence (Murdoch 1994).

Time-lags in population dynamics caused by life history have not, to our knowledge, previously been incorporated into methods for detecting and estimating density dependence from population time-series (Bulmer 1975; Pollard et al. 1987; Turchin 1990, 1995; Royama 1992; Turchin & Taylor 1992; Hanski et al. 1993; Dennis & Taper 1994; Zeng et al. 1998).