Autocorrelated Exogenous Factors and the Detection of Delayed Density Dependence

Abstract

Coupled trophic interactions with specialist predators or resources are thought to be primarily responsible for generating delayed density dependence. Previous theoretical studies suggest that autocorrelation in exogenous factors could generate apparent negative delayed density dependence in populations regulated only by direct density dependence. Using both linear and nonlinear models, we show that autocorrelated exogenous factors can generate the spurious appearance of not only negative, but also positive, delayed density dependence in populations regulated only by direct density dependence. Evidence for negative delayed density dependence is found mainly in populations exhibiting monotonic deterministic stability, whereas evidence for positive delayed density dependence is found mainly in populations exhibiting damped or persistent two-point cycles, or more complex deterministic dynamics. We argue that fluctuating resources (e.g., mast seeding) in bottom-up controlled communities could qualify as autocorrelated exogenous factors and cause apparent delayed density dependence in the population of their consumers.

Red environmental noise and the appearance of delayed density dependence in age–structured populations

“…In keeping with predictions from unstructured population models (Royama 1981;Williams & Leibhold 1995;Jiang & Shao 2003), our simulations demonstrate that both negative and positive spurious DDD could arise in age-structured populations subjected to red environmental noise. We have also demonstrated that different densitydependent scenarios can lead to qualitatively different patterns of spurious DDD in age-structured populations.…”

“…We have also demonstrated that different densitydependent scenarios can lead to qualitatively different patterns of spurious DDD in age-structured populations. In unstructured population models, negative spurious DDD is associated with deterministic monotonic damping dynamics and positive spurious DDD is associated with deterministic oscillatory damping or limit cycles ( Jiang & Shao 2003). We show that these simple predictions from unstructured models may not necessarily hold in structured models, even for the simple age-structured models explored here.…”

“…It has become increasingly clear, however, that physical environmental noise may often be red (positively autocorrelated over time) (Mandelbrot & Wallis 1969;Steele 1985;Halley, 1996;Cuddington & Yodzis 1999). Some biotic factors may also act in the form of autocorrelated noise for organisms that are affected by them (Jiang & Shao 2003). Recent theoretical studies suggest that red noise leads to different risks of population extinction than white noise (Ripa & Lundberg 1996;Petchey et al 1997;Cuddington & Yodzis 1999;Halley & Kunin 1999;Morales 1999;Ripa & Heino 1999;Heino et al 2000;Heino & Sabadell 2003).…”

“…Several researchers have used simple unstructured models to show that populations experiencing only direct density dependence appear to be influenced by DDD, when subjected to red noise (Royama 1981;Ives 1995;Williams & Liebhold 1995;Jiang & Shao 2003). Furthermore, Jiang & Shao (2003) demonstrated that red noise may cause the appearance of either negative or positive DDD, depending on deterministic population dynamics. Such apparent DDD does not arise from intrinsic density-dependent processes alone, but from the interplay between noise and density dependence, and may therefore be perceived as spurious (Williams & Liebhold 1995Berryman & Turchin 1997).…”

“…Previous studies on this topic have focused on unstructured models of homogenous populations (Royama 1981;Williams & Liebhold 1995;Jiang & Shao 2003), despite the fact that many organisms go through multiple stages during their life cycle or have spatially structured populations. We focus on age-structured populations here.…”