Temporal autocorrelation and stochastic population growth

Abstract

How much does environmental autocorrelation matter to the growth of structured populations in real life contexts? Interannual variances in vital rates certainly do, but it has been suggested that between-year correlations may not. We present an analytical approximation to stochastic growth rate for multistate Markovian environments and show that it is accurate by testing it in two empirically based examples. We find that temporal autocorrelation has sizeable effect on growth rates of structured populations, larger in many cases than the effect of interannual variability. Our approximation defines a sensitivity to autocorrelated variability, showing how demographic damping and environmental pattern interact to determine a population's stochastic growth rate.

Poor environmental tracking can make extinction risk insensitive to the colour of environmental noise

“…By contrast, our study-the first to our knowledge to specifically look at extinction risk-suggests that extinction risk is less sensitive to environmental autocorrelation than to interannual variability (figure 2). Our model differs in several ways from that of Tuljapurkar & Haridas [37]: specifically, we included demographic stochasticity, density dependence and environmental tracking as well as a different stage structure. Although the type of density dependence and stage structure may also influence how autocorrelation affects the population dynamics [56], the poor environmental tracking suggests that it is unlikely that these mechanisms alone caused the large differences in relative impact of variability and autocorrelation of the environment on extinction risk.…”

“…(f) Extinction risk: environmental autocorrelation versus variability Tuljapurkar & Haridas [37] made an important theoretical contribution by modelling the relative effects of environmental autocorrelation and variability on population dynamics. In their models, the population growth rate was often more sensitive to environmental autocorrelation than to interannual variability, and they hypothesized that the same may hold for extinction risk.…”

“…Consequently, for predicting the impact of future climate change, we need to identify which aspect of change in environmental variables is most important, and under which circumstances. Interestingly, two studies suggested that for certain parameter conditions and model assumptions, the growth rate of populations might be more sensitive to noise colour than to interannual variability [36,37] and it was proposed that this may also hold for extinction risk [37].…”

Persistence of structured populations in random environments

“…These correlations can influence extinction risk (Lawton 1988, Petchey et al 1997, Cuddington and Yodzis 1999, Heino et al 2000, inflate population abundances Holt 2002, Holt et al 2003), and facilitate persistence of couple sink populations (Roy et al 2005). While there have been some work on computing or approximating the stochastic growth rate with correlated noise (Tuljapurkar 1982, Tuljapurkar 1990, Tuljapurkar and Haridas 2006, there have been no theoretical results connecting these results for the linear models to the dynamics of the nonlinear models. Here, we extend the results of Chesson, Ellner and Hardin et al to stationary environments (i.e.…”

Bounds on the dynamics of sink populations with noisy immigration

“…In reality, environmental fluctuations will influence not just the magnitude of immigration but also the demographic parameters of the ambient population (Tuljapurkar and Haridas, 2006) and thus machinery to handle such stochasticity is required. As demonstrated, the material presented here extends to such a situation when an estimate on the size of the perturbations is known.…”