Weak population regulation in ecological time series

Abstract

How strongly natural populations are regulated has a long history of debate in ecology. Here, we discuss concepts of population regulation appropriate for stochastic population dynamics. We then analyse two large collections of data sets with autoregressive-moving average (ARMA) models, using model selection techniques to find best-fitting models. We estimated two metrics of population regulation: the characteristic return rate of populations to stationarity and the variability of the stationary distribution (the long-term distribution of population abundance). Empirically, longer time series were more likely to show weakly regulated population dynamics. For data sets of length > or = 20, more than 35% had characteristic return times > 6 years, and more than 29% had stationary distributions whose coefficients of variation were more than two times greater than would be the case if they were maximally regulated. These results suggest that many natural populations are weakly regulated.

Effects of weather and climate on the dynamics of animal population time series

“…The database has been used to analyse density dependence [22,23,25], population cycles [27], extinction risk [28] and population variability [20]. We applied selection criteria to choose suitable datasets from the database.…”

“…We limited our analysis to simple AR models (equation (2.1)), rather than including either state-space models to incorporate measurement error [31] or autoregressive moving average (ARMA) models [25]. Many of the GPDD time series are short, which could cause high imprecision in parameter estimates of more complex models owing to shallow likelihoods (see [32] for state-space models).…”

Density dependence: an ecological Tower of Babel

“…Secondly, the recent turn from DD testing to modelling (Bjørnstad and Grenfell 2001) makes DD parameters implicit in mathematical equations (although not necessarily biologically meaningful, Clark et al 2010), which might theoretically account for population regulation-so again, with one stroke, statistical evidence for a given model is assumed to bring about joint evidence for both DD and population regulation (e.g. Ziebarth et al 2010). Thirdly, both the conceptual and mathematical definitions of the concept population regulation remain to be unified, which is exemplified by Murdoch's (1994) droll observation that ''…regulation seems best defined by defining non-regulation''.…”

An updated perspective on the role of environmental autocorrelation in animal populations

“…The Gompertz model has been widely used in ecology to detect density dependence in animal populations (Morris, 1959; Sibly et al, 2007; Ziebarth et al, 2010). It has also been the basis for the development of measurement error models (Dennis et al, 2006) and for analysis of density dependence in large datasets (Sibly et al, 2007; Abbott et al, 2009; Knape and de Valpine, 2010; Ziebarth et al, 2010; Knape and de Valpine, 2011). The Ricker model was originally derived by William Ricker (1954) emerging from a cannibalistic interaction between adults and juveniles in a population.…”