Statistical indicators and state–space population models predict extinction in a population of bobwhite quail

Abstract

Early warning systems of extinction thresholds have been developed for and tested in microcosm experiments, but have not been applied to populations of wild animals. We used state-space population models and a statistical indicator to detect a transcritical bifurcation extinction threshold in a population of bobwhite quail (Colinus virginianus) located in an agricultural region experiencing habitat deterioration and loss. The extinction threshold was detectible using two independent data sets. We compared predictions from state-space population models to predictions from a statistical indicator and found that predictions were corroborated. Using state-space population models, we estimated that our study population crossed the extinction threshold in 2010 ; 95 % confidence intervals [CI]) using the whistle count (WC) data set and in 2008 (1999-2064; 95 % CI) using the Breeding Bird Survey (BBS) data. With the statistical indicator, we estimated that the extinction threshold will be crossed in 2018 ; 95 % CI) using the WC data and will be crossed in 2012 (2006-2018; 95 % CI) using the BBS data. We expect extinction in our study population soon after crossing the extinction threshold, but the time to extinction and potential reversibility of the threshold are unknown. Our results suggest that neither small nor decreasing population size will warn of the transcritical bifurcation extinction threshold. We suggest that managers of wildlife populations in regions experiencing land use change should try to predict extinction thresholds and make management decisions to ensure the persistence of the species.

Factors Influencing the Detectability of Early Warning Signals of Population Collapse

“…These generic leading indicators arise from mathematical properties of stochastic dynamical systems as they approach a tipping point and appear to be present in vastly different systems, including stock markets, global climatic change, and populations (for a review, see Scheffer et al 2009). The development and testing of these statistical early warning signals suggests that a predictive framework for population risk might be developed that requires only a relatively limited amount of demographic data (Hefley et al 2013;Krkošek and Drake 2014). From a conservation perspective, such a framework could provide an important tool for prioritizing conservation efforts and funding to target those species approaching a critical transition.…”

“…Typically, a subset of the population is counted (say, along a transact or within a defined area), with this subset being assumed to reflect the true (total) population abundance (e.g., Franzetti et al 2012; but see Hefley et al 2013). However, in itself, this subsampling generates uncertainty, as chance events such as the movement of organisms, the heterogeneous distribution of individuals, and the skill of the observers influence recorded population abundance (Muhlfeld et al 2006).…”

“…Previous work has suggested that generic statistical indicators will perform poorly when observational errors are large (Dai et al 2012;Ives and Dakos 2012; but see Hefley et al 2013). One method that may be used to ameliorate some of these issues would be the use of state-space models (which allow the data collection process to be incorporated into dynamic population models of a species, where the model can pass through a critical transition), which could explicitly account for observational errors (Hefley et al 2013).…”

“…One method that may be used to ameliorate some of these issues would be the use of state-space models (which allow the data collection process to be incorporated into dynamic population models of a species, where the model can pass through a critical transition), which could explicitly account for observational errors (Hefley et al 2013). Previous work has used this approach to detect potential transcritical bifurcations in wild populations (Hefley et al 2013). However, this approach is significantly more complicated to implement and more problem specific than the methods of, say, Dakos et al (2008) and Scheffer et al (2009).…”

“…However, this approach is significantly more complicated to implement and more problem specific than the methods of, say, Dakos et al (2008) and Scheffer et al (2009). Moreover, Hefley et al (2013) found that even with significant observational error generated by spatial subsampling, statistical leading indicators may still perform reasonably well. Given this additional complexity and the apparent robustness of statistical approaches, state-space model approaches are not considered further here.…”