Likelihood based population viability analysis in the presence of observation error

Abstract

Population viability analysis (PVA) entails calculation of extinction risk, as defined by various extinction metrics, for a study population. These calculations strongly depend on the form of the population growth model and inclusion of demographic and/or environmental stochasticity. Form of the model and its parameters are determined based on observed population time series data. A typical population time series, consisting of estimated population sizes, inevitably has some observation error and likely has missing observations. In this paper, we present a likelihood based PVA in the presence of observation error and missing data. We illustrate the importance of incorporation of observation error in PVA by reanalyzing the population time series of song sparrow Melospiza melodia on Mandarte Island, British Columbia, Canada from 1975–1998. Using Akaike information criterion we show that model with observation error fits the data better than the one without observation error. The extinction risks predicted by with and without observation error models are quite different. Further analysis of possible causes for observation error revealed that some component of the observation error might be due to unreported dispersal. A complete analysis of such data, thus, would require explicit spatial models and data on dispersal along with observation error. Our conclusions are, therefore, two‐fold: 1) observation errors in PVA matter and 2) integrating these errors in PVA is not always enough and can still lead to important biases in parameter estimates if other processes such as dispersal are ignored.

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

“…When observational ecological data is available, statespace time series analysis methods have allowed researchers to model the data collection process along with realistic dynamical systems models capable of threshold dynamics (Ives et al , 2008Schooler et al 2011). Methods to fit state-space population growth models to observational time series data are well developed and it would be straightforward to estimate model parameters and determine if the growth rate has decreased and if an extinction threshold has or will be crossed (de Valpine and Hastings 2002;Williams et al 2003;Clark and Bjørnstad 2004;Dennis et al 2006;Wang 2007;Pedersen et al 2011;Nadeem and Lele 2012).…”

“…Parameter estimation for state-space population models is well developed using maximum likelihood (ML) or posterior sampling under a Bayesian paradigm (de Valpine and Hastings 2002;Clark and Bjørnstad 2004;Dennis et al 2006;Wang 2007;Ponciano et al 2009;Pedersen et al 2011;Nadeem and Lele 2012). For our situation, we feel that ML estimation is desirable because our results could be sensitive to the specification of vague priors.…”

“…A sensitivity analysis to justify our conclusions would be cumbersome. We used the data cloning (DC) algorithm to obtain ML parameter estimates (Lele et al 2007(Lele et al , 2010Ponciano et al 2009;Nadeem and Lele 2012). The DC algorithm uses Markov chain Monte Carlo (MCMC) posterior sampling to obtain ML parameter estimates and the associated asymptotic variance-covariance matrix.…”

“…All quantities derived from the population models (e.g., population prediction intervals and distributions of statistical indicators) and confidence intervals (CI) were obtained by bootstrap integration over the asymptotic distribution of the model parameters using 50,000 bootstrap samples (Nadeem and Lele 2012). For these bootstrap simulations, we assumed that r t ≥0, K t ≥0.01, and N t ≥1 for all t. These restrictions were required to avoid numerical issues associated with the population models postbifurcation.…”

“…Much focus has been given to the effects of demographic and environmental stochasticity on population extinction (Melbourne and Hastings 2008), forecasting quasi-extinction probabilities (Holmes et al 2007), and population viability analyses (Nadeem and Lele 2012) with less focus directed on identifying and forecasting critical threshold crossings that result in transitions to alternative population states including extinction (Wissel 1984;Abrams 2002;Drake and Griffen 2010;Dai et al 2012Dai et al , 2013. This shortage of research and application is particularly evident in the management of declining populations, where it is often assumed that a decreasing or small population size warns of future extinction (International Union for Conservation of Nature 2001; Abrams 2002).…”