Methods for Joint Inference From Multiple Data Sources for Improved Estimates of Population Size and Survival Rates

Abstract

Critical conservation decisions often hinge on estimates of population size, population growth rate, and survival rates, but as a practical matter it is difficult to obtain enough data to provide precise estimates. Here we discuss Bayesian methods for simultaneously drawing on the information content from multiple sorts of data to get as much precision as possible for the estimates. The basic idea is that an underlying population model can connect the various sorts of observations, so this can be elaborated into a joint likelihood function for joint estimation of the respective parameters. The potential for improved estimates derives from the potentially greater effective sample size of the aggregate of data, even though some of the data types may only bear directly on a subset of the parameters. The achieved improvement depends on specifics of the interactions among parameters in the underlying model, and on the actual content of the data. Assuming the respective data sets are unbiased, notwithstanding the fact that they may be noisy, we may gauge the average improvement in the estimates of the parameters of interest from the reduction, if any, in the standard deviations of their posterior marginal distributions. Prospective designs may be evaluated from analysis of simulated data. Here this approach is illustrated with an assessment of the potential value in various ways of merging mark‐resight and carcass‐survey data for the Florida manatee, as could be made possible by various modifications in the data collection protocols in both programs.

A Bayesian Capture–Recapture Population Model With Simultaneous Estimation of Heterogeneity

“…This approach is similar to ours, but we also integrate a dynamic population model and an observation model into the estimation process. Goodman (2004) also implemented a population model in a Bayesian context that combines capture-recapture data with carcass-recovery data, but assumes the absence of heterogeneity in capture probabilities. Durban et al (2005) estimated abundance for the same population as us, but used a multisite Bayesian log-linear model and model averaging (King and Brooks 2001) across the possible models with varying combinations of interactions.…”

Insights into processes of population decline using an integrated population model: The case of the St. Lawrence Estuary beluga (Delphinapterus leucas)

“…This integration is achieved by measuring relative model fit to each data set in a common currency, the likelihood, and then combining them to obtain a global measure of fit. The objective is then to maximise this value (Goodman, 2004;Hoyle and Maunder, 2004). We described changes in population size and parameters with two linked components: the state and the observation processes (State−space models; De Valpine and Hastings, 2002;Buckland et al, 2004).…”

Precautionary design of a marine protected area based on a habitat model

“…Estimation of density and habitat relationships may also be combined in a single analysis (Hedley et al 2004, Royle et al 2004, Johnson et al 2010, Niemi & Fernández 2010. Inference about population processes is improved when combined with an observation model into a single likelihood framework (Goodman 2004, Buckland et al 2007, Royle & Dorazio 2008.…”