Using Statistical Population Reconstruction to Estimate Demographic Trends in Small Game Populations

Abstract

Statistical population reconstruction offers a robust approach to demographic assessment for harvested populations, but current methods are restricted to big‐game species with multiple age classes. We extended this approach to small game and analyzed 14 years of age‐at‐harvest data for greater sage‐grouse (Centrocercus urophasianus) in Oregon, USA, in conjunction with radiotelemetry data to reconstruct annual abundance levels, recruitment, and natural survival probabilities. Abundance estimates ranged from a low of 26,236 in 1995 to a high of 39,492 in 2004. Annual abundance estimates for adult males were correlated with a spring lek count index (r = 0.849, P < 0.029). We estimated the average annual harvest mortality for the population to be 0.028, ranging from 0.021 to 0.031 across years. We estimated the probability of natural survival of adult females to be 0.818 ( = 0.052), somewhat higher than that of adult males (Ŝ = 0.609, = 0.163). Our precision in reconstructing the population was hampered by low harvest rates and the few birds tagged in the radiotelemetry investigations. Despite these issues, our analysis illustrates how modern statistical reconstruction procedures offer a flexible framework for demographic assessment using commonly collected data. This approach offers a useful alternative to small‐game indices and would be most appropriate for species with 5 or more years of age‐at‐harvest data and moderate‐to‐heavy harvest rates.

AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models

“…where p θ (y) is given by (10). When element (i, j ) of the Hessian H is zero, u i and u j become conditionally independent under (16), given the remaining u's.…”

Random Effects Models and Multistage Estimation Procedures for Statistical Population Reconstruction of Small Game Populations

“…Some of the most recent developments require estimation of initial animal cohort abundance as a parameter [3], [4], [7], [8], or as a latent variable [5] in a frequentist or Bayesian framework, respectively. Recently, models for statistical population reconstruction (SPR) of harvested large game animals have been developed that utilize the same likelihood-based inference techniques, but instead consider estimating animal abundance following optimization, outside of the likelihood framework with a Horvitz-Thompson-type estimator, which adjusts the observed harvest count by the estimated probability of harvest in accordance with the assumption of a binomial sampling scheme [9].…”

“…Previous work has examined a modeling framework for small game animals that provides a way to accommodate the unknown contribution of prior cohorts to the adult age group of a given cohort [1], [7]. These models, however, suffer from similar difficulties associated with the big game models of Gove et al [3], Skalski et al [4], and Skalski et al [8] inasmuch as they assume constancy of demographic rates across time periods when additional data are not available to inform estimation of year- or age-specific rates.…”

“…In addition, models with only fixed effects have proven in fully aged simulation studies to provide biased estimates of annual abundance and poor confidence interval covariate [9]. It is therefore of interest to extend the modeling framework of Broms et al [7] in a manner similar to Gast et al [9], and to determine what impact this has on statistical population reconstructions of small game populations with pooled age classes.…”

Integrated Population Modeling of Black Bears in Minnesota: Implications for Monitoring and Management

“…Recently, several authors have suggested applying modern statistical age-at-harvest models to monitor population trends, either in concert or as an alternative to more labor intensive survey methods [1]–[7]. Methods for analyzing age-at-harvest data have largely been adapted from fisheries' statistical catch-age models [8]–[9], which fall under the broader classification of integrated population (or “hidden process”) models [10]–[13].…”