Integrating population dynamics models and distance sampling data: a spatial hierarchical state‐space approach

Abstract

Stochastic versions of Gompertz, Ricker, and various other dynamics models play a fundamental role in quantifying strength of density dependence and studying long-term dynamics of wildlife populations. These models are frequently estimated using time series of abundance estimates that are inevitably subject to observation error and missing data. This issue can be addressed with a state-space modeling framework that jointly estimates the observed data model and the underlying stochastic population dynamics (SPD) model. In cases where abundance data are from multiple locations with a smaller spatial resolution (e.g., from mark-recapture and distance sampling studies), models are conventionally fitted to spatially pooled estimates of yearly abundances. Here, we demonstrate that a spatial version of SPD models can be directly estimated from short time series of spatially referenced distance sampling data in a unified hierarchical state-space modeling framework that also allows for spatial variance (covariance) in population growth. We also show that a full range of likelihood based inference, including estimability diagnostics and model selection, is feasible in this class of models using a data cloning algorithm. We further show through simulation experiments that the hierarchical state-space framework introduced herein efficiently captures the underlying dynamical parameters and spatial abundance distribution. We apply our methodology by analyzing a time series of line-transect distance sampling data for fin whales (Balaenoptera physalus) off the U.S. west coast. Although there were only seven surveys conducted during the study time frame, 1991-2014, our analysis detected presence of strong density regulation and provided reliable estimates of fin whale densities. In summary, we show that the integrative framework developed herein allows ecologists to better infer key population characteristics such as presence of density regulation and spatial variability in a population's intrinsic growth potential.

Estimation of population size and trends for highly mobile species with dynamic spatial distributions

“…Hierarchical models enable the joint estimation of an ecological process submodel that describes the ecological processes of interest (such as population size and distribution), and an observation submodel that describes the relationship between unobserved ecological state variables and the observed data (Royle & Dorazio, ). Moore and Barlow (, , ) designed a series of BHMs with ecological submodels for population dynamics to estimate population size and trends for fin whales ( Balaenoptera physalus ), beaked whales (family Ziphiidae ) and sperm whales ( Physeter macrocephalus ) (see also Nadeem, Moore, Zhang, & Chipman, ). BHMs designed to estimate distribution patterns as a function of habitat covariates have generally built on the multinomial N ‐mixture model developed by Royle, Dawson, and Bates () (e.g., Chelgren, Samora, Adams, & McCreary, ; Gerrodette & Eguchi, ; Oedekoven et al., ).…”

Private land conservation has landscape‐scale benefits for wildlife in agroecosystems

“…Pradel, ); however, spatially and temporally replicated counts can be sufficient to estimate population growth rates (Dail & Madsen, ; Royle, ). Modelling growth allows us to use classical population models that do not assume resources are unlimited (Hostetler & Chandler, ; Nadeem, Moore, Zhang, & Chipman, ). Realistic growth models facilitate population forecasting and allow us to compare the ramifications of alternative management scenarios.…”

“…Pradel, 1996); however, spatially and temporally replicated counts can be sufficient to estimate population growth rates (Dail & Madsen, 2011;Royle, 2004). Modelling growth allows us to use classical population models that do not assume resources are unlimited (Hostetler & Chandler, 2015;Nadeem, Moore, Zhang, & Chipman, 2016 In agricultural landscapes, grassland bird populations are driven by resource availability (Butler, Boccaccio, Gregory, Vorisek, & Norris, 2010), specifically food and nesting resources (Benton, Bryant, Cole, & Crick, 2002;Butler, Vickery, & Norris, 2007).…”

An open‐population distance sampling framework for assessing population dynamics in group‐dwelling species

“…In the N-mixture framework, repeated counts allow the estimation of parameters such as survival and recruitment (Dail & Madsen, 2011) and can be further extended to stagestructured data (Zipkin et al, 2014). Distance sampling protocols are not typically conducted under the robust design framework, and although survival and recruitment are theoretically estimable under single-visit protocols, in most cases, estimation is functionally limited to the population rate of change (Kery & Royle, 2016;Sollmann et al, 2015; but see Nadeem, Moore, Zhang, & Chipman, 2016). However, group composition data (e.g.…”

“…Koenen, DeStefano, & Krausman, 2002;Schmidt & Rattenbury, 2013) but has not been incorporated in an open-population framework (e.g. Nadeem et al, 2016;Sollmann et al, 2015). Therefore, the extension of open-distance models to groupdwelling species where composition information is collected would provide sex and age class-specific estimates of rate of change over time, partially mitigating the limitations of the single-visit design.…”