An integrated open population distance sampling approach for modelling age-structured populations

Estimation of abundance and demographic rates for populations of wild species is a challenging but fundamental issue for both management and research into ecology and evolution. One set of approaches that has been used extensively to estimate abundance of wildlife populations is Distance Sampling (DS) methods for line or point transect survey data. Historically, DS models were only available as closed population models, and did not allow for the estimation of changes in abundance through time. The advent of open population formulations based on the DS framework greatly extended the scope of the models, but much untapped potential remains in models that estimate temporal dynamics not only in abundance but also in the underlying demographic rates. Here, we present an integrated distance sampling approach that utilize age-structured survey data and auxiliary data from marked individuals to jointly estimate population density and the demographic rates (recruitment rate and survival probability) that drive temporal changes density. The core of the resulting model is, in essence, equivalent to both an integrated population model and a matrix population model with two age classes: juveniles and adults. The integrated framework allows making full use of the available data by effectively combining line transect and telemetry data, and can easily be adapted to include additional and/or different data types. Moreover, as demographic rates often respond to environmental variation, our approach also supports direct estimation of the effects of such environmental covariates on demographic rates. Through a comprehensive simulation study we show that the model is able to adequately recover true population and vital rate dynamics. Subsequent application to data from a study of willow ptarmigan (Lagopus lagopus) in Norway showcases the frameworks ability to recover both fluctuations and trends in population dynamics and highlights its potential applicability to a wide range of species surveyed using distance sampling approaches.