Open integrated distance sampling for modelling age-structured population dynamics
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Abstract
Estimation of abundance and demographic rates for populations of wild species is a challenging but fundamental issue for both ecological research and wildlife management. One set of approaches that has been used extensively to estimate abundance of wildlife populations is Distance Sampling (DS) for line or point transect survey data. The first implementations of 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 utilizes 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 in density. The resulting model is equivalent to an integrated 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.
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Introduction
In their paper, Nilsen and Nater (2025) introduce a novel method, Integrated Distance Sampling Modelling (IDSM), designed to address the challenges of estimating population density and demographic rates (such as recruitment and survival) in age/size-structured populations. Unlike traditional approaches, IDSM leverages both distance sampling data and auxiliary data from marked individuals, providing a comprehensive framework for monitoring wildlife populations over time.
Main findings
Innovative Model Structure At the heart of the IDSM is a matrix-based population model that differentiates juveniles from adults, enabling the simulation of population dynamics over successive time intervals. By combining transect survey data with survival data of marked individuals, the model can estimate both population sizes and the demographic …Introduction
In their paper, Nilsen and Nater (2025) introduce a novel method, Integrated Distance Sampling Modelling (IDSM), designed to address the challenges of estimating population density and demographic rates (such as recruitment and survival) in age/size-structured populations. Unlike traditional approaches, IDSM leverages both distance sampling data and auxiliary data from marked individuals, providing a comprehensive framework for monitoring wildlife populations over time.
Main findings
Innovative Model Structure At the heart of the IDSM is a matrix-based population model that differentiates juveniles from adults, enabling the simulation of population dynamics over successive time intervals. By combining transect survey data with survival data of marked individuals, the model can estimate both population sizes and the demographic processes that drive changes in population, such as survival and recruitment rates. Application to Willow Ptarmigan IDSM was utilised with a data set concerning Willow Ptarmigan in Norway, covering a period of 15 years. The model successfully detected both trends and variations in population density, while also uncovering crucial patterns in survival and recruitment. Specifically, survival rates were observed to remain largely constant over time, while recruitment rates exhibited considerable temporal variability. This study of Nilsen and Nater (2025) highlights IDSM’s proficiency in managing intricate population dynamics within species characterised by markedly fluctuating reproductive success. Environmental Covariates The IDSM exhibits sufficient flexibility to accommodate environmental variables. This study tried to investigate how the abundance of small mammals could impact the recruitment rates of ptarmigans. Although a rodent effect was not clearly highlighted, the authors propose that this absence of a definitive link might result from data limitations regarding rodents or dynamic ecological factors.
Conclusion
The IDSM method goes beyond traditional population modeling by integrating multiple data sources, offering an adaptable tool for wildlife researchers and managers. Although this paper focused on a bird species in Norway, the model can be applied to a wide range of taxa and ecological settings, provided sufficient data is available. The approach is particularly well-suited for long-term monitoring programs, as it maximises data usage and allows for the estimation of key demographic parameters that are often difficult to capture using a single data source. By providing detailed insights into both population sizes and the drivers of population changes, IDSM should enhance our ability to make informed decisions about wildlife management and conservation.References
Nilsen, E.B. and Chloé R. Nater, C.R. (2025) Open integrated distance sampling for modelling age-structured population dynamics. EcoEvoRxiv, ver.3 peer-reviewed and recommended by PCI Ecology https://doi.org/10.32942/X2Q899
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