Spatially explicit models of density improve estimates of Eastern Bering Sea beluga (Delphinapterus leucas) abundance and distribution from line-transect surveys

Megan C. Ferguson; Paul B. Conn; James T. Thorson

doi:10.7717/peerj.20077

journal article Open Access Sep 30, 2025

Spatially explicit models of density improve estimates of Eastern Bering Sea beluga (Delphinapterus leucas) abundance and distribution from line-transect surveys

Megan C. Ferguson Paul B. Conn James T. Thorson

PeerJ Vol. 13 pp. e20077 · PeerJ

View at Publisher Save 10.7717/peerj.20077

Abstract

We investigate spatially explicit models and ensemble modeling techniques for estimating animal abundance from line-transect survey data. Spatially explicit models are expected to be statistically more efficient, resulting in more precise abundance estimates, than design-based abundance estimators that rely heavily on assumptions about survey design and realization. Ensemble modeling reduces error by averaging among models, and allows for model selection uncertainty to propagate to the abundance estimator. We develop density surface models using Matérn covariance functions and spline-based smooths for a case study, belugas (Delphinapterus leucas) from the Eastern Bering Sea (EBS) stock. EBS belugas are upper trophic level predators in a rapidly changing ecosystem and are a vital nutritional and cultural resource for Alaska Natives. Effective management of this stock requires regular monitoring to derive accurate and unbiased estimates of abundance. Since 1992, aerial line-transect surveys have been the primary means of surveying and estimating abundance of EBS belugas in the region. We compare EBS beluga abundance estimates for 2017 and 2022 that were derived using post-stratified, design-based abundance estimators with analogous estimates the we derive using spatially explicit and ensemble modeling methods. The estimated precision in the abundance estimates from the individual density surface models (DSMs) and the ensemble average of DSMs is higher than for the design-based estimator in both survey years. The design-based models estimated that there were 12,269 belugas in 2017 (coefficient of variation (CV) = 0.118) and 19,811 belugas within a larger study area in 2022 (CV = 0.343). The ensemble spatial models estimate that there were 11,654 belugas in 2017 (CV = 0.118) and 13,313 belugas in 2022 (CV = 0.216). Among the individual spatially explicit models, abundance estimates range from 11,242 to 11,963 (CV = 0.111 to 0.114) in 2017 and 12,023 to 15,593 (CV = 0.172 to 0.198) in 2022. Because spatial models identify spatial patterns in beluga density at finer resolutions than design-based models, we argue that ensembles of spatially explicit density models provide a reasonable path forward for estimating EBS beluga abundance and distribution in a way that is useful to management and conservation efforts.

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References

59

[1]

Adams "Alaska and Inuvialuit Beluga Whale Committee (AIBWC)—an initiative in “at home management”" Arctic (1993) 10.14430/arctic1334

[2]

Ensemble forecasting of species distributions

M ARAUJO, M NEW

Trends in Ecology & Evolution 2007 10.1016/j.tree.2006.09.010

[3]

Bakka "Non-stationary Gaussian models with physical barriers" Spatial Statistics (2019) 10.1016/j.spasta.2019.01.002

[4]

Belmont "Building the mesh" (2022)

[5]

Bravington "Variance propagation for density surface models" Journal of Agricultural, Biological and Environmental Statistics (2021) 10.1007/s13253-021-00438-2

[6]

Buckland (2001) 10.1093/oso/9780198506492.001.0001

[7]

Buckland (2015) 10.1007/978-3-319-19219-2

[8]

Burnham (2002)

[9]

Burt "Using mark—recapture distance sampling methods on line transect surveys" Methods in Ecology and Evolution (2014) 10.1111/2041-210x.12294

[10]

Citta "Satellite telemetry reveals population specific winter ranges of beluga whales in the Bering Sea" Marine Mammal Science (2017) 10.1111/mms.12357

[11]

Cochran (1977)

[12]

Conn "On extrapolating past the range of observed data when making statistical predictions in ecology" PLOS ONE (2015) 10.1371/journal.pone.0141416

[13]

Cook "Influential observations in linear regression" Journal of the American Statistical Association (1979) 10.1080/01621459.1979.10481634

[14]

Dorfman "A note on the delta-method for finding variance formulae" The Biometric Bulletin (1938)

[15]

Dormann "Model averaging in ecology: a review of Bayesian, information-theoretic, and tactical approaches for predictive inference" Ecological Monographs (2018) 10.1002/ecm.1309

[16]

Dunn "Randomized quantile residuals" Journal of Computational & Graphical Statistics (1996) 10.1080/10618600.1996.10474708

[17]

Dunn "Series evaluation of Tweedie exponential dispersion model densities" Statistics and Computing (2005) 10.1007/s11222-005-4070-y

[18]

Ferguson "Distribution and estimated abundance of eastern Bering Sea belugas from aerial line-transect surveys in 2017" NOAA technical memorandum NMFS-AFSC-471 (2023)

[19]

Ferguson "Spatially-explicit models of density improve estimates of Eastern Bering Sea beluga (Delphinapterus leucas) abundance and distribution from line-transect surveys" Paper SC/69B/SM01 presented to the 69B IWC scientific committee (2024)

[20]

Frost "Alaska Beluga Whale Committee—a unique model of co-management" Polar Research (2021) 10.33265/polar.v40.5611

[21]

Frost "Radio tag based correction factors for use in beluga whale population estimates" (1995)

[22]

Frost "Radiotagging studies of belukha whales (Delphinapterus leucas) in Bristol Bay, Alaska" Marine Mammal Science (1985) 10.1111/j.1748-7692.1985.tb00008.x

[23]

Hartig "DHARMa: residual diagnostics for hierarchical (multi-level/mixed) regression models" (2022)

[24]

Hedley "Comments on design-based and model-based abundance estimates for the RMP and other contexts" Paper SC/65B/RMP11 presented to the 65B IWC Scientific Committee (2014)

[25]

Spatial models for line transect sampling

Sharon L. Hedley, Stephen T. Buckland

Journal of Agricultural, Biological and Environmen... 2004 10.1198/1085711043578

[26]

Huntington "Traditional knowledge of the ecology of beluga whales (Delphinapterus lencas) in the Eastern Chukchi and Northern Bering Seas, Alaska" Arctic (1999) 10.14430/arctic909

[27]

Johnson "A model-based approach for making ecological inference from distance sampling data" Biometrics (2010) 10.1111/j.1541-0420.2009.01265.x

[28]

Exponential Dispersion Models

Bent Jørgensen

Journal of the Royal Statistical Society Series B:... 1987 10.1111/j.2517-6161.1987.tb01685.x

[29]

Kass "Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models)" Journal of the American Statistical Association (1989) 10.1080/01621459.1989.10478825

[30]

Kendal "Spatial aggregation of the Colorado potato beetle described by an exponential dispersion model" Ecological Modelling (2002) 10.1016/s0304-3800(01)00494-x

[31]

Kendal "Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models" Ecological Complexity (2004) 10.1016/j.ecocom.2004.05.001

[32]

Kristensen "TMB: automatic differentiation and Laplace approximation" Journal of Statistical Software (2015) 10.18637/jss.v070.i05

[33]

Laake "Methods for incomplete detection at distance zero" (2004) 10.1093/oso/9780198507833.003.0006

[34]

Bayesian Spatial Modelling withR-INLA

Finn Lindgren, Håvard Rue

Journal of Statistical Software 2015 10.18637/jss.v063.i19

[35]

Lindgren "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach" Journal of the Royal Statistical Society B (2011) 10.1111/j.1467-9868.2011.00777.x

[36]

Lowry "Distribution, abundance, harvest, and status of Western Alaska Beluga Whale, Delphinapterus leucas, stocks" Marine Fisheries Review (2019) 10.7755/mfr.81.3-4.2

[37]

Lowry "Aerial survey estimates of abundance of the eastern Chukchi Sea stock of beluga whales (Delphinapterus leucas) in 2012" Arctic (2017) 10.14430/arctic4667

[38]

Marsh "Correcting for visibility bias in strip transect aerial surveys of aquatic fauna" Journal of Wildlife Management (1989) 10.2307/3809604

[39]

Spatial models for distance sampling data: recent developments and future directions

David L. Miller, M. Louise Burt, Eric A. Rexstad et al.

Methods in Ecology and Evolution 2013 10.1111/2041-210x.12105

[40]

Miller "Understanding the stochastic partial differential equation approach to smoothing" Journal of Agricultural, Biological and Environmental Statistics (2020) 10.1007/s13253-019-00377-z

[41]

Miller "dsm: density surface modelling of distance sampling data" (2022)

[42]

Miller "Finite area smoothing with generalized distance splines" Environmental and Ecological Statistics (2014) 10.1007/s10651-014-0277-4

[43]

Oceana and Kawerak Inc Bering strait marine life and subsistence use data synthesis (2014)

[44]

O’Corry-Crowe "Genetic history and stock identity of beluga whales in Kotzebue sound" Polar Research (2021) 10.33265/polar.v40.7623

[45]

O’Corry-Crowe "Migratory culture, population structure and stock identity in North Pacific beluga whales (Delphinapterus leucas)" PLOS ONE (2018) 10.1371/journal.pone.0194201

[46]

R Core Team "R: A language and environment for statistical computing" (2023)

[47]

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Håvard Rue, Sara Martino, Nicolas Chopin

Journal of the Royal Statistical Society Series B:... 2009 10.1111/j.1467-9868.2008.00700.x

[48]

Siddon "Ecosystem assessment" Ecosystem status report 2023: eastern bering sea, stock assessment and fishery evaluation report (2023)

[49]

Sigourney "Developing and assessing a density surface model in a Bayesian hierarchical framework with a focus on uncertainty: insights from simulations and an application to fin whales (Balaenoptera physalus)" PeerJ (2020) 10.7717/peerj.8226

[50]

Taylor "Aggregation, variance and the mean" Nature (1961) 10.1038/189732a0

Showing 50 of 59 references

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Details

Published: Sep 30, 2025
Vol/Issue: 13
Pages: e20077
License: View

Authors

M

Megan C. Ferguson

Marine Mammal Laboratory, Alaska Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Seattle, WA, United States of America; Biodiversity Research Institute, Portland, ME, United States of America

P

Paul B. Conn

Marine Mammal Laboratory, Alaska Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Seattle, WA, United States of America

J

James T. Thorson

Resource Ecology and Fisheries Management, Alaska Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Seattle, WA, United States of America

Funding

National Oceanic and Atmospheric Administration and the Alaska Beluga Whale Committee

Cite This Article

Megan C. Ferguson, Paul B. Conn, James T. Thorson (2025). Spatially explicit models of density improve estimates of Eastern Bering Sea beluga (Delphinapterus leucas) abundance and distribution from line-transect surveys. PeerJ, 13, e20077. https://doi.org/10.7717/peerj.20077

Spatially explicit models of density improve estimates of Eastern Bering Sea beluga (Delphinapterus leucas) abundance and distribution from line-transect surveys

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