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Animal movement models for multiple individuals

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Frances E. Buderman, Henry R. Scharf

Published Online: Mar 09 2020

DOI: 10.1002/wics.1506

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Abstract Statistical models for animal movement provide tools that help ecologists and biologists learn how animals interact with their environment and each other. Efforts to develop increasingly realistic, implementable, and scientifically valuable methods for analyzing remotely observed trajectories have provided practitioners with a wide selection of models to help them understand animal behavior. Increasingly, researchers are interested in studying multiple animals jointly, which requires methods that can account for dependence across individuals. Dependence can arise for many reasons, including shared behavioral tendencies, familial relationships, and direct interactions on the landscape. We provide a synopsis of recent statistical methods for animal movement data applicable to settings in which inference is desired across multiple individuals. Highlights of these approaches include the ability to infer shared behavioral traits across a group of individuals and the ability to infer unobserved social networks summarizing dynamic relationships that manifest themselves in movement decisions. This article is categorized under: Statistical Models > Bayesian Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Data: Types and Structure > Social Networks

Population‐level spatial quantities of residence time (a,b), speed (c,d), and tortuosity (e,f). For reference, county boundaries and major roads are shown for Colorado (a,c,e). Not included are rare movements to eastern states (Nebraska, Kansas, and Iowa) (Reprinted with permission from Buderman, Hooten, Ivan, and Shenk (). Copyright 2018 John Wiley & Sons Ltd; and refers to quantities related to Canada lynx movement)

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Points and lines in the bottom of the figure represent the effects of attraction (dashed line) and alignment (dotted line) between individual i and its “ego‐network” (polygons), defined as the collection all individuals that share a connection with i (Reprinted with permission from Scharf et al. (). Copyright 2016 Institute of Mathematical Statistics)

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Location uncertainty for five individual cranes over time indicated by the radius of the 95% credible circle for μ on the y‐axis. The dashed lines represent the uncertainty inferred from models fit independently to each individual, whereas the solid lines represent the uncertainty resulting from the migratory network model. Rug plots show observation times (Reprinted with permission from Hooten et al. (). Copyright 2018 John Wiley & Sons Ltd)

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Group movement paths. (a) Plotted paths of a shoal of 10 guppies from Bode et al. (). (b) Plotted paths of a simulated realization from the CTCRW model without interactions. (c) Plotted paths of a simulated realization from the DPPI model with the attraction‐repulsion point process interaction function (Reprinted with permission from Russell et al. (); Copyright 2016 Springer Nature)

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Selection of the 21 possible pairs of seven individuals in the killer whale study. The plots displayed are for all (inter‐type) pairs of killer whales that include the sole individual of type B1. The dotted line shows the proximity‐based network defined such that individuals are deemed connected whenever they are separated by a distance less than 10 km. The solid line in each plot shows the inferred probability of a social connection during the 1 week study period (i.e., Pr(A_ij(t) = 1)), and the gray region depicts uncertainty as one standard deviation above and below the probability computed using samples from the posterior distribution (Reprinted with permission from Scharf et al. (). Copyright 2016 Institute of Mathematical Statistics)

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Posterior means and 95% equi‐tailed credible intervals for the individual‐ (each named row) and population‐level (μ) effects of distance to nearest potential kill site on cougar motility. Population‐level effects represent the mean coefficient across all individuals (Reprinted with permission from Buderman, Hooten, Alldredge, et al. (). Copyright 2018 BioMed Central Ltd)

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References

Aarts,, G., Fieberg,, J., & Matthiopoulos,, J. (2012). Comparative interpretation of count, presence–absence and point methods for species distribution models. Methods in Ecology and Evolution, 3(1), 177–187.
Anderson‐Sprecher,, R. C., & Ledolter,, J. (1991). State‐space analysis of wildlife telemetry data. Journal of the American Statistical Association, 86(415), 596–602.
Avgar,, T., Potts,, J. R., Lewis,, M. A., & Boyce,, M. S. (2016). Integrated step selection analysis: Bridging the gap between resource selection and animal movement. Methods in Ecology and Evolution, 7(5), 619–630.
Bachl,, F. E., Lindgren,, F., Borchers,, D. L., & Illian,, J. B. (2019). inlabru: An R package for Bayesian spatial modelling from ecological survey data. Methods in Ecology and Evolution, 10, 760–766.
Barocas,, A., Hefner,, R., Ucko,, M., Merkle,, J. A., & Geffen,, E. (2018). Behavioral adaptations of a large carnivore to human activity in an extremely arid landscape. Animal Conservation, 21(5), 433–443.
Berdahl,, A. M., Biro,, D., Westley,, P. A., & Torney,, C. J. (2018). Collective movement ecology [special issue]. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1746), 2017004–2017017.
Berliner,, L. M. (1996). Hierarchical Bayesian time series models. In K. M. Hanson, & R. N. Silver, (Eds.), Maximum entropy and Bayesian methods (pp. 15–22). Netherlands: Springer.
Blackwell,, P. (1997). Random diffusion models for animal movement. Ecological Modelling, 100(1), 87–102.
Bode,, N. W. F., Franks,, D. W., Wood,, A. J., Piercy,, J. J. B., Croft,, D. P., & Codling,, E. A. (2012). Distinguishing social from nonsocial navigation in moving animal groups. The American Naturalist, 179(5), 621–632.
Boyce,, M. S., & McDonald,, L. L. (1999). Relating populations to habitats using resource selection functions. Trends in Ecology and Evolution, 14(7), 268–272.
Brennan,, A., Hanks,, E. M., Merkle,, J. A., Cole,, E. K., Dewey,, S. R., Courtemanch,, A. B., & Cross,, P. C. (2018). Examining speed versus selection in connectivity models using elk migration as an example. Landscape Ecology, 33(6), 955–968.
Brillinger,, D. R., Preisler,, H. K., & Wisdom,, M. J. (2011). Modelling particles moving in a potential field with pairwise interactions and an application. Brazilian Journal of Probability and Statistics, 25(3), 421–436.
Brillinger,, D. R., & Stewart,, B. S. (1998). Elephant‐seal movements: Modelling migration. Canadian Journal of Statistics, 26(3), 431–443.
Brost,, B. M., Hooten,, M. B., Hanks,, E. M., & Small,, R. J. (2015). Animal movement constraints improve resource selection inference in the presence of telemetry error. Ecology, 96(10), 2590–2597.
Buderman,, F. E., Hooten,, M. B., Alldredge,, M. W., Hanks,, E. M., & Ivan,, J. S. (2018). Time‐varying predatory behavior is primary predictor of fine‐scale movement of wildland‐urban cougars. Movement Ecology, 6(22), 1–16.
Buderman,, F. E., Hooten,, M. B., Ivan,, J. S., & Shenk,, T. M. (2016). A functional model for characterizing long‐distance movement behaviour. Methods in Ecology and Evolution, 7(3), 264–273.
Buderman,, F. E., Hooten,, M. B., Ivan,, J. S., & Shenk,, T. M. (2018). Large‐scale movement behavior in a reintroduced predator population. Ecography, 41(1), 126–139.
Calabrese,, J. M., Fleming,, C. H., Fagan,, W. F., Rimmler,, M., Kaczensky,, P., Bewick,, S., … Mueller,, T. (2018). Disentangling social interactions and environmental drivers in multi‐individual wildlife tracking data. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1746), 1–10.
Craiu,, R. V., Duchesne,, T., Fortin,, D., & Baillargeon,, S. (2011). Conditional logistic regression with longitudinal follow‐up and individual‐level random coefficients: A stable and efficient two‐step estimation method. Journal of Computational and Graphical Statistics, 20(3), 767–784.
Craiu,, R. V., Duchesne,, T., Fortin,, D., & Baillargeon,, S. (2016). Twostepclogit: Conditional logistic regression: A two‐step estimation method. (R package version 1.2.5).
Croft,, D. P., James,, R., & Krause,, J. (2008). Exploring animal social networks. Princeton, NJ: Princeton University Press.
DeMars,, C. A., & Boutin,, S. (2018). Nowhere to hide: Effects of linear features on predator–prey dynamics in a large mammal system. Journal of Animal Ecology, 87(1), 274–284.
Duchesne,, T., Fortin,, D., & Rivest,, L. P. (2015). Equivalence between step selection functions and biased correlated random walks for statistical inference on animal movement. PLoS One, 10(4), 1–12.
Dunn,, J. E., & Gipson,, P. S. (1977). Analysis of radio telemetry data in studies of home range. Biometrics, 33(1), 85–101.
Eckert,, S. A., Moore,, J. E., Dunn,, D. C., van Buiten,, R. S., Eckert,, K. L., & Halpin,, P. N. (2008). Modeling loggerhead turtle movement in the Mediterranean: Importance of body size and oceanography. Ecological Applications, 18(2), 290–308.
Fieberg,, J., Rieger,, R. H., Zicus,, M. C., & Schildcrout,, J. S. (2009). Regression modelling of correlated data in ecology: Subject‐specific and population averaged response patterns. Journal of Applied Ecology, 46(5), 1018–1025.
Fortin,, D., Beyer,, H. L., Boyce,, M. S., Smith,, D. W., Duchesne,, T., & Mao,, J. S. (2005). Wolves influence elk movements: Behavior shapes a trophic cascade in Yellowstone National Park. Ecology, 86(5), 1320–1330.
Frair,, J. L., Fieberg,, J., Hebblewhite,, M., Cagnacci,, F., DeCesare,, N. J., & Pedrotti,, L. (2010). Resolving issues of imprecise and habitat‐biased locations in ecological analyses using GPS telemetry data. Philosophical Transactions of the Royal Society B: Biological Sciences, 365(1550), 2187–2200.
Gelman,, A., Carlin,, J. B., Stern,, H. S., Dunson,, D. B., Vehtari,, A., & Rubin,, D. B. (2013). Bayesian data analysis. Boca Raton, FL: Chapman and Hall/CRC.
Goldenberg,, A., Zheng,, A. X., Fienberg,, S. E., & Airoldi,, E. M. (2010). A survey of statistical network models. Foundations and Trends® in Machine Learning, 2(2), 129–233.
Goldenberg,, S. Z., de Silva,, S., Rasmussen,, H. B., Douglas‐Hamilton,, I., & Wittemyer,, G. (2014). Controlling for behavioural state reveals social dynamics among male African elephants, Loxodonta africana. Animal Behaviour, 95, 111–119.
Hanks,, E. M., Hooten,, M. B., %26 Alldredge,, M. W. (2015). Continuous‐time discrete‐space models for animal movement. The Annals of Applied Statistics, 9(1), 145–165.
Hanks,, E. M., Hooten,, M. B., Johnson,, D. S., & Sterling,, J. T. (2011). Velocity‐based movement modeling for individual and population level inference. PLoS One, 6(8), e22795.
Hoff,, P. D., Raftery,, A. E., & Handcock,, M. S. (2002). Latent space approaches to social network analysis. Journal of the American Statistical Association, 97(460), 1090–1098.
Hooten,, M. B., Buderman,, F. E., Brost,, B. M., Hanks,, E. M., & Ivan,, J. S. (2016). Hierarchical animal movement models for population‐level inference. Environmetrics, 27(6), 322–333.
Hooten,, M. B., Johnson,, D. S., Hanks,, E. M., & Lowry,, J. H. (2010). Agent‐based inference for animal movement and selection. Journal of Agricultural, Biological and Environmental Statistics, 15(4), 523–538.
Hooten,, M. B., Johnson,, D. S., McClintock,, B. T., & Morales,, J. M. (2017). Animal movement: Statistical models for telemetry data. Boca Raton, FL: Chapman and Hall/CRC.
Hooten,, M. B., King,, R., & Langrock,, R. (2017). Animal movement modeling [special issue]. Journal of Agricultural, Biological, and Environmental Statistics, 22(3), 221–425.
Hooten,, M. B., Scharf,, H. R., Hefley,, T. J., Pearse,, A. T., & Weegman,, M. D. (2018). Animal movement models for migratory individuals and groups. Methods in Ecology and Evolution, 9(7), 1692–1705.
Horne,, J. S., Garton,, E. O., Krone,, S. M., & Lewis,, J. S. (2007). Analyzing animal movements using brownian bridges. Ecology, 88(9), 2354–2363.
Hurford,, A. (2009). GPS measurement error gives rise to spurious 180 turning angles and strong directional biases in animal movement data. PLoS One, 4(5), e5632.
Johnson,, D. S., London,, J. M., Lea,, M.‐A., & Durban,, J. W. (2008). Continuous‐time correlated random walk model for animal telemetry data. Ecology, 89(5), 1208–1215.
Jonsen,, I. D. (2016). Joint estimation over multiple individuals improves behavioural state inference from animal movement data. Scientific Reports, 6, 20625.
Jonsen,, I. D., Flemming,, J. M., & Myers,, R. A. (2005). Robust state‐space modeling of animal movement data. Ecology, 86(11), 2874–2880.
Jonsen,, I. D., Myers,, R. A., & James,, M. C. (2006). Robust hierarchical state‐space models reveal Diel variation in travel rates of migrating leatherback turtles. Journal of Animal Ecology, 75(5), 1046–1057.
Kays,, R., Crofoot,, M. C., Jetz,, W., & Wikelski,, M. (2015). Terrestrial animal tracking as an eye on life and planet. Science, 348(6240), aaa2478.
Kohl,, M. T., Stahler,, D. R., Metz,, M. C., Forester,, J. D., Kauffman,, M. J., Varley,, N., … MacNulty,, D. R. (2018). Diel predator activity drives a dynamic landscape of fear. Ecological Monographs, 88(4), 638–652.
Langrock,, R., Hopcraft,, J. G. C., Blackwell,, P. G., Goodall,, V., King,, R., Niu,, M., … Schick,, R. S. (2014). Modelling group dynamic animal movement. Methods in Ecology and Evolution, 5(2), 190–199.
Langrock,, R., King,, R., Matthiopoulos,, J., Thomas,, L., Fortin,, D., & Morales,, J. M. (2012). Flexible and practical modeling of animal telemetry data: Hidden Markov models and extensions. Ecology, 93(11), 2336–2342.
Leos‐Barajas,, V., Gangloff,, E. J., Adam,, T., Langrock,, R., Van Beest,, F. M., Nabe‐Nielsen,, J., & Morales,, J. M. (2017). Multi‐scale modeling of animal movement and general behavior data using hidden Markov models with hierarchical structures. Journal of Agricultural, Biological and Environmental Statistics, 22(3), 232–248.
Long,, J. A., Nelson,, T. A., Webb,, S. L., & Gee,, K. L. (2014). A critical examination of indices of dynamic interaction for wildlife telemetry studies. Journal of Animal Ecology, 83(5), 1216–1233.
Lunn,, D., Barrett,, J., Sweeting,, M., & Thompson,, S. (2013). Fully Bayesian hierarchical modelling in two stages, with application to meta‐analysis. Journal of the Royal Statistical Society: Series C (Applied Statistics), 62(4), 551–572.
Manly,, B. F. J., McDonald,, L. L., & Thomas,, D. D. L. (2002). Resource selection by animals: Statistical design and analysis for field studies (2nd ed.). Dordrecht, Netherlands: Kluwer Academic Publishers.
McClintock,, B. T. (2017). Incorporating telemetry error into hidden Markov models of animal movement using multiple imputation. Journal of Agricultural, Biological and Environmental Statistics, 22(3), 249–269.
McClintock,, B. T., & Michelot,, T. (2018). momentuHMM: R package for generalized hidden Markov models of animal movement. Methods in Ecology and Evolution, 9(6), 1518–1530.
McClintock,, B. T., Russell,, D. J., Matthiopoulos,, J., & King,, R. (2013). Combining individual animal movement and ancillary biotelemetry data to investigate population‐level activity budgets. Ecology, 94(4), 838–849.
McKellar,, A. E., Langrock,, R., Walters,, J. R., & Kesler,, D. C. (2014). Using mixed hidden markov models to examine behavioral states in a cooperatively breeding bird. Behavioral Ecology, 26(1), 148–157.
Michelot,, T., Langrock,, R., Bestley,, S., Jonsen,, I. D., Photopoulou,, T., & Patterson,, T. A. (2017). Estimation and simulation of foraging trips in land‐based marine predators. Ecology, 98(7), 1932–1944.
Michelot,, T., Langrock,, R., & Patterson,, T. A. (2016). moveHMM: An R package for the statistical modelling of animal movement data using hidden Markov models. Methods in Ecology and Evolution, 7(11), 1308–1315.
Morales,, J. M., Haydon,, D. T., Frair,, J. J. L. J., Holsinger,, K. E., & Fryxell,, J. M. (2004). Extracting more out of relocation data: Building movement models as mixtures of random walks. Ecology, 85(9), 2436–2445.
Muff,, S., Signer,, J., & Fieberg,, J. (2019). Accounting for individual‐specific variation in habitat‐selection studies: Efficient estimation of mixed‐effects models using Bayesian or frequentist computation. Journal of Animal Ecology, 89(1), 80–92.
NIMBLE Development Team. (2019). Nimble: Mcmc, particle filtering, and programmable hierarchical modeling. (R package version 0.9.0).
Niu,, M., Blackwell,, P. G., & Skarin,, A. (2016). Modeling interdependent animal movement in continuous time. Biometrics, 72(2), 315–324.
Noonan,, M. J., Fleming,, C. H., Akre,, T. S., Drescher‐Lehman,, J., Gurarie,, E., Harrison,, A.‐L., … Calabrese,, J. M. (2019). Scale‐insensitive estimation of speed and distance traveled from animal tracking data. Movement Ecology, 7(1), 1–15.
Northrup,, J. M., Rivers,, J. W., Yang,, Z., & Betts,, M. G. (2019). Synergistic effects of climate and land‐use change influence broad‐scale avian population declines. Global Change Biology, 25(5), 1561–1575.
Plummer,, M. (2018). rjags: Bayesian graphical models using MCMC [Computer software manual]. (R package version 4‐8).
Prokopenko,, C. M., Boyce,, M. S., & Avgar,, T. (2017). Characterizing wildlife behavioural responses to roads using integrated step selection analysis. Journal of Applied Ecology, 54(2), 470–479.
Raynor,, E. J., Beyer,, H. L., Briggs,, J. M., & Joern,, A. (2017). Complex variation in habitat selection strategies among individuals driven by extrinsic factors. Ecology and Evolution, 7(6), 1802–1822.
Russell,, J. C., Hanks,, E. M., & Haran,, M. (2016). Dynamic models of animal movement with spatial point process interactions. Journal of Agricultural, Biological, and Environmental Statistics, 21(1), 22–40.
Sawyer,, H., Kauffman,, M. J., Nielson,, R. M., & Horne,, J. S. (2009). Identifying and prioritizing ungulate migration routes for landscape‐level conservation. Ecological Applications, 19(8), 2016–2025.
Scharf,, H. R., Hooten,, M. B., Fosdick,, B. K., Johnson,, D. S., London,, J. M., & Durban,, J. W. (2016). Dynamic social networks based on movement. Annals of Applied Statistics, 10(4), 2182–2202.
Scharf,, H. R., Hooten,, M. B., & Johnson,, D. S. (2017). Imputation approaches for animal movement modeling. Journal of Agricultural, Biological, and Environmental Statistics, 22(3), 335–352.
Scharf,, H. R., Hooten,, M. B., Johnson,, D. S., & Durban,, J. W. (2018). Process convolution approaches for modeling interacting trajectories. Environmetrics, 29(3), e2487.
Scrafford,, M. A., Avgar,, T., Heeres,, R., & Boyce,, M. S. (2018). Roads elicit negative movement and habitat‐selection responses by wolverines (Gulo gulo luscus). Behavioral Ecology, 29(3), 534–542.
Signer,, J., Fieberg,, J., & Avgar,, T. (2019). Animal movement tools (amt): R package for managing tracking data and conducting habitat selection analyses. Ecology and Evolution, 9, 880–890.
Smith,, J. A., Donadio,, E., Pauli,, J. N., Sheriff,, M. J., & Middleton,, A. D. (2019). Integrating temporal refugia into landscapes of fear: Prey exploit predator downtimes to forage in risky places. Oecologia, 189(4), 883–890.
Stan Development Team. (2019). RStan: The R interface to Stan. (R package version 2.19.2).
Tremblay,, Y., Robinson,, P. W., & Costa,, D. P. (2009). A parsimonious approach to modeling animal movement data. PLoS One, 4(3), e4711.
Turchin,, P. (1998). Quantitative analysis of movement: Measuring and modeling population redistribution in animals and plants. Sunderland, MA: Sinauer Associates.
Warton,, D. I., & Shepherd,, L. C. (2010). Poisson point process models solve the “pseudo‐absence problem” for presence‐only data in ecology. Annals of Applied Statistics, 4(3), 1383–1402.

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