Uncovering hidden states in African lion movement data using hidden Markov models
Victoria L. Goodall A B F , Sam M. Ferreira C , Paul J. Funston D and Nkabeng Maruping-Mzileni EA Department of Statistics, Nelson Mandela University, PO Box 77000, Port Elizabeth 6031, South Africa.
B Centre for African Conservation Ecology, Zoology Department, Nelson Mandela University, PO Box 77000, Port Elizabeth 6031, South Africa.
C Scientific Services, SANParks, Private Bag X402, Skukuza 1350, South Africa.
D Panthera, 8th West 40th Street, New York, USA.
E Scientific Services Kimberley, SANParks, PO Box 110040, Kimberley 8306, South Africa.
F Corresponding author. Email: victoriagoodall@gmail.com
Wildlife Research 46(4) 296-303 https://doi.org/10.1071/WR18004
Submitted: 12 January 2018 Accepted: 18 February 2019 Published: 3 May 2019
Abstract
Context: Direct observations of animals are the most reliable way to define their behavioural characteristics; however, to obtain these observations is costly and often logistically challenging. GPS tracking allows finer-scale interpretation of animal responses by measuring movement patterns; however, the true behaviour of the animal during the period of observation is seldom known.
Aims: The aim of our research was to draw behavioural inferences for a lioness with a hidden Markov model and to validate the predicted latent-state sequence with field observations of the lion pride.
Methods: We used hidden Markov models to model the movement of a lioness in the Kruger National Park, South Africa. A three-state log-normal model was selected as the most suitable model. The model outputs are related to collected data by using an observational model, such as, for example, a distribution for the average movement rate and/or direction of movement that depends on the underlying model states that are taken to represent behavioural states of the animal. These inferred behavioural states are validated against direct observation of the pride’s behaviour.
Key results: Average movement rate provided a useful alternative for the application of hidden Markov models to irregularly spaced GPS locations. The movement model predicted resting as the dominant activity throughout the day, with a peak in the afternoon. The local-movement state occurred consistently throughout the day, with a decreased proportion during the afternoon, when more resting takes place, and an increase towards the early evening. The relocating state had three peaks, namely, during mid-morning, early evening and about midnight. Because of the differences in timing of the direct observations and the GPS locations, we had to compare point observations of the true behaviour with an interval prediction of the modelled behavioural state. In 75% of the cases, the model-predicted behaviour and the field-observed behaviour overlapped.
Conclusions: Our data suggest that the hidden Markov modelling approach is successful at predicting a realistic behaviour of lions on the basis of the GPS location coordinates and the average movement rate between locations. The present study provided a unique opportunity to uncover the hidden states and compare the true behaviour with the inferred behaviour from the predicted state sequence.
Implications: Our results illustrated the potential of using hidden Markov models with movement rate as an input to understand carnivore behavioural patterns that could inform conservation management practices.
Additional keywords: behaviour, Panthera leo, state validation.
References
Beukes, M., Radloff, F. G. T., and Ferreira, S. M. (2017). Estimating lion’s prey species profile in an arid environment. Journal of Zoology 303, 136–144.| Estimating lion’s prey species profile in an arid environment.Crossref | GoogleScholarGoogle Scholar |
Beyer, H. L., Morales, J. M., Murray, D., and Fortin, M. J. (2013). The effectiveness of Bayesian state–space models for estimating behavioural states frommovement paths. Methods in Ecology and Evolution 4, 433–441.
| The effectiveness of Bayesian state–space models for estimating behavioural states frommovement paths.Crossref | GoogleScholarGoogle Scholar |
Bissett, C., and Bernard, R. T. F. (2007). Habitat selection and feeding ecology of the cheetah (Acinonyx jubatus) in thicket vegetation: is the cheetah a savanna specialist? Journal of Zoology 271, 310–317.
Buchholz, R. (2007). Behavioural biology: an effective and relevant conservation tool. Trends in Ecology & Evolution 22, 401–407.
| Behavioural biology: an effective and relevant conservation tool.Crossref | GoogleScholarGoogle Scholar |
Cagnacci, F., Boitani, L., Powell, R. A., and Boyce, M. S. (2010). Animal ecology meets GPS-based radiotelemetry: a perfect storm of opportunities and challenges. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 365, 2157–2162.
| Animal ecology meets GPS-based radiotelemetry: a perfect storm of opportunities and challenges.Crossref | GoogleScholarGoogle Scholar | 20566493PubMed |
Caro, T. (1999). The behaviour–conservation interface. Trends in Ecology & Evolution 14, 366–369.
| The behaviour–conservation interface.Crossref | GoogleScholarGoogle Scholar |
Di Orio, A. P., Callas, R., and Schaefer, R. J. (2003). Performance of two GPS telemetry collars under different habitat conditions. Wildlife Society Bulletin 31, 372–379.
Estes, R. D. (1992) ‘Behavior Guide to African Mammals.’ (The University of California Press: Berkeley, CA.)
Ferreira, S. M., and Funston, P. J. (2010). Estimating lion population variables: prey and disease effects in Kruger National Park, South Africa. Wildlife Research 37, 194–206.
| Estimating lion population variables: prey and disease effects in Kruger National Park, South Africa.Crossref | GoogleScholarGoogle Scholar |
Forester, J. D., Ives, A. R., Turner, M. G., Anderson, D. P., Fortin, D., Beyer, H. L., Smith, D. W., and Boyce, M. S. (2007). State-space models link elk movement patterns to landscape characteristics in Yellowstone National Park. Ecological Monographs 77, 285–299.
| State-space models link elk movement patterns to landscape characteristics in Yellowstone National Park.Crossref | GoogleScholarGoogle Scholar |
Franke, A., Caelli, T., and Hudson, R. J. (2004). Analysis of movements and behaviour of caribou (Rangifer tarandus) using hidden Markov models. Ecological Modelling 173, 259–270.
| Analysis of movements and behaviour of caribou (Rangifer tarandus) using hidden Markov models.Crossref | GoogleScholarGoogle Scholar |
Franke, A., Caelli, T., Kuzyk, G., and Hudson, R. J. (2006). Prediction of wolf (Canis lupus) kill-sites using hidden Markov models. Ecological Modelling 197, 237–246.
| Prediction of wolf (Canis lupus) kill-sites using hidden Markov models.Crossref | GoogleScholarGoogle Scholar |
Funston, P. J., Mills, M. G. L., Biggs, H. C., and Richardson, P. R. K. (1998). Hunting by male lions: ecological influences and socioecological implications. Animal Behaviour 56, 1333–1345.
| Hunting by male lions: ecological influences and socioecological implications.Crossref | GoogleScholarGoogle Scholar | 9933529PubMed |
Funston, P. J., Mills, M. G. L., and Biggs, H. C. (2001). Factors affecting the hunting success of male and female lions in the Kruger National Park. Journal of Zoology 253, 419–431.
| Factors affecting the hunting success of male and female lions in the Kruger National Park.Crossref | GoogleScholarGoogle Scholar |
Gertenbach, W. P. D. (1983). Landscapes of the Kruger National Park. Koedoe 26, 9–121.
| Landscapes of the Kruger National Park.Crossref | GoogleScholarGoogle Scholar |
Goodall, V. L., Fatti, L. P., and Owen-Smith, N. (2017). Animal movement modelling: independent or dependent models? South African Statistical Journal 51, 295–315.
Langrock, R., King, R., Matthiolpoulos, J., Thomas, L., Fortin, D., and Morales, J. M. (2012). Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions. Ecology 93, 2336–2342.
| Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions.Crossref | GoogleScholarGoogle Scholar | 23236905PubMed |
Langrock, R., Hopcraft, J. G. C., Blackwell, P. G., Goodall, V. L., King, R., Niu, M., Patterson, T. A., Pedersen, M. W., Skarin, A., and Schick, R. S. (2014). Modelling group dynamic animal movement. Methods in Ecology and Evolution 5, 190–199.
| Modelling group dynamic animal movement.Crossref | GoogleScholarGoogle Scholar |
Leroux, B. G., and Puterman, M. L. (1992). Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 48, 545–558.
| Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models.Crossref | GoogleScholarGoogle Scholar | 1637977PubMed |
MacDonald, I. L., and Raubenheimer, D. (1995). Hidden Markov models and animal behaviour. Biometrical Journal. Biometrische Zeitschrift 37, 701–712.
| Hidden Markov models and animal behaviour.Crossref | GoogleScholarGoogle Scholar |
McLachlan, G., and Peel, D. (2000) ‘Finite Mixture Models.’ (John Wiley & Sons: New York.)
Michel, A. L., Bengis, R. G., Keet, D. F., Hofmeyr, M., de Klerk, L. M., Cross, P. C., Jolles, A. E., Cooper, D., Whyte, I. J., Buss, P., and Godfroid, J. (2006). Wildlife tuberculosis in South African conservation areas: Implications and challenges. Veterinary Microbiology 112, 91–100.
| Wildlife tuberculosis in South African conservation areas: Implications and challenges.Crossref | GoogleScholarGoogle Scholar | 16343819PubMed |
Michelot, T., Langrock, R., and 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, 1308–1315.
| moveHMM: an R package for the statistical modelling of animal movement data using hidden Markov models.Crossref | GoogleScholarGoogle Scholar |
Ogutu, J. O., and Dublin, H. T. (2004). Spatial dynamics of lions and their prey along an environmental gradient. African Journal of Ecology 42, 8–22.
| Spatial dynamics of lions and their prey along an environmental gradient.Crossref | GoogleScholarGoogle Scholar |
Ogutu, J. O., Bhola, N., and Reid, R. (2005). The effects of pastoralism and protection on the density and distribution of carnivores and their prey in the Mara ecosystem of Kenya. Journal of Zoology 265, 281–293.
| The effects of pastoralism and protection on the density and distribution of carnivores and their prey in the Mara ecosystem of Kenya.Crossref | GoogleScholarGoogle Scholar |
Owen-Smith, N., and Goodall, V. (2014). Coping with savanna seasonality: comparative daily activity patterns of African ungulates as revealed by GPS telemetry. Journal of Zoology 293, 181–191.
| Coping with savanna seasonality: comparative daily activity patterns of African ungulates as revealed by GPS telemetry.Crossref | GoogleScholarGoogle Scholar |
Owen-Smith, N., and Mills, M. G. L. (2006). Manifold interactive influences on the population dynamics of multispecies ungulate assemblage. Ecological Monographs 76, 73–92.
| Manifold interactive influences on the population dynamics of multispecies ungulate assemblage.Crossref | GoogleScholarGoogle Scholar |
Owen-Smith, N., Fryxell, J., and Merrill, E. H. (2010). Foraging theory upscaled: the behavioural ecology of herbivore movement. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 365, 2267–2278.
| Foraging theory upscaled: the behavioural ecology of herbivore movement.Crossref | GoogleScholarGoogle Scholar | 20566503PubMed |
Owen-Smith, N., Goodall, V. L., and Fatti, L. P. (2012). Applying mixture models to derive activity states of large herbivores from movement rates obtained using GPS telemetry. Wildlife Research 39, 452–462.
| Applying mixture models to derive activity states of large herbivores from movement rates obtained using GPS telemetry.Crossref | GoogleScholarGoogle Scholar |
Packer, C., and Pusey, A. E. (1997). Divided we fall: cooperation among Lions. Scientific American 276, 52–59.
| Divided we fall: cooperation among Lions.Crossref | GoogleScholarGoogle Scholar |
Packer, C., Hilborn, R., Mosser, A., Kissui, B., Borner, M., Hopcraft, G., Wilmshurst, J., Mduma, S., and Sinclair, A. R. (2005). Ecological change, group territoriality, and population dynamics in Serengeti lions. Science 307, 390–393.
| Ecological change, group territoriality, and population dynamics in Serengeti lions.Crossref | GoogleScholarGoogle Scholar | 15662005PubMed |
Patterson, T. A., Basson, M., Bravington, M. V., and Gunn, J. S. (2009). Classifying movement behaviour in relation to environmental conditions using hidden Markov models. Journal of Animal Ecology 78, 1113–1123.
| Classifying movement behaviour in relation to environmental conditions using hidden Markov models.Crossref | GoogleScholarGoogle Scholar | 19563470PubMed |
Pedersen, M. W., Righton, D., Thygesen, U. H., Andersen, K. H., and Madsen, H. (2008). Geolocation of North Sea cod (Gadus morhua) using hidden Markov models and behavioural switching. Canadian Journal of Fisheries and Aquatic Sciences 65, 2367–2377.
| Geolocation of North Sea cod (Gadus morhua) using hidden Markov models and behavioural switching.Crossref | GoogleScholarGoogle Scholar |
R Core Team (2016). ‘R: a Language and Environment for Statistical Computing.’ (R Foundation for Statistical Computing: Vienna, Austria.)
Roughgarden, J., Running, S. W., and Matson, P. A. (1991). What does remote sensing do for ecology? Ecology 72, 1918–1922.
| What does remote sensing do for ecology?Crossref | GoogleScholarGoogle Scholar |
Schaller, G. B. (1972) ‘The Serengeti Lion.’ (University of Chicago Press: Chicago, IL.)
Schick, R. S., Loarie, S. R., Colchero, F., Best, B. D., Boustany, A., Conde, D. A., Halpin, P. N., Joppa, L. N., McClellen, C. M., and Clark, J. S. (2008). Understanding movement data and movement processes: current and emerging directions. Ecology Letters 11, 1338–1350.
| Understanding movement data and movement processes: current and emerging directions.Crossref | GoogleScholarGoogle Scholar | 19046362PubMed |
Tambling, C. J., Cameron, E. Z., du Toit, J. T., and Getz, W. M. (2010). Methods for locating African lion kills using global positioning system movement data. The Journal of Wildlife Management 74, 549–556.
| Methods for locating African lion kills using global positioning system movement data.Crossref | GoogleScholarGoogle Scholar |
Tambling, C. J., Laurence, S. D., Bellan, S. E., Cameron, E. Z., du Toit, J. T., and Getz, W. M. (2011). Estimating carnivoran diets using a combination of carcass observations and scats from GPS clusters. Journal of Zoology 286, 102–109.
| Estimating carnivoran diets using a combination of carcass observations and scats from GPS clusters.Crossref | GoogleScholarGoogle Scholar |
Valeix, M., Chamaille´-Jammes, S., Loveridge, A. J., Davidson, Z., Hunt, J. E., Madzikanda, H., and Macdonald, D. W. (2011). Understanding patch departure rules for large carnivores: lion movements support a patch-disturbance hypothesis. American Naturalist 178, 269–275.
| Understanding patch departure rules for large carnivores: lion movements support a patch-disturbance hypothesis.Crossref | GoogleScholarGoogle Scholar | 21750389PubMed |
van Niekerk, B. (2018). ‘Application of Hidden Markov Models and their Extensions to Animal Movement Data.’ (Nelson Mandela University: Port Elizabeth, South Africa.)
Viterbi, A. (1967). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory 13, 260–269.
| Error bounds for convolutional codes and an asymptotically optimum decoding algorithm.Crossref | GoogleScholarGoogle Scholar |
Walton, L. R., Cluff, H. D., Paquet, P. C., and Ramsay, M. A. (2001). Performance of 2 models of satellite collars for wolves. Wildlife Society Bulletin 29, 180–186.
Zucchini, W., and MacDonald, I. L. (2009). ‘Hidden Markov Models for Time Series: An Introduction Using R.’ (Chapman & Hall/CRC: Boca Raton, FL.)
