Non-Markovian maximum likelihood estimation of autocorrelated movement processes

Methods in Ecology and Evolution

Volumn 5, Issue 5, 2014, Pages 462-472

  Fleming, Christen H ^a,b   Calabrese, Justin M ^a   Mueller, Thomas ^a,b   Olson, Kirk A ^a   Leimgruber, Peter ^a   Fagan, William F ^b  

^a SMITHSONIAN CONSERVATION BIOLOGY INSTITUTE   (United States)

^b University of Maryland   (United States)

Author keywords

Autocorrelation function; Characteristic scale; Home range; Irregular sampling; Mongolian gazelle; Movement ecology; Procapra gutturosa; Satellite collar movement data; Time series; Tracking data gaps

Indexed keywords

EID: 84900547819     PISSN: None     EISSN: 2041210X     Source Type: Journal    
DOI: 10.1111/2041-210X.12176     Document Type: Article

References (48)

1. Adelman, S.A. (1976) Fokker-Planck equations for simple non-Markovian systems. The Journal of Chemical Physics 64, 124-130.
2. Bailey, D.W., Gross, J.E., Laca, E.A., Rittenhouse, L.R., Coughenour, M.B., Swift, D.M. & Sims P.L. (1996) Mechanisms that result in large herbivore grazing distribution patterns. Journal of Range Management 49, 386-400.
3. Blackwell, P.G. (2003) Bayesian inference for Markov processes with diffusion and discrete components. Biometrika 90, 613-627.
4. Bovet, P. & Benhamou, S. (1988) Spatial analysis of animals' movements using a correlated random walk model. Journal of theoretical biology 131, 419-433.
5. Boyce, M.S., Pitt, J., Northrup, J.M., Morehouse, A.T., Knopff, K.H., Cristescu, B. & Stenhouse, G.B. (2010) Temporal autocorrelation functions for movement rates from global positioning system radiotelemetry data. Philosophical Transactions of the Royal Society B: Biological Sciences 365, 2213-2219.
6. Brillinger, D.R. & Stewart, B.S. (1998) Elephant-seal movements: modelling migration. Canadian Journal of Statistics 26, 431-443.
7. Calzetta, E., Roura, A. & Verdaguer, E. (2003) Stochastic description for open quantum systems. Physica A: Statistical Mechanics and its Applications 319, 188-212.
8. Codling, E.A. & Hill, N.A. (2005) Sampling rate effects on measurements of correlated and biased random walks. Journal of Theoretical Biology 233, 573-588.
9. Codling, E.A., Plank, M.J. & Benhamou, S. (2008) Random walk models in biology. Journal of the Royal Society Interface 5, 813-834.
10. Cover, T.M. & Thomas, J.A. (2006) Elements of Information Theory. Wiley Interscience, Hoboken, NJ.
11. Cressie, N. (1993) Statistics for Spatial Data, Revised edn. Wiley, New York.
12. Dembo, A. (1986) The relation between maximum likelihood estimation of structured covariance matrices and periodograms. Acoustics, Speech and Signal Processing, IEEE Transactions on 34, 1661-1662.
13. Dunn, J.E. & Gipson, P.S. (1977) Analysis of radio telemetry data in studies of home range. Biometrics 33, 85-101.
14. Fan, J. & Yao, Q. (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag, New York.
15. Fleming, C.H. & Calabrese, J.M. (2013) On the estimators of autocorrelation model parameters ArXiv:1301.4968 [stat.ME].
16. Fleming, C.H., Calabrese, J.M., Mueller, T., Olson, K.A., Leimgruber, P. & Fagan, W.F. (2013) Data from: From fine-scale foraging to home ranges: A semi-variance approach to identifying movement modes across spatiotemporal scales. Dryad Digital Repository. doi:10.5061/dryad.45157.
17. Fleming, C.H., Calabrese, J.M., Mueller, T., Olson, K.A., Leimgruber, P. & Fagan, W.F. (2014) From fine-scale foraging to home ranges: A semi-variance approach to identifying movement modes across spatiotemporal scales. The American Naturalist 183. doi:10.1086/675504.
18. Gardiner, C.W. (2009) Handbook of Stochastic Methods. Springer-Verlag, Berlin, Heidelberg, New York.
19. Gautestad, A.O. (2012) Animal space use: distinguishing a two-level superposition of scale-specific walks from scale-free Lévy walk. Oikos 122, 612-620.
20. Gurarie, E. & Ovaskainen, O. (2011) Characteristic spatial and temporal scales unify models of animal movement. The American Naturalist 178, 113-123.
21. Gurarie, E., Andrews, R.D. & Laidre, K.L. (2009) A novel method for identifying behavioural changes in animal movement data. Ecology Letters 12, 395-408.
22. Hillery, M., O'Connell, R.F., Scully M.O. & Wigner E.P. (1984) Distribution functions in physics: Fundamentals. Physics Reports 106, 121-167.
23. Horne, J.S., Garton, E.O. Krone, S.M. & Lewis, J.S. (2007) Analyzing animal movements using Brownian bridges. Ecology 88, 2354-2363.
24. Jiang, Z., Takatsuki, S., Li, J., Wang, W., Ma, J. & Gao, Z. (2002) Feeding type and seasonal digestive strategy of Mongolian gazelles in China. Journal of Mammalogy 83, 91-98.
25. 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, 1208-1215.
26. Jonsen, I.D., Flemming, J.M. & Myers, R.A. (2005) Robust state-space modeling of animal movement data. Ecology 86, 2874-2880.
27. Kareiva, P.M. & Shigesada, N. (1983) Analyzing insect movement as a correlated random walk. Oecologia 56, 234-238.
28. Krige, D.G. (1951) A statistical approach to some basis mine valuation problems on the Witwatersrand. Journal of the Chemical Metal and Mining Society of South Africa 52, 119-139.
29. Legendre, P. (1993) Spatial autocorrelation: trouble or new paradigm? Ecology 74, 1659-1673.
30. Lomb, N.R. (1976) Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 39, 447-462.
31. Marcotte, D. (1996) Fast variogram computation with FFT. Computers & Geosciences 22, 1175-1186.
32. Mardia, K.V. & Marshall, R.J. (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71, 135-146.
33. McClintock, B.T., King, R., Thomas, L., Matthiopoulos, J., McConnell, B.J. & Morales, J.M. (2012) A general discrete-time modeling framework for animal movement using multistate random walks. Ecological Monographs 82, 335-349.
34. Moorcroft, P.R. & Lewis, M.A. (2006) Mechanistic Home Range Analysis. Princeton University Press, Princeton, NJ.
35. Moorcroft, P.R., Lewis, M.A. & Crabtree, R.L. (2006) Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone. Proceedings of the Royal Society B: Biological Sciences 273, 1651-1659.
36. Morales, J.M., Haydon, D.T., Frair, J., Holsinger, K.E. & Fryxell, J.M. (2004) Extracting more out of relocation data: building movement models as mixtures of random walks. Ecology 85, 2436-2445.
37. Mueller, T., Olson, K.A., Dressler, G., Leimgruber, P., Fuller, T.K., Nicolśon, C. et al. (2011) How landscape dynamics link individual- to population-level movement patterns: A multispecies comparison of ungulate relocation data. Global Ecology and Biogeography 20, 683-694.
38. Nouvellet, P., Bacon, J. & Waxman, D. (2009) Fundamental insights into the random movement of animals from a single distance-related statistic. The American Naturalist 174, 506-514.
39. Olson, K.A., Fuller, T.K., Mueller, T., Murray, M.G., Nicolson, C., Odonkhuu, D., Bolortsetseg, S. & Schaller, G.B. (2010) Annual movements of Mongolian gazelles: Nomads in the eastern steppe. Journal of Arid Environments 74, 1435-1442.
40. Pawitan, Y. (2001) In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, Oxford.
41. Polansky, L., Wittemyer, G., Cross, P.C., Tambling, C.J. & Getz, W.M. (2010) From moonlight to movement and synchronized randomness: Fourier and wavelet analyses of animal location time series data. Ecology 91, 1506-1518.
42. Scargle, J.D. (1982) Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal 263, 835-853.
43. Southwood, T.R. (2000) Ecological Methods, 3rd edn. Wiley Blackwell, Hoboken, NJ.
44. Swihart, R.K., & Slade N.A. (1985) Testing for independence of observations in animal movements. Ecology 66, 1176-1184.
45. Turchin, P. (1998) Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants. Sinauer Associates, Sunderland, MA.
46. Ville, J. (1948) Théorie et applications de la notion de signal analytique. Câbles et Transmission 2, 61-74.
47. Whittle, P. (1953) Estimation and information in stationary time series. Arkiv for Matematik 2, 423-434.
48. Worton, B.J. (1989) Kernel methods for estimating the utilization distribution in home-range studies. Ecology 70, 164-168.