Sampling Animal Movement Paths Causes Turn Autocorrelation

Animal movement models allow ecologists to study processes that operate over a wide range of scales. In order to study them, continuous movements of animals are translated into discrete data points, and then modelled as discrete models. This discretization can bias the representation of the movement path. This paper shows that discretizing correlated random movement paths creates a biased path by creating correlations between successive turning angles. The discretization also biases statistical tests for correlated random walks (CRW) and causes an overestimate in distances travelled; a correction is given for these biases. This effect suggests that there is a natural scale to CRWs, but that distance-discretized CRWs are in a sense, scale invariant. Perhaps a new null model for continuous movement paths is needed. Authors need to be aware of the biases caused by discretizing correlated random walks, and deal with them appropriately.

[1]  Nicolas Schtickzelle,et al.  Quantitative analysis of changes in movement behaviour within and outside habitat in a specialist butterfly , 2007, BMC Evolutionary Biology.

[2]  Peter A. Burrough,et al.  Using fractal dimensions for characterizing tortuosity of animal trails , 1988 .

[3]  Simon Benhamou,et al.  An analysis of movements of the wood mouse Apodemus sylvaticus in its home range , 1991, Behavioural Processes.

[4]  S. Harris,et al.  Predicting oscillatory dynamics in the movement of territorial animals , 2012, Journal of The Royal Society Interface.

[5]  Juan M. Morales,et al.  EXTRACTING MORE OUT OF RELOCATION DATA: BUILDING MOVEMENT MODELS AS MIXTURES OF RANDOM WALKS , 2004 .

[6]  Stephen P. Rice,et al.  Flow‐ and substratum‐mediated movement by a stream insect , 2006 .

[7]  N. Haddad.  Corridor Length and Patch Colonization by a Butterfly, Junonia coenia , 2000 .

[8]  Peter Turchin,et al.  Quantifying insect movement in the field , 1991 .

[9]  M. Colyn,et al.  Efficiency of fluorescent powder tracking for studying use of space by small mammals in an African rainforest , 2007 .

[10]  Vilis O. Nams,et al.  Using animal movement paths to measure response to spatial scale , 2005, Oecologia.

[11]  Effect of fire on northern bettong (Bettongia tropica) foraging behaviour , 2001 .

[12]  Vilis O. Nams,et al.  Detecting oriented movement of animals , 2006, Animal Behaviour.

[13]  Chris J. Johnson,et al.  Movement parameters of ungulates and scale‐specific responses to the environment , 2002 .

[14]  C. McCulloch,et al.  Analyzing Discrete Movement Data as a Correlated Random Walk , 1989 .

[15]  Eliezer Gurarie,et al.  A novel method for identifying behavioural changes in animal movement data. , 2009, Ecology letters.

[16]  N. Haddad.  Corridor Use Predicted from Behaviors at Habitat Boundaries , 1999, The American Naturalist.

[17]  Devin S Johnson,et al.  Continuous-time correlated random walk model for animal telemetry data. , 2008, Ecology.

[18]  A. Hofgaard,et al.  Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights , 2002 .

[19]  Stephen P. Ellner,et al.  SCALING UP ANIMAL MOVEMENTS IN HETEROGENEOUS LANDSCAPES: THE IMPORTANCE OF BEHAVIOR , 2002 .

[20]  Lars Edenius,et al.  Field test of a GPS location system for moose Alces alces under Scandinavian boreal conditions , 1997, Wildlife Biology.

[21]  J. A. Schaefer,et al.  Caribou movement as a correlated random walk , 2000, Oecologia.

[22]  O. Mitesser,et al.  Host plant finding in the specialised leaf beetle Cassida canaliculata: an analysis of small‐scale movement behaviour , 2007 .

[23]  Peter Turchin,et al.  Fractal Analyses of Animal Movement: A Critique , 1996 .

[24]  H. Whitehead,et al.  Movements of sperm whales in the tropical Pacific , 2008 .

[25]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[26]  Helen Bailey,et al.  Quantitative analysis of bottlenose dolphin movement patterns and their relationship with foraging. , 2006, The Journal of animal ecology.

[27]  Bruce Page,et al.  SHORT-DURATION DAYTIME MOVEMENTS OF A COW HERD OF AFRICAN ELEPHANTS , 2007 .

[28]  Michael L. Cain,et al.  Random Search by Herbivorous Insects: A Simulation Model , 1985 .

[29]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[30]  P. Kareiva,et al.  Analyzing insect movement as a correlated random walk , 1983, Oecologia.

[31]  Timothy D. Reynolds,et al.  Time intervals for estimating pronghorn and coyote home ranges and daily movements , 1990 .

[32]  Bruce J. West,et al.  Lévy dynamics of enhanced diffusion: Application to turbulence. , 1987, Physical review letters.

[33]  E. McCoy,et al.  ALTERNATIVE FORAGING TACTICS OF JUVENILE GOPHER TORTOISES (GOPHERUS POLYPHEMUS) EXAMINED USING CORRELATED RANDOM WALK MODELS , 2007 .

[34]  Victoria J. Bakker,et al.  Gap‐Crossing Decisions by the Red Squirrel, a Forest‐Dependent Small Mammal , 2004 .

[35]  S. Benhamou.  How to reliably estimate the tortuosity of an animal's path: straightness, sinuosity, or fractal dimension? , 2004, Journal of theoretical biology.

[36]  Michael J Plank,et al.  Sampling rate and misidentification of Lévy and non-Lévy movement paths. , 2009, Ecology.

[37]  D. DeAngelis,et al.  Evaluating the effect of salinity on a simulated American crocodile (Crocodylus acutus) population with applications to conservation and Everglades restoration , 2004 .

[38]  N. Fisher,et al.  A correlation coefficient for circular data , 1983 .

[39]  Eliezer Gurarie,et al.  Characteristic Spatial and Temporal Scales Unify Models of Animal Movement , 2011, The American Naturalist.

[40]  J. Byers.  CORRELATED RANDOM WALK EQUATIONS OF ANIMAL DISPERSAL RESOLVED BY SIMULATION , 2001 .

[41]  P. Turchin.  Quantitative Analysis Of Movement , 1998 .

[42]  Deborah Austin,et al.  Intraspecific variation in movement patterns: modeling individual behaviour in a large marine predator , 2004 .

[43]  More on the meanderings of mangabeys: how to test whether bounded walks are random , 2000 .

[44]  Wolf M. Mooij,et al.  Search paths of swans foraging on spatially autocorrelated tubers , 2002 .

[45]  Nicolas Schtickzelle,et al.  Behavioural responses to habitat patch boundaries restrict dispersal and generate emigration-patch area relationships in fragmented landscapes. , 2003, The Journal of animal ecology.

[46]  Frederic Bartumeus,et al.  ANIMAL SEARCH STRATEGIES: A QUANTITATIVE RANDOM‐WALK ANALYSIS , 2005 .