Using Fractal Analyses to Characterize Movement Paths of White-Tailed Deer and Response to Spatial Scale

Abstract It is often difficult to test hypotheses about how and why animal movement responds to environmental conditions, and at what spatial scales movement decisions are made, all of which are critical for sound management. We used fractal dimension (D) as a measure of tortuosity because it described animal movement patterns and was useful for testing hypotheses about effects of sex, home-range size, monthly rainfall, and reproductive phase on movement paths and for detecting changes in movement patterns of animals across a range of movement distances. We captured and fitted 33 (18 females and 15 males) white-tailed deer (Odocoileus virginianus) with global positioning system collars. We found that females moved more tortuously (D  =  1.75 ± 0.035 SE) than males (D  =  1.549 ± 0.025). These differences in movement were related to home-range size of females but not of males. Rainfall predicted D for females; thus, females may have been able to forage more intensively in a smaller area due to increased forage availability. Fractal D of females was greatest during the parturition period (1.468 ± 0.02), likely due to restricted movements in smaller areas or increased foraging. Home-range size of males was similar in spring and rut, but D was lower during rut, indicating that deer changed movement patterns within previously established home ranges. Movement patterns were similar at path lengths related to foraging patches and home ranges, whereas movement patterns changed as path length approximated the size of habitat patches.

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

[2]  T. J. Breen,et al.  Biostatistical Analysis (2nd ed.). , 1986 .

[3]  John G. Kie,et al.  LANDSCAPE HETEROGENEITY AT DIFFERING SCALES: EFFECTS ON SPATIAL DISTRIBUTION OF MULE DEER , 2002 .

[4]  K. Miller,et al.  Seasonal Ranges and Site Fidelity of Adult Male White-Tailed Deer (Odocoileus virginianus) in Southern Texas , 2008 .

[5]  John G. Kie,et al.  Habitat selection and survival of mule deer : Tradeoffs associated with migration , 1997 .

[6]  S. Stevenson.  Managing second-growth forests as caribou habitat , 1990 .

[7]  J. Bascompte,et al.  Fractals and search paths in mammals , 1997, Landscape Ecology.

[8]  S. Nusser,et al.  ANALYSIS OF PREDATOR MOVEMENT IN PRAIRIE LANDSCAPES WITH CONTRASTING GRASSLAND COMPOSITION , 2004 .

[9]  F. Messier,et al.  Fractal measures of female caribou movements , 2011 .

[10]  C. Bienz,et al.  Parturition Behavior and Territoriality in White-Tailed Deer: Impact on Neonatal Mortality , 1982 .

[11]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[12]  Vilis O. Nams,et al.  Fractal analysis measures habitat use at different spatial scales: an example with American marten , 2004 .

[13]  David R. Anderson,et al.  Model selection and inference : a practical information-theoretic approach , 2000 .

[14]  Benoit B. Mandelbrot,et al.  Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality , 1984 .

[15]  J. Kilgo,et al.  White-tailed deer , 2005 .

[16]  Douglas H. Johnson.  THE COMPARISON OF USAGE AND AVAILABILITY MEASUREMENTS FOR EVALUATING RESOURCE PREFERENCE , 1980 .

[17]  L. J. Verme.  Reproduction Studies on Penned White-Tailed Deer , 1965 .

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

[19]  R. Relyea,et al.  Home range of Desert Mule Deer : Testing the body-size and habitat-productivity hypotheses , 2000 .

[20]  N. J. Karberg,et al.  White-tailed deer (Odocoileus virginianus) fecal pellet decomposition is accelerated by the invasive earthworm Lumbricus terrestris , 2009, Biological Invasions.

[21]  Stephen L. Webb,et al.  Efficacy of a 15-Strand High-Tensile Electric Fence to Control White-tailed Deer Movements , 2009 .

[22]  David R. Anderson,et al.  Model Selection and Inference: A Practical Information-Theoretic Approach , 2001 .

[23]  Vilis O Nams,et al.  Improving Accuracy and Precision in Estimating Fractal Dimension of Animal movement paths , 2006, Acta biotheoretica.

[24]  J. Wiens,et al.  Interactions between landscape structure and animal behavior: the roles of heterogeneously distributed resources and food deprivation on movement patterns , 1999, Landscape Ecology.

[25]  A. Harestad,et al.  Home Range and Body Weight‐‐A Reevaluation , 1979 .

[26]  A. O. Haugen,et al.  Breeding records of whitetail deer in the Upper Peninsula of Michigan. , 1950 .

[27]  C. W. Severinghaus.  Tooth Development and Wear as Criteria of Age in White-Tailed Deer , 1949 .

[28]  D. Diefenbach,et al.  FOREST COVER INFLUENCES DISPERSAL DISTANCE OF WHITE-TAILED DEER , 2005 .

[29]  Veronica A. J. Doerr,et al.  FRACTAL ANALYSIS CAN EXPLAIN INDIVIDUAL VARIATION IN DISPERSAL SEARCH PATHS , 2004 .

[30]  Gino J. D'Angelo,et al.  Daily movements of female white-tailed deer relative to parturition and breeding. , 2005 .

[31]  Charles W. Ramsey,et al.  A Drop-Net Deer Trap , 1968 .

[32]  J. Wiens.  Spatial Scaling in Ecology , 1989 .

[33]  F. Golley.  Gestation Period, Breeding and Fawning Behavior of Columbian Black-Tailed Deer , 1957 .

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

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

[36]  B. McNab,et al.  Bioenergetics and the Determination of Home Range Size , 1963, The American Naturalist.

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

[38]  Steven R. Beissinger,et al.  Effects of parturition on home ranges and social affiliations of female white-tailed deer , 1996 .

[39]  Donald E. Spalinger,et al.  Foraging behavior of browsing ruminants in a heterogeneous landscape , 1998, Landscape Ecology.

[40]  L. K. Halls,et al.  White-tailed deer : ecology and management , 1985 .

[41]  John A. Wiens,et al.  Fractal patterns of insect movement in microlandscape mosaics , 1995 .

[42]  A. O. Haugen.  Breeding Records of Captive White-Tailed Deer in Alabama , 1959 .

[43]  Stephen L. Webb,et al.  Scale of Management for Mature Male White-Tailed Deer as Influenced by Home Range and Movements , 2007 .

[44]  R. Sikes,et al.  Guidelines of the American Society of Mammalogists for the Use of Wild Mammals in Research , 2007 .

[45]  Bruce T. Milne,et al.  Applications of Fractal Geometry in Wildlife Biology , 1997 .

[46]  Vilis O. Nams,et al.  The VFractal: a new estimator for fractal dimension of animal movement paths , 1996, Landscape Ecology.

[47]  B. Worton.  Kernel methods for estimating the utilization distribution in home-range studies , 1989 .

[48]  John A. Wiens,et al.  Animal movement in heterogeneous landscapes : an experiment with Eleodes beetles in shortgrass prairie , 1992 .

[49]  M. Kenward,et al.  Small sample inference for fixed effects from restricted maximum likelihood. , 1997, Biometrics.

[50]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .