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Appendix S1:
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Descriptive analysis of Florida panther movement
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Animal movement patterns can be characterized using descriptors such as
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step length and turning angle. These descriptors can vary between individuals of
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different age, sex, residency or reproductive status. Due to the tortuosity of
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animal trajectories, movement descriptors differ when locations are collected at
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different time intervals. Therefore, we limited our analyses to locations that were
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collected at hourly intervals. For the movement trajectory of each individual, the
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step lengths and turning angles between successive locations were calculated
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using the package adehabitatLT
(Calenge 2006)
in R 2.2.14
computing
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environment (R Development Core Team 2011). Because turning angles range
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from -180 to 180 on a continuous circular scale, arithmetic mean turning angles
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may not be meaningful. Therefore, we used the R package CircStats (Agostinelli
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& Lund 2009) to calculate the vectorized mean turning angle, which indicates the
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direction of the resultant vector when each observation is treated as a vector on
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the unit circle (Jammalamadaka & SenGupta 2001).
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The mean squared displacement (MSD) quantifies the average straight-
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line distance traveled within a certain time interval (Kareiva & Shigesada 1983;
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Codling, Plank & Benhamou 2008; Nouvellet, Bacon & Waxman 2009). MSD was
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calculated following the methods described by Nouvellet, Bacon & Waxman
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(2009), except that MSD was calculated for each individual separately as:
MSD(Dt) =
1 N-Dt
(x(tk+Dt ) - x(tk )) 2 + (y(tk+Dt ) - y(tk )) 2
å
N - Dt k=1
22
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where x and y are the UTM coordinates, N is the total number of locations for
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each individual, and Δt is the successive time interval with Δt = 1,2,3,…, T (T ≤
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150).
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Panther movement patterns may be affected by factors such as sex,
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residency status (territorial or dispersing) of males, and reproductive status of
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females. When a resident female gives birth, her movement patterns may change
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drastically because she needs to provide care for dependent kittens. Using
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observations of adult females and/or kittens from tracking aircraft and camera
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traps, we identified females that had no kittens, a female with kittens <8 weeks
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of age (likely still in the den), and a female with kittens >8 weeks of age
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(dependent but no longer in the den). Movement descriptors were compared
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between these three groups. We also used sex, age and MSD to distinguish
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dispersing males, whose movement is not constrained in space, from territorial
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males, who move within their territory
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To understand the pattern of panther movement over the diel period,
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movement descriptors were graphically compared for each hour of the day.
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Movement descriptors were also estimated during diurnal (0700 to 1559 hrs) and
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nocturnal (1600 to 0659 hrs) periods separately. These cut-off points were used
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because
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substantially after these hours. Finally, we tested for differences in movement
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descriptors between the wet (May 15 to Oct 14) and dry (Oct 15 to May 14)
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seasons.
movement
patterns
(step
lengths
and
turning
angles)
changed
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On average, the hourly step length of male and female panthers was
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297±44m and 166±48m, respectively. However, it varied substantially over the
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diel period, with both males and females being most active around 1900 to 0100
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hrs and least active around 1000 to 1500 hrs (Fig. S1a). The vectorized mean
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turning angles were 0.00080 and 0.00050 for males and females, respectively,
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indicating that panthers of both sexes turned left or right with approximately
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equal frequencies. Both male and female panthers were more active during the
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night, when their step lengths were longer (males: 384±59m; females:
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228±49m) and their turning angles were not uniform and averaged 0o (Rayleigh
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test of uniformity with alternative hypothesis mean direction =0; males:R=0.13,
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P<0.001; females:R=0.02, P<0.001). Panthers were less active during the day,
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characterized by shorter step lengths (males: 112±21m; females: 122±35m),
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and turning angles not significantly different from the uniform distribution
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(Rayleigh test of uniformity with alternative hypothesis mean direction =0;
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males:R=-0.19, P=1, females:R=-0.07, P=1).
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The MSD increased steadily and then reached an asymptote for most
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individuals, indicating that movement is generally constrained within home
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ranges. However, MSD increased faster, and asymptotes were generally higher,
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for males than for females, suggesting that males traveled faster and had larger
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home ranges than females (Fig. S1b).
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One female produced a litter during the time she was tracked, and we
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compared movement patterns of this female before and during denning, and
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when she was with dependent kittens. Her movement trajectory changed
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substantially when she denned and when she was accompanied by dependent
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kittens. Step lengths of this female were longest when she was without kittens,
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and shortest when she had dependent kittens (Fig. S1c:a). Likewise, her turning
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angles were larger when she had kittens than when she did not (Fig. S1c:b).
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Based on age, movement patterns and MSD, it was determined that one
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male, FP130, (aged 1.8 when fitted with GPS collars) was dispersing. During the
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day, this male had shorter step lengths (88±4m) than resident males (114±23m),
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but step lengths during the night (dispersing male: 543±10m; resident males:
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370±63m) were substantially longer for the dispersing male compared to resident
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males.
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Step lengths were generally shorter during the wet season compared to
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the dry season, but the difference varied depending on sex and time of the day
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(Fig. S1d).
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References:
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Agostinelli, C. & Lund, U. (2009) CircStats: Circular Statistics, from “Topics in
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circular Statistics” (2001). Version 0.2-4. http://cran.r-
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project.org/package=CircStats.
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Calenge, C. (2006) The package adehabitat for the R software: a tool for the
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analysis of space and habitat use by animals. Ecological Modelling, 197,
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516–519.
88
89
90
91
92
93
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Codling, E.A., Plank, M.J. & Benhamou, S. (2008) Random walk models in
biology. Journal of the Royal Society, Interface, 5, 813–34.
Jammalamadaka, S.R. & SenGupta, A. (2001) Topics in Circular Statistics. World
Scientific Press, Singapore.
Kareiva, P.M. & Shigesada, N. (1983) Analyzing insect movement as a correlated
random-walk. Oecologia, 56, 234–238.
Nouvellet, P., Bacon, J.P. & Waxman, D. (2009) Fundamental insights into the
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random movement of animals from a single distance-related statistic. The
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American Naturalist, 174, 506–14.
97
98
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R Development Core Team. (2011) R: A language and environment for statistical
computing. Version 3.0.2. http://www.r-project.org/.
FIGURES
Figure S1a. Average (± 95% CI) step length per hour for male (n=13; 32,468
locations) and female (n=5; 17,357 locations) Florida panthers during the diel
period.
Figure S1b. The mean squared displacement (MSD) over different time intervals
for the trajectory of each individual male (n=10; 32,316 locations) and female
(n=3; 17,164 locations) panther with sufficient hourly location data. Each line
represents MSD for an individual panther. MSDs for males increased faster
initially than MSDs of females, indicating faster movement. MSDs reaching an
asymptote indicates movement within a home range, and male MSDs reaching a
higher asymptote indicates larger home ranges for males compared to females.
b
Figure S1c. (a) Step length (mean ± 95% CI), and (b) turning angle distribution
for females without kittens (n=3 females; 12,935 locations), a female with
kittens <8 weeks of age (in den, n=1; 524 locations), and a female with
dependent kittens >8 weeks of age (dependent kitten, n=1; 71 locations).
Figure S1d. Average hourly step length (± 95% CI) for female and male Florida
panthers during the dry and wet seasons. Sample sizes for the dry season were:
13 males, 21,379 locations; 5 females, 11,607 locations. Sample sizes for the wet
season were: 9 males, 11,089 locations; 2 females, 5,750 locations.