Statistical inference for home range overlap

Winner, Kevin; Noonan, Michael; Fleming, Christen H.; Olson, Kirk A.; Mueller, Thomas; Sheldon, Daniel; Calabrese, Justin M.

doi:10.1111/2041-210x.13027

Cited by 89 publications

(134 citation statements)

References 40 publications

(141 reference statements)

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“…We then used the Battacharryya distance (BD; Bhattacharyya , Winner et al. ) as a measure of dissimilarity between the normal distributions corresponding to the fitted movement models from

T_{1}

and

T_{2}

, and asked if the CIs on this distance contained 0 (for full details see Appendix ), where the BD can be expressed in terms of the arithmetic and geometric means of the covariance matrices (AM and GM respectively)

AM = \frac{{boldσ}_{1} + {boldσ}_{2}}{2}, GM = \sqrt{{boldσ}_{1} {boldσ}_{2}}

and the Mahalanobis distance (MD; Mahalanobis )

MD = \sqrt{{({boldμ}_{1} - {boldμ}_{2})}^{normalT} {AM}^{- 1} false(μ_{1} - μ_{2} false)} .

such that

BD = \frac{1}{8} {MD}^{2} + \frac{1}{2} tr log (\frac{AM}{GM}) .

…”

Section: Methodsmentioning

confidence: 99%

“…Movement models for each subset half were fit using the methods described above, which provided estimates of the mean, l, and covariance, r, parameters of the models' distributions. We then used the Battacharryya distance (BD; Bhattacharyya 1946, Winner et al 2018 as a measure of dissimilarity between the normal distributions corresponding to the fitted movement models from T 1 and T 2 , and asked if the CIs on this distance contained 0 (for full details see Appendix S1), where the BD can be expressed in terms of the arithmetic and geometric means of the covariance matrices (AM and GM respectively)…”

Section: Estimator Evaluationmentioning

confidence: 99%

See 1 more Smart Citation

A comprehensive analysis of autocorrelation and bias in home range estimation

Noonan

Tucker

Fleming

et al. 2019

Ecological Monographs

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157

231

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Home range estimation is routine practice in ecological research. While advances in animal tracking technology have increased our capacity to collect data to support home range analysis, these same advances have also resulted in increasingly autocorrelated data. Consequently, the question of which home range estimator to use on modern, highly autocorrelated tracking data remains open. This question is particularly relevant given that most estimators assume independently sampled data. Here, we provide a comprehensive evaluation of the effects of autocorrelation on home range estimation. We base our study on an extensive data set of GPS locations from 369 individuals representing 27 species distributed across five continents. We first assemble a broad array of home range estimators, including Kernel Density Estimation (KDE) with four bandwidth optimizers (Gaussian reference function, autocorrelated‐Gaussian reference function [AKDE], Silverman's rule of thumb, and least squares cross‐validation), Minimum Convex Polygon, and Local Convex Hull methods. Notably, all of these estimators except AKDE assume independent and identically distributed (IID) data. We then employ half‐sample cross‐validation to objectively quantify estimator performance, and the recently introduced effective sample size for home range area estimation (normalNfalse^area) to quantify the information content of each data set. We found that AKDE 95% area estimates were larger than conventional IID‐based estimates by a mean factor of 2. The median number of cross‐validated locations included in the hold‐out sets by AKDE 95% (or 50%) estimates was 95.3% (or 50.1%), confirming the larger AKDE ranges were appropriately selective at the specified quantile. Conversely, conventional estimates exhibited negative bias that increased with decreasing normalNfalse^area. To contextualize our empirical results, we performed a detailed simulation study to tease apart how sampling frequency, sampling duration, and the focal animal's movement conspire to affect range estimates. Paralleling our empirical results, the simulation study demonstrated that AKDE was generally more accurate than conventional methods, particularly for small normalNfalse^area. While 72% of the 369 empirical data sets had >1,000 total observations, only 4% had an normalNfalse^area >1,000, where 30% had an normalNfalse^area <30. In this frequently encountered scenario of small normalNfalse^area, AKDE was the only estimator capable of producing an accurate home range estimate on autocorrelated data.

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“…We then used the Battacharryya distance (BD; Bhattacharyya , Winner et al. ) as a measure of dissimilarity between the normal distributions corresponding to the fitted movement models from

T_{1}

and

T_{2}

AM = \frac{{boldσ}_{1} + {boldσ}_{2}}{2}, GM = \sqrt{{boldσ}_{1} {boldσ}_{2}}

and the Mahalanobis distance (MD; Mahalanobis )

MD = \sqrt{{({boldμ}_{1} - {boldμ}_{2})}^{normalT} {AM}^{- 1} false(μ_{1} - μ_{2} false)} .

such that

BD = \frac{1}{8} {MD}^{2} + \frac{1}{2} tr log (\frac{AM}{GM}) .

…”

Section: Methodsmentioning

confidence: 99%

Section: Estimator Evaluationmentioning

confidence: 99%

A comprehensive analysis of autocorrelation and bias in home range estimation

Noonan

Tucker

Fleming

et al. 2019

Ecological Monographs

Self Cite

157

231

View full text Add to dashboard Cite

show abstract

“…Finally, in the local-perception limit (q = 0), the mean encounter rate can be written in terms of the overlap between each individual's home range, measured either through the Bhattacharyya coefficient (BC) (Fieberg and Kochanny, 2005;Winner et al, 2018) or through the scalar product of both individual-position PDFs, f 1 · f 2 . f 1 and f 2 are, respectively, the PDFs for the position of the predator and the prey, and the scalar product, denoted by the symbol ·, is defined as the spatial integral of the product of both PDFs.…”

Section: Ornstein-uhlenbeckmentioning

confidence: 99%

How range residency and long-range perception change encounter rates

Martínez-García

Fleming

Seppelt

et al. 2019

Preprint

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AbstractEncounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can systematically bias encounter rate predictions.

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“…To identify the transition between exploration and home range establishment for each oryx, we used the Bhattacharyya coefficient, a metric initially derived to measure similarity among probability distributions (Bhattacharyya, 1943). This metric is proportional to areal overlap among distributions, does not depend on ad hoc parameters (such as isopleths), displays consistency across large sample sizes, and incorporates a correction for small sample sizes (Winner et al, 2018). We calculated Bhattacharyya coefficients and recorded confidence intervals for all pairwise comparisons of AKDE home ranges for each individual.…”

Section: Exploratory Movements and Home Range Establishmentmentioning

confidence: 99%

“…We calculated Bhattacharyya coefficients and recorded confidence intervals for all pairwise comparisons of AKDE home ranges for each individual. When the confidence interval of the Bhattacharya coefficient does not overlap 1, AKDE home range estimates may be considered significantly different (Winner et al, 2018). Thus, we use the time after release at which the Bhattacharya confidence interval for the entire and subsampled trajectory no longer overlaps 1 to determine when exploratory movements were satisfactorily excluded.…”

Section: Exploratory Movements and Home Range Establishmentmentioning

confidence: 99%

Management Background and Release Conditions Structure Post-release Movements in Reintroduced Ungulates

et al. 2019

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One of the greatest challenges in restoring species to the wild is insufficient knowledge about their habitat requirements and movement ecology. This is especially true for wide-ranging species such as the scimitar-horned oryx (Oryx dammah). Once widespread across Sahelo-Saharan grasslands, oryx were declared Extinct in the Wild in 1999. Here, we integrate GPS/satellite tracking, remote sensing, and movement analyses to assess how reintroduced oryx respond to wild conditions. We monitored two groups of oryx, reared under different captive management regimes and released in different seasons, for 12 months after release. Our study provides the first movement trajectories and home range estimates for this species. We expected oryx movements after release to represent trade-offs between risky, energetically expensive exploration and resource exploitation. Oryx raised under semi-free ranging conditions and released during the wet season ("ranging") exhibited this pattern of exploration followed by home range establishment. In contrast, oryx raised in small pens and released during the dry season ("penned") explored far less novel terrain. Ranging oryx exhibited seasonal shifts in activity and movement timing, while penned oryx simply reduced overall movement and continuously accessed supplemental food and water. Sahelian ecosystems exhibit strong seasonal cycles and extensive spatial variation. In this highly variable environment, reintroduced oryx will need to disperse from the release site to acquire adequate forage throughout the year. Thus, we experimentally varied acclimation period, and expected dispersal to decrease with acclimation period length. Post-release dispersal ranged from 2 to 90 km: ranging oryx acclimated for ca. 6 months moved 40-60 km from the release site, while penned oryx acclimated for ca. 1 month remained within 5-25 km. Our results demonstrate that captive management and environmental conditions at release strongly influence the extent to which reintroduced oryx disperse and adapt to wild conditions. We also show that-in contrast to previous studies-longer acclimation periods do not necessarily lead to site fidelity. Finally, our findings demonstrate the importance of tracking a large proportion of reintroduced individuals to (1) accurately record post-release behaviors and vital rates, and (2) adaptively evaluate pre-and post-release management actions to improve conservation outcomes.

show abstract

Statistical inference for home range overlap

Cited by 89 publications

References 40 publications

A comprehensive analysis of autocorrelation and bias in home range estimation

A comprehensive analysis of autocorrelation and bias in home range estimation

How range residency and long-range perception change encounter rates

Management Background and Release Conditions Structure Post-release Movements in Reintroduced Ungulates

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