Home range

Last updated
Simple schema of four bird nests (in black), their defended territories (red), and their partly overlapping home ranges (green) Home range - simple schema.svg
Simple schema of four bird nests (in black), their defended territories (red), and their partly overlapping home ranges (green)

A home range is the area in which an animal lives and moves on a periodic basis. It is related to the concept of an animal's territory which is the area that is actively defended. The concept of a home range was introduced by W. H. Burt in 1943. He drew maps showing where the animal had been observed at different times. An associated concept is the utilization distribution which examines where the animal is likely to be at any given time. Data for mapping a home range used to be gathered by careful observation, but in more recent years, the animal is fitted with a transmission collar or similar GPS device.

Contents

The simplest way of measuring the home range is to construct the smallest possible convex polygon around the data but this tends to overestimate the range. The best known methods for constructing utilization distributions are the so-called bivariate Gaussian or normal distribution kernel density methods. More recently, nonparametric methods such as the Burgman and Fox's alpha-hull and Getz and Wilmers local convex hull have been used. Software is available for using both parametric and nonparametric kernel methods.

History

The concept of the home range can be traced back to a publication in 1943 by W. H. Burt, who constructed maps delineating the spatial extent or outside boundary of an animal's movement during the course of its everyday activities. [1] Associated with the concept of a home range is the concept of a utilization distribution, which takes the form of a two dimensional probability density function that represents the probability of finding an animal in a defined area within its home range. [2] [3] The home range of an individual animal is typically constructed from a set of location points that have been collected over a period of time, identifying the position in space of an individual at many points in time. Such data are now collected automatically using collars placed on individuals that transmit through satellites or using mobile cellphone technology and global positioning systems (GPS) technology, at regular intervals.

Methods of calculation

The simplest way to draw the boundaries of a home range from a set of location data is to construct the smallest possible convex polygon around the data. This approach is referred to as the minimum convex polygon (MCP) method which is still widely employed, [4] [5] [6] [7] but has many drawbacks including often overestimating the size of home ranges. [8]

The best known methods for constructing utilization distributions are the so-called bivariate Gaussian or normal distribution kernel density methods. [9] [10] [11] This group of methods is part of a more general group of parametric kernel methods that employ distributions other than the normal distribution as the kernel elements associated with each point in the set of location data.

Recently, the kernel approach to constructing utilization distributions was extended to include a number of nonparametric methods such as the Burgman and Fox's alpha-hull method [12] and Getz and Wilmers local convex hull (LoCoH) method. [13] This latter method has now been extended from a purely fixed-point LoCoH method to fixed radius and adaptive point/radius LoCoH methods. [14]

Although, currently, more software is available to implement parametric than nonparametric methods (because the latter approach is newer), the cited papers by Getz et al. demonstrate that LoCoH methods generally provide more accurate estimates of home range sizes and have better convergence properties as sample size increases than parametric kernel methods.

Home range estimation methods that have been developed since 2005 include:

Computer packages for using parametric and nonparametric kernel methods are available online. [21] [22] [23] [24] In the appendix of a 2017 JMIR article, the home ranges for over 150 different bird species in Manitoba are reported. [25]

See also

Related Research Articles

A histogram is a visual representation of the distribution of quantitative data. To construct a histogram, the first step is to "bin" the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) are adjacent and are typically of equal size.

The following outline is provided as an overview of and topical guide to statistics:

<span class="mw-page-title-main">Convex hull</span> Smallest convex set containing a given set

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset.

Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as is parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated.

<span class="mw-page-title-main">Density estimation</span> Estimate of an unobservable underlying probability density function

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population.

<span class="mw-page-title-main">Kernel density estimation</span> Estimator

In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy.

Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data. That is, no parametric equation is assumed for the relationship between predictors and dependent variable. Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the parameter estimates.

In statistics, semiparametric regression includes regression models that combine parametric and nonparametric models. They are often used in situations where the fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the regressors or the density of the errors is not known. Semiparametric regression models are a particular type of semiparametric modelling and, since semiparametric models contain a parametric component, they rely on parametric assumptions and may be misspecified and inconsistent, just like a fully parametric model.

Truncated regression models are a class of models in which the sample has been truncated for certain ranges of the dependent variable. That means observations with values in the dependent variable below or above certain thresholds are systematically excluded from the sample. Therefore, whole observations are missing, so that neither the dependent nor the independent variable is known. This is in contrast to censored regression models where only the value of the dependent variable is clustered at a lower threshold, an upper threshold, or both, while the value for independent variables is available.

Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals (e.g. a pack of wolves, a pride of lions, or herd of buffaloes), and for constructing a utilization distribution. The latter is a probability distribution that represents the probabilities of finding an animal within a given area of its home range at any point in time; or, more generally, at points in time for which the utilization distribution has been constructed. In particular, different utilization distributions can be constructed from data pertaining to particular periods of a diurnal or seasonal cycle.

In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy.

The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics.

In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y.

A utilization distribution is a probability distribution giving the probability density that an animal is found at a given point in space. It is estimated from data sampling the location of an individual or individuals in space over a period of time using, for example, telemetry or GPS based methods.

Mean shift is a non-parametric feature-space mathematical analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm. Application domains include cluster analysis in computer vision and image processing.

In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.

Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series. Kernel density estimators were first introduced in the scientific literature for univariate data in the 1950s and 1960s and subsequently have been widely adopted. It was soon recognised that analogous estimators for multivariate data would be an important addition to multivariate statistics. Based on research carried out in the 1990s and 2000s, multivariate kernel density estimation has reached a level of maturity comparable to its univariate counterparts.

<span class="mw-page-title-main">Yacine Aït-Sahalia</span> American economist

Yacine Aït-Sahalia is the Otto Hack 1903 Professor of Finance and Economics at Princeton University. His primary areas of research are financial econometrics and mathematical statistics. He served as the inaugural director of the Bendheim Center for Finance at Princeton University from 1998 until 2014.

Èlizbar Nadaraya is a Georgian mathematician who is currently a Full Professor and the Chair of the Theory of Probability and Mathematical Statistics at the Tbilisi State University. He developed the Nadaraya-Watson estimator along with Geoffrey Watson, which proposes estimating the conditional expectation of a random variable as a locally weighted average using a kernel as a weighting function.

References

  1. Burt, W. H. (1943). "Territoriality and home range concepts as applied to mammals". Journal of Mammalogy . 24 (3): 346–352. doi:10.2307/1374834. JSTOR   1374834.
  2. Jennrich, R. I.; Turner, F. B. (1969). "Measurement of non-circular home range". Journal of Theoretical Biology . 22 (2): 227–237. Bibcode:1969JThBi..22..227J. doi:10.1016/0022-5193(69)90002-2. PMID   5783911.
  3. Ford, R. G.; Krumme, D. W. (1979). "The analysis of space use patterns". Journal of Theoretical Biology . 76 (2): 125–157. Bibcode:1979JThBi..76..125F. doi:10.1016/0022-5193(79)90366-7. PMID   431092.
  4. Baker, J. (2001). "Population density and home range estimates for the Eastern Bristlebird at Jervis Bay, south-eastern Australia". Corella. 25: 62–67.
  5. Creel, S.; Creel, N. M. (2002). The African Wild Dog: Behavior, Ecology, and Conservation. Princeton, New Jersey: Princeton University Press. ISBN   978-0691016559.
  6. Meulman, E. P.; Klomp, N. I. (1999). "Is the home range of the heath mouse Pseudomys shortridgei an anomaly in the Pseudomys genus?". Victorian Naturalist. 116: 196–201.
  7. Rurik, L.; Macdonald, D. W. (2003). "Home range and habitat use of the kit fox (Vulpes macrotis) in a prairie dog (Cynomys ludovicianus) complex". Journal of Zoology. 259 (1): 1–5. doi:10.1017/S0952836902002959.
  8. Burgman, M. A.; Fox, J. C. (2003). "Bias in species range estimates from minimum convex polygons: implications for conservation and options for improved planning" (PDF). Animal Conservation. 6 (1): 19–28. Bibcode:2003AnCon...6...19B. doi:10.1017/S1367943003003044. S2CID   85736835.
  9. Silverman, B. W. (1986). Density estimation for statistics and data analysis . London: Chapman and Hall. ISBN   978-0412246203.
  10. Worton, B. J. (1989). "Kernel methods for estimating the utilization distribution in home-range studies". Ecology . 70 (1): 164–168. Bibcode:1989Ecol...70..164W. doi:10.2307/1938423. JSTOR   1938423.
  11. Seaman, D. E.; Powell, R. A. (1996). "An evaluation of the accuracy of kernel density estimators for home range analysis". Ecology. 77 (7): 2075–2085. Bibcode:1996Ecol...77.2075S. doi:10.2307/2265701. JSTOR   2265701.
  12. Burgman, M. A.; Fox, J. C. (2003). "Bias in species range estimates from minimum convex polygons: implications for conservation and options for improved planning" (PDF). Animal Conservation . 6 (1): 19–28. Bibcode:2003AnCon...6...19B. doi:10.1017/S1367943003003044. S2CID   85736835.
  13. Getz, W. M.; Wilmers, C. C. (2004). "A local nearest-neighbor convex-hull construction of home ranges and utilization distributions" (PDF). Ecography. 27 (4): 489–505. Bibcode:2004Ecogr..27..489G. doi:10.1111/j.0906-7590.2004.03835.x. S2CID   14592779.
  14. Getz, W. M; Fortmann-Roe, S.; Cross, P. C.; Lyonsa, A. J.; Ryan, S. J.; Wilmers, C. C. (2007). "LoCoH: nonparametric kernel methods for constructing home ranges and utilization distributions" (PDF). PLoS ONE . 2 (2): e207. Bibcode:2007PLoSO...2..207G. doi: 10.1371/journal.pone.0000207 . PMC   1797616 . PMID   17299587.
  15. Getz, W. M.; Wilmers, C. C. (2004). "A local nearest-neighbor convex-hull construction of home ranges and utilization distributions" (PDF). Ecography. 27 (4): 489–505. Bibcode:2004Ecogr..27..489G. doi:10.1111/j.0906-7590.2004.03835.x. S2CID   14592779.
  16. Horne, J. S.; Garton, E. O.; Krone, S. M.; Lewis, J. S. (2007). "Analyzing animal movements using Brownian Bridges". Ecology. 88 (9): 2354–2363. Bibcode:2007Ecol...88.2354H. doi:10.1890/06-0957.1. PMID   17918412. S2CID   15044567.
  17. Steiniger, S.; Hunter, A. J. S. (2012). "A scaled line-based kernel density estimator for the retrieval of utilization distributions and home ranges from GPS movement tracks". Ecological Informatics. 13: 1–8. doi:10.1016/j.ecoinf.2012.10.002.
  18. Downs, J. A.; Horner, M. W.; Tucker, A. D. (2011). "Time-geographic density estimation for home range analysis". Annals of GIS. 17 (3): 163–171. Bibcode:2011AnGIS..17..163D. doi: 10.1080/19475683.2011.602023 . S2CID   7891668.
  19. Long, J. A.; Nelson, T. A. (2012). "Time geography and wildlife home range delineation". Journal of Wildlife Management . 76 (2): 407–413. Bibcode:2012JWMan..76..407L. doi:10.1002/jwmg.259. hdl: 10023/5424 .
  20. Steiniger, S.; Hunter, A. J. S. (2012). "OpenJUMP HoRAE – A free GIS and Toolbox for Home-Range Analysis". Wildlife Society Bulletin. 36 (3): 600–608. Bibcode:2012WSBu...36..600S. doi:10.1002/wsb.168. (See also: OpenJUMP HoRAE - Home Range Analysis and Estimation Toolbox)
  21. LoCoH: Powerful algorithms for finding home ranges Archived 2006-09-12 at the Wayback Machine
  22. "AniMove – Animal movement methods". Archived from the original on 2007-01-04. Retrieved 2007-01-12.
  23. OpenJUMP HoRAE - Home Range Analysis and Estimation Toolbox (open source; methods: Point-Kernel, Line-Kernel, Brownian-Bridge, LoCoH, MCP, Line-Buffer)
  24. adehabitat for R (open source; methods: Point-Kernel, Line-Kernel, Brownian-Bridge, LoCoH, MCP, GeoEllipse)
  25. Nasrinpour, Hamid Reza; Reimer, Alex A.; Friesen, Marcia R.; McLeod, Robert D. (July 2017). "Data preparation for West Nile Virus agent-based modelling: protocol for processing bird population estimates and incorporating ArcMap in AnyLogic". JMIR Research Protocols. 6 (7): e138. doi: 10.2196/resprot.6213 . PMC   5537560 . PMID   28716770.