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B. J. Worton developed statistical methods for estimating animal space use. A 1989 paper applied kernel density estimation to the utilization distribution, comparing fixed and adaptive kernels and choices of smoothing parameter.^[ref]

A location sample is a collection of points, while a utilization distribution describes how use varies across a region. Smoothing connects those descriptions, but the choice changes the resulting map. A very narrow kernel around each recorded location emphasizes isolated peaks; a broader kernel can merge nearby clusters. Neither choice creates additional observations.

The contribution matters because a home range outline alone cannot express every difference in intensity of use. Estimating a spatial probability density function makes those differences quantitative, while keeping assumptions about observation times and sampling visible. The methodological paper supplies a reusable estimator, not a guarantee that every recorded movement sample is independent or representative.

By B. J. Worton. Ecology 70(1), 164–168 (February 1989). DOI doi.org/10.2307/1938423

Original methodological paper, publisher abstract: nonparametric estimation from animal locations, fixed/adaptive kernels, and smoothing-parameter choice. Full-text equations were not inspected; article examples here are independent teaching models.

A utilization distribution is a probability distribution describing an animal's location during a specified period and sampling regime. When represented by a probability density function $u(x,y)$, it obeysThe probability assigned to a region is the integral of the density over that region. A home range boundary can summarize this pattern, but the utilization distribution also distinguishes frequently used patches from rarely visited ones.

Consider an invented animal that spends probability $0.8$ uniformly in a feeding patch of $1{\mathrm{km}}^2$ and probability $0.2$ uniformly in a disjoint resting patch of $4{\mathrm{km}}^2$. Their densities are $0.8{\mathrm{km}}^{-2}$ and $0.05{\mathrm{km}}^{-2}$, respectively. Multiplying each density by its patch area recovers $0.8+0.2=1$. The larger patch has lower total use as well as lower density: occupied area and intensity of use answer different questions.

B. J. Worton's 1989 methodological paper used kernel density estimation to estimate a utilization distribution from animal locations, comparing fixed and adaptive approaches and choices of smoothing parameter.^[ref] A contour containing $95\%$ of estimated probability is defined by an integral, not by taking $95\%$ of the maximum density. Unequal observation intervals and serial dependence between positions also matter when using animal radiotelemetry to infer space use.