= Utilization distribution
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 obeys
$$
u(x,y)\geq0,\qquad \iint u(x,y)\,dx\,dy=1.
$$
The 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>.<Kernel Methods for Estimating the Utilization Distribution in Home-Range Studies by B. J. Worton>[Abstract; fixed/adaptive kernel estimates from sampled locations]{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.
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