  A theory is provided for the estimation of home ranges of animals from the
standard mark-recapture technique in which data are collected by capturing,
tagging and recapturing the animals. The theoretical tool used is the
Fokker-Planck equation, its characteristic quantities being the diffusion
constant which describes the motion of the animals, and the attractive
potential which addresses their tendency to live near their burrows. The
measurement technique is shown to correspond to the calculation of a certain
kind of mean square displacement of the animals relevant to the specific
probing window in space corresponding to the trapping region. The output of the
theory is a sigmoid curve of the observable mean square displacement as a
function of the ratio of distances characteristic of the home range and the
trapping region, along with an explicit prescription to extract the home range
form observations. Applications of the theory to rodent movement in Panama and
New Mexico are pointed out. An analysis is given of the sensitivity of our
theory to the choice of the confining potential via the use of various
representative cases. A comparison is provided between home range size inferred
from our method and from other procedures employed in the literature.
Consequences of home range overlap are also discussed.
