Data from: Overcoming the challenge of small effective sample sizes in home-range estimation

Technological advances have steadily increased the detail of animal
tracking datasets, yet fundamental data limitations exist for many species
that cause substantial biases in home‐range estimation. Specifically, the
effective sample size of a range estimate is proportional to the number of
observed range crossings, not the number of sampled locations. Currently,
the most accurate home‐range estimators condition on an autocorrelation
model, for which the standard estimation frame‐works are based on
likelihood functions, even though these methods are known to underestimate
variance—and therefore ranging area—when effective sample sizes are small.
Residual maximum likelihood (REML) is a widely used method for reducing
bias in maximum‐likelihood (ML) variance estimation at small sample sizes.
Unfortunately, we find that REML is too unstable for practical application
to continuous‐time movement models. When the effective sample size N is
decreased to N ≤
urn:x-wiley:2041210X:media:mee313270:mee313270-math-0001(10), which is
common in tracking applications, REML undergoes a sudden divergence in
variance estimation. To avoid this issue, while retaining REML’s
first‐order bias correction, we derive a family of estimators that
leverage REML to make a perturbative correction to ML. We also derive AIC
values for REML and our estimators, including cases where model structures
differ, which is not generally understood to be possible. Using both
simulated data and GPS data from lowland tapir (Tapirus terrestris), we
show how our perturbative estimators are more accurate than traditional ML
and REML methods. Specifically, when
urn:x-wiley:2041210X:media:mee313270:mee313270-math-0002(5) home‐range
crossings are observed, REML is unreliable by orders of magnitude, ML home
ranges are ~30% underestimated, and our perturbative estimators yield home
ranges that are only ~10% underestimated. A parametric bootstrap can then
reduce the ML and perturbative home‐range underestimation to ~10% and ~3%,
respectively. Home‐range estimation is one of the primary reasons for
collecting animal tracking data, and small effective sample sizes are a
more common problem than is currently realized. The methods introduced
here allow for more accurate movement‐model and home‐range estimation at
small effective sample sizes, and thus fill an important role for animal
movement analysis. Given REML’s widespread use, our methods may also be
useful in other contexts where effective sample sizes are small.