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We developed ‘movedesign’, a user‐friendly Shiny application, which can be utilized to investigate the precision of three estimates regularly reported in movement and spatial ecology studies: home range area, speed and distance travelled. Conceptually similar to statistical power analysis, this application enables users to assess the degree of estimate precision that may be achieved with a given sampling design; that is, the choices regarding data resolution (sampling interval) and battery life (sampling duration).

Leveraging the ‘ctmm’Rpackage, we utilize two methods proven to handle many common biases in animal movement datasets: autocorrelated kernel density estimators (AKDEs) and continuous‐time speed and distance (CTSD) estimators. Longer sampling durations are required to reliably estimate home range areas via the detection of a sufficient number of home range crossings. In contrast, speed and distance estimation requires a sampling interval short enough to ensure that a statistically significant signature of the animal's velocity remains in the data.

This application addresses key challenges faced by researchers when designing tracking studies, including the trade‐off between long battery life and high resolution of GPS locations collected by the devices, which may result in a compromise between reliably estimating home range or speed and distance. ‘movedesign’ has broad applications for researchers and decision‐makers, supporting them to focus efforts and resources in achieving the optimal sampling design strategy for their research questions, prioritizing the correct deployment decisions for insightful and reliable outputs, while understanding the trade‐off associated with these choices.

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 sizeNis decreased toN ≤ (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(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.

Here, we bridge this gap by introducing a method for describing the long‐term encounter location probabilities for movement within home ranges, termed the conditional distribution of encounters (CDE). We then derive this distribution, as well as confidence intervals, implement its statistical estimator into open‐source software and demonstrate the broad ecological relevance of this distribution.

We first use simulated data to show how our estimator provides asymptotically consistent estimates. We then demonstrate the general utility of this method for three simulation‐based scenarios that occur routinely in biological systems: (a) a population of individuals with home ranges that overlap with neighbours; (b) a pair of individuals with a hard territorial border between their home ranges; and (c) a predator with a large home range that encompassed the home ranges of multiple prey individuals. Using GPS data from white‐faced capuchinsCebus capucinus, tracked on Barro Colorado Island, Panama, and sleepy lizardsTiliqua rugosa,tracked in Bundey, South Australia, we then show how the CDE can be used to estimate the locations of territorial borders, identify key resources, quantify the potential for competitive or predatory interactions and/or identify any changes in behaviour that directly result from location‐specific encounter probability.

The CDE enables researchers to better understand the dynamics of populations of interacting individuals. Notably, the general estimation framework developed in this work builds straightforwardly off of home range estimation and requires no specialized data collection protocols. This method is now openly available via thectmm Rpackage.