Measuring effects of linear obstacles on wildlife movements: accounting for the relationship between step length and crossing probability

Animal movements in the landscape are influenced by linear features such as rivers, roads and power lines. Prior studies have investigated how linear features, particularly roads, affect movement rates by comparing animal's movement rate measured as step lengths (i.e., the distance between consecutive observations such as GPS locations) before, during and after crossing of a linear feature. The null hypothesis has been that the length of crossing steps should not differ from other steps, and a deviation from this, mainly that steps are longer during crossing, has been taken as support for a disturbance effect of the linear feature. However, based on the simple relationship between the length of a step and its probability to cross a linear feature, we claim that this assumption is inappropriate to test for behavioural responses to linear features. The probability is related to the proportion of the total length of the trajectory (i.e., the path of movement) a step constitutes. Consequently, care should be taken when formulating hypotheses about how animal moves in relation to linear features in the landscape. Statistical tests should be set up with respect to the expected length based on the distribution of step lengths in the trajectory. We propose two methods that accounts for the bias in crossing frequency that is caused by step lengths, and illustrates their applications by using simulated animal trajectories as well as empirical data on reindeer in an area with a power line.