'You shall not pass!': quantifying barrier permeability and proximity avoidance by animals.

Impediments to animal movement are ubiquitous and vary widely in both scale and permeability. It is essential to understand how impediments alter ecological dynamics via their influence on animal behavioural strategies governing space use and, for anthropogenic features such as roads and fences, how to mitigate these effects to effectively manage species and landscapes. Here, we focused primarily on barriers to movement, which we define as features that cannot be circumnavigated but may be crossed. Responses to barriers will be influenced by the movement capabilities of the animal, its proximity to the barriers, and habitat preference. We developed a mechanistic modelling framework for simultaneously quantifying the permeability and proximity effects of barriers on habitat preference and movement. We used simulations based on our model to demonstrate how parameters on movement, habitat preference and barrier permeability can be estimated statistically. We then applied the model to a case study of road effects on wild mountain reindeer summer movements. This framework provided unbiased and precise parameter estimates across a range of strengths of preferences and barrier permeabilities. The quality of permeability estimates, however, was correlated with the number of times the barrier is crossed and the number of locations in proximity to barriers. In the case study we found that reindeer avoided areas near roads and that roads are semi-permeable barriers to movement. There was strong avoidance of roads extending up to c. 1 km for four of five animals, and having to cross roads reduced the probability of movement by 68·6% (range 3·5-99·5%). Human infrastructure has embedded within it the idea of networks: nodes connected by linear features such as roads, rail tracks, pipelines, fences and cables, many of which divide the landscape and limit animal movement. The unintended but potentially profound consequences of infrastructure on animals remain poorly understood. The rigorous framework for simultaneously quantifying movement, habitat preference and barrier permeability developed here begins to address this knowledge gap.