  The two dominant approaches for the analysis of species-habitat associations
in animals have been shown to reach divergent conclusions. Models fitted from
the viewpoint of an individual (step selection functions), once scaled up, do
not agree with models fitted from a population viewpoint (resource selection
functions). We explain this fundamental incompatibility, and propose a solution
by introducing to the animal movement field a novel use for the well-known
family of Markov chain Monte Carlo (MCMC) algorithms. By design, the step
selection rules of MCMC lead to a steady-state distribution that coincides with
a given underlying function: the target distribution. We therefore propose an
analogy between the movements of an animal and the movements of a MCMC sampler,
to guarantee convergence of the step selection rules to the parameters
underlying the population's utilisation distribution. We introduce a
rejection-free MCMC algorithm, the local Gibbs sampler, that better resembles
real animal movement, and discuss the wide range of biological assumptions that
it can accommodate. We illustrate our method with simulations on a known
utilisation distribution, and show theoretically and empirically that locations
simulated from the local Gibbs sampler give rise to the correct resource
selection function. Using simulated data, we demonstrate how this framework can
be used to estimate resource selection and movement parameters.
