  Species distribution models (SDMs) are important statistical tools for
ecologists to understand and predict species range. However, standard SDMs do
not explicitly incorporate dynamic processes like dispersal. This limitation
may lead to bias in inference about species distribution. Here, we adopt the
theory of ecological diffusion that has recently been introduced in statistical
ecology to incorporate spatio-temporal processes in ecological models. As a
case study, we considered the wolf (Canis lupus) that has been recolonizing
Eastern France naturally through dispersal from the Apennines since the early
90's. Using partial differential equations for modelling species diffusion and
growth in a fragmented landscape, we develop a mechanistic-statistical
spatio-temporal model accounting for ecological diffusion, logistic growth and
imperfect species detection. We conduct a simulation study and show the ability
of our model to i) estimate ecological parameters in various situations with
contrasted species detection probability and number of surveyed sites and ii)
forecast the distribution into the future. We found that the growth rate of the
wolf population in France was explained by the proportion of forest cover, that
diffusion was influenced by human density and that species detectability
increased with increasing survey effort. Using the parameters estimated from
the 2007-2015 period, we then forecasted wolf distribution in 2016 and found
good agreement with the actual detections made that year. Our approach may be
useful for managing species that interact with human activities to anticipate
potential conflicts.
