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 modeling 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.

物种分布模型（SDM）是生态学家了解和预测物种范围的重要统计工具。但是，标准SDM并未明确包含诸如分散之类的动态过程。此限制可能导致在推断物种分布时出现偏差。在这里，我们采用统计生态学中最近引入的生态扩散理论，将时空过程纳入生态模型。作为案例研究，我们考虑了狼（Canis lupus）自90年代初以来就一直通过从亚平宁山脉撤离而自然地重新定居了法国东部。使用偏微分方程对一个零散的景观中的物种扩散和生长进行建模，我们开发了一种机械-统计的时空模型，该模型考虑了生态扩散，逻辑生长和不完善的物种检​​测。我们进行了仿真研究，并证明了我们的模型具有以下能力：i）估计各种情况下的生态参数，并具有相反的物种检测概率和被调查地点的数量，以及ii）预测未来的分布。我们发现，法国狼群的增长率可以由森林覆盖率解释，扩散受到人类密度的影响，物种的可检测性随着调查工作的增加而增加。使用从2007年至2015年期间估算的参数，我们随后预测了2016年的狼分布，并发现与当年的实际发现有很好的一致性。我们的方法对于管理与人类活动相互作用的物种以预期潜在的冲突可能有用。