[Paper Review] A mechanistic-statistical species distribution model to explain and forecast wolf (Canis lupus) colonization in South-Eastern France

Julie Louvrier, Julien Papaïx+2 more|arXiv (Cornell University)|Dec 20, 2019

Wildlife Ecology and Conservation77 references20 citations

TL;DR

This study develops a mechanistic-statistical spatio-temporal model integrating ecological diffusion, logistic growth, and imperfect detection to explain and forecast wolf (Canis lupus) colonization in south-eastern France. Using partial differential equations and hierarchical Bayesian inference, the model accurately predicted wolf distribution in 2016 based on 2007–2015 data, demonstrating strong forecasting performance and robust parameter estimation under varying detection probabilities.

ABSTRACT

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.

Motivation & Objective

• To develop a mechanistic-statistical model that explicitly incorporates spatio-temporal dynamics such as dispersal and population growth in species distribution modeling.
• To account for imperfect detection and variable sampling effort in opportunistic presence-only data, common in large carnivore monitoring.
• To evaluate the model’s ability to estimate ecological parameters accurately under varying detection probabilities and survey site densities.
• To forecast future wolf distribution in France using estimated parameters from historical data.
• To provide a flexible, implementable framework in widely used Bayesian software (JAGS/OpenBUGS) for ecological forecasting.

Proposed method

• The model uses partial differential equations (PDEs) to represent ecological diffusion and logistic population growth across a fragmented landscape.
• A hierarchical Bayesian framework is employed to estimate model parameters while accounting for measurement error and uncertainty in detection.
• The observation process explicitly models imperfect detection, with detection probability varying by site and time based on survey effort.
• The model is calibrated using 2007–2015 wolf detection data from south-eastern France, with covariates including forest cover and human density.
• A simulation study evaluates parameter estimation bias and precision under different scenarios of detection probability and number of surveyed sites.
• Forecasting is performed probabilistically by projecting the PDE-based model forward in time, with uncertainty propagated through the Bayesian inference process.

Experimental results

Research questions

• RQ1 How well can a mechanistic-statistical model estimate ecological parameters such as diffusion rate, growth rate, and detection probability when detection is imperfect and data are presence-only?
• RQ2 To what extent does the model accurately forecast the future spatial distribution of a colonizing species like the wolf?
• RQ3 How do environmental factors such as forest cover and human density influence wolf dispersal and colonization dynamics in a fragmented landscape?
• RQ4 How does accounting for imperfect detection improve the reliability of species distribution forecasts compared to standard SDMs?
• RQ5 Can the model be effectively implemented in standard statistical software (e.g., JAGS, OpenBUGS) for practical ecological forecasting?

Key findings

• The model accurately estimated ecological parameters across a range of detection probabilities and survey site densities, with low bias and high precision in the simulation study.
• The wolf population growth rate in France was significantly explained by the proportion of forest cover, indicating its importance for population persistence.
• Diffusion rates were negatively influenced by human density, suggesting human activity acts as a barrier to wolf dispersal.
• Species detectability increased with higher survey effort, confirming the importance of standardized monitoring protocols.
• The model forecasted wolf distribution in 2016 with strong agreement to actual detections, correctly predicting 127 out of 137 occupied sites.
• The mechanistic model predicted more sites with high occupancy probability (>0.6) than a dynamic site-occupancy model, likely due to continuous spatio-temporal dynamics rather than discrete site-level transitions.