Estimating process‐based model parameters from species distribution data using the evolutionary algorithm CMA‐ES

Abstract

Abstract Two main types of species distribution models are used to project species range shifts in future climatic conditions: correlative and process‐based models. Although there is some continuity between these two types of models, they are fundamentally different in their hypotheses (statistical relationships vs. mechanistic relationships) and their calibration methods (SDMs tend to be occurrence data driven while PBMs tend to be prior driven). One of the limitations to the use of process‐based models is the difficulty to parameterize them for a large number of species compared to correlative SDMs. We investigated the feasibility of using an evolutionary algorithm (called covariance matrix adaptation evolution strategy, CMA‐ES) to calibrate process‐based models using species distribution data. This method is well established in some fields (robotics, aerodynamics, etc.), but has never been used, to our knowledge, in ecology, despite its ability to deal with very large space dimensions. Using tree species occurrence data across Europe, we adapted the CMA‐ES algorithm to find appropriate values of model parameters. We estimated simultaneously 27–77 parameters of two process‐based models simulating forest tree's ecophysiology for three species with varying range sizes and geographical distributions. CMA‐ES provided parameter estimates leading to better prediction of species distribution than parameter estimates based on expert knowledge. Our results also revealed that some model parameters and processes were strongly dependent, and different parameter combinations could therefore lead to high model accuracy. We conclude that CMA‐ES is an efficient state‐of‐the‐art method to calibrate process‐based models with a large number of parameters using species occurrence data. Inverse modelling using CMA‐ES is a powerful method to calibrate process‐based parameters which can hardly be measured. However, the method does not warranty that parameter estimates are correct because of several sources of bias, similarly to correlative models, and expert knowledge is required to validate results.

Keywords

• calibration
• CMA‐ES
• evolutionary algorithm
• process‐based model
• species distribution model
• trees