Bayesian model averaging of climate-dependent forest models using Expectation–Maximization

Abstract

In the context of rapid climate change, climate-dependent models are essential for assessing species vulnerability. However, variation in model structure and divergence in their predictions introduce substantial uncertainty. Rather than selecting a single “best” model, a more robust strategy is to integrate predictions across models. Bayesian model averaging with Expectation–Maximization (BEM) provides an alternative to simple model averaging (SMA) and weighted model averaging (WMA) for combining ensemble predictions. To date, BEM has been rarely applied to tree species distribution models. We developed a BEM framework for models predicting either species occurrence or proxy variables linked to occurrence. The approach was applied to European beech (Fagus sylvatica) in France, using an ensemble of six models: four species distribution models, one model predicting the probability of hydraulic failure, and one model predicting juvenile productivity. In contrast to SMA and WMA, which assigned similar weights across models, BEM concentrated 85% of the weight on two models. Furthermore, BEM enabled spatially explicit decomposition of model weights, allowing us to identify regions where predictions diverged most strongly. The resulting probability maps revealed a specific zone in environmental space where model agreement on beech occurrence was particularly limited. Focusing on this zone may help refine projections and shed light on the ecological mechanisms that enable local persistence.