The influence of climate on biodiversity is an important ecological question. Various theories try to link climate change to allelic richness and therefore to predict the impact of global warming on genetic diversity. We model the relationship between genetic diversity in the European beech forests and curves of temperature and precipitation reconstructed from pollen databases. Our model links the genetic measure to the climate curves through a linear functional regression. The interaction in climate variables is assumed to be bilinear. Since the data are georeferenced, our methodology accounts for the spatial dependence among the observations. The practical issues of these extensions are discussed.