Fitting models predicting dates of flowering of temperate‐zone trees using simulated annealing

The aim of the present study was to test the four commonly used models to predict the dates of flowering of temperate‐zone trees, the spring warming, sequential, parallel and alternating models. Previous studies concerning the performance of these models have shown that they were unable to make accurate predictions based on external data. One of the reasons for such inaccuracy may be wrong estimations of the parameters of each model due to the non‐convergence of the optimization algorithm towards their maximum likelihood. We proposed to fit these four models using a simulated annealing method which is known to avoid local extrema of any kind of function, and thus is particularly well adapted to fit budburst models, as their likelihood function presents many local maxima. We tested this method using a phenological dataset deduced from aeropalynological data. Annual pollen spectra were used to estimate the dates of flowering of the populations around the sampling station. The results show that simulated annealing provides a better fit than traditional methods. Despite this improvement, classical models still failed to predict external data. We expect the simulated annealing method to allow reliable comparisons among models, leading to a selection of biologically relevant ones.