Spatially limited pollen exchange and a long-range synchronization of trees

Many trees in mature forests show intermittent reproduction. Intensive flowering and seed production occur only once in several years, often synchronized over a long distance. In a previous paper, we showed that the limitation of fruit production by the outcross pollen availability can bring about synchronized reproduction of trees in a constant environment, assuming that pollen availability depends on the mean flowering intensity of the trees. However, pollen exchange normally occurs within a distance much shorter than the extent of the whole forest. We studied a coupled map lattice, in which each tree engages in the chaotic dynamics of energy reserve level, but different trees are coupled by pollen exchange with neighbors. We first derived a relation between two statistics of spatial covariance (dynamic spatial covariance and snapshot spatial covariance). A strong synchronization of tree reproduction can develop over the whole forest that may be orders of magnitude larger than the distance of direct pollen exchange between trees. The fluctuation is close to a cycle with a period of two years. The model of local coupling always generates non-uniform spatial patterns, but the enhanced spatial covariance caused by the spatial heterogeneity is restricted to a short range, only a few times larger than the spatial range of direct interaction. When pollen exchange occurs beyond the nearest neighbors, the local spatial pattern becomes proportionally larger, but the condition for synchronization of the whole forest and its magnitude are the same as for the case with the nearest neighbor pollen exchange. When a fraction of the seeds are sired by globally dispersed pollen and the rest are sired by local pollen, long-range synchronization can occur for a wide-parameter region, and trees may engage in a fluctuation with a masting interval longer than two years. We discuss alternative explanations for the long-range synchronization of beech forests.