Pollen Coupling of Forest Trees: Forming Synchronized and Periodic Reproduction out of Chaos

Many of the tree species in mature forests show masting; their reproductive activity has a large variance between years and is often synchronized between different individuals. In this paper, we analyse a globally coupled map model in which trees accumulate photosynthate every year, produce flowers when the energy reserve level exceeds a threshold, and set seeds and fruits at a rate limited by pollen availability. Without pollen limitation, the trees in the forest show independent chaotic fluctuation. Coupling of trees via pollen exchange results in reproduction being synchronized partially or completely over the forest. The whole forest shows diverse dynamical behaviors determined by the values of two essential parameters; the depletion coefficient k and the coupling strength β. We find perfectly synchronized periodic reproduction, synchronized reproduction with a chaotic time series, clustering phenomena, and chaotic reproduction of trees without synchronization over individuals. There are many parameter windows in which synchronized reproduction of trees shows a stable periodic fluctuation. For perfectly synchronized forests, we can calculate all the Lyapunov exponents analytically. They show that synchronized reproduction of all the trees in the forest can only occur when trees flower at low (but positive) levels in a significant fraction of years, resulting in small fruit sets due to outcrossed pollen limitation. This is consistent with the observation that the distinction between mast years and non-mast years is often not clear cut.