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 betw een 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 t rees 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 behav iors determined by the values of two essential parameters; the depletion co efficient k and the coupling strength beta. We find perfectly synchronized periodic reproduction, synchronized reproduction with a chaotic time series , clustering phenomena, and chaotic reproduction of trees without synchroni zation over individuals. There are many parameter windows in which synchron ized reproduction of trees shows a stable periodic fluctuation. For perfect ly synchronized forests, we can calculate all the Lyapunov exponents analyt ically. They show that synchronized reproduction of all the trees in the fo rest can only occur when trees flower at low (but positive) levels in a sig nificant fraction of years, resulting in small fruit sets due to outcrossed pollen limitation. This is consistent with the observation that the distin ction between mast years and non-mast years is often not clear cut. (C) 200 0 Academic Press.