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Talk Abstract
Pollen-Coupling of Forest Trees, Forming Synchronized and Periodic Reproduction out of Chaos

Yoh Iwasa
Department of Biology
Faculty of Science
Kyushu University
Fukuoka 812-8581
Japan
yiwasscb@mbox.nc.kyushu-u.ac.jp
http://bio-math10.biology.kyushu-u.ac.jp/~iwasa/


Many tree species in mature forests show masting - their reproductive activity has a large variance between years and is often synchronized over different individuals. I here analyze a globally coupled map model in which trees accumulate photosynthate every year, put flowers when the energy reserve level exceeds a threshold, and set seeds and fruits at a rate limited by pollen availability. Without pollen limitation, trees in a forest show chaotic fluctuation independently. Coupling of trees via pollen exchange makes reproduction synchronized partially or completely over the forest. Depending on two essential parameters, depletion coefficient k and coupling strength , the whole forest shows diverse dynamical behaviors, such as 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 show a stable periodic fluctuation. Analysis of Lyapunov exponents reveals that synchronized reproduction of all the trees in the forest can occur only 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 distinction between mast years and non-mast years is often not clear-cut. I will also discuss a coupled map lattice model for spatially limited pollen exchange and the synchronization of different tree species in tropical rain forest via sharing common pollinators.

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1998-1999 Mathematics in Biology

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