Yoh Iwasa
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan
E-mail: yiwasscb@mbox.nc.kyushu-u.ac.jp

Synchronized reproduction of trees in the forests

1.      Many trees in mature forests, including beaches and oaks, show intermittent reproduction (masting).  Intensive flowering and seed production occur only once in several years, often synchronized over a long distance.  The reserve of a tree is affected by the flowering activity of other individuals in the same forest because successful fruit production requires pollen produced by other individuals.  We study a coupled map model for the dynamics of energy reserve of individuals: a single tree grows in each site of a 2-dimensional finite lattice.
2.      Without pollen limitation, 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.  When the coupling is global, 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 show a stable periodic fluctuation.  For perfectly synchronized forests, we can calculate all the Lyapunov exponents analytically.  They shows that synchronized reproduction of trees can occur only if trees flower at low (but positive) levels in a significant fraction of years, resulting in small fruit sets due to the shortage of outcross pollen.
3.      Next, we study a coupled map lattice in which the pollen availability for a tree is the average flowering intensity within its local neighborhood.  Analysis of dynamic spatial covariance shows that 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 of period 2.  In addition, non-uniform spatial patterns are generated, 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 proportionalily larger but the condition for synchronization of the whole forest and its magnitude are the same as the case with the nearest neighbor pollen exchange.  When a fraction of seeds are sired by globally dispersed pollen and the rest are by local pollen, the long-range synchronization can occur for a wide parameter region, and trees may engage in a fluctuation with masting interval longer than 2.
4.      We then examine the effect of common environmental fluctuation experienced by different individuals.  The fluctuation in the annual productivity and that in the reproductive threshold can be studied by the same model that includes additional fluctuation terms.  Without pollen coupling, environmental fluctuation strongly correlated between individuals (Moran effect) fails to produce a high positive correlation between individuals of seed production.  In contrast, positive correlation can be maintained at a high level if both pollen coupling and correlated environmental fluctuation are at work.  We conclude that both pollen coupling and environmental fluctuation correlated between individuals are needed to explain the masting with an interval longer than two years.
5.      We also discuss the reproductive synchronization between different species who share common pollinators, which is applicable to the synchronization in the tropical rain forest in Southeast-Asia.