Theoretical Study of Spatio-Temporal Dynamics of Synchronized Flowering and Reproduction of Trees in Forests

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Trees in mature forests often show intermittent reproduction. Intensive flowering and seed production occur only once in several years, often synchronized over a long distance. We study a coupled map model for the dynamics of energy reserve of individuals, and show that trees become synchronized in reproduction when their fruit production is limited by the availability of outcross pollen. Without pollen limitation, the trees show independent chaotic fluctuation. With global pollen coupling, trees show various degree of reproductive synchronization. Lyapunov exponents are calculated analytic ally for perfectly synchronized forests, demonstrating 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. We then study a coupled map lattice with local pollen exchange. Dynamic spatial covariance shows that a strong synchronization over the whole forest can develop from rather short range pollen exchange. We then examined the synchronization caused by common environmental fluctuation either in the annual productivity or the reproductive threshold level. Without pollen coupling, positive correlation between individuals are difficult to emerge even under environmental fluctuation correlated between individuals. Positive correlation can be maintained at high level only in the presence of both pollen coupling and correlated environmental fluctuation. 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. The first paper was printed in JTB, the second in now (in press) in Ecology, and another was submitted to J Ecology.