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Snapback Repellers in Chaos Theory and their Application in Ecology Resource Budget Model reserve reproductive threshold income by photosynthesis resource depletion coefficient investment pollen availability to flowers reproduction investment to fruits with normalized reserve resource depletion coeff. pollen availability year year year reproduce every year Pollen Coupling Pollination efficiency for a tree depends on the reproductive activity of others pollen availability: pollen coupling strength Pi(t) β=0.2 β=1.0 β=1.5 Flowering intensity of the forest Phase Diagram Coherent periodic Coherent chaotic β : pollen coupling strength Coherent Annual Annual Coherent Clustering Clustering Desynchronized Desynchronize (Satake and Iwasa 2000, JTB) ki : resource depletion coefficient To discuss the evolution, We trace the whole life cycle, not just the number of seeds produced. Forest is composed of a number of canopy trees, and new recruit is possible only when a canopy tree dies. Lottery Competition Life cycle of trees within a year growth reproduction recruitment death Growth Trees accumulates resources obtained by photosynthesis Reproduction Trees with large reserve produce flower and fruits. This depletes the reserve. Reproduction Trees with large reserve produce flower and fruits. This depletes the reserve. Seed crop： Whole forest： Death of canopy trees Annual mortality A gap is created. Young individuals from seeds compete for the gap. An offspring from Free seeds produced in the Site year wins the site. Recruitment A new individual (haploid) inherits the trait from one of the parents. It inherits the trait k of the i th tree with probability: Small mutations Adaptive Dynamics Repeating these processes many times, what remains in the end is evolutionary advantageous. Thank you for your attention!
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