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Numerical Computations in Ecological Models

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Numerical Computations in Ecological Models Powered By Docstoc
					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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posted:9/1/2011
language:English
pages:14