Post on 17-Jan-2016
transcript
Snapback Repellers in Chaos Theory and their Application in Ecology
Resource Budget Model
reserve
Si t
income byphotosynthesis
PS
investment to flowers
investmentto fruits
reproduction
reproductive threshold
pollen availability
resource depletion coefficient
ki
Pi t
LT
Si t 1 Si t PS if Si t PS LT
Si t PS 1 Pi t ki Si t PS LT otherwise
Yi t1 Yi t 1
kiPi t Yi t 1
if Yi 0
otherwise pollen availability
resource depletion coeff.
ki
Pi t
Yi t normalized reserve
Si t1 Si t PS if Si t PS LT
Si t PS 1 Pi t ki Si t PS LT otherwise
year
Y (t)
reproduce every year
year year
ki 0.7
ki 1.5
ki 4.3
Yi t Si t PS LT PSwith
Pollen Coupling
Pi t 1
N 1Y j t
ji
N
Pollination efficiency for a tree depends on the reproductive activity of others
Yi t1 Yi t 1
kiPi t Yi t 1
if Yi 0
otherwise
β=0.2 β=1.0 β=1.5
Pi(t) pollen coupling strength
Flowering intensity of the forest
pollen availability:
Phase Diagram
Clustering
Desynchronize
Coherent chaoticCoherent periodic
CoherentAnnual
β : po
llen
cou
plin
g st
reng
th
ki : resource depletion coefficient
(Satake and Iwasa 2000, JTB)
1 2 3 4
0
1
2
Annual
CoherentClustering
Desynchronized
To discuss the evolution,
We trace the whole life cycle, not just the number of seeds produced.
Lottery Competition
Forest is composed of a number of canopy trees, and new recruit is possible only when a canopy tree dies.
Life cycle of trees within a year
growth reproduction
deathrecruitment
Growth
Treesaccumulatesresources obtained by photosynthesis
Trees with large reserve produceflower and fruits.This depletes the reserve.
Reproduction
Seed crop :
i t kiPi t Yi t Whole forest :
t i t i 2
Trees with large reserve produceflower and fruits.This depletes the reserve.
Reproduction
Death of canopy trees
Annual mortality
A gap is created.Young individuals from seedscompete forthe gap.
FreeSite
An offspring from seeds produced in the 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:
i t 1
2
i t t
Yi t
Y t i 1
j t t ji i 1
N
Small mutations
Adaptive Dynamics
Repeating these processes many times, what remains in the end is evolutionary advantageous.
Thank you for your attention!