?
Graphic from http://spongebob-plankton.tripod.com
Evolution of coexisting density compensation strategies in the
Maynard Smith and Slatkin equation
Florian Hartig, Tamara Münkemüller, Karin Johst, Ulf Dieckmann
http://www.ufz.de/index.php?en=10623
Florian Hartig
Department of Ecological Modelling
Introduction: Niches, coexistence mechanisms
and the paradox of the plankton
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Classic picture: Competitive exclusion -> Niche partitioning
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Problem: Often, several species appear to coexist within one niche
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A number of equalizing/stabilizing mechanisms exist which are based
on the spatio-temporal dynamics of resources / competitors
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E.g. storage effect, colonization-competition trade-offs
Relative Nonlinearity of Competition
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Page 2
Hutchinson ‘61 Paradox of the plankton
Hubbel ‘01 - UNTB
Different relative competitive strength at different resource levels
Huisman ‘99, Nature
Florian Hartig
Department of Ecological Modelling
The Maynard Smith-Slatkin model
?
Graphic from http://spongebob-plankton.tripod.com
Page 3
Florian Hartig
Department of Ecological Modelling
The Maynard Smith-Slatkin model
Discrete time steps
Non-overlapping generations
►
-1.0
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Both act positively on growth
r/b combination determines shape
0.0
2 free parameters r and b
-0.5
►
Growthrate
0.5
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Growth rates - varying r
1.0
►
0.0
0.5
1.0
1.5
Population size in units of the capacity
Page 4
Florian Hartig
Department of Ecological Modelling
2.0
Properties of the MMS model
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r/b determines reproductive success in
fluctuating environments. Larger b mean
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The larger r/b the stronger the fluctuations
Higher average growth at low fluctuations
Lower average growth at high fluctuations
0
For large r/b chaotic population dynamics
Individuals
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1000 2000 3000
r=6, b=7
430
440
450
460
470
480
Generation
Self-induded fluctuations and
fluctuation-dependent growth may
stabilize the coexistence of 2 or more
different b/r strategies!
Münkemüller, T.; Bugmann, H. & Johst, K.
Hutchinson revisited: Patterns of density regulation and the coexistence
of strong competitors
Journal of Theoretical Biology, 2009, 259, 109-117
Page 5
Florian Hartig
Department of Ecological Modelling
490
500
Questions:
Questions:
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►
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Page 6
Will
Willevolution
evolutionlead
leadto
tocoexisting
coexisting
strategies
strategiesin
inthe
theMMS
MMSequation?
equation?
Are
Arethese
thesecoexisting
coexistingstrategies
strategies
evolutionary
evolutionarystable?
stable?
Florian Hartig
Department of Ecological Modelling
Methods: Model description
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Individual-based
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Each individual has its own r/b strategy and
reproduces according to the MMS equation
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Scheduling within one generation
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Reproduction (Poisson-distributed)
Mutation of b (r, …) (small probability, normally distributed
mutation)
External disturbance (uniform)
Graphic from http://spongebob-plankton.tripod.com
Page 7
Florian Hartig
Department of Ecological Modelling
Results: Coexistence and invasibility
Confirms the results of:
Münkemüller, T.; Bugmann, H. & Johst, K.
Hutchinson revisited: Patterns of density regulation and the coexistence of strong competitors
Journal of Theoretical Biology, 2009, 259, 109-117
Page 8
Florian Hartig
Department of Ecological Modelling
Conclusion:
Conclusion:
►
► Existence
Existenceof
ofcoexisting
coexistingb-strategies
b-strategies
in
inthe
theMMS
MMSmodel
model
Question:
Question:
►
► bb subject
subjectto
toevolution,
evolution,what
whatisisgoing
going
to
tohappen?
happen?
Page 9
Florian Hartig
Department of Ecological Modelling
Evolution of b: ESS and the influence of
disturbance
Evolutionary stable b strategy
0.5
8
14
0.4
7
0.0
9
1.0
3
1.5
5
6
10
0.3
0.1
disturbance
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Only one ESS
Depends on r and on the
external disturbance
0.2
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4
2
2.0
2.5
r
Page 10
Florian Hartig
Department of Ecological Modelling
3.0
Other factors tested:
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►
1
0
One ESS
Left skewed shape favored
-1
Coevolution r/b
-2
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Growthrate
2
3
ESS coevolution
0.0
0.5
1.0
1.5
2.0
2.5
Population size in units of the capacity
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Intraspecific < interspecific competition
Evolution of intraspecific competition and niches
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Page 11
At no costs, intraspecific competition is always disfavored
Florian Hartig
Department of Ecological Modelling
Conclusions
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For populations development governed by the
MMS equation, relative nonlinearity of competition
acts as stabilizing coexistence mechanism
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Coexistence only an intermediate state during
evolution:
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Page 12
0.5
8
14
0.4
6
10
0.3
5
disturbance
0.2
3
2
0.1
9
1.0
1.5
4
2.0
r
Possibilities for evolution to coexisting strategies:
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7
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Evolution towards one single ESS
Depends on the disturbance regime
Evolution is slow because of the stabilizing effect
0.0
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Evolutionary stable b strategy
Physiological trade-offs
Conjecture: Shifts in the disturbance regime on larger
time/spatial scales may be sufficient to maintain
coexistence
?
Florian Hartig
Department of Ecological Modelling
2.5
3.0