A SESSION ON CHESSON
OR
MORE EQUATIONS THAN YOU PROBABLY WANT TO
SEE AT 10:30AM
Benjamin Adams
Contents
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Background
Interest and Role in Community Ecology
His work
 The
Lottery Model
 Variable Environment Theory
 The Storage Effect
 Scale-Transition Theory
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Issues
Background
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1974 B.Sc. University of Adelaide, Australia
1978 Ph.D. (Departments of Statistics and Zoology), University of Adelaide,
Australia
http://www.environment.arizona.edu/peter-chesson
1978-81 Postgraduate Research Biologist, University of California, Santa
Barbara
1981-90 Professor of Zoology, Botany and Statistics, Ohio State University
1990-97 Senior Fellow, Research School of Biological Sciences, Australian
National University
1998-05 Professor, Section of Evolution and Ecology, University of
California, Davis
2005-present Professor, Ecology and Evolutionary Biology, University of
Arizona
https://www.facebook.com/peter.chesson
Interest
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How organisms interactions and adaptation to
variability promotes species diversity and affects
ecosystem functioning.
http://www.futurity.org/earth-environment/nature%E2%80%99s-eternal-rock-paper-scissors/
Role
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Theoretical Biologist or Mathematical Modeler
Chesson and Warner 1981
Chesson and Elner1989
The Work
The Lottery Model
and derivatives
The Storage Effect
Variable Environmental Theory
Scale-Transition Theory
http://whitneyfehr.wordpress.com/2010/03/13/exploring-biomes/
http://www.intelligentspeculator.net/2009/08/page/2/
http://www.vector1media.com/spatialsustain/neon-aims-to-create-a-common-ecological-observation-platform.html
The Work
The Lottery Model
and derivatives
The Sale’s Lottery System
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L is the number of larvae of species i available
c is a constant representing the relative competitive
ability of species i
Chesson and Warner 1981
Chesson’s Population Model
Portion of
homes filled
by species “i”
Chesson and Warner 1981
Surviving
individuals in
species “i”
Dead Incorporates
Birthrate of “i”
stochasticity
individuals of
divided by the
among of
all othervariable birthrate
speciesthe rest
species
Population Model - Non-overlapping
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Population Model - Non-overlapping
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Population Model - Overlapping
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Chesson and Warner 1981
Chesson and Warner 1981
The Work
Variable Environmental Theory
Variable Environment Model
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ri = Long term growth rate of species i
ΔE = relative mean effect of the environment
ΔC = relative mean effect of competition
ΔI = relative mean of the interactions between
environment and competition.
Chesson 1989
ΔC – the competition term
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Consists of two parts:
 The
difference between inter- and intraspecific
competition independent of fluctuation
 The difference between inter- intraspecific competition
which is dependent on competition in the previous time
period and nonlinear response.
 Example
of nonlinear: two species with different
dependence on same resource.
Chesson 1994
ΔI – the interaction term
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Composed of three parts
 Species
 e.g.
specific response to the environment
different responses to temperature fluctuation
 Covariance
between environment and competition
 e.g.
improved condition increase density thereby increasing
demand on resources
 The
growth rates response to both competition and
environmental fluctuation
 Three
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different results – additive, subadditive, superadditive
Storage Effect
Chesson 1994
The Work
The Storage Effect
The Storage Effect
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Competing species can coexist when intraspecific
competition outweighs interspecific competition
Fluctuation-dependent 3 part mechanism (ΔI)
 Fluctuation
must effect birth rate, death rate, or
recruitment
 Buffered population
 Examples
= seed banks, hibernation, long-lived adults,
refuges for spatial storage effect
Chesson 1994
Chesson 2000a
Chesson 2000b
Buffered population growth
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Subadditive results from previous model.
The equation
Long term
growth rate at
low populatons
Equalizing
mechanism
Stabilizing
mechanism
Storage effect
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Test of Storage Effect
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Pake and Venable 1995 – Sonoran annuals use
seed banks to store maintain populations. Variation
due to germination factors.
Caceres 1997 – 30 years of plankton data of two
species. Diapaused eggs. Extinction for one definite
without storage effect
Sears and Chesson 2007 – use of neighborhood
competition to show spatial storage effect.
The Work
Scale-Transition Theory
Scale-transition Theory
Chesson 2009
Chesson 2011
Scale-transition equation
Number of
individuals in
following time
point
Chesson 2009
Variability
introduced to
local dynamics
or physical
environment
Variability
introduced by
nonlinearity on
population
density
Scale-transition models
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Allows you to incorporate emergent variability
produced into a model where data is scaled up to a
larger perspective.
Produces testable prediction as to how those
emergent properties will relate to smaller scale
data (i.e. through nonlinearity and variation)
Propose as a potential alternative to metacommunity theory for large scale ecological systems
The Work
The Lottery Model
and derivatives
The Storage Effect
Variable Environmental Theory
Scale-Transition Theory
http://whitneyfehr.wordpress.com/2010/03/13/exploring-biomes/
http://www.intelligentspeculator.net/2009/08/page/2/
http://www.vector1media.com/spatialsustain/neon-aims-to-create-a-common-ecological-observation-platform.html
Issues with models
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No Allee effects
No extinction possible
No effect of location on dispersal
Deriving actual numbers to represent variables still
difficult
References
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Caceres, C. 1997. Temporal variation, dormancy, and coexistence: a field test of the storage effect. Proc.
Natl. Acad. Sci. USA 94:9171–75
Chesson P, Warner R. 1981 Environmental variability promotes coexistence in lottery competitive systems.
Am. Nat. 117 (6): 923-943
Chesson P, Ellner S. 1989. Invasibility and stochastic boundedness in monotonic competition models. J. Math.
Biol. 27:117–38
Chesson, P. 1989. A general model of the role of environmental variability in communities of competing
species, in “Lectures of Mathematics in Life Sciences,” 20:97-123 Amer. Math. Soc., Providence.
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Chesson, P. 1994. Multispecies competition in variable environments. Theo. Pop. Bio. 45:227–276.
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Chesson, P. 2000a. Mechanisms of maintenance of species diversity. Ann. Rev. Ecol. System. 31: 343-366.
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Chesson, P. 2000b. General theory of competitive coexistence in spatially varying environments. Theor.
Popul. Biol. 58:211-237
Chesson, P. 2009. Scale transition theory with special reference to species coexistence in variable
environments. J. Bio. Dynamics. 3 (2-3):149-163
Chesson, P. 2012. Scale transition theory: Its aims, motivations and predictions. Ecol. Complex.
doi:10.1016/j.ecocom.2011.11.002
Pake C, Venable L. 1995. Is coexistence of Sonoran desert annual plants mediated by temporal variability
reproductive success. Ecology 76 (1): 246–261.
Sears A, Chesson P. 2007. New methods for quantifying the spatial storage effect: an illustration with desert
annuals. Ecology 88 (9): 2240–2247