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A SESSION ON CHESSON OR MORE EQUATIONS THAN YOU PROBABLY WANT TO SEE AT 10:30AM Benjamin Adams Contents Background Interest and Role in Community Ecology His work The Lottery Model Variable Environment Theory The Storage Effect Scale-Transition Theory Issues Background 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 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 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 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 i i J i i J J J J i J J i i i J i i J i i i i J i i i i i J J i J i J J i J i J i J Population Model - Non-overlapping i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Population Model - Overlapping i i J i i J J J J i J J i i i J i i J i i i i J i i i i i J J i J i J J i J i J i J Chesson and Warner 1981 Chesson and Warner 1981 The Work Variable Environmental Theory Variable Environment Model 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 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 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 different results – additive, subadditive, superadditive Storage Effect Chesson 1994 The Work The Storage Effect The Storage Effect 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 Subadditive results from previous model. The equation Long term growth rate at low populatons Equalizing mechanism Stabilizing mechanism Storage effect i i Ji i i Ji iJ iJ Ji i iJ Ji i i i Ji i i iJ i i i i Ji i i i i i Ji iJ i iJ i Ji Ji i iJ i Ji iJ Ji Test of Storage Effect 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 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 No Allee effects No extinction possible No effect of location on dispersal Deriving actual numbers to represent variables still difficult References 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. Chesson, P. 1994. Multispecies competition in variable environments. Theo. Pop. Bio. 45:227–276. Chesson, P. 2000a. Mechanisms of maintenance of species diversity. Ann. Rev. Ecol. System. 31: 343-366. 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