1. Mary L. Frost Introduction The diversity-promoting effects of nonlinear dynamics in variable environments (1, 2) may be an important component of the maintenance of the renowned diversity of coral reef fish communities. Model Structure REEF FISH LIFE HISTORY Indicates environmentally sensitive parameter in model Local larval biomass: Juvenile biomass: Adult biomass: growth/survival of existing adults maturation of juveniles Parameters and notation 1,…,n species 1,…,k patches reproductive rate parameters varying with the environment larval survival rate fraction of locally produced larvae retained in patch fraction of locally produced larvae dispersing to common larval pool maximum per capita growth rate for stage X, where X is L, J or A sets reduction in per capita growth rate of stage X (where X is L, J, or A) due to density-dependence competitive effect of stage Z (L, J, or A) on stage Y (L, J, or A) i j R E S p 1-p a X b X c YZ ==================== REEF ENVIRONMENT OFFSHORE ENVIRONMENT p 1-p REPRODUCTION (R) SETTLEMENT ADULTS (A) JUVENILES (J) LOCAL LARVAL BIOMASS (L) RETAINED PELAGIC LARVAE COMMON LARVAL POOL E E LOCAL DENSITY DEPENDENCE VARIABLE RECRUITMENT X DIVERSITY PROMOTION Summary Nonlinear competitive processes (local density dependence) and environmental stochasticity (recruitment variation) are prevalent in coral reef fish communities and interact in a way that tends to promote coexistence. These mechanisms potentially make a major contribution to the maintenance of the high diversity of coral reef fish communities. Applications Specific to marine fishes… Marine Protected Area analysis/design Yield assessment of tropical, multispecies fisheries In general… Appropriate for patchily distributed populations in general, whether insects in an agricultural mosaic or birds in forest fragments. Future goals Experimental guidelines for documenting these mechanisms in natural systems. Continued exploration of how different mechanisms influence dynamics in variable, spatially structured, populations. References (1)Warner, R. and P. Chesson. 1985. Coexistence mediated by recruitment fluctuations: a field guide to the storage effect. Am. Nat. 125(6): 769-787. (2) Chesson, P. 1994. Multispecies competition in variable environments. Theor. Popul. Biol. 45: 227-276. (3) Chesson, P. 1998. Making sense of spatial models in Ecology. In Modeling Spatiotemporal Dynamics in Ecology, J. Bascompte and R. V. Sole, Eds., pp. 151-16. Springer- Verlag, New York. Peter Chesson and Chesson lab group members NCEAS workgroup “Advances in Competition Theory” members: Sally Holbrook, Russ Schmitt, Craig Osenberg, Colette St. Mary Funding: NCEAS Competition Theory working group, NSF OCE 9911386 Acknowledgements Nonlinear Processes in Variable Environments: Mechanisms of Diversity Maintenance in Coral Reef Fishes Barbara A. Byrne – Section of Evolution and Ecology, UC-Davis Steve Turek Kevin Roland David F. Colvard Chuck Savall Local growth rate = ƒ(local density) Regional growth rate = ƒ(local density)  ƒ(local density) SCALE TRANSITION methods (3) provide an appropriate spatial average of a locally acting, nonlinear process, where: ƒ(local density)  ƒ(local density) + c  2 REGIONAL SCALE MODEL SPECIES A SPECIES B REEFS LARVAL POOL Reproduction and dispersal Recruitment of dispersive larvae Recruitment of retained larvae TIME BIOMASS PATCH 1 + - - + TIME BIOMASS PATCH 2 + - - + TIME BIOMASS REGIONAL AVERAGE + - - + Environmental variation… …present (+) …absent (-) Exclusion of by Coexistence of and BA AB Scaling Up Population Growth Variance in local recruit density Degree of nonlinearity * actual regional growth rate growth rate at regional density interaction b/w c and  2 = the storage effect FINITE RATE OF INCREASE COMPETITOR RECRUIT DENSITY actual regional growth rate growth rate at regional density contribution to regional population growth rate from the storage effect in regionin patch type 2 in patch type 1 ƒ, the MEASURING COEXISTENCE PROMOTION Coexistence occurs if all species can recover from low density. Species at a fitness disadvantage relative to the rest of the community will not recover without variation, but may recover with variation if the storage effect can compensate for the fitness disadvantage. The surmountable fitness disadvantage (SFD) is a measure of the promotion of coexistence by the storage effect. 0.5 0.25 0 0 increasing variation (from 0) SFD Long-term growth rate from low density Relative fitness Level of variation SFD 01234 1 0.5 0 1.5 As predicted by theory (2), interaction between local density dependent competition and variable recruitment promotes coexistence in systems with: species-specific variation in larval supply (feature of model) buffered population growth provided by an adult stage with relatively low mortality or by dispersal to independent environmental conditions (feature of model) covariance between environment and competition (results only from coexistence promoting combinations of competition, retention, and variable recruitment) How do competition, recruitment variation, and larval retention combine to promote coexistence? Simulation Results 0% larval retention 40% larval retention PC = promotes coexistence DNPC = does not promote coexistence Competition with own & adult stage TEMPORAL 01234 1 0.5 0 1.5 Type of recruitment variation SFD SPATIAL 01234 1 0.5 0 1.5 Level of variation SPATIOTEMPORAL 01234 1 0.5 0 1.5 PC Competition with adult stage only TEMPORAL 01234 1 0.5 0 1.5 SFD SPATIAL 01234 1 0.5 0 1.5 Type of recruitment variation Level of variation SPATIOTEMPORAL 01234 1 0.5 0 1.5 PC DNPC PC DNPC