Mary L. Frost

1. Nonlinear Processes in Variable Environments: Mechanisms of Diversity Maintenance in Coral Reef Fishes Barbara A. Byrne – Section of Evolution and Ecology, UC-Davis David F. Colvard Chuck Savall Chuck Savall Kevin Roland Steve Turek Steve Turek 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 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 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. Simulation Results MEASURING COEXISTENCE PROMOTION REGIONAL SCALE MODEL 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. A B …present (+) Coexistence of and Environmental variation… LOCAL DENSITY DEPENDENCE VARIABLE RECRUITMENT DIVERSITY PROMOTION A B X …absent (-) Exclusion of by - PATCH 1 PATCH 2 - + + 0.5 + increasing variation (from 0) + SFD 1.5 - - 1 0.25 Long-term growth rate from low density SFD 0.5 Applications 0 0 0 -1 0 1 2 3 4 Level of variation Relative fitness REPRODUCTION (R) SPECIES A SPECIES B 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. REEF FISH LIFE HISTORY - REGIONAL AVERAGE + Indicates environmentally sensitive parameter in model E + How do competition, recruitment variation, and larval retention combine to promote coexistence? - 1-p p ADULTS (A) COMMON LARVAL POOL RETAINED PELAGIC LARVAE PC = promotes coexistence DNPC = does not promote coexistence 0% larval retention SETTLEMENT 40% larval retention Future goals REEF ENVIRONMENT OFFSHORE ENVIRONMENT Competition with own & adult stage JUVENILES (J) Type of recruitment variation Scaling Up Population Growth LOCAL LARVAL BIOMASS (L) E SPATIAL SPATIOTEMPORAL TEMPORAL Local larval biomass: Experimental guidelines for documenting these mechanisms in natural systems. Continued exploration of how different mechanisms influence dynamics in variable, spatially structured, populations. 1.5 1.5 1.5 PC PC PC PC PC PC 1 1 1 Juvenile biomass: SFD 0.5 0.5 0.5 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 Level of variation Adult biomass: References Competition with adult stage only Type of recruitment variation Degree of nonlinearity SPATIAL SPATIOTEMPORAL TEMPORAL • 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. Variance in local recruit density 1.5 1.5 1.5 maturation of juveniles DNPC DNPC PC PC DNPC PC 1 1 1 SFD * 0.5 0.5 0.5 0 0 0 growth/survival of existing adults actual regional growth rate growth rate at regional density interaction b/w c and 2 = the storage effect 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 BIOMASS BIOMASS BIOMASS Level of variation Parameters and notation • 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) TIME TIME TIME 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 aX bX cYZ = = = = = = = = = = FINITE RATE OF INCREASE contribution to regional population growth rate from the storage effect ƒ, the Acknowledgements actual regional growth rate 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 REEFS LARVAL POOL growth rate at regional density Reproduction and dispersal in patch type 1 in region in patch type 2 Recruitment of dispersive larvae Recruitment of retained larvae COMPETITOR RECRUIT DENSITY Mary L. Frost