1. A SCALING TOOL TO ACCOUNT FOR INHERENT STOCHASTICITY IN LARVAL DISPERSAL Mitarai S., Siegel D. A., Warner R.R., Kendall B.E., Gaines S.D., Costello C.J. University of California, Santa Barbara Winters K.B. Scripps Institution of Oceanography A Biocomplexity Project - Flow, Fish and Fishing ROLE OF TURBULENCE IN STOCK DYNAMICS

2. HABITAT CONNECTIVITY Habitat connectivity via larval dispersal is key in predicting stock dynamics A Fish’s Life Cycle Source yDestination x x Cowen et al, Science (2006) Connectivity Matrix y x

3. POPULAR TOOLS Eddy diffusion modelsLarval pool assumption Largier, Ecol. App. (2003) Pineda, Ocean. E. Pacific (2000) All sites have equal probability Yield homogeneous, unstructured connectivity

4. MODIS-NASA Chlorophyl distribution in south Atlantic HYPOTHESIS Coastal eddies connect only a few habitats for a given season, resulting in important consequences in stock predictions Ohlmann et al, JGR (2003) Surface drifter track Abundance of fish larvae Surface Velocity Nishimoto & Washburn (2002)

5. COASTAL CIRCULATION SIMULATIONS Nearshore habitat: < 10 km from coast 1000 / d x 90 d = 90000 particles Competency window = 20 - 40 d Red dots: successful settlers In Central California Larvae are accumulated & transported by coastal eddies

6. N Three different seasons Season #1#2#3 Source location (km) Destination location (km) SAMPLE CONNECTIVITY MATRICES Only a few strong connections Different patterns for different seasons Source location (km) As a function of observation time Diffusion 1 season 5 seasons10 seasons Destination location (km) Smoothed out if averaged 10+ seasons Unavoidable uncertainties for a given season What sets these patterns?

7. Describes larval settlement as arrival of N “larval packets” A SIMPLE SCALING TOOL L: Domain size l: Eddy size (~ 50 km) T: Larval release duration t: Eddy turn-over time (~ 14 d) eddy size (l) N larval packets

8. SIMULATIONS VS. PACKET MODEL (L = 256 km, l = 50 km, T = 90*n d, t = 14 d) Circulation simulationsPacket model Destination location (km) Source location (km) Packet model represents heterogeneity & stochasticity without expensive simulations

9. DOES EDDY STOCHASTICITY MATTER? Diffusion model breaks up packet & lowers density Recruitment rate Density of settling larvae Beverton - Holt density dependence A Fish’s Life Cycle Recruitment rate = f(settlement density) Yes, because of the post-settlement density dependence

10. SAMPLE STOCK DYNAMICS Eddy-diffusion model Packet model Predictions... Model equation New Stock = Survivors + Recruits Production ~ local abundance Diffusion or packet model Adult life time ~ 20 years Beverton - Holt density dependence Consider single, unharvested species with sessile adult stage

11. CONCLUSIONS Coastal eddies set unavoidable uncertainties in connectivity for a given season & have important consequences in predicting stock dynamics Conventional eddy-diffusion modeling approach, which ignores turbulent eddy structures, can substantially overestimate future stock Turbulent eddy structures play an important role in stock dynamics Turbulent eddy structures play an important role in stock dynamics