1. Scaling of Larval Transport in the Coastal Ocean Satoshi Mitarai, Dave Siegel, Kraig Winters Postdoctoral Researcher University of California, Santa Barbara

2. BACKGROUND Quantitative description of larval transport is important in marine ecology Quantitative description of larval transport is important in marine ecology e.g., marine population dynamics, fishery stock management, design of MPA’s e.g., marine population dynamics, fishery stock management, design of MPA’s For many important applications, eddy- diffusion model (or dispersal kernel) has been used For many important applications, eddy- diffusion model (or dispersal kernel) has been used F3 idea: eddy-diffusion modeling approach is not appropriate F3 idea: eddy-diffusion modeling approach is not appropriate

3. EDDY DIFFUSION MODELS EDDY DIFFUSION MODELS Describe probability distribution of larval source locations (or destination locations) Describe probability distribution of larval source locations (or destination locations) Often called dispersal kernel Often called dispersal kernel Not larval transport for a single season (or year) Not larval transport for a single season (or year) Steneck (2006) Dispersal Kernel Larval source # of successful recruits

4. SIEGEL ET AL (2003) Larval transport for a single season should be described somehow in a stochastic way based on dispersal kernel Larval transport for a single season should be described somehow in a stochastic way based on dispersal kernel

5. F3 STOCK/HARVEST MODEL # of adults harvested # of adults at x in year n+1 # of recruits to x from everywhere # of survivors at x in year n Natural mortality x’ x Fraction of settlers successfully recruit at x Fraction of larvae settling at x # of larvae produced at x’ Stochasticity in larval transport will lead to unavoidable uncertainty in recruitment patterns Stochasticity in larval transport will lead to unavoidable uncertainty in recruitment patterns Connectivity matrix

6. COASTAL OCEAN IS TURBULENT Falkland Islands MODIS - NASA Characteristics of turbulence is coherent structures (eddies)

7. SURFACE DRIFTERS AROUND EDDIES Ohlmann et al, JGR (2001) Cold eddies Warm eddies Drifters are advected by currents around eddies

8. LARVAL TRANSPORT AROUND EDDIES Nishimoto & Washburn (2002) Red bars = juvenile fish abundance High juvenile fish abundance near the center of the eddy

9. IDEA Turbulent eddy motions set stochasticity in larval transport Turbulent eddy motions set stochasticity in larval transport Temporal & spatial patterns in larval transport should be related with eddy motions Temporal & spatial patterns in larval transport should be related with eddy motions e.g., eddy size, eddy turn-over time, … e.g., eddy size, eddy turn-over time, …

10. GOALS Scale temporal & spatial patterns induced by eddies in larval transport Scale temporal & spatial patterns induced by eddies in larval transport As a function of upwelling condition, PLD & larval behavior As a function of upwelling condition, PLD & larval behavior Propose simple scaling tool that describes larval transport (connectivity matrix) for a single season Propose simple scaling tool that describes larval transport (connectivity matrix) for a single season Along with eddy-diffusion model Along with eddy-diffusion model

11. COASTAL CIRCULATION SIMULATIONS Modeled after circulation processes in Central California under strong & weak upwelling Modeled after circulation processes in Central California under strong & weak upwelling Strong UpwellingWeak Upwelling

12. SIMULATION SETUP Top View Alongshore pressure gradient obtained from observation data Stochastic wind stress estimated from observation data Side View Periodic Wall Open  Poleward

13. ADDING LARVAE Released daily for 90 d, uniformly distributed in nearshore waters at near top surface Released daily for 90 d, uniformly distributed in nearshore waters at near top surface Nearshore = within 10 km from coast Nearshore = within 10 km from coast Larvae settle when found in nearshore during competency time window Larvae settle when found in nearshore during competency time window Competency = 10-20, 20-40, 30-60, 40-80 d Competency = 10-20, 20-40, 30-60, 40-80 d Two types of larval behavior Two types of larval behavior Surface-following Surface-following Vertically-migrating (shift 30 m 5 d after release) Vertically-migrating (shift 30 m 5 d after release)

14. LARVAL TRANSPORT & SETTLEMENT Red dots = settling larvae Strong UpwellingWeak Upwelling

15. DISPERSAL & KERNEL

16. MEAN ADVECTION & DISPERSAL Strongly depend on upwelling condition, PLD & behavior Dispersal is not sensitive to behavior, though Surface following larvae (solid lines) Migrating larvae (dashed lines) 28 realizations of simulations used

17. SETTLEMENT RATE & VARIATION Strongly depend on upwelling condition, PLD & behavior Variation is not sensitive to behavior, though Surface following larvae (solid lines) Migrating larvae (dashed lines) 28 realizations of simulations used

18. DISPERSAL KERNEL In all cases, substantial portion of larvae are retained in natal area In all cases, substantial portion of larvae are retained in natal area

19. SETTLEMENT TIME SERIES & CONNECTIVITY Only a few settlement pulses are observed, leading to heterogeneous connectivity Only a few settlement pulses are observed, leading to heterogeneous connectivity

20. TIME & LENGTH OF SETTLEMENT PULSES Arrival ScalesDeparture scales Rather consistent regardless upwelling, PLD or behavior Rather consistent regardless upwelling, PLD or behavior ~ eddy turn-over time (a few weeks) ~ eddy turn-over time (a few weeks) ~ eddy size (40 to 60 km)

21. CONNECTIVITY IS STOCHASTIC

22. PACKET MODEL Idea: portrays settlement processes in terms of N statistically-independent, equally-sized (eddy size) packets of individual larvae Idea: portrays settlement processes in terms of N statistically-independent, equally-sized (eddy size) packets of individual larvae N = (L/l) (T/t) f L = domain size = 256 km l = eddy size ~ 50 km T = observation time = 90 d + mean PLD t = eddy turn-over time ~ 2 weeks f = packet survivability ~ 0.5 Source of each packet is determined randomly based on dispersal kernel (random sampling) Source of each packet is determined randomly based on dispersal kernel (random sampling)

23. PACKET MODEL VS SIMULATIONS Shows a good agreement with simulation data Shows a good agreement with simulation data As observation time increases, heterogeneity is smoothed out As observation time increases, heterogeneity is smoothed out

24. MORE EVALUATION Stochasticity in larval transporte-folding time scale Shows a reasonable quantitative agreement Shows a reasonable quantitative agreement

25. CONCLUSIONS (1/2) Simulation results suggest Simulation results suggest Larvae are accumulated & delivered by eddies, leading to high variation in settlement patterns Larvae are accumulated & delivered by eddies, leading to high variation in settlement patterns Temporal & spatial scales are rather consistent regardless upwelling, PLD or behavior, reflecting eddy motions Temporal & spatial scales are rather consistent regardless upwelling, PLD or behavior, reflecting eddy motions

26. CONCLUSIONS (2/2) Propose simple scaling tool that describes larval transport for a single season based upon dispersal kernel Propose simple scaling tool that describes larval transport for a single season based upon dispersal kernel Without performing expensive numerical simulations of coastal circulation processes Without performing expensive numerical simulations of coastal circulation processes Handy tool to be used in applications in marine ecology Handy tool to be used in applications in marine ecology

27. MORE CONNECTIVITY,…