Scaling of larval dispersal in the coastal ocean Satoshi Mitarai Postdoctoral Researcher University of California, Santa Barbara

BACKGROUND Larval dispersal is important in fish population dynamics Larval dispersal is important in fish population dynamics A major source of uncertainty in juvenile fish recruitment A major source of uncertainty in juvenile fish recruitment Diffusion model is used for many applications Diffusion model is used for many applications Issue: not properly used Issue: not properly used

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’ Connectivity matrix Dispersal kernel (when x is fixed)

DIFFUSION MODEL DIFFUSION MODEL Describes probability of larval source locations Describes probability of larval source locations Can be used as a model for dispersal kernel only when observation time is very long Can be used as a model for dispersal kernel only when observation time is very long Steneck, Science (2006) X’ Dispersal Kernel Not true in annual time scale

SIEGEL ET AL (2003) Dispersal kernel should be described somehow in a stochastic way based on diffusion model Dispersal kernel should be described somehow in a stochastic way based on diffusion model

COASTAL OCEAN IS TURBULENT California Current Falkland Islands MODIS - NASA SeaWiFS - NASA Characteristics of turbulence is coherent structures (eddies)

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

LARVAL DISPERSAL IN EDDIES Nishimoto & Washburn (2002) Red bars = juvenile fish abundance Idea: turbulent eddy motions set stochasticity in larval dispersal

IDEA Turbulent eddy motions set stochasticity in larval dispersal Turbulent eddy motions set stochasticity in larval dispersal Temporal & spatial patterns in larval dispersal should be related with eddy size, eddy turn-over speed, etc. Temporal & spatial patterns in larval dispersal should be related with eddy size, eddy turn-over speed, etc.

GOALS Scale temporal & spatial patterns induced by eddies in larval dispersal Scale temporal & spatial patterns induced by eddies in larval dispersal As a function of upwelling condition, PLD & larval behavior As a function of upwelling condition, PLD & larval behavior Propose simple scaling tool to describe stochastic larval dispersal using conventional diffusion model Propose simple scaling tool to describe stochastic larval dispersal using conventional diffusion model

COASTAL CIRCULATION SIMULATIONS Simulate circulation processes in Central California under strong & weak upwelling Simulate circulation processes in Central California under strong & weak upwelling

ADDING LARVAE Released daily for 90 d, uniformly distributed in nearshore waters near top surface Released daily for 90 d, uniformly distributed in nearshore waters 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, d Competency = 10-20, 20-40, 30-60, d Two types of larval behavior Two types of larval behavior Surface-following Surface-following Vertically-migrating (shift 30 m 5d after release) Vertically-migrating (shift 30 m 5d after release)

LARVAL DISPERSAL & SETTLEMENT Red dots = settling larvae Strong UpwellingWeak Upwelling

LARVAL DISPERSAL

MEAN DISPERSAL DISTANCE Strongly depends on upwelling condition, PLD & behavior Strongly depends on upwelling condition, PLD & behavior Spread is not sensitive to behavior, though Spread is not sensitive to behavior, though

SETTLEMENT RATE & VARIATION Strongly depends on upwelling condition, PLD & behavior Strongly depends on upwelling condition, PLD & behavior Variation is not sensitive to behavior, though Variation is not sensitive to behavior, though

PDF OF LARVAL SOURCE For all cases, there are significant probability in natal area

DISPERSAL TIME SERIES & CONNECTIVITY Connectivity is heterogeneous

EDDY-INDUCED SCALES 0 Arrival Scales Departure Scales Rather consistent regardless upwelling, PLD or behavior ~ eddy size 40 to 60 km ~ eddy turn-over time (a few weeks) ~ eddy turn-over time (a few weeks)

PACKET MODEL IDEA Portray settlement processes in terms of N statistically-independent, equally-sized (eddy size) packets of individual larvae Portray 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 diffusion model Source of each packet is determined randomly based on diffusion model

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

MORE EVALUATION Shows a reasonable quantitative agreement Shows a reasonable quantitative agreement e-folding time scale Coefficient of Variation

CONCLUSION (1/2) 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

CONCLUSIONS (2/2) Simple scaling analysis that introduces stochasticity in conventional diffusion model Simple scaling analysis that introduces stochasticity in conventional diffusion model Dispersal kernel (or connectivity) is described without expensive numerical simulations Dispersal kernel (or connectivity) is described without expensive numerical simulations Handy tool to be used in many applications in marine population dynamics Handy tool to be used in many applications in marine population dynamics

EDDY-INDUCED PATTERNS Only a few strong settlement pulses Only a few strong settlement pulses Connectivity is heterogeneous Connectivity is heterogeneous Behavior changes patterns moderately, while stochasticity remains Behavior changes patterns moderately, while stochasticity remains