Scaling of larval Scaling of larval dispersal in the dispersal in the coastal oceancoastal ocean

Satoshi MitaraiSatoshi Mitarai

Postdoctoral ResearcherPostdoctoral ResearcherUniversity of California, Santa University of California, Santa

BarbaraBarbara

BACKGROUNDBACKGROUND Larval dispersal is important in fish Larval dispersal is important in fish

population dynamicspopulation dynamics A major source of uncertainty in A major source of uncertainty in

juvenile fish recruitment juvenile fish recruitment Diffusion model is used for many Diffusion model is used for many

applicationsapplications• Issue: not properly usedIssue: not properly used

STOCK/HARVEST STOCK/HARVEST MODELMODEL

Ax

n+11 M A

x

n Hx

n Px'

n Kx,x'

n Rx

n dx'

# 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 mortalit

y

x’ x

Rx

n

Kx,x'

n

Fraction of settlers successfully recruit at

x Px'

n

Fraction of larvae settling at x

# of larvae produced at

x’

Connectivity matrix

Dispersal kernel (when x is fixed)

DIFFUSION MODELDIFFUSION MODEL Describes probability of larval source locationsDescribes probability of larval source locations Can be used as a model for dispersal kernel Can be used as a model for dispersal kernel

only when observation time is very longonly when observation time is very long

Steneck, Science (2006)

Kx,x'

n

X’

Dispersal Kernel

Not true in annual time scale

SIEGEL ET AL (2003)SIEGEL ET AL (2003)

Dispersal kernel should be described Dispersal kernel should be described somehow in a stochastic way based somehow in a stochastic way based on diffusion modelon diffusion model

COASTAL OCEAN IS COASTAL OCEAN IS TURBULENTTURBULENT

California Current Falkland Islands

MODIS - NASA

SeaWiFS - NASA

Characteristics of turbulence is coherent structures (eddies)

SURFACE DRIFTERS IN SURFACE DRIFTERS IN EDDIESEDDIES

Ohlmann et al, JGR (2001)

Cold eddies Warm eddies

Drifters are advected by currents around eddies

LARVAL DISPERSAL IN LARVAL DISPERSAL IN EDDIESEDDIES

Nishimoto & Washburn (2002)

Red bars = juvenile fish abundance

Idea: turbulent eddy motions set stochasticity in larval dispersal

IDEAIDEA Turbulent eddy motions set Turbulent eddy motions set

stochasticity in larval dispersalstochasticity in larval dispersal Temporal & spatial patterns in larval Temporal & spatial patterns in larval

dispersal should be related with eddy dispersal should be related with eddy size, eddy turn-over speed, etc.size, eddy turn-over speed, etc.

GOALSGOALS Scale temporal & spatial patterns Scale temporal & spatial patterns

induced by eddies in larval dispersal induced by eddies in larval dispersal • As a function of upwelling condition, PLD As a function of upwelling condition, PLD

& larval behavior& larval behavior Propose simple scaling tool to Propose simple scaling tool to

describe stochastic larval dispersal describe stochastic larval dispersal using conventional diffusion modelusing conventional diffusion model

COASTAL CIRCULATION COASTAL CIRCULATION SIMULATIONSSIMULATIONS

Simulate circulation processes in Simulate circulation processes in Central California under strong & Central California under strong & weak upwelling weak upwelling

ADDING LARVAEADDING LARVAE

Released daily for 90 d, uniformly Released daily for 90 d, uniformly distributed in nearshore waters near top distributed in nearshore waters near top surfacesurface• Nearshore = within 10 km from coastNearshore = within 10 km from coast

Larvae settle when found in nearshore Larvae settle when found in nearshore during competency time windowduring competency time window• Competency = 10-20, 20-40, 30-60, 40-80 dCompetency = 10-20, 20-40, 30-60, 40-80 d

Two types of larval behaviorTwo 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 DISPERSALLARVAL DISPERSAL& SETTLEMENT& SETTLEMENT

Red dots = settling larvae

Strong Upwelling Weak Upwelling

LARVAL DISPERSALLARVAL DISPERSAL

MEAN DISPERSAL MEAN DISPERSAL DISTANCEDISTANCE

Strongly depends Strongly depends on upwelling on upwelling condition, PLD & condition, PLD & behavior behavior

Spread is not Spread is not sensitive to sensitive to behavior, though behavior, though

SETTLEMENT RATE & SETTLEMENT RATE & VARIATIONVARIATION

Strongly depends Strongly depends on upwelling on upwelling condition, PLD & condition, PLD & behavior behavior

Variation is not Variation is not sensitive to sensitive to behavior, though behavior, though

PDF OF LARVAL SOURCEPDF OF LARVAL SOURCE

For all cases, there are significant probability in natal area

DISPERSAL TIME SERIES DISPERSAL TIME SERIES & CONNECTIVITY& CONNECTIVITY

• Connectivity is heterogeneous

x

x'

Kx,x'

n

EDDY-INDUCED SCALESEDDY-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 IDEAPACKET MODEL IDEA

Portray settlement processes in terms of N Portray settlement processes in terms of N statistically-independent, equally-sized statistically-independent, equally-sized (eddy size) packets of individual larvae(eddy size) packets of individual larvae

N = (L/l) (T/t) fN = (L/l) (T/t) fL = domain size = 256 kmL = domain size = 256 km

l = eddy size ~ 50 kml = eddy size ~ 50 km

T = observation time = 90 d + mean PLDT = observation time = 90 d + mean PLD

t = eddy turn-over time ~ 2 weekst = eddy turn-over time ~ 2 weeks

f = packet survivability ~ 0.5f = packet survivability ~ 0.5

Source of each packet is determined Source of each packet is determined randomly based on diffusion modelrandomly based on diffusion model

PACKET MODEL VS PACKET MODEL VS SIMULATIONSSIMULATIONS

Shows a good Shows a good agreement with agreement with simulation datasimulation data

As observation As observation time increases, time increases, heterogeneity is heterogeneity is smoothed outsmoothed out

MORE EVALUATIONMORE EVALUATION

Shows a reasonable quantitative Shows a reasonable quantitative agreementagreement

e-folding time scaleCoefficient of Variation

CONCLUSION (1/2)CONCLUSION (1/2) Larvae are accumulated & delivered Larvae are accumulated & delivered

by eddies, leading to high variation in by eddies, leading to high variation in settlement patternssettlement patterns

Temporal & spatial scales are rather Temporal & spatial scales are rather consistent regardless upwelling, PLD consistent regardless upwelling, PLD or behavior, reflecting eddy motionsor behavior, reflecting eddy motions

CONCLUSIONS (2/2) CONCLUSIONS (2/2) Simple scaling analysis that Simple scaling analysis that

introduces stochasticity in introduces stochasticity in conventional diffusion modelconventional diffusion model• Dispersal kernel (or connectivity) is Dispersal kernel (or connectivity) is

described without expensive numerical described without expensive numerical simulationssimulations

• Handy tool to be used in many Handy tool to be used in many applications in marine population applications in marine population dynamicsdynamics

EDDY-INDUCED EDDY-INDUCED PATTERNSPATTERNS

Only a few strong Only a few strong settlement pulsessettlement pulses

Connectivity is Connectivity is heterogeneousheterogeneous

Behavior changes Behavior changes patterns patterns moderately, while moderately, while stochasticity stochasticity remainsremains