A SCALING TOOL TO ACCOUNT A SCALING TOOL TO ACCOUNT FOR INHERENT STOCHASTICITY FOR INHERENT STOCHASTICITY

IN LARVAL DISPERSAL 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 DYNAMICSROLE OF TURBULENCE IN STOCK DYNAMICS

HABITAT CONNECTIVITYHABITAT CONNECTIVITY

• Habitat connectivity via larval dispersal is key in predicting stock dynamics

A Fish’s Life Cycle

Source y Destination x

x

Cowen et al, Science (2006)

Connectivity Matrix

y

x

POPULAR TOOLSPOPULAR TOOLS

Eddy diffusion models Larval pool assumption

Largier, Ecol. App. (2003)Pineda, Ocean. E. Pacific (2000)

All sites have equal probability

• Yield homogeneous, unstructured connectivity

MODIS-NASA

Chlorophyl distribution in south Atlantic

HYPOTHESISHYPOTHESIS

• 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)

COASTAL CIRCULATION SIMULATIONSCOASTAL 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

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• Larvae are accumulated & transported by coastal eddies

N

Three different seasonsSeason #1 #2 #3

Sou

rce

loca

tion

(km

)

Destination location (km)

SAMPLE CONNECTIVITY MATRICESSAMPLE CONNECTIVITY MATRICES

• Only a few strong connections

• Different patterns for different seasons

Sou

rce

loca

tion

(km

)

As a function of observation time Diffusion1 season 5 seasons 10 seasons

Destination location (km)

• Smoothed out if averaged 10+ seasons

• Unavoidable uncertainties for a given season

What sets these patterns?What sets these patterns?

• Describes larval settlement as arrival of N “larval packets”

A SIMPLE SCALING TOOLA SIMPLE SCALING TOOL

L: Domain sizel: Eddy size (~ 50 km)T: Larval release durationt: Eddy turn-over time (~ 14 d)

eddy size (l)

N larval packets

SIMULATIONS VS. PACKET MODELSIMULATIONS VS. PACKET MODEL

(L = 256 km, l = 50 km, T = 90*n d, t = 14 d)

Circulation simulations Packet model

Destination location (km) Destination location (km)

Sou

rce

loca

tion

(km

)

Sou

rce

loca

tion

(km

)

• Packet model represents heterogeneity & stochasticity without expensive simulations

DOES EDDY STOCHASTICITY MATTER?DOES EDDY STOCHASTICITY MATTER?

Diffusion model breaks up packet& lowers density

Rec

ruitm

ent

rate

Density of settling larvae

Beverton - Holt density dependenceA Fish’s Life Cycle

Recruitment rate = f(settlement density)

• Yes, because of the post-settlement density dependence

SAMPLE STOCK DYNAMICSSAMPLE 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

CONCLUSIONSCONCLUSIONS

• 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