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
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