flow, fish and fishing
DESCRIPTION
Flow, Fish and Fishing. Dave Siegel University of California, Santa Barbara Moss Landing Marine Laboratory – September 8, 2006. U.S. West Coast Rockfish. Source: Pacific Fisheries Management Council, 2001. I was a victim of public service. - PowerPoint PPT PresentationTRANSCRIPT
Flow, Fish and FishingDave Siegel
University of California, Santa Barbara
Moss Landing Marine Laboratory – September 8, 2006
U.S. West Coast Rockfish
Source: Pacific Fisheries Management Council, 2001
0%
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1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
widowdarkblotchedcanarybocacciocowcodPOP
unfished
overfishedthreshold
rebuildingtarget
I was a victim of public service...
• Served on Science Panel for the Channel Islands Marine Reserve Working Group
• Build a marine protected area to achieve both conservation & fishery objectives – protect biodiversity– maintain fishery yields & incomes
Approved Oct. 24, 2002State waters are
implemented
How a MPA might work
Key: Spatial Management of a Fishery
Fish(x)MPA
• MPA’s increase local stocks• Leads to spillover of fish for harvest
Distance ->
Spillover
Who are we talking about??• Harvested species with limited home ranges• Rockfish, kelp bass, urchin, …• Not tuna, sardine, whales, ...
So, How a MPA might work??• MPA’s allow adults grow to maturity
(especially for sedentary fish & inverts)
• Elimination of harvest enables more “natural” communities & food webs to exist
• Fecundity for many fish increase with age• Fishery benefits if progeny disperse broadly
or adults “spill out” of the MPA
Conservation vs. FisheriesVa
lue
Fractional Set Aside
Conservation Goal
Fishery Goal
Will a MPA Work for Conservation?
• Yes, the “field of dreams” works– If you build an MPA, fish will come...
• Lots of empirical evidence– Larger, more productive adults, more
robust, “natural” food webs, etc.
• Biodiversity goals will be satisfied
MPA’s Work WithinTheir
Borders
From Halpern [2002]
Will a MPA Work for Fisheries?
• A few case studies show nearby fisheries benefiting from a MPA
• BUT, what about the general case?
• How do we predict spillover from a MPA & its role on nearby fisheries?
• Theory is not well advanced...
Organism Life Cycle is Critical
A Typical Life Cycle• Larvae are released to develop in plankton• They disperse in the currents • A select few settle on suitable habitat• Even fewer recruit to adults• The cycle repeats (if they’re lucky)
KEY ELEMENT => Larval Transport
Fishery Models for MPA’s
Next generation stocks = survivors - harvest + new recruits
SURVIVORS are those naturally surviving adultsHARVEST are those extractedNEW RECRUITS are a function of fecundity of the
survivors, larval dispersal & mortality, settlement & recruitment to adult stages
Mathematically...t 1 t tx x x
t t t tx x x x x x
A (1 M)(A H )
(A H )F K P L dx
' ' ' ' '
t
x
tx
tx
x'
tx
[#/km]
[#/km]
[#/year]
(=f(A & fishing effort))
[spawned larvae/adult]
[settled larvae/spawner]
A Adult density
H Harvest YieldM Natural mortalityF FecundityP Larval mortality
L Post-settlementrecru
x x'
[adult/settler]
[(settler/km)/total settled larvae]
itmentK Dispersion kernel
Dispersal Kernel
Dispersal Kernels• A dispersal kernel defines probability of
successful larval settling as function of distance from a site
• Units of [settlers / km / total settlers]
Distance alongshore [km]
K(x)
X=0
K(x)dx 1
Objectives of this talk• Characterize the larval dispersal
Address the time/space scales of “connectivity”Understand competing roles of biology & physics
• Develop bio-physical models of larval transport
• Markov chain modeling of larval dispersal • Regional Ocean Modeling System (ROMS)
– Release & advect larvae using simulated flows– Assess where they settle -> connectivity matrices
Kinlan & Gaines [2003], Ecology
Dispersal Scales for Marine Organisms
Dispersal & Time in Plankton
Siegel et al. [2003; Marine Ecology Progress Series 260: 83-96]Pelagic Larval Duration (days)
Gene
tic D
isper
sal S
cale
(k
m)
The longer the development time,the further the mean dispersal
Modeling Larval Dispersal
• Larvae are advected & dispersed by coastal circulations as they develop competency to settle in suitable habitat
• Important elements for modeling dispersal– Pelagic larval duration (PLD)
What is the development time window for the organism?
– Ocean circulation (mean & fluctuating currents)– Larval behavior (depth strata that larvae prefer)
Coastal flows are highly variable...
HF Radar Surface Currents - Libe Washburn [UCSB]
-120.6 -120.4 -120.2 -120 -119.8 -119.6 -119.4 -119.233.8
33.9
34
34.1
34.2
34.3
34.4
34.5
Longitude (oE)
Latit
ude
(o N)
All drifter tracks from GOIN - Data from CCS/SIO
Lagrangian paths are too..
Location of “settlement” of GOIN drifters - Winant et al. [1999]
Where do drifters settle?
• Model trajectories of many individual larvae• Correlated random walk - Markov chain • Use realistic ocean velocity statistics for surface flow
– Homogeneous ocean with different values of U, u & L
– A “CODE-like” scenario following Davis [1981]
• Requires larval development time scenario - biology• Ensemble averaging provides dispersal kernel
Siegel, Kinlan, Gaylord & Gaines [2003; MEPS]
Modeling of Larval Transport - 1
Example Trajectories
-50 -40 -30 -20 -10 0 10 20 30 40 500
10
20
30
40
50
60
70
80
90
100
along-shore distance [km]
cros
s-sh
elf d
ista
nce
[km
]
0/5d settlers
-300 -200 -100 0 100 200 300 400 500 6000
100
200
300
400
500
600
700
8006/8w settlers
along-shore distance [km]
cros
s-sh
elf d
ista
nce
[km
]
PLD = 0 to 5 days PLD = 6 to 8 weeks
U = 5 cm/s & u = 15 cm/s
Estimate of Dispersion Kernels
-150 -100 -50 0 50 100 1500
50
100
150
200
250U = 5 ustd = 15 To = 0 Tf = 5
tota
l set
tlers
= 13
66 t
otal
par
t = 5
000
alongcoast (km) (a,b,c = 205.2 5.6392 18.974)-600 -400 -200 0 200 400 600 800 10000
10
20
30
40
50
60
70
80
90
100
U = 5 ustd = 15 To = 42 Tf = 56
tota
l set
tlers
= 10
24 t
otal
par
t = 5
000
alongcoast (km) (a,b,c = 84.815 200.39 216.62)
PLD = 0 to 5 days PLD = 6 to 8 weeks
• K(x) defines along shore settling probability distribution• Trajectories are summed to determine K(x)
A Gaussian form for K(x) seemed to hold for nearly all flow/settling protocols
Mean currents regulate offset (xd)
RMS flow drives spread (d) & amplitude (Ko)
Kernel Modeling Results
Kernel Modeling Scaling
Ko = f(1/(PLD u))
d = f(PLD u2)
xd = f(PLD U)
Dd = dispersion scale“Spread”
“Amplitude” “Offset”
A Model Validation?
Genetic Dispersion Scale (km)
Mod
eled
Disp
ersio
n Sc
ale,
Dd
(km
)
Another Model Validation??
Scripps/MMS Drifter Beachings o = release site & + = beaching
Data from Ed Dever (OSU)
Drifter Model Validation??
PLD = 2 d
U = 15 cm/su = 15 cm/s
PLD = 7 d
U = 5 cm/su = 15 cm/s
•Dispersal kernels can be estimated using simple particle dispersion theory
•K(x)’s are to O(1) Gaussian & are parameterized using simple flow & life history information
•Dispersal modeling is roughly consistent with genetic & beached drifter estimates
•Time scales are important… but ignored here
Markov Chain Results
PISCO / SBC-LTER [UCSB]
160 180 200 220 240 260 280 300 3200
10
20
30
40
50
60
70
JD 2001
# se
ttler
s/de
ploy
men
tEllwood Invert Setttlment Time Series
Mytilus Clams (excl razor & HIAARC) any marine snail (excl. veligers, limp)Limpet species Snail veliger any seastar Hiatella arctica
Invert Settlement Time Series – Ellwood, CA
Interpreting Settlement Time Series
• Stochastic, quasi-random time series• No correlation in settling among species • Relatively few settlement events for each species• Events are short (typically 2
days)
160 180 200 220 240 260 280 300 3200
10
20
30
40
50
60
70
JD 2001
# se
ttler
s/de
ploy
men
t
Ellwood Invert Setttlment Time Series
Mytilus Clams (excl razor & HIAARC) any marine snail (excl. veligers, limp)Limpet species Snail veliger any seastar Hiatella arctica
• Annual recruitment may be a small sampling of a dispersal kernel (N = 10?, or less!!)– (300 releases / year) * (10% survival) / (3 day L)
Time, continued...
-100 -50 0 50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
U = 5 Ustd = 15 To = 14 Tf = 21
tota
l set
tlers
= 13
tot
al p
art =
100
alongcoast (km)
• Example for N= 100 ->
• Implies that connectivity is stochastic & intermittent
N=5000
A Stirred, Not Mixed Ocean!
• Stochasticity in larval settlement is created from sampling only a few trajectories
• Larval transport occurs in a stirred, not mixed ocean
• Need to model the correlations in the flow to understand time / space scales of larval transport– To do this we use a coastal circulation model
•Advect “larvae” using an ocean circulation model– Time dependent, 3D, quasi-realistic circulations – Regional Ocean Modeling System (ROMS)– Model summer-time conditions offshore of Pt Sur
(CalCOFI line 70 – maximum upwelling conditions)– Uniform domain in the alongshore direction– Forcings based on observations
Modeling of Larval Transport - 2
Mitarai et al. in press, Journal of Marine SystemsSiegel et al. in review, PNAS
Numerical Setting
2-km horizontal resolution 20 vertical levels
• Unstructured in alongshore direction (periodic BC)• Stochastic wind forcing at surface (stats from buoys)• Alongshore pressure gradient as a body force• Free slip inshore BC & open BC offshore
Shows good agreement with CalCOFI mean
Model ValidationCalCOFI data (July, Line #70)
Simulation field(mean over 180 days)
• Good agreement with surface drifter observations
• Model disperses particles appropriately
Model Validation
Time scale Length scale Diffusivity
2.7/2.9 d 29/31 km 4.0/4.3 x107 cm2/s
2.9/3.5 d 32/38 km 4.3/4.5 x107 cm2/sSurface drifter data(Swenson & Niiler)
Simulation data
(along/cross shore)
Adding Larvae…• Pattern after rocky reef fish, BUT we want large
number of successful settlement events• Large, uniform nearshore habitat (< 20 km)• Larvae are released daily for 90 days every 2
km• Settlement occurs for larvae aged 20 to 40 days• Biotic larval mortality is not considered• Source-destination relationship are calculated -> Assumptions lead to large settlement rates
Connectivity is
Heterogeneous
Connectivity diagrams show connection strength & locations of “hot spots”
Settlement is patchyPeak is ~120 km upstream
Self settlement happensSettlement is heterogeneous in an unstructured domain
Destination Location (km)
Sou
rce
Loca
tion
(km
)
Self se
ttlemen
t
Connectivity is Not Diffusive
Destination Location (km)
Sou
rce
Loca
tion
(km
)
Self se
ttlemen
t
simulated diffusive
Connectivity is Intermittent
4 different realizations -> 4 different connectivity patterns
Connectivity Can Differ for Differing Life Histories
Same flowDifferent PLD’s
Different patterns caused by life history diff’s for the same flowDestination Location (km)
Sou
rce
Loca
tion
(km
)
20-40 d 5-10 d
Connectivity Can Differ for Differing Larval Behaviors
Same flowEnable simple vertical migration
Different patterns arise due to larval behavior diff’s
Destination Location (km)
Sou
rce
Loca
tion
(km
)
surface migration
Connectivity is Still Stochastic for a Sinuous
CoastlineSame flow but a sinuous coastline
Patterned after CA coast
“Hot spots” do NOT follow coastline features
surface migration
Summary of Modeling Results
• Larval connectivity patterns are heterogeneous & intermittent & NOT diffusive (even for a uniform region!!)
• Life history can alter connectivity patterns (for same flow)
• Arriving larvae come in “packets” (scaling theory developed)
• Self-seeding & distant transport occur as rare, discrete settlement events (influencing alee effects)
• Present case optimizes successful settlementNearly any change will make stochasticity worse!!
Implications• Larval settlement on annual scales is noisy
– Makes stock [& MPA] assessments difficult– Local stocks & recruits are [largely] unrelated– Noise is unavoidable
• Successful settlement will occur for only a few “larval packets” each year– Role in self recruitment & colonization– Critical for spatial fishery management
Flow, Fish and Fishing
Dave Siegel, Chris Costello, Steve Gaines, Bruce Kendall, Satoshi Mitarai & Bob Warner
[UCSB]Ray Hilborn [UW]
Steve Polasky [UMn]Kraig Winters [SIO/UCSD]
A Biocomplexity in the Environment Project
The Flow, Fish & Fishing Idea
• Larval transport is stochastic driven by stirring• Fish stocks, yields & their assessment are
affected directly by this & other forcings • Management under this uncertainty must be
accounted for robustly
• Key ingredients are notion of scale and the flows & values of information
Flow
Fish
Settlement
Habitat Recruitment
Harvest
RegulationFisherm
en
Market INFO
Climate
What sets the scales of fish stocks & harvest?
larval transport, recruitment to adult stages, habitat, adult migration, fishery regulation, natural & fishing mortality, fisherman behavior, prices vs. costs, ??
Fishermen
A Coupled Human-Natural System
• Couple oceanographic, population dynamics, fish life cycle, management, fisherman behavior, regulatory and economic processes
• Approach - analytical & simulation modeling– From groundfish to “roundfish”
• Focus on mechanisms which are generalizable & not on the results of detailed case studies
F3 Modeling Approach• Circulation & Larval Transport – time / space
scales of larval transport & their settlement
• Stock / Harvest Dynamics – implications of uncertainty on fish stocks, yields & profits
• Fleet Dynamics – How do fishermen choose when, where & how to fish?
• Value of Information – How does amount & quality of data available inform the management process?
Flow, Fish & Fishing in a Nutshell
• Larval transport is stochastic which impacts fish stocks, yields, profits & their assessment
• Approach is to build models which assess processes linking uncertainty & management
• Goal is to help change the best science that drives fishery management
• Fundamental disciplinary achievements can come from interdisciplinary research program
Flow, Fish & Fishing Webpage
www.icess.ucsb.edu/~satoshi/f3
Mathematically ...x x t u Ui
t 1it
it c h
x x location of particle i at time t
u fluctuating x - velocityof particle iU mean x - velocity
t timestep Repeat for y - direction
it
it
i
x x t u Uit 1
it
it c h
x x location of particle i at time t
u fluctuating x - velocity of particle iU mean x - velocity
t time step Repeat for y - direction
it
it
i
Modeling Fluctuating Velocity
u ut t
it 1
it FHG IKJ 1
2
RN u
Lagrangian autocorrelation timescaleRoot mean squared x velocity
RN Normal randomdeviateu
Here, spatial homogeneity in velocity statistics is assumed
u u t tit 1
it FHG IKJ 1 2
RN u
Lagrangian autocorrelation time scaleRoot mean squared x velocity
RN Normal random deviateu
Dispersion Modeling• Choose a velocity field
Mean flow - U = 0, 5 & 10 cm/s & V = 0RMS fluctuation - u = 5, 10, 15 & 20 cm/sAlternatives - CODE (Davis, 1985) varies from 0.5 to 3 d from on- to off-shore
• Choose a Planktonic Larval Duration (PLD)Many macroalgae 0 to 5 daysSome inverts & fish 2 to 3 weeksMany others 1 to 3 months
• Need demographic parameters (F, P, L, M)• Specify a harvest policy (constant effort)• Need density dependence (Ricker for Lt
x)• Example of yields for a MPA network
Application to MPA Modeling
t 1 t t t t tx x x x x x x xA (1 M)(A H ) Y F K P L dx
' ' ' '
A Fish’s View of Larval Transport
• My fecundity rates are huge • The probability of success for my babies is tiny• My population’s spawning season is short • The time for my babies in the pelagic (PLD) is
relatively short -> Larval connectivity of populations are
stochastic on annual time scales
My Goals• Provide a predictive understanding for
nearshore fisheries
• Illustrate using the MPA example
• Assess mechanisms linking ocean, life cycle & demographic processes & policy
• Introduce Flow, Fish & Fishing (F3)
My Modeling Philosophy
• Model simple, generalizable scenarios• Consider process -> organism’s life cycle
• Ignore exceptional attributes • Match impedance among physical, ecological
& management modeling approaches • Confront model results with data
Example Flow Field
Mitarai et al. in press, Journal of Marine SystemsSiegel et al. in review, Science
Factors Affecting Nearshore Fisheries
• “Intrinsic” dynamicsmortality, fecundity, recruitment, migration, etc.
• “Extrinsic” dynamicslarval transport, settlement, community interactions
• Exogenous processesENSO, climate change, man-made disaster, etc.
• Anthropogenic processesharvest mortality, its regulation, learning, etc.
Consider a spherical fish...
• 1-D domain– simplified spatial domain - alongcoast
changes• Single species only
– no community feedback• Sessile adult stages
– no adult movement among subpopulations• Demographics & life cycles are known
Larval Transport• Many nearshore fishes & inverts have an
obligate larval stage & are [nearly] sessile as adults
• Planktonic larval durations (PLD) range from days to months
• To O(1), larvae will disperse with the currents• During this time they can disperse 100’s m to
100’s of km
A Stirred, Not Mixed Ocean!
• Stochasticity in larval settlement is created from sampling only a few trajectories
• Larval transport occurs in a stirred, not mixed ocean
• Alternative conceptual model...
“Threads of Connectivity”
Threads of Connectivity??
Distance ->
Implications of Stirring
• Few trajectories make source-destination relationships noisy & kernels “spiky”
• Makes experimental work difficult – Hard to relate larval sources to settlement
• Limits applicability of smooth kernels– Evolution/genetics/biogeography? Probably– Annual management of a fisheries? No!!
Benefits of Being Old & Fat
Larval Transport, Time & Fish Stock Uncertainty
• Larval dispersal measured or modeled represents ensemble mean conditions
• The implied time to construct similar mean estimates is 10 to 50 years!!
• However, fish life cycles & management time scales are much shorter
Fishery Models for MPA’s
Next generation stocks = survivors - harvest + new recruits
SURVIVORS are those naturally surviving adultsHARVEST are those extractedNEW RECRUITS are a function of fecundity of the
survivors, larval dispersal & mortality, settlement & recruitment to adult stages
Mathematically...t 1 t t t t tx x x x x x x xA (1 M)(A H ) Y F K P L dx
' ' ' '
t t
x x
tx
tx
tx
x'
tx
[#/km]
[#/km]
[#/year]
( A H )
[spawned larvae/adult]
[settled larvae/spawner]
A Adult density
H Harvest Yield
Y Escapedadult densityM Natural mortalityF FecundityP Larval mortality
L Post-settlem
x x'
[adult/settler]
[(settler/km)/total settled larvae]
ent recruitmentK Dispersion kernel
• Need demographic parameters (F, P, L, M)• Specify a harvest policy (constant effort)• Need density dependence (Ricker for Lt
x)• Example of yields for a MPA network
Application to MPA Modeling
t 1 t t t t tx x x x x x x xA (1 M)(A H ) Y F K P L dx
' ' ' '
The “Larval Pool” Hypothesis
Distance ->
Well-Mixed Larval Pool
Settlement Sites
Cross-Shelf Transport
Larval Pool Hypothesis is Inconsistent!
• A mixed larval pool would necessitate the co-settlement of species
• Only a few co-settlement events are seen• No “gate-keeping” at the innershelf• At least for this site
(& others like it)
160 180 200 220 240 260 280 300 3200
10
20
30
40
50
60
70
JD 2001
# se
ttler
s/de
ploy
men
t
Ellwood Invert Setttlment Time Series
Mytilus Clams (excl razor & HIAARC) any marine snail (excl. veligers, limp)Limpet species Snail veliger any seastar Hiatella arctica
Are Dispersion Kernels Consistent??
• Kernels should diffuse larvae down-gradient
• Events should follow releases smoothly
• Settlement time scales suggest the ocean works differently...
160 180 200 220 240 260 280 300 3200
10
20
30
40
50
60
70
JD 2001
# se
ttler
s/de
ploy
men
t
Ellwood Invert Setttlment Time Series
Mytilus Clams (excl razor & HIAARC) any marine snail (excl. veligers, limp)Limpet species Snail veliger any seastar Hiatella arctica
Distance alongshore [km]
K(x)
X=0
Larval Transport, Time & Fish Stock Uncertainty
• Larval dispersal measured or modeled represents ensemble mean conditions
• The implied time to construct similar mean estimates is 10 to 50 years!!
• However, fish life cycles & management time scales are much shorter
A Stirred, Not Mixed Ocean!
• Stochasticity in larval settlement is created from sampling only a few trajectories
• Larval transport occurs in a stirred, not mixed ocean
• Alternative conceptual model...
“Threads of Connectivity”
Threads of Connectivity??
Distance ->
Implications of Stirring
• Few trajectories make source-destination relationships noisy & kernels “spiky”
• Makes experimental work difficult – Hard to relate larval sources to settlement
• Limits applicability of smooth kernels– Evolution/genetics/biogeography? Probably– Annual management of a fisheries? No!!
Fishery Management in a Stirred Ocean
• Stock-recruitment relationships will be noisy due to stochasticity from larval transport
• Present estimates of excess fish production (total allowable catch) will be highly uncertain
• Huge amounts of information will be required to reduce this noise (at correspondingly huge costs)
• How should nearshore fisheries be managed?
Modeling Larval Transport
• Parameterize source-to-destination exchange among nearshore populations
• Incorporate important oceanographic & life history characteristics
• Constrain using field observations• Useful for modeling spatial population
dynamics
The Flow, Fish & Fishing Idea
• Larval transport is stochastic driven by stirring• Fish stocks, yields & their assessment are
directly affected by this stochastic forcing • Management under this uncertainty must be
accounted for in real & robust ways• The key is assessing the flow & value of
information to management
Bocaccio (MacCall et al. 1999)
0
10,000
20,000
30,000
40,000
50,000
0 2,000 4,000 6,000 8,000 10,000 12,000Spawning Output
Recr
uits
(x 10
00)
Pacifi c whiting (Dorn et al. 1999)
02468
101214
0.0 0.5 1.0 1.5 2.0 2.5 3.0Female Spawning Biomass
Recr
uits
(x 10
00)
• Used by PFMC for determining quotas & stock rebuilding plans
Real Stock-Recruitment Relationships