Application of quantitative dispersal models to the design of MPAs eddy diffusivity and exchange on

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Application of quantitative dispersal models to
the design of MPAseddy diffusivity and exchange
on shallow continental shelves

• Karen Pehrson Edwards
• Oral Exam
• Sept. 26, 2005

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History of MPAs in the SAFMC
1990
2004
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Fisheries Effects of MPAs
Russ, 2001.
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Outline

• Measuring Larval Dispersal
• Strategic models MPAs
• Tactical models
• Georges Bank Scallops
• Great Barrier Reef
• Application of quantitative models to the SAB
• Eddy diffusivity and dispersion
• Conclusions

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Methods to Study Dispersal

• Movement-redistribution methods or direct
  tracking of individuals
• Depends on relative body size and dispersal
  distance (Nathan 2001)
• Genetic Analysis
• Relate mean dispersal distance to the increase in
  genetic differentiation with distance, or
  isolation-by-distance (IBD) (Kinlan and Gaines,
  2003).
• Models
• Simplest models estimate larval dispersal from
  the duration of the pelagic larval stage combined
  with the movement of passive particles in
  low-frequency currents (Grantham et al., 2003
  Shanks et al., 2003, and references therein)

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Strategic Models for MPAs

• Larval movement is typically represented by one
  of 3 simple abstractions

Pure diffusion

• Question answered

Predicted area needed in reserves

• Schematic of marine reserve network

Gell Roberts 2003
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Source-Sink Dynamics and MPAs
Model design hypothetical archipelago of reefs
includes 20 reefs in a 4x5 array. Looked at
population response to reserve placement.
Suggests that not only habitat quality (sources
and sinks) but spatial location of reserves
relative to physical factors is important in MPA
design.
Crowder et al. 2000
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Tactical Models Georges Bank Scallops
1998 Scallop abundance from dredge survey tows
John Quinlan, ECOHAB/GLOBEC Portland ME, June
17-18, 2002 Murawski et al., 2000
http//www-nml.dartmouth.edu/Publications/internal
_reports/NML-00-2/
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Scallop source/sink dynamics along the east coast
Settlement Distributions
John Quinlan, ECOHAB/GLOBEC Portland ME, June
17-18, 2002
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Larval dispersal on the Great Barrier Reef
Larval Retention
1985
1989
gt0.2 0.1 - 0.2 lt 0.1
gt0.02 0.01 - 0.02 0.005 - 0.01 lt0.005
1996
Avg
Creation of Connectivity Matrix
James et al., 2002
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Quantitative dispersal models and MPAs on the SAB

• Use dispersal kernels to create connectivity
  matrices of hard bottom reefs on the SAB shelf.

All Spring Runs
Provided by Harvey Walsh, NOAA Beaufort
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Current SAFMC Proposed MPAs

• Deepwater snapper/ grouper complex rely on
  estuarine habitats for juvenile stage - larvae
  must cross the shelf.
• Lack information linking spawning sites to
  estuarine habitat and which spawning sites
  (proposed MPAs) have most successful larvae.

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Quantitative dispersal models and MPAs on the SAB

• Quantifying Arrival Kernels Use arrival kernels
  to quantify larval transport from the shelf-edge
  proposed MPA/ spawning sites to inlets.
• The figure shows the starting locations of
  larvae arriving at each inlet.

Hare et al, 1999 John Quinlan, ECOHAB/GLOBEC
Portland ME, June 17-18, 2002
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Quantitative dispersal models and MPAs on the SAB

• For reef fish populations on the shelf and for
  deepwater snapper/grouper proposed MPAs
• With realistic 3D flow fields available,
• Spawning sites and times, and estimates of larval
  behavior,
• Create quantitative dispersal/arrival kernels.
• Aggregating the kernels to create Connectivity
  Matrices (aij(t)),
• A network of MPAs could be designed or tested.

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Eddy diffusivity and exchange on shallow
continental shelves
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Dispersion
http//marine.rutgers.edu/cool/latte/images/CT_plu
me.jpg

• Diffusive mixing by turbulence.
• Effect of different eddy scales on
  transport and spreading of a patch of material
• Eddies which are larger than the patch transport
  it without affecting its shape
• Intermediate-scale eddies cause distortions which
  lengthen the boundary with the surrounding liquid
• Eddies which are smaller than the patch play a
  diffusive role, smoothing out distortions or
  irregularities in shape
• Dispersion in estuaries and coastal waters.

1926 Richardson observed the relative motion of
two floating pieces of parsnip, Dispersion in
estuaries and coastal waters.
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Shear Diffusion
Spatial variations in velocity increase the
surface area over which diffusive mixing can act.
u
z
Kz

• Spreading due to vertical shear in horizontal
  advection.

Include vertical diffusion or mixing, Kz.
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Measuring Diffusion
(Okubos ?rc (cm))

• In dye studies, eddy diffusivity, K (m2s-1), is a
  measure of the rate of increase of a patch of
  dye.
• In modeling, K provides for diffusion due to
  sub-grid-scale processes or processes not
  included in the model. Calculate displacement
  added to particle velocity

Lewis, Dispersion in estuaries and coastal waters.
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Oceanic Diffusion
?rc (km)
Ka100 m2/sec
month
Sundermeyer (2001)
?2rc 0.0108t2.34 Ka? ?2rc/4t
Ka 0.0103l1.15 l ? 3?rc
Okubo, 1971.
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Model K-test
From Okubo (1971) l (typical length scale
3?rc) ? 100 km after 1 month K1 m2/sec, l ?
50 km K10 m2/sec, l ? 80 km K100 m2/sec, l ?
180 km
Using K10 m2/sec in the model provides the
appropriate length scale after one month.
?2rc2 s11 s22
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Application to Larvae
Dispersion studies of larvae and eggs in relation
to Okubos Ka
Dispersion vs. Age of Larvae
Hare et al. (1999)
McGurk, 1989
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Conclusions

• With simple climatology and M2 tides, reduce K
  from 100 m2s-1 (observed after 30 days) to 10
  m2s-1 in model.
• As larvae become capable of more behavior,
  passive diffusivity coefficients may no longer be
  valid.
• Application of quantitative models to the SAB
• Connectivity matrices from an ensemble of
  dispersal kernels can be used to create network
  of MPAs.
• Ideally, couple physics with metapopulation
  models.

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I know that the human being and the fish can
coexist. - George Bush
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Questions/Open Issues?

• Need to define level of connectivity that is
  ecologically feasible? What level of
  self-recruitment is needed in MPAs to maintain
  populations?
• Need to define how close a larval fish gets to a
  reef before assuming that it finds it.
• Important to know how much variability in the
  connectivity interseasonal, interannual, longer
  term
• How big should MPAs be? GRNMS is 58km2.
  Individual reefs too small and too difficult to
  enforce. Larger areas would have benefit of
  including between-reef habitat.
• Need larval and adult fish surveys to validate
  models. Are larvae dispersing where models say?
  Are adults living and spawning on identified
  source reefs?

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Putting Effort Catch Together
Murawski GLOBEC Talk
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Ensemble Modelling

• Ensemble forecasting cover a larger part of the
  possible future through introduction of variation
  in initial conditions.
• Perturb initial conditions (NCEP uses 11 member
  ensemble).
• Multi-scheme ensemble uses variations in same
  model
• Multi-model ensemble uses different models
• Poor mans ensemble initial conditions from
  overlapping runs of Met Model

Giebel et al., 2003
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Population Markers in Larval Dispersal Studies

• Artificial Tags
• Flourescent compounds (Jones et al., 1999)
• Elemental tags
• Radioactive isotopes
• Thermal marks
• Disadvantages
• Requires recapture of significant number of
  tagged individuals to draw valid conclusions

• Natural Tags
• Genetic Markers
• Environmental Tags (Swearer et al., 1999)
• Disadvantages
• Natural tags are rarely unequivocal
• Need signatures from all likely source regions

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A mark and recapture study of reef fish dispersal

• Marked the otoliths (using tetracycline) of 10
  million larval damselfish at six reef sites on
  the GBR
• Later collected juveniles and found that 15 out
  of 5000 were originally from that reef
• Estimated a retention of 15 to 60
• Jones et al., 1999

Map of Lizard Island on the North Great Barrier
Reef
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Benefits of MPAs - Higher density of target
species inside reserve. Adult Spillover Adults
have to spend most of their time in reserves
Tagging and tracking large vertebrates Bluefin
Tuna movements Block et al
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Ascidians (sea squirts)
Colonial organism that is highly organized and
closely related to vertebrates. They are filter
feeders. Some form colonies, larger ones are
solitary.
home.att.net/ mmkdomanski/ascidians.jpg
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ECOSPACE (ECOPATH/ECOSIM)

• Results indicate larger/ fewer MPAs more
  effective than smaller/ many.
• May be more appropriate for studying adult
  spillover.
• Does not include physical transport or
  circulation even at a coarse scale.

Salomon et al., 2002. 1,2,3,4 represent depth
categories 40-30m, 331-50m, 251-70m and 170m
Walters et al., 1999, Walters 2000 www.ecopath.org
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Dispersal and connectivity
Why are they important to measure?

• Population and community ecology understanding
  the basics
• Management and conservation Design and evaluate
  MPAs
• Evolution What causes genetic isolation and
  speciation?
• Biogeography Evaluate the extent to which range
  limits are set by barriers to dispersal rather
  than physical tolerances of adults
• Introduced Species What controls rates of spread
  of exotics
• Dynamics of infectious diseases Evaluate the
  role of linkages in the epidemiology of diseases.