An individual-based population dynamic model of seas scallop, with application to Georges Bank

Rucheng TianDepartment of Fisheries Oceanography

SMAST, UMASSD

Supervisors: Drs. C.S. Chen, K. Stokesbury, B. Rothschild

Participants: the FVCOM group, Q.C. Xu, S. Hu, G. Cowles, B. Harris and M. Marino

Outline: - Model structure - Parameterization - Model set up for application - Results - Findings

Scallop life cycle

(Stewart, P.L. and S.H. Arnold. 1994. Can. Tech. Rep. Fish. Aquat. Sci. 2005: 1-36).

1 2 3 4 5

f1

f2

G1 G2 G3 G4

P1 P2 P3 P4 P5

(EPA RI). Stage-based population model f1, f2: Reproduction; G1-4: recruitments; P1-5: survivorship (Hinchey, Chintal, & Gleason 2004 ).

A stage-based population model for bay scallop

r

n1 n1 n1 n1

n2 n2 n2

n3 n3 n3

n4 n4

nn

nk nk

t t+1 t+2 t+n

e e e e

Time

m m m

mmm

m m m

m m

m m

m

Weigh

t

r rMinimum harvest weight

G

n: number of mussels; e: spawning; m: mortality; r: harvesting; G: growth (Gangnery et al., 2001)

Population dynamics model of mussels

Egg

Z

Pediveliger

P

N

Veliger

D

Adult

Sed

imen

t

Biodeposits Young adultJuvenile

F

F

R G

ST S S

H

Eulerian Lagrangian

Wat

er

TrochophoreSV

SV

D: Detritus; N: Nitrogen; P: Phytoplankton; Z: ZooplanktonF: Feeding; G: Growth; H: Hatching; R: Recruitment; S: Spawning; ST: Settlement; SV: Survivorship;

A Lagrangian individual-based population dynamic model of scallop, coupled with an Eulerian concentration-based ecosystem model

Parameterization

Ross and Nisbet, 1990.

Starvation mortality:

RGwhen

RGwhenGR

MS

SSS

S

0

)( R : Respiration.G : GrowthS: Constant. S : Constant.

)release after theMortality ( ;),(

)release thebefore Spawning(;2

1

),(

1

2

12

tMi

t

t

tt

eggscallop

i

etnP

eSN

tnP

m

ttagePtageP ii ),(),(

)1)(,(),( lii gtthPthP

)1)(,(),( wii gttwPtwP

Biological attributes of Lagrangian ensemble particles

Number of

larvae:

Age:

Height:

Pi(n,t): Number of eggs at t in an ensemble particle;Nscallop: Total scallop in a simulation cell; Segg: Total eggs spawned by each individual adult scallop in one season;M: Mortality (0.25 d-1; McGarvey et al., 1993)

Biomass:

),()()(),( tPWKRARtutxP imxxxi

2/11 ('2'))( ttKKrtKKR xxxx

)(35);(7.1

)(355);(1.0

)(52);(3.0

)(2;0

),(

1

1

1

dayagewhensmm

dayagewhensmm

dayagewhensmm

dayagewhen

agePW im

Lagrangian trajectory

Trajectory:

Random walking:

A : Horizontal diffusivity. K : Vertical diffusivity; Pi : Particle i at x and t; Wm: Vertical migration; r : Random process; σ : Std of r; t : Time; u : Current; x : Spatial position. (Visser, 1997)

Behavior:

(eggs, at 1 m above the bottom)

(trochphores)

(veligers)

(pediveligers)

41.4

66.0067.00 66.8 66.6 66.4 66.2

41.7

41.8

42.1

41.5

41.6

41.9

42.0

CAI

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

Provided by K. Stokesbury

Thouzou et al., 1991

)1(87.144)1()( )5566.0(2813.0)(max

0 tttk eeHtH

H(3) = 72.03 (mm)

F(>age 3) = 76% (average on GB)

Estimation of the spawning stock

von Bertalanffy growth function:

22

168

600

2

1

1

72

1

1 1682

1100.5

2

1),(

t

t

tscallop

ttt

teggscallopi eNeSNtnPm

The simulation starts on Aug 15;

tm (maximum spawning day) is assumed to be on Sep. 10;

(deviation) is assumed to be 1 week;

One adult spawns in average 50 million eggs (Langton, 1987; McGarvey et al., 1992, 1993)

Abundance of scallop > age 3 (N m-2 )

Spawning

21

2

1

2

1)(

2

2

1 xerfetF

tt

The normal distribution was integrated using the error function:

Substrate distribution and larvae-settlement probability

Settlement probability

Settlement probability: Gravel: 0.2; Sand: 0.05; Fine sand: 0.01.

The scallop simulation was conducted with the framework of FVCOM

- Surface forcing from MM5.

- Tide.

- Monthly boundary conditions.

- Daily SST data assimilation.

- River discharges.

Larvae settlement

Movie of simulated larval trajectory for 1995

Hor

izon

tal t

raje

ctor

y Vertical trajectory

Movie of simulated larval trajectories for 1995 and 1998

Drifter trajectories

(Lozer & Gawarkiewicz, 2001, JPO. 31: 2498-2510)

0

2

4

6

8

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005Year

Lar

vae

(1012

)

GB GSC MAB

0

2

4

6

8

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005Year

Lar

vae

(1012

)

GB GSC MAB

Total larvae settled on Georges Bank (GB), in the Great Southern Channel (GSC) and to the Middle Atlantic Bight (MAB)

Late spawning is unfavorable for larvae retention on Georges Bank

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Temp. run 79% 37% 47% 23% 26% 32% 36% 48% 74% 25% 16%

Larvae exchange between scallop subpopulations

Closed area selection and rotation

Closed area selection and rotation

Closed area selection and rotation

Closed area selection and rotation

Schematic of the scallop benthic module

Phytoplankton

Suspended sedimentsDetritus

Sediment Biodeposits SedimentScallop

Watercolumn

Boundary layer

Detritus

Phytoplankton

Suspended sediments

Mixing Mixing

Sedimentation SuspensionSedimentation Suspension Feeding Feeding

Forcing TemperatureCurrent/turbulence Predator

Natural & fishing MortalityPredation ResuspensionStarvation Temperature stress

Sinking Sinking

SUMMARY

- Construct your model based on your question.

- Better using prognostic parameterizations than diagnostic one.

- Model set up can be specific to each ecosystems.

- Long-distance larval transport from GB to the MAB.

- Interannual variability due to physical forcing.

- Larval exchanges between scallop beds.

- Closed-area selection and rotation.

END