Intermingling of two Pseudocalanus species on Georges Bank D.J. McGillicuddy, Jr. Woods Hole Oceanographic Institution A. Bucklin University of New Hampshire Journal of Marine Research 60, pp , 2002.

P. moultoni P. newmani 1997 Broadscale Survey Data Species-specific PCR (Bucklin et al., 2001)

The forward model: an advection-diffusion-reaction equation C concentration v velocity K diffusivity Advection Tendency Diffusion Reaction (biological sources and sinks) C obs (t 0 ) C obs (t 1 ) time The forward problem

Observations: P. Moultoni Models Observations: P. newmani

Are the inverse solutions ecologically realistic? R(x,y,t) bounded by –100 to +100 individuals m -3 day -1 [most fall between -10 to +10] C 5 moulting potential: Mean C 5 abundance 2500 individuals m -3 (Incze pump samples: April 1997, May 1997, June 1995) Stage duration in GB conditions: 5 days (McLaren et al., 1989) Implied moulting flux of 500 individuals m -3 day -1

Are the inverse solutions ecologically realistic? Predation potential: Model predicted rates of 3-10% day -1 Bollens et al. specific rates of predation on C. finmarchicus and Pseudocalanus spp. copepodites based on observed predator abundance and feeding rates

Inverse method results in convergent solutions Geographically specific regions of growth/mortality These vary seasonally according to animal abundance patterns, the circulation, and their orientation Two main balances: –Tendency / source (weak currents or aligned gradients) –Tendency / source / advection Conclusions (I)

Resulting biological sources and sinks ecologically realistic -- R(x,y,t) bounded by independent rate estimates C 5 moulting flux Predation by invertebrates and vertebrates Emerging conceptual model: -- Distinct source regions in late winter P. moultoni on NW flank P. newmani on NE peak and Browns Bank -- During the growing season, GB circulation blends these reproducing (not interbreeding) populations such that their distributions overlap by early summer. Conclusions (II)

Physics -- errors in the circulation -- vertical shear Biology -- density dependence vs. “geographic” formulation -- multistage models, behavior, etc. Observational limitations -- only adults -- upper 40m Caveats

Are the inverse solutions ecologically realistic? R(x,y,t) bounded by –100 to +100 individuals m -3 day -1 [most fall between -10 to +10] C 5 moulting potential: Mean C 5 abundance 2500 individuals m -3 (Incze pump samples) Stage duration in GB conditions: 5 days (McLaren et al., 1989) Implied moulting flux of 500 individuals m -3 day -1 Predation potential: Hydroid ingestion rate: 0.25 cop. hydr -1 day -1 (Madin et al., 1996) Characteristic abundance: 10,000 hydranths m -3 Potential consumption rate: 2500 copepods m -3 day -1 Pseudocalanus adults ~15% of total postlarvae (Davis, 1987) Hydroid predation on Pseudocalanus: 200 individuals m -3 day -1

Pseudocalanus spp. MARMAP Concentration (# m -3 ) Two population centers: Western Gulf of Maine Georges Bank Davis (1984) hypothesis: Western Gulf of Maine is a source region for the Georges Bank population

General circulation during the stratified season Beardsley et al. (1997)

A first attempt to simulate the data…

Derivation of the adjoint model (1) Problem: Given observations C 0 (t 0 ) and C 1 (t 1 ), find R(x,y) that minimizes J Define a cost function J: Where λ=λ(x,y,t) are Lagrange multipliers

Derivation of the adjoint model (2) Adjoint model: We require R at the minimum of (and therefore J) where It can be shown that:

Convergence of the iterative procedure

Example results: Mar-Apr to May-Jun Red: source Blue: sink

Term-by-Term Diagnosis Observations Biological Source/Sink Advection Diffusion Tendency JF-MA MA-MJ MJ-JA

Chlorophyll-a MARMAP O’Reilly and Zetlin (1996) Jan-Feb Mar-Apr May-JunJul-Aug Sep-Oct Nov-Dec Davis (1984) Cutoff for food limitation 0.6 – 1.2 μg Chl l -1 Cutoff range

Chaetognaths MARMAP Sullivan and Meise (1996) Jan-FebMar-Apr May-JunJul-Aug Sep-OctNov-Dec

ECOHAB-GOM Observations Townsend et al. (2001) 1)Gulf-wide distribution 2) Association with coastal current 3) Center of mass shifts west-to-east as season progresses

Some thoughts on model design for HAB applications Forward models Inverse approaches McG et al. (1998) Fisheries Oceanography, 7(3/4), McG and Bucklin (2002) Journal of Marine Research, 60,

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Term-by-Term Diagnosis Continued… Observations Biological Source/Sink Advection Diffusion Tendency JA-SO SO-ND ND-JF

Pseudocalanus spp. MARMAP Concentration (# m -3 )

Term-by-Term Diagnosis Obs Src Adv Dif Ten JF-MA MA-MJ MJ-JA JA-SO SO-ND ND-JF

Term-by-Term Diagnosis Obs Src Adv Dif Ten JF-MA MA-MJ MJ-JA JA-SO SO-ND ND-JF

A first attempt to simulate the data…

Term-by-term diagnosis Red: source Blue: sink

Observations: P. Moultoni Models Observations: P. newmani