Inverse Modeling of the Microbial Loop

J. Steele & A. Beet

Woods Hole Oceanographic Institution

Benthivorous Fish

Pelagic Invertebrate

Predators

Micro-Phytoplankton

(>20m)

Seabirds

Deposit-feedingBenthos

Suspension- feeding Benthos

Detritus Ammonia

Fishing

R

Micro-Zooplankton(2-200m)

Meso-Zooplankton

(>200m)

Nitrate

Nano-Phytoplankton

(<20m)

PlanktivorousFish

Piscivorous Fish

Pre-recruits Pre-recruits Pre-recruits

MarineMammals

spawning

recruitment

Bi

Ni

Losses from Systemdue to inefficiency, ei

ExternalInputs, Ki

Ni = ei ( aij Nj ) + Ki

0 < ei < 1.0 , “Ecopath type” solution; specify ei, aij Ki solve for Ni

i

ija 1

There are an equal number of variables and equationsA unique solution exists

jij Na

Benthivorous FishB: 0.88

Pelagic InvertebratePredators

Sullivan & Meise 1996

1197Phytoplankton

Seabirds0.08

55.54Deposit-feeding

Benthos

30.19Suspension-

feeding Benthos

DOC 638Detritus 2.2x10^6 mg at N s^ -1

Ammonia

FishingLobsters: 0.9Shellfish: 0.9

Fish: 0.24+0.48+0.24

Phyto 501 RZoo ?

285Micro-

Zooplankton

202Meso-

Zooplankton

4.8x10^5 mg at N s^ -1Nitrate+Nitrite

2793Nano-

Phytoplankton

PlanktivorousFish

B: 9.85

Piscivorous FishB: 2.76

6.2

Pre-recruits Pre-recruits Pre-recruits

MarineMammals

6.0 from fish & Squid

1.8 from Zoo

7.8 total

spawning

recruitment

900Bacteria

Bi

Ni

ExternalInputs, Ki

Ni = ei ( aij Nj ) + Ki

“Inverse” solution: set bounds on ei , , and solve for

Ni = bi . Bi where bi is turnover rate

Losses from Systemdue to inefficiency, ei

ija

Problem: There are more variables than equationsThere is no unique solution

ib jij Na

jij Na

To obtain a unique solution the introduction of an objective function is needed. The maximization or minimization of this function provides a unique solution.

Vezina and Platt, 1988

Question

ecological; how appropriate is this function?

Alternative

maximize resilience

2FlowsMin

Phyto

Microz mesoZ

Detritus

NO3

Pel.F.

Dem.F

Regn.

S.P. L.P.

Phyto

Microz mesoZ

Detritus

NO3

Pel.F.

Dem.F

Regn.

S.P. L.P.

Phyto

Microz mesoZ

Detritus

NO3

Pel.F.

Dem.F

Regn.

S.P. L.P.

N1Phyto

N2Microz

N3mesoZ

N4 Detritus

NO3

Pel.F.

Dem.F

S.P. L.P.

R3

R2

R1

R4Fluxes

Regn

Losses

Regn

Graz

jij Na

Proportion of intake to Z, D to higher levels

F-ratio Fraction of detritus regeneration

0.75 .34 / .40 .90 / .40

0.4 <= P->M <= 1(Resilience / Sum of squares)

Proportion of intake to Z, D to higher levels

F-ratio Fraction of detritus regeneration

0.75 .44/ .39 .10 / .40

0.5 <= P->M <= 1(Resilience / Sum of squares)

Proportion of intake to Z, D to higher levels

F-ratio Fraction of detritus regeneration

0.75 .34 / .40 .90 / .40

0.5 .56 / .62 .90 / .30

0.25 .73 / .77 .90 / .10

0.4 <= P->M <= 1(Resilience / Sum of squares)

Proportion of intake to Z, D to higher levels

F-ratio Fraction of detritus regeneration

0.75 .44/ .39 .10 / .40

0.5 .62 / .60 .10 / .30

0.25 .74 / .74 .10 / .10

0.5 <= P->M <= 1(Resilience / Sum of squares)