inverse modeling of the microbial loop j. steele & a. beet woods hole oceanographic institution
DESCRIPTION
BiBi NiNi Losses from System due to inefficiency, e i External Inputs, K i N i = e i ( a ij N j ) + K i 0 < e i < 1.0, “Ecopath type” solution; specify e i, a ij K i solve for N i There are an equal number of variables and equations A unique solution existsTRANSCRIPT
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Inverse Modeling of the Microbial Loop
J. Steele & A. Beet
Woods Hole Oceanographic Institution
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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
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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
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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
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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
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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, 1988Question
ecological; how appropriate is this function?
Alternative
maximize resilience
2FlowsMin
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Phyto
Microz mesoZ
Detritus
NO3
Pel.F.
Dem.F
Regn.
S.P. L.P.
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Phyto
Microz mesoZ
Detritus
NO3
Pel.F.
Dem.F
Regn.
S.P. L.P.
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Phyto
Microz mesoZ
Detritus
NO3
Pel.F.
Dem.F
Regn.
S.P. L.P.
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N1Phyto
N2Microz
N3mesoZ
N4 Detritus
NO3
Pel.F.
Dem.F
S.P. L.P.
R3
R2
R1
R4FluxesRegnLosses
Regn
Graz
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jij Na
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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)
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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)