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
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, 1988Question
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
R4FluxesRegnLosses
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)