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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 (>20 m) Seabirds Deposit-feeding Benthos Suspension- feeding Benthos Detritus Ammonia Fishing R Micro- Zooplankton (2-200 m) Meso- Zooplankton (>200 m) Nitrate Nano- Phytoplankton (<20 m) Planktivorous Fish Piscivorous Fish Pre-recruits Marine Mammals spawning recruitment
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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 exists
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Benthivorous Fish B: 0.88 Pelagic Invertebrate Predators Sullivan & Meise 1996 1197 Phytoplankton Seabirds 0.08 55.54 Deposit-feeding Benthos 30.19 Suspension- feeding Benthos DOC 638 Detritus 2.2x10^6 mg at N s^ -1 Ammonia Fishing Lobsters: 0.9 Shellfish: 0.9 Fish: 0.24+0.48+0.24 Phyto 501 R Zoo ? 285 Micro- Zooplankton 202 Meso- Zooplankton 4.8x10^5 mg at N s^ -1 Nitrate+Nitrite 2793 Nano- Phytoplankton Planktivorous Fish B: 9.85 Piscivorous Fish B: 2.76 6.2 Pre-recruits Marine Mammals 6.0 from fish & Squid 1.8 from Zoo 7.8 total spawning recruitment 900 Bacteria
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BiBi NiNi External Inputs, K i N i = e i ( a ij N j ) + K i “Inverse” solution: set bounds on e i,, and solve for N i = b i. B i where b i is turnover rate Losses from System due to inefficiency, e i Problem: There are more variables than equations There is no unique solution
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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, 1988 Question ecological; how appropriate is this function? Alternative maximize resilience
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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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N1 Phyto N2 Microz N3 mesoZ N4 Detritus NO3 Pel.F. Dem.F S.P. L.P. R3 R2 R1 R4 Fluxes Regn Losses Reg n Graz
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Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration 0.75.34 /.40.90 /.40 0.4 M <= 1 (Resilience / Sum of squares) Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration 0.75.44/.39.10 /.40 0.5 M <= 1 (Resilience / Sum of squares)
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Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration 0.75.34 /.40.90 /.40 0.5.56 /.62.90 /.30 0.25.73 /.77.90 /.10 0.4 M <= 1 (Resilience / Sum of squares) Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration 0.75.44/.39.10 /.40 0.5.62 /.60.10 /.30 0.25.74 /.74.10 /.10 0.5 M <= 1 (Resilience / Sum of squares)
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