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Andrew J. Melville and Rod M. Connolly "Spatial analysis of stable isotope data to determine primary sources of nutrition for fish" Oecologia (2003) 136:499-507 http://www.springerlink.com/content/u70cyrwdd2wyv5tc/fulltext.pdf

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Research Problem 1) Levels of certain stable isotopes within fish species can provide insight into their behavior and diet. Melville and Connolly use Carbon (C) and Nitrogen (N) stable isotopes to investigate the autotrophic sources that supported three commercially important fish species over unvegetated mudflats located in a subtropical estuary. 2) Understanding the variations in behavior and diet can help to explain questions about species behavior while improving management and conservation efforts. 3) As in this paper one way to better understand variation through time and across landscapes is to utilize such research.

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Location of the nine study sites in Southern Moreton Bay.

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Models 1) Whole Estuary Modeling for fish and autotroph sources a)IsoSource b)Utilized to indicates feasible combinations of autotrophs 2) Spatial Analysis a) Utilized to further test variability of isotropic values b) Two-dimensional spatial correlation between fish and autotrophs at each location

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Fish Sources Investigated Yellowfin Bream, Acanthopagurs australis *42-263 mm, 7 sites Sand Whiting, Sillage ciliata *15-337 mm, 6 sites Winter Whiting, Sillago maculata *19-103 mm, 7 sites

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Seven Autotroph Sources Investigated Saltmarsh Succulents (SMU) Mangroves (MAN) Microphytobenthos (MPB) Particulate Organic Matter (POM) Seagrass Epiphytes (EPI) Saltmarsh Grass (SMG) Seagrass (SG)

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Sources of data Accounting for fractionation of nitrogen, subtract 3‰ by two trophic levels (-6‰) from the fish d13C d15N ID Species Name d13C d15N ID Species Name -17.1 10.2 AA A. australis -17.0 9.9 SM S. maculata -16.1 9.4 SC S. ciliata -28.9 1.8 SMU saltmarsh succulents -28.6 2.7 MAN mangroves -23.4 3.7 MPB microphytobenthos -19.8 5.3 POM particulate organic matter -14.8 5.5 EPI seagrass epiphytes -14.4 0.7 SMG saltmarsh grass -12.6 4.6 SG seagrass

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Solving for proportions With k=2 isotopes and the additional linear constraint that proportions of sources must add to 1, the proportions of n=3 sources can be solved for uniquely. With more than n=3 sources, eg. n=7, the solution may not be unique, instead be a n-(k+1)=4-dimensinoal space of possible solutions. d13C = p1(C_SMU) + p2(C_MAN) + p3(C_MPB) + p4(C_POM) + p5(C_EPI) + p6(C_SMG) + p7(C_SG) d15N = p1(N_SMU) + p2(N_MAN) + p3(N_MPB) + p4(N_POM) + p5(N_EPI) + p6(N_SMG) + p7(N_SG) 1 = p1 + p2 + p3 + p4 + p5 + p6 + p7

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For fish A. australis, we want to find all sets of {p1,..., p7} that satisfy these three equations: 17.1 = p1(28.9) + p2(28.6) + p3(23.4) + p4(19.8) 17.1 = p1(28.9) + p2(28.6) + p3(23.4) + p4(19.8) + p5(14.8) + p6(14.4) + p7(12.6) + p5(14.8) + p6(14.4) + p7(12.6) 10.2+a= p1( 1.8) + p2( 2.7) + p3( 3.7) + p4( 5.3) + p5( 5.5) + p6( 0.7) + p7( 4.6) + p5( 5.5) + p6( 0.7) + p7( 4.6) 1= p1 + p2 + p3 + p4 + p5 + p6 + p7 1= p1 + p2 + p3 + p4 + p5 + p6 + p7 where a=-6‰ is the adjustment in d15N due to the tropic level increase. where a=-6‰ is the adjustment in d15N due to the tropic level increase.

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An elimination view of finding solutions with n sources and k isotopes With n sources, create an n-dimensional normal hypercubic regular grid with increments specified by the user (eg. 1%). With n sources, create an n-dimensional normal hypercubic regular grid with increments specified by the user (eg. 1%). Eliminate linear combinations of the n proportions of the sources that do not sum to 100%. Eliminate linear combinations of the n proportions of the sources that do not sum to 100%. Eliminate linear combinations of the n isotopic values of the sources that do not result in the k isotopic values simultaneously of the organism of interest (within a tolerance). Eliminate linear combinations of the n isotopic values of the sources that do not result in the k isotopic values simultaneously of the organism of interest (within a tolerance). The remaining combinations are the possible solutions. The remaining combinations are the possible solutions. The results of IsoSource are these same solutions. The results of IsoSource are these same solutions.

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Model Constraints The linear mixture model assumes that: The linear mixture model assumes that: 1) the only inputs to the organism of interest are the sources listed 2) no measurement error in the input (source) or output (organism) isotopic values 2a) measurement error can be crudely accounted for by increasing the IsoSource tolerance specification 3) sources contribute in an additive way to the isotopic values appearing in the organism

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Results of fitted model Our fitted model provides close to the same distributional quantiles for each of the seven sources appearing in the paper. Our fitted model provides close to the same distributional quantiles for each of the seven sources appearing in the paper. SMU MAN MPB POM EPI SMG SG

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Overview of Results Yellowfish Bream, A. Australis Yellowfish Bream, A. Australis *MAN – very low whole estuary modeling *MAN – Spatial analysis – up to 33% contribution Sand Whiting, S. ciliata Sand Whiting, S. ciliata *MAN & microalgae – Unimportant based on whole estuary modeling *MAN & microalgae – Spatial analysis – up to 25% contribution Winter Whiting, S. maculata Winter Whiting, S. maculata *No spatial correlations found *No spatial correlations found *Fish moved among locations *Fish relied on different autotrophs at different locations

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Overview of Results (cont.) Overview of Results (cont.) Size-dependent isotopic signature Size-dependent isotopic signature –Isotopic values tested for fish species –Regression analysis – C and N tested separately Result Result –No correlation between length and 13C for any fish (P>0.05) –No correlation between length and 15N Sand Whiting (S. ciliata) Winter Whiting (S. maculata) –Positive relationship between length and 15N signature of Yellowfin Bream (A. Australia)

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Constraints Previous studies indicate that 15N fractionation levels vary considerably around the mean for different trophic levels Previous studies indicate that 15N fractionation levels vary considerably around the mean for different trophic levels Weakness of whole estuary model Weakness of whole estuary model - Correcting for N fractionation based on assumption of 3‰ per trophic level - Correcting for N fractionation based on assumption of 3‰ per trophic level Differences in diet can skew isotopic levels Differences in diet can skew isotopic levels due to different rates of assimilation. due to different rates of assimilation.

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Constraints (cont.) Melville and Connolly suggest IsoSource is not reliable enough to distinguish major sources contributing to foodwebs Melville and Connolly suggest IsoSource is not reliable enough to distinguish major sources contributing to foodwebs Spatial Analysis Spatial Analysis –Can supplement information, but can not resolve dietary patterns on its own

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Constraint Resolutions Constraint Resolutions Multi-Model Approach Multi-Model Approach Melville and Connolly suggest utilizing a combination of spatial analysis and whole estuary modeling Melville and Connolly suggest utilizing a combination of spatial analysis and whole estuary modeling Use both models when numerous potential sources are available to consumers and/or changes in ecology exist. Use both models when numerous potential sources are available to consumers and/or changes in ecology exist.

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