Andrew J. Melville Andrew J. Melville and Rod M. Connollyand Rod M. Connolly

"Spatial analysis of stable "Spatial analysis of stable isotope data to determine isotope data to determine

primary sources of nutrition primary sources of nutrition for fish"for fish"

Oecologia (2003) 136:499-507Oecologia (2003) 136:499-507http://www.springerlink.com/contenthttp://www.springerlink.com/content

/u70cyrwdd2wyv5tc/fulltext.pdf/u70cyrwdd2wyv5tc/fulltext.pdf

Research ProblemResearch Problem

1)1) Levels of certain stable isotopes within fish species Levels of certain stable isotopes within fish species can provide insight into their behavior and diet. can provide insight into their behavior and diet. Melville and Connolly use Carbon (C) and Nitrogen Melville and Connolly use Carbon (C) and Nitrogen (N) stable isotopes to investigate the autotrophic (N) stable isotopes to investigate the autotrophic sources that supported three commercially sources that supported three commercially important fish species over unvegetated mudflats important fish species over unvegetated mudflats located in a subtropical estuary. located in a subtropical estuary.

2)2) UnderstandingUnderstanding the variations in behavior and diet the variations in behavior and diet can help to explain questions about species can help to explain questions about species behavior while improving management and behavior while improving management and conservation efforts. conservation efforts.

3)3) As in this paper one way to better understand As in this paper one way to better understand variation through time and across landscapes is to variation through time and across landscapes is to utilize such research. utilize such research.

Location of the nine

study sites in Southern

Moreton Bay.

ModelsModels

1) Whole Estuary Modeling for fish 1) Whole Estuary Modeling for fish and autotroph sourcesand autotroph sources

a) IsoSource

b)Utilized to indicates feasible combinations of autotrophs

2) Spatial Analysis

a) Utilized to further test variability of isotropic valuesb) Two-dimensional spatial correlation between fish and autotrophs at each location

Fish Sources InvestigatedFish Sources Investigated

Yellowfin Bream, Yellowfin Bream, Acanthopagurs australis Acanthopagurs australis

*42-263 mm, 7 sites*42-263 mm, 7 sites

Sand Whiting, Sillage ciliata*15-337 mm, 6 sites

Winter Whiting, Sillago maculata *19-103 mm, 7 sites

Seven Autotroph Sources Seven Autotroph Sources Investigated Investigated

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

Sources of data Sources of data Accounting for fractionation of nitrogen, Accounting for fractionation of nitrogen,

subtract 3‰ by two trophic levels (-6‰) from the fishsubtract 3‰ by two trophic levels (-6‰) from the fish

d13C d15N ID Species Named13C d15N ID Species Name-17.1 10.2 AA A. australis-17.1 10.2 AA A. australis-17.0 9.9 SM S. maculata-17.0 9.9 SM S. maculata-16.1 9.4 SC S. ciliata-16.1 9.4 SC S. ciliata-28.9 1.8 SMU saltmarsh succulents-28.9 1.8 SMU saltmarsh succulents-28.6 2.7 MAN mangroves-28.6 2.7 MAN mangroves-23.4 3.7 MPB microphytobenthos-23.4 3.7 MPB microphytobenthos-19.8 5.3 POM particulate organic matter-19.8 5.3 POM particulate organic matter-14.8 5.5 EPI seagrass epiphytes-14.8 5.5 EPI seagrass epiphytes-14.4 0.7 SMG saltmarsh grass-14.4 0.7 SMG saltmarsh grass-12.6 4.6 SG seagrass-12.6 4.6 SG seagrass

Solving for proportionsSolving for proportions

With k=2 isotopes and the additional linear With k=2 isotopes and the additional linear constraint that proportions of sources must add to constraint that proportions of sources must add to 1, the proportions of n=3 sources can be solved for 1, the proportions of n=3 sources can be solved for uniquely.uniquely.

With more than n=3 sources, eg. n=7, the solution With more than n=3 sources, eg. n=7, the solution may not be unique, instead be a n-(k+1)=4-may not be unique, instead be a n-(k+1)=4-dimensinoal space of possible solutions.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

For fish A. australis, we want to find all sets For fish A. australis, we want to find all sets ofof{p1, ..., p7}{p1, ..., p7} that satisfy these three equations: that satisfy these three equations:

17.1 17.1 = p1(28.9) + p2(28.6) + p3(23.4) + p4(19.8)= 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+a10.2+a = p1( 1.8) + p2( 2.7) + p3( 3.7) + p4( 5.3)= 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)

11 = p1 + p2 + p3 + p4 + p5 + p6 + p7= p1 + p2 + p3 + p4 + p5 + p6 + p7

• where where a=-6‰a=-6‰ is the adjustment in is the adjustment in d15N due to the tropic level increase.d15N due to the tropic level increase.

An elimination view of finding solutions An elimination view of finding solutions with n sources and k isotopeswith n sources and k isotopes

• With n sources, create an n-dimensional normal With n sources, create an n-dimensional normal hypercubic regular grid with increments specified hypercubic regular grid with increments specified by the user (eg. 1%).by the user (eg. 1%).

• Eliminate linear combinations of the n proportions Eliminate linear combinations of the n proportions of the sources that do not sum to 100%.of the sources that do not sum to 100%.

• Eliminate linear combinations of the n isotopic Eliminate linear combinations of the n isotopic values of the sources that do not result in the k values of the sources that do not result in the k isotopic values simultaneously of the organism of isotopic values simultaneously of the organism of interest (within a tolerance).interest (within a tolerance).

• The remaining combinations are the possible The remaining combinations are the possible solutions.solutions.

• The results of IsoSource are these same solutions.The results of IsoSource are these same solutions.

Model ConstraintsModel Constraints

• The linear mixture model assumes that:The linear mixture model assumes that:1) the only inputs to the organism of interest are 1) the only inputs to the organism of interest are

the sources listedthe sources listed2) no measurement error in the input (source) or 2) no measurement error in the input (source) or

output (organism) isotopic valuesoutput (organism) isotopic values2a) measurement error can be crudely accounted for 2a) measurement error can be crudely accounted for

by increasing the IsoSource tolerance specificationby increasing the IsoSource tolerance specification

3) sources contribute in an additive way to the 3) sources contribute in an additive way to the isotopic values appearing in the organismisotopic values appearing in the organism

ResultResults of s of

fitted fitted modelmodel• Our fitted model Our fitted model

provides close to provides close to the same the same distributional distributional quantiles for quantiles for each of the each of the seven sources seven sources appearing in the appearing in the paper.paper.

SMU

MAN

MPB

POM

EPI

SMG

SG

Overview of ResultsOverview of Results

• Yellowfish Bream, Yellowfish Bream, A. AustralisA. Australis*MAN – very low whole estuary modeling*MAN – very low whole estuary modeling*MAN – Spatial analysis – up to 33% contribution*MAN – Spatial analysis – up to 33% contribution

• Sand Whiting, Sand Whiting, S. ciliataS. ciliata*MAN & microalgae – Unimportant based on whole *MAN & microalgae – Unimportant based on whole estuary modeling estuary modeling*MAN & microalgae – Spatial analysis – up to 25% *MAN & microalgae – Spatial analysis – up to 25%

contribution contribution

• Winter Whiting, Winter Whiting, S. maculataS. maculata *No spatial correlations found*No spatial correlations found

*Fish moved among locations*Fish moved among locations*Fish relied on different autotrophs at *Fish relied on different autotrophs at

different locations different locations

Overview of Results Overview of Results (cont.)(cont.)

• Size-dependent isotopic signatureSize-dependent isotopic signature– Isotopic values tested for fish speciesIsotopic values tested for fish species– Regression analysis – C and N tested separatelyRegression analysis – C and N tested separately

• Result Result – No correlation between length and 13C for any No correlation between length and 13C for any

fish (P>0.05)fish (P>0.05)– No correlation between length and 15NNo correlation between length and 15N

Sand Whiting (S. ciliata) Sand Whiting (S. ciliata) Winter Whiting (S. maculata)Winter Whiting (S. maculata)

– Positive relationship between length and 15N Positive relationship between length and 15N signature of signature of Yellowfin Bream (A. Australia)Yellowfin Bream (A. Australia)

ConstraintsConstraints

• Previous studies indicate that 15N Previous studies indicate that 15N fractionation levels vary considerably fractionation levels vary considerably around the mean for different trophic levelsaround the mean for different trophic levels

• Weakness of whole estuary modelWeakness of whole estuary model

-- Correcting for N fractionation based on Correcting for N fractionation based on assumption of 3‰ per trophic levelassumption of 3‰ per trophic level

• Differences in diet can skew isotopic Differences in diet can skew isotopic levelslevels

due to different rates of assimilation.due to different rates of assimilation.

ConstraintsConstraints (cont.)(cont.)

• Melville and Connolly suggest Melville and Connolly suggest IsoSource is not reliable enough to IsoSource is not reliable enough to distinguish major sources contributing distinguish major sources contributing to foodwebsto foodwebs

• Spatial AnalysisSpatial Analysis– Can supplement information, but can Can supplement information, but can

not resolve dietary patterns on its ownnot resolve dietary patterns on its own

Constraint ResolutionsConstraint Resolutions

• Multi-Model ApproachMulti-Model Approach

•• Melville and Connolly suggest utilizing Melville and Connolly suggest utilizing a a combination of spatial analysis combination of spatial analysis and whole and whole estuary modeling estuary modeling

•Use both models when numerous Use both models when numerous potential sources are available to potential sources are available to consumers and/or changes in ecology consumers and/or changes in ecology exist.exist.