USEPA Risk Assessment Paradigm

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RESEARCH RISK ASSESSMENT Regulatory decision Information on extrapolation methods Field measurements, characterization of populations Research needs identified Laboratory and field observations Development of regulatory options Evaluation of public health, environmental, economic, social, and political consequences of regulatory options RISK MANAGEMENT Problem Formulation and Hazard Identification ANALYSIS Dose-response charactertization Exposure characterization Risk Characterization USEPA Risk Assessment Paradigm

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USEPA Risk Assessment Paradigm. Risk Identification : “Qualitative evaluation of the potential for a substance to cause an adverse effect.”. Types of Data used in Developing Exposure & Toxicity Profiles Laboratory data Field Observations Model output QSARs. - PowerPoint PPT Presentation

Transcript of USEPA Risk Assessment Paradigm

  • USEPA Risk Assessment Paradigm

  • Risk Identification:

    Qualitative evaluation of the potential for a substance to cause an adverse effect.

  • Types of Data used in Developing Exposure & Toxicity Profiles

    Laboratory dataField ObservationsModel outputQSARs

  • Common Difficulties/Sources of Uncertainty with the Use of Data

  • Distribution of ConcentrationsVariability of Effects Concentration,EC50

  • What is an Exposure Profile?

    Range of concentrations/doses associated with the stressor in time and placeMagnitude in uncertainty due to sampling and/or measurements errorIdentify the variability in concentrations and their causes

  • What is an Ecological Effects Profile

    Relationship between stressor level and ecological effect (Dose-Response Relationship) as a function of time and spaceEcological effects can include: single species, populations, multiple species, general trophic levels, communities, ecosystems, landscapes

  • Ecological Effects Profile : Single Species

  • Risk Estimation for Single SpeciesOne Dose Response Curve One Species

  • Distribution of ConcentrationsUncertainty of Effects Concentrations, e.g LC5

  • Risk Estimation for Single SpeciesCumulative distribution of EC5Comparison of 50th percentile exposure with EC5Multiple Dose Response Curves One Species

  • Risk Estimation for Single SpeciesCumulative distribution of EC5Comparison of 50th percentile exposure with EC5Multiple Dose Response Curves One Species

  • Distribution of ConcentrationsDistribution of Effects Concentrations among different organisms

  • Ecological Effects Profile : Multiple SpeciesRank Order Method100 x n / ( N + 1)6n = rankN = Total Number of observations (6)

  • Ecological Effects Profile : Multiple SpeciesStatistical Distribution Method

    Sheet4

    Column1

    Mean38.9833333333

    Standard Error15.2824608984

    Median26

    Mode

    Standard Deviation37.4342312151

    Sample Variance1401.3216666667

    Kurtosis-0.3110762239

    Skewness0.9551100993

    Range94.1

    Minimum5.9

    Maximum100

    Sum233.9

    Count6

    Sheet5

    PointColumn1RankPercent

    61001100.00%

    565280.00%

    440360.00%

    312440.00%

    211520.00%

    15.96.00%

    Sheet6

    PointColumn1RankPercent

    621100.00%

    51.8129133566280.00%

    41.6020599913360.00%

    31.079181246440.00%

    21.0413926852520.00%

    10.77085201166.00%

    Sheet1

    EC50%

    5.9140.77085201162.665

    11291.0413926852220.595

    12431.0791812462450

    40571.6020599913

    65711.8129133566

    100862

    1.384399881824.2325926458

    0.4893294531

    0.9590857281

    2.3434856099220.539106092

    0.42531415372.662650433

    EC50log EC50

    5.90.7708520116

    111.0413926852

    121.079181246

    401.6020599913

    651.8129133566

    1002

    Mean38.981.3824.2350%

    std37.430.493.09

    1.96*std73.370.969.10

    Mean+1.96*std112.352.34220.5495%

    Mean-1.96*std-34.390.432.665%

    Sheet1

    %

    EC50 (umol/L)

    %

    Ecological Risk Profile

    Sheet2

    14

    29

    43

    57

    71

    86

    %

    EC50 (umol/L)

    %

    Ecological Risk Profile

    Sheet3

  • Risk estimation involving multiple species

  • Risk estimation involving multiple species

  • Risk Characterization

    Develop an estimate of the risk posed to ecological entities included in the assessment end-points identified in the problem formulationDescribe the risk estimate in the context of the significance of any adverse effects and the strength of evidence supporting itQualify the risk estimates by summarizing uncertainties and assumptions.

  • Strengths:

    Estimates likelihood that a certain percentage of species may be adversely affected.

    But:consider whether the subset of species for which toxicity test are available represent the range of species present in the environmentconsider whether particular sensitive groups of organisms are includedIf a criterion is selected, often protect 95% of the species, consider whether the 5% potentially affected organisms are of ecological, commercial or recreational significance

  • Mixtures of Chemicals

    PCBsChlorinated dibenzo-p-dioxinsChlorinated dibenzo-furansChlorinated diphenyl ethersPolychlorinated naphthalenesPBBsPolybrominated diphenyl ethers

  • Body weight lossthymus atrophyimpairment of immune response hepatotoxicityearly life stage mortalitydelayed responsedisruption of the endocrine systemchanges in vitamin A levels

    Toxic Responses

    neurotoxicityteratogenicitycarcinogenicity

  • Structure-Activity Relationship for dioxin- like compounds10 A4 APlanarityelectronegative substituents groups in the corners

  • Compounds

    Toxic Equivalency

    Factor

    PCBs

    3,3',4,4'-tetra- (#77)

    0.00016

    3,4,4',5-tetra- (#81)

    0.00056

    3,3',4,4',5-penta- (#126)

    0.005

    PCDDs

    2,3,7,8-tetra-

    1.0

    1,2,3,7,8-penta-

    0.730

    1,2,3,4,7,8-hexa-

    0.319

    1,2,3,6,7,8-hexa-

    0.024

    PCDFs

    2,3,7,8-tetra-

    0.028

    1,2,3,7,8-penta-

    0.034

    2,3,4,7,8-penta-

    0.359

    1,2,3,4,7,8-hexa-

    0.280

  • Additivity

    ChemicalConcentration (ng/kg)TEFTEQ(ng/kg)

    2,3,7,8-TCDD101103,3,4,4,5-PCB10000.005 52,3,7,8-TCDF1000.0282.8

    Mixture111017.8

  • A Probabilistic Risk Assessment of the Reproductive Effects of Polychlorinated Biphenyls, Dibenzo-p-dioxins and Dibenzofurans in Lake Ontario Lake Trout Stocks

    Frank A.P.C. Gobas1, *Cherie M. Gelowitz1, Philip M. Cook2, Susan Y. Huestis3, Mark R. Servos4

  • Figure 3.1: Predicted and observed concentrations of 3,3',4,4',5-pentachlorobiphenyl (# 126) in the sediments of Lake Ontario as a function of time.

    _1015412550.xls

    Sheet: 126

    Sheet: fitting

    Sheet: n

    Sheet: o

    Sheet: 1

    Sheet: 2

    Sheet: Sheet7

    Sheet: Sheet8

    Sheet: Sheet9

    Sheet: Sheet10

    p126

    Year

    Water-Total

    Water-Diss

    SedimentSol

    Phytoplankton

    Zooplankton

    Diporeia

    Alewife-0

    Alewife-1

    Alewife-2

    Alewife-3

    Alewife-4

    Alewife-5

    Alewife-6

    Alewife-7

    Alewife-8

    Sculpin-0

    Sculpin-1

    Sculpin-2

    Sculpin-3

    Sculpin-4

    Sculpin-5

    Smelt-0

    Smelt-1

    Smelt-2

    Smelt-3

    Smelt-4

    Smelt-5

    Trout-0

    Trout-1

    Trout-2

    Trout-3

    Trout-4

    Trout-5

    Trout-6

    Trout-7

    Lake Trout-8

    1927.0

    1928.0

    4.77106887963275E-13

    2.34451002117444E-13

    2.78894782235987E-8

    9.09959571921865E-9

    5.45975743153119E-8

    3.09883091373319E-8

    1.27394340069061E-7

    4.50132011066503E-8

    2.60637298954962E-7

    3.70986477881391E-7

    4.49411836024125E-7

    4.76944174575114E-7

    4.82315231508304E-7

    4.93526300373332E-7

    4.67848555689814E-7

    1.15746857548461E-7

    4.25819241066055E-8

    1.61958877738508E-7

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    2.36864525416E-7

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    3.91282615926402E-8

    4.82757223408144E-8

    4.52606956322028E-7

    7.408240337695E-7

    9.54910606544187E-7

    1.26410706857719E-6

    1.50535221726834E-6

    1.75215936180669E-6

    2.06110108527634E-6

    4.88751425239383E-13

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    9.58180428022798E-8

    1.1676489951107E-7

    1.26019879605457E-7

    1.2934338321744E-7

    1.34340343448198E-7

    1.30228173107351E-7

    2.50405040542288E-8

    5.56297507087693E-8

    2.27177341428523E-7

    2.43059389429822E-7

    2.7771953070504E-7

    3.00848327217369E-7

    1.91740966578764E-8

    2.21658627871311E-8

    1.08386431942916E-7

    1.5256199722164E-7

    1.66901443396586E-7

    1.79455016952913E-7

    8.46495026990437E-9

    2.55381649386139E-8

    3.62168113905557E-7

    5.07872243794097E-7

    5.91494168056974E-7

    7.27887296846351E-7

    8.41827981454824E-7

    8.5094214740893E-7

    9.3711706890303E-7

    9.12343032491465E-14

    4.48326661464918E-14

    4.23140675732539E-8

    1.74006139134955E-9

    1.04403683480973E-8

    4.70156306369488E-8

    2.43608594788937E-8

    1.08886699390489E-8

    6.49941290977859E-8

    8.46940938546674E-8

    1.03208587864663E-7

    1.11388518119687E-7

    1.1432563328427E-7

    1.18741875076825E-7

    1.15106519099567E-7

    2.21335808979663E-8

    4.91726696627279E-8

    2.00808338148075E-7

    2.14846789741301E-7

    2.45483825519105E-7

    2.65928009960919E-7

    1.69481979517446E-8

    1.95928777175483E-8

    9.58049090304831E-8

    1.34852081860991E-7

    1.47526729249832E-7

    1.58622759546358E-7

    7.48226398280306E-9

    2.25737360414663E-8

    3.20128968104208E-7

    4.48918696660391E-7

    5.22832028879169E-7

    6.43389327441006E-7

    7.44099249458925E-7

    7.52147753938976E-7

    8.28307082091539E-7

    8.06436364494804E-14

    3.96283974450414E-14

    3.74025807184496E-8

    1.53807146266646E-9

    9.22842877599875E-9

    4.15584230204996E-8

    2.15330004773304E-8

    9.6247139463228E-9

    5.74494902526939E-8

    7.48623538740485E-8

    9.12273093549482E-8

    9.84573668773906E-8

    1.01053248216814E-7

    1.04956525602065E-7

    1.01742883691247E-7

    1.95642690051174E-8

    4.34650671751129E-8

    1.77499993571241E-7

    1.89908899757898E-7

    2.16989804173143E-7

    2.35060979749204E-7

    1.49808160463713E-8

    1.73186096723203E-8

    8.46841500901031E-8

    1.1919859504672E-7

    1.30401867770951E-7

    1.40209739908993E-7

    6.61370728946577E-9

    1.99534655546816E-8

    2.82970034689563E-7

    3.96809699640082E-7

    4.6214250288278E-7

    5.68704192717365E-7

    6.57721713510467E-7

    6.64832074023743E-7

    7.32144762595766E-7

    7.12826701626273E-14

    3.50284053214541E-14

    3.30611690067742E-8

    1.35953493154399E-9

    8.15720958926395E-9

    3.67346322297491E-8

    1.90334890416159E-8

    8.50750653401365E-9

    5.0780865598183E-8

    6.61723295804054E-8

    8.06374998777495E-8

    8.70281384264426E-8

    8.93225488445903E-8

    9.27725796918835E-8

    8.99318266902645E-8

    1.72932843292396E-8

    3.84199559404104E-8

    1.56897082284408E-7

    1.67865619301171E-7

    1.91803163163095E-7

    2.07776768135062E-7

    1.32418702332385E-8

    1.53083546831924E-8

    7.48544083070445E-8

    1.05362453547499E-7

    1.15265232638469E-7

    1.23934570182064E-7

    5.84600020563917E-9

    1.76373723510947E-8

    2.501245546408E-7

    3.50749977087494E-7

    4.08498806268553E-7

    5.02690468048779E-7

    5.81374092754798E-7

    5.87657140039786E-7

    6.47153300535488E-7

    6.3008466374427E-14

    3.09624498326354E-14

    2.92236698313177E-8

    1.20172562031719E-9

    7.21035372190312E-9

    3.24707442570197E-8

    1.68241586844406E-8

    7.51999562016705E-9

    4.48864322291293E-8

    5.849124348143E-8

    7.12772688413673E-8

    7.69260233852608E-8

    7.8954034049739E-8

    8.200351757916E-8

    7.9492434286166E-8

    1.52859498904346E-8

    3.39604420739484E-8

    1.38685593837159E-7

    1.48380964791665E-7

    1.69540007326026E-7

    1.83659510941734E-7

    1.17048075418894E-8

    1.35314521109847E-8

    6.61657335542922E-8

    9.31325154897921E-8

    1.01885800831726E-7

    1.09548809183635E-7

    5.1674201673639E-9

    1.55901324651207E-8

    2.21091701251752E-7

    3.10036962366769E-7

    3.61082409258688E-7

    4.44340410873095E-7

    5.13890301085454E-7

    5.19443046847008E-7

    5.7203161663195E-7

    5.56947794151012E-14

    2.73684936772189E-14

    2.58315964818851E-8

    1.06223571517059E-9

    6.37341429102352E-9

    2.87017738687612E-8

    1.48713000123882E-8

    6.64711765068966E-9

    3.96762564245006E-8

    5.17018562088196E-8

    6.30037040648646E-8

    6.79967384539378E-8

    6.97893110406928E-8

    7.24847853573095E-8

    7.02651380247132E-8

    1.35116382969699E-8

    3.0018555330065E-8

    1.22587957528087E-7

    1.31157950274222E-7

    1.49861000350375E-7

    1.62341612612823E-7

    1.03461758657615E-8

    1.19608081052865E-8

    5.84856296814165E-8

    8.23222447412681E-8

    9.00594856227608E-8

    9.68329988362106E-8

    4.56761357523352E-9

    1.37805306730108E-8

    1.95428855228688E-7

    2.74049839866695E-7

    3.19170136523778E-7

    3.92763854554018E-7

    4.54240532377092E-7

    4.59148242862866E-7

    5.05631843079017E-7

    4.92300671959332E-14

    2.41917249144475E-14

    2.28332490496156E-8

    9.38937835555717E-10

    5.6336270133343E-9

    2.53702767217951E-8

    1.314512969778E-8

    5.87556208863203E-9

    3.50708782608379E-8

    4.57006003651972E-8

    5.56905760423861E-8

    6.01040275813425E-8

    6.16885102609519E-8

    6.4071089290551E-8

    6.21090663001258E-8

    1.19432892682687E-8

    2.65342140892502E-8

    1.08358816751494E-7

    1.15934061169325E-7

    1.32466193089791E-7

    1.43498144436048E-7

    9.14525451831269E-9

    1.05724775606608E-8

    5.1697003857195E-8

    7.27668059043384E-8

    7.96059498456028E-8

    8.5593227651236E-8

    4.03743269288958E-9

    1.21809792209475E-8

    1.7274481123527E-7

    2.42239956613209E-7

    2.82122929012898E-7

    3.47174264419511E-7

    4.01514984854272E-7

    4.05852783692585E-7

    4.46940459910665E-7

    4.3515760323074E-14

    2.13837064042398E-14

    2.01829276098047E-8

    8.29952021956281E-10

    4.97971213173769E-9

    2.24254751220052E-8

    1.16193283073879E-8

    5.19356573398838E-9

    3.1000078751817E-8

    4.03959620510914E-8

    4.92263548947573E-8

    5.31275106033561E-8

    5.45280672084023E-8

    5.66340812910965E-8

    5.48997876521999E-8

    1.05569897192839E-8

    2.34543101450615E-8

    9.57812919710443E-8

    1.02477253414082E-7

    1.17090452057883E-7

    1.26841892571006E-7

    8.08373269385418E-9

    9.3452967552002E-9

    4.56963668925162E-8

    6.43205213275336E-8

    7.03658193006939E-8

    7.56581291547996E-8

    3.56879369441201E-9

    1.07670947144534E-8

    1.52693791273807E-7

    2.14122394945642E-7

    2.49375993458911E-7

    3.06876556257827E-7

    3.54909698821534E-7

    3.58743865199028E-7

    3.95062153097781E-7

    3.84647436375339E-14

    1.89016296337867E-14

    1.78402362676271E-8

    7.33616775140518E-10

    4.40170065084311E-9

    1.98224847418079E-8

    1.02706348519673E-8

    4.59073196191776E-9

    2.74017984734745E-8

    3.57070659928223E-8

    4.351248055025E-8

    4.69608107781068E-8

    4.81987953265895E-8

    5.00603520801029E-8

    4.85273587401931E-8

    9.33160537978738E-9

    2.07318994947E-8

    8.46636763857401E-8

    9.05824168238469E-8

    1.03499418437015E-7

    1.12118980652185E-7

    7.14542738986864E-9

    8.26055951665896E-9

    4.03922481504286E-8

    5.68546352126113E-8

    6.21982344071182E-8

    6.68762467323985E-8

    3.15455213310423E-9

    9.51732511064374E-9

    1.34970162508478E-7

    1.8926854921738E-7

    2.20430138535188E-7

    2.71256404892203E-7

    3.13714153293874E-7

    3.1710321011691E-7

    3.49205815511004E-7

    3.40000203171566E-14

    1.67076582553644E-14

    1.57694677482066E-8

    6.48463577317208E-10

    3.89078146390325E-9

    1.75216308313407E-8

    9.07849008244092E-9

    4.05787151924252E-9

    2.42211860180896E-8

    3.15624326516853E-8

    3.84618454018469E-8

    4.1509914313981E-8

    4.26041996505039E-8

    4.42496769499361E-8

    4.28946204996241E-8

    8.24845670347489E-9

    1.83254869527362E-8

    7.48365146083272E-8

    8.00682488817647E-8

    9.14859360544402E-8

    9.91050003544495E-8

    6.31603524306961E-9

    7.30173147090899E-9

    3.57037974463539E-8

    5.02553432427619E-8

    5.49786934975539E-8

    5.91137133613501E-8

    2.788393382464E-9

    8.41262053583225E-9

    1.19303772731324E-7

    1.67299576616926E-7

    1.94844138241968E-7

    2.39770831516681E-7

    2.77300360771269E-7

    2.80296006054492E-7

    3.08672310799665E-7

    3.00535341367634E-14

    1.47683493432972E-14

    1.39390592987061E-8

    5.73194429754984E-10

    3.4391665785299E-9

    1.5487843665229E-8

    8.02472201656977E-9

    3.58686208263655E-9

    2.14097590756546E-8

    2.78988835475057E-8

    3.39974589308244E-8

    3.66917277476682E-8

    3.7658994794534E-8

    3.91134751365714E-8

    3.79157029838604E-8

    7.29103314648339E-9

    1.61983937461215E-8

    6.61500201563407E-8

    7.07744913529424E-8

    8.08668939312164E-8

    8.76015910229264E-8

    5.58291374581354E-9

    6.45419769942231E-9

    3.15595507321044E-8

    4.44220539628241E-8

    4.85971502066982E-8

    5.2252205225645E-8

    2.46473604794643E-9

    7.43614257554283E-9

    1.05455829604204E-7

    1.47880614506362E-7

    1.72227992533453E-7

    2.11939902724447E-7

    2.45113257190454E-7

    2.47761172012229E-7

    2.72843726748953E-7

    p126

    pg/g to g/kg

    1.0E-9

    sediment

    lake trout -4 years

    lake trout-5years

    year

    observed

    observed

    predicted

    ss of squares

    predicted

    year

    observed

    Observed

    predicted

    s of squares

    predicted

    year

    observed

    Observed

    predicted

    s of squares

    predicted

    sed.conc.

    sed. conc.

    sed. conc.

    sed conc.

    4-yr Lake

    4-yr Lake

    4-yr Lake

    4-yr lake

    5-yr Lake

    5-yr Lake

    5-yr Lake

    5-yr Lake

    (pg/g)

    (g/kg)

    (g/kg)

    (pg/g)

    trout

    trout

    trout

    trout

    trout

    trout

    trout

    trout

    1929.0

    2.78894782235987E-8

    27.8894782235987

    (pg/g)

    (g/kg)

    (g/kg)

    (pg/g)

    (pg/g)

    (g/kg)

    (g/kg)

    (pg/g)

    1930.0

    3.23020331797585E-8

    32.302033179758496

    1977.0

    2.64954412099498E-6

    2649.54412099498

    2.8393400000000003E-6

    3.28594051668586E-6

    1.9945202150407693E-13

    3285.94051668586

    3.7E-8

    3.62339824723595E-8

    5.8678285265246E-19

    36.2339824723595

    1978.0

    2.32363552462406E-6

    2323.63552462406

    3.25406E-6

    1.0163673441574016E-15

    1932.0

    3.97331823915252E-8

    39.7331823915252

    1979.0

    2.04441677307364E-6

    2044.4167730736397

    2.88464E-6

    1.610421046923382E-13

    1933.0

    4.28469189809863E-8

    42.846918980986295

    1.7559300000000002E-6

    1.80222320772382E-6

    2.143061081360733E-15

    1802.22320772382

    1978.0

    2.87260383833978E-6

    2872.60383833978

    1934.0

    4.56188597123138E-8

    45.61885971231379

    9.4654E-7

    7.321937519805261E-13

    1979.0

    2.52260280518448E-6

    2522.60280518448

    1935.0

    4.80883041990866E-8

    48.0883041990866

    1980.0

    2017.0713999999998

    2.0170713999999997E-6

    4.615974572434228E-14

    1980.0

    2.2212550752118E-6

    2221.2550752118

    4.4000000000000004E-8

    5.02902518177951E-8

    3.956726793127456E-17

    50.2902518177951

    8.520000000000001E-7

    1.59052728723952E-6

    5.454225539973644E-13

    1590.5272872395199

    1.5921900000000001E-6

    1.95904497519525E-6

    1.3458257282550738E-13

    1959.04497519525

    1937.0

    5.22557408564591E-8

    52.2557408564591

    8.909900000000001E-7

    4.893524162384266E-13

    5.7106E-7

    1.9265022913677584E-12

    1938.0

    5.40122419638876E-8

    54.0122419638876

    1.34659E-6

    1.40462971963091E-6

    3.368609054834621E-15

    1404.62971963091

    1982.0

    1.72941203648293E-6

    1729.41203648293

    5.1E-8

    5.5584052872879E-8

    2.101354074135021E-17

    55.584052872879

    1.04208E-6

    1.3144229920445138E-13

    1983.0

    1.52753111195987E-6

    1527.53111195987

    1940.0

    5.69926545667994E-8

    56.992654566799395

    9.6964E-7

    1.892160561845776E-13

    1984.0

    1.34964419338926E-6

    1349.64419338926

    1941.0

    5.82570385977094E-8

    58.257038597709396

    1.0254400000000002E-6

    1.24093757689114E-6

    4.643920564595273E-14

    1240.93757689114

    1985.0

    1.1926911593345E-6

    1192.6911593344998

    1942.0

    5.93939911125652E-8

    59.393991112565196

    7.308200000000001E-7

    1.09656624881538E-6

    1.3377031852252175E-13

    1096.5662488153798

    8.5468E-7

    1.05410169246004E-6

    3.9769011423626806E-14

    1054.10169246004

    5.8E-8

    6.04342381306813E-8

    5.925515276862784E-18

    60.4342381306813

    8.4292E-7

    6.43364195381136E-14

    1.1436500000000003E-6

    8.018899383271286E-15

    1944.0

    6.17806001072209E-8

    61.7806001072209

    1.9533E-6

    7.339927204188704E-13

    1.05473E-6

    3.9477036477048476E-19

    1945.0

    6.37115440545815E-8

    63.711544054581495

    1985.0

    9.69115792160582E-7

    969.115792160582

    1987.0

    9.31672740098381E-7

    931.6727400983809

    1946.0

    6.63396391717331E-8

    66.3396391717331

    1986.0

    8.56541965005205E-7

    856.5419650052049

    7.9042E-7

    8.23492060431435E-7

    1.0937611811804878E-15

    823.492060431435

    6.5E-8

    6.97210559968526E-8

    2.2288369725417852E-17

    69.72105599685258

    1.10553E-6

    7.57077136053783E-7

    1.2141939839232085E-13

    757.077136053783

    1.01404E-6

    3.63085172738255E-14

    1948.0

    7.38966924965127E-8

    73.8966924965127

    6.2463E-7

    1.75422438488493E-14

    1.10458E-6

    7.901042977090128E-14

    1949.0

    7.89077252053395E-8

    78.9077252053395

    7.575000000000001E-7

    1.7881391701027599E-19

    1.1862300000000002E-6

    1.3157881280244804E-13

    1.0000000000000001E-7

    8.48016416958489E-8

    2.3099009514135906E-16

    84.80164169584889

    6.2227E-7

    1.8172963931023163E-14

    1.3729000000000002E-6

    3.018490840609762E-13

    1951.0

    9.16347802291067E-8

    91.6347802291067

    6.4348E-7

    1.2904309319621671E-14

    9.064600000000001E-7

    7.27887296846351E-7

    3.188821031160127E-14

    727.887296846351

    1952.0

    9.94736308237684E-8

    99.47363082376839

    9.9369E-7

    6.69178916917427E-7

    1.053074430434246E-13

    669.178916917427

    7.9354E-7

    4.310277431381159E-15

    1.35E-7

    1.08395757089638E-7

    7.077857408335473E-16

    108.39575708963798

    1.35248E-6

    4.669003701418174E-13

    8.745000000000001E-7

    2.1495284726020015E-14

    1954.0

    1.1849032834514E-7

    118.49032834513999

    4.5283E-7

    5.91494168056974E-7

    1.9227751502932715E-14

    591.4941680569739

    7.1029E-7

    6.43389327441006E-7

    4.475699988845739E-15

    643.389327441006

    1955.0

    1.29858775904806E-7

    129.85877590480598

    6.1808E-7

    5.22832028879169E-7

    9.072176002634667E-15

    522.832028879169

    7.0782E-7

    5.68704192717365E-7

    1.9353207835899246E-14

    568.704192717365

    1.71E-7

    1.42616882971426E-7

    8.056013322577285E-16

    142.61688297142598

    1991.0

    4.6214250288278E-7

    462.14250288278

    1992.0

    5.02690468048779E-7

    1957.0

    1.56895427225116E-7

    156.89542722511598

    5.95E-7

    4.08498806268553E-7

    3.478269526325473E-14

    408.498806268553

    1993.0

    4.44340410873095E-7

    2.3100000000000002E-7

    1.72841488840775E-7

    3.382412420257702E-15

    172.84148884077499

    9.176000000000001E-7

    3.61082409258688E-7

    3.0971182880451463E-13

    361.08240925868796

    1959.0

    1.90619948775028E-7

    190.61994877502798

    sum =

    4.232878516655652E-12

    sum =

    3.1017469486941807E-12

    1960.0

    2.10415176236099E-7

    210.41517623609897

    2.7800000000000003E-7

    2.32432943042609E-7

    2.0763566797581186E-15

    232.43294304260897

    1962.0

    2.56902550031004E-7

    256.902550031004

    log

    log

    log

    log

    1963.0

    2.84079189971611E-7

    284.079189971611

    year

    Observed

    predicted

    logpre-log-obs

    year

    Observed

    predicted

    logpre-logobs

    3.2600000000000003E-7

    3.14246622941574E-7

    1.3814187227753602E-16

    314.24662294157395

    4-yr Lake

    4-yr Lake

    5-yr Lake

    5-yr Lake

    1965.0

    3.47720129441463E-7

    347.720129441463

    trout

    trout

    trout

    trout

    1966.0

    3.84849780158128E-7

    384.84978015812794

    (g/kg)

    (g/kg)

    (g/kg)

    (g/kg)

    4.16E-7

    4.26024101488634E-7

    1.0048261065443366E-16

    426.02410148863396

    1977.0

    -5.576828844088842

    1977.0

    -5.546782599273146

    -5.483340302589611

    0.06344229668353485

    1968.0

    4.58769205114874E-7

    458.769205114874

    1978.0

    -5.633831992485762

    1977.0

    -5.487574443584569

    0.004234140994957336

    1969.0

    4.62286675244045E-7

    462.286675244045

    1979.0

    -5.689430564606135

    1977.0

    -5.539908378615351

    0.05656807602573988

    4.6000000000000004E-7

    4.4305815215013E-7

    2.870262085681465E-16

    443.05815215012996

    1980.0

    -5.7554928011973905

    -5.744191422080828

    0.011301379116562593

    1978.0

    -5.54172426356121

    1971.0

    4.11199637618173E-7

    411.19963761817297

    1980.0

    -6.023861028385644

    0.2796696063048163

    1979.0

    -5.598151125660114

    1972.0

    3.74180740115494E-7

    374.180740115494

    1980.0

    -5.695278728422246

    -0.04891269365858175

    1980.0

    -5.653401566892231

    1973.0

    3.36472857850493E-7

    336.47285785049297

    1981.0

    -6.069560405233299

    -5.798458875694692

    0.27110152953860744

    1981.0

    -5.798005108063206

    -5.707955593482085

    0.09004951458112131

    3.08E-7

    3.00429261466473E-7

    5.731608194303025E-17

    300.429261466473

    1981.0

    -6.050127170227087

    0.25166829453239536

    1981.0

    -6.243318259004667

    0.535362665522582

    1975.0

    2.6712519661643E-7

    267.12519661643

    1982.0

    -5.870764614998732

    -5.852438146872913

    0.018326468125819062

    1982.0

    -5.762101522716747

    2.3600000000000002E-7

    2.36929021535198E-7

    8.630810128615946E-19

    236.929021535198

    1982.0

    -5.982098939169993

    0.12966079229707983

    1983.0

    -5.816009935511011

    1977.0

    2.09844088751298E-7

    209.844088751298

    1982.0

    -6.01338947710832

    0.16095133023540686

    1984.0

    -5.86978070944171

    1.64E-7

    1.85699858676082E-7

    4.708838665619305E-16

    185.699858676082

    1983.0

    -5.989089745760008

    -5.906250064346209

    0.08283968141379905

    1985.0

    -5.923471999884675

    1979.0

    1.64253845103219E-7

    164.25384510321896

    1984.0

    -6.136189576028332

    -5.959965125385617

    0.17622445064271464

    1986.0

    -6.068196458660803

    -5.9771174893665115

    0.09107896929429149

    1.4400000000000002E-7

    1.45243796872064E-7

    1.5470306589561178E-18

    145.24379687206397

    1984.0

    -6.074213641516686

    0.11424851613106934

    1986.0

    -5.941706865687774

    -0.03541062367873771

    1.2500000000000002E-7

    1.28413089538634E-7

    1.164918019873271E-17

    128.41308953863398

    1984.0

    -5.709231049933441

    -0.25073407545217563

    1986.0

    -5.976858701046332

    -2.587883201794483E-4

    1982.0

    1.13522115359262E-7

    113.522115359262

    1985.0

    -6.013624329355826

    1987.0

    -6.030736611388867

    9.5E-8

    1.00352533626154E-7

    2.8649616219109294E-17

    100.352533626154

    1986.0

    -6.067251354562185

    1988.0

    -6.102142079326618

    -6.084340583655658

    0.017801495670959788

    1984.0

    8.87080056107954E-8

    88.7080056107954

    1987.0

    -5.956429467777553

    -6.120859869435375

    -0.16443040165782197

    1988.0

    -5.993944913408357

    -0.09039567024730122

    6.5E-8

    7.84132748631966E-8

    1.7991594255566184E-16

    78.41327486319659

    1987.0

    -6.204377161121551

    0.08351729168617616

    1988.0

    -5.956802824563612

    -0.12753775909204634

    1986.0

    6.93125624747884E-8

    69.3125624747884

    1987.0

    -6.120617362825658

    -2.4250660971691929E-4

    1988.0

    -5.925831096767273

    -0.15850948688838518

    1987.0

    6.12677293350809E-8

    61.267729335080894

    1987.0

    -6.2060211361013655

    0.08516126666599089

    1988.0

    -5.862361094977244

    -0.22197948867841433

    1988.0

    5.41564468892991E-8

    54.1564468892991

    1987.0

    -6.191464946855351

    0.07060507741997668

    1989.0

    -6.042651355564677

    -6.137935859899677

    -0.0952845043350008

    1989.0

    4.78704718202409E-8

    47.870471820240894

    1988.0

    -6.002749080680724

    -6.174457750331669

    -0.1717086696509451

    1989.0

    -6.100431176859431

    -0.03750468304024679

    1990.0

    4.23140675732539E-8

    42.3140675732539

    1988.0

    -5.868869148368424

    -0.3055886019632448

    1989.0

    -6.058240186185305

    -0.07969567371437236

    1991.0

    3.74025807184496E-8

    37.4025807184496

    1989.0

    -6.344064808845255

    -6.228049533019417

    0.1160152758258377

    1990.0

    -6.148564299611192

    -6.191526147462525

    -0.04296184785133317

    1992.0

    3.30611690067742E-8

    33.06116900677419

    1990.0

    -6.208955309199255

    -6.281637815239521

    -0.07268250604026605

    1991.0

    -6.150077170199601

    -6.2451135699414255

    -0.09503639974182487

    1993.0

    2.92236698313177E-8

    29.2236698313177

    1991.0

    -6.335224087922301

    1992.0

    -6.298699349729285

    1994.0

    2.58315964818851E-8

    25.8315964818851

    1992.0

    -6.22548303427145

    -6.388809208242307

    -0.1633261739708569

    1993.0

    -6.352284187724443

    1995.0

    2.28332490496156E-8

    22.8332490496156

    1993.0

    -6.037346595106789

    -6.442393668449298

    -0.40504707334250867

    1996.0

    2.01829276098047E-8

    20.1829276098047

    log mean =

    0.011679054677831919

    antimean

    1.0272568707024796

    log mean

    -0.0070020981563697505

    antimean

    0.9840063518343208

    1997.0

    1.78402362676271E-8

    17.8402362676271

    log sd =

    0.18462752424705534

    95%conlim

    0.36186994752422846

    antisd

    1.5297748765793806

    log sd =

    0.16042238462522873

    95%conlim

    antisd

    1.4468462554053214

    1998.0

    1.57694677482066E-8

    15.769467748206598

    -0.18462752424705534

    95%conlim

    -0.36186994752422846

    antisd

    0.6536909549959586

    log sd =

    -0.16042238462522873

    95%conlim

    antisd

    0.691158439443076

    1999.0

    1.39390592987061E-8

    13.939059298706098

    sum

    8.569003235426411E-15

    sed sum =

    8.569003235426411E-15

    sheet

    sed sum

    4yrlt sum

    5yrlt sum

    4yrlogmean

    0.011679054677831919

    sheet

    4yrlogmean

    5yrlogmean

    4yrltsum =

    4.232878516655652E-12

    n

    8.89E-15

    4.31E-12

    3.32E-12

    5yrlogmean

    -0.0070020981563697505

    n

    0.01637

    0.00368

    5yrltsum =

    3.1017469486941807E-12

    o

    8.57E-15

    4.77E-12

    4.09E-12

    o

    0.0358

    0.0237

    1.0

    8.57E-15

    4.47E-12

    3.52E-12

    1.0

    0.02363

    0.00817

    2.0

    8.75E-15

    4.23E-15

    3.1E-12

    2.0

    0.01168

    -0.007

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0