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A Model to Evaluate Recreational Management Measures Objective I – Stock Assessment Analysis Create a model to distribute estimated landings (A + B1 fish) by size class. Create a model to distribute estimated catch (A + B1 +B2 fish) by size class

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A Model to Evaluate Recreational Management Measures Objective II – Estimates of landings and catch for different proposed recreational fishery regulations Size limits Possession limits Abundance

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Summer Flounder Size Class 2011

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I. Logistic Analysis The logit model where multiple possible outcomes exist can be extended to a multinomial model referred to as a generalized or baseline-category logit model of the form (McFadden, 1974): Log(Pr(Y=i|x)/Pr(Y=k+1|x)) = α i + β’ i xi = 1,....,k α i = the intercept parameters, and β i = the vector of the slope parameters.

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Analysis of Maximum Likelihood Estimates for the Probability that a Fish will be Landed in a Given Size Category Extra-Fishery Variables Parameter DF Estimate Standard Wald Error Chi-Square Pr > ChiSq sfldp 1 -0.83730.0477308.1836<.0001 FPPI 1 0.00340.000272156.1948<.0001 pr 1 0.07020.00567153.3822<.0001 NP 1 7.46E-092.71E-097.5450.006 NPd 1 -0.47410.048894.5362<.0001 omega3 1 -0.18240.039721.0956<.0001

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Analysis of Maximum Likelihood Estimates for the Probability that a Fish will be Landed in a Given Size Category Recreational Fishing Experience Variables Parameter DF Estimate Standard Wald Error Chi-Square Pr > ChiSq Weight1 -12.25330.041886011.0892<.0001 TotSFL 1 0.0000366.19E-0633.7463<.0001 SSB 1 -8.86E-062.03E-0619.0343<.0001 PARTY 1 -0.002680.00062118.646<.0001

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Analysis of Maximum Likelihood Estimates for the Probability that a Fish will be Landed in a Given Size Category Regulatory Variables Parameter DF Estimate Standard Wald Error Chi-Square Pr > ChiSq minsLm 1 -0.02110.0132.61740.1057 minslmi 1 0.02870.0049733.3697<.0001 PosLmt 1 0.002310.001532.2790.1311 ARecTrgt 1 -0.002140.00029651.966<.0001

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Numbers of Summer Flounder Landed Minimum Size = 16 Possession Limit = 3 StATotnszclnszcl11nszcl12nszcl13nszcl14nszcl15nszcl16nszcl17nszcl18nszcl19nszcl20nszcl21nszcl22nszcl23nszcl24nszcl25 CT6105400000198211331267437270944643180 DE434040001950361290819581179532388147600 MA1349790001637273232825969786452576318837310 MD268060000425181147611036121681799113400 NC480393161036505135163291907558218366440000 NJ9512860021091529385432267297157509018101445665225650 NY5263180000000232469820715434334165220717891 RI109727000001548668882559137386392357452 VA266436003171518786253440941518535755053103151200 Coastwi de Total2168049316108679539617850300118902650826569736624132321153834479120776893

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II. Quick Assessment Method The first model (m1) predicts the number of fish landed (Type A + B1 fish) in a state that have been intercepted, identified, measured, and in some cases weighted by observers (TotSFLnmbr). The second model (m2) predicts the total number of fish (Type A+B1+B2 fish) reported to observers by anglers who did not necessarily allow them to be identified, measured, and weighted by observers (TotSFLnd).

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M1: Parameters of Interest Variable Parameter EstimateStandard ErrorF ValuePr > F Offshore Minimum Size limit 0.839480.016132710.07<.0001 Inshore Minimum Size Limit -0.254230.00801003.64<.0001 Possession Limit Offshore 0.396670.012341034.15<.0001 Possession Limit Inshore -0.314160.007841604.92<.0001 Open Season -0.178280.00640776.85<.0001

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QAM: Scatter Plot Two scatter plots at the end of the program provide a comparison of the actual and predicted values of these two dependent variables. These plots indicate that most predicted values fall within narrow bands around the actual values of the variables; this reflects the coefficient of determination of 76.7 and 76.8 percent, respectively.

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Summer flounder recreational management measures by state, 2012.

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Estimated Landed and Caught StateLandedCaught MA39.116106.159 RI213.724516.305 CT182.143273.405 NY224.219800.370 NJ417.6041034.970 DE250.582526.213 MD51.9624150.618 VA230.185485.789 NC273.608354.256 Coast Wide1883.1464218.085

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Fluke MRIP 2012 Number of Fish STATE123456 Grand TotalSum W1-4 % W1-4 from 2011Proj Total MASSACHUSETTS 1971756503 76,220 56.47%134,981 RHODE ISLAND 6029942987103,286 94.13%109,727 CONNECTICUT 120524900461,056 100.00%61,056 NEW YORK 0196649291676488,325 92.78%526,319 NEW JERSEY 0361997566851928,848 97.64%951,286 DELAWARE 074922888736,379 83.81%43,404 MARYLAND 8871599516,882 62.98%26,806 VIRGINIA 4299577605132149252,749 94.85%266,473 NORTH CAROLINA701706193861088732,049 66.71%48,039 1,995,794 2,168,092 2,168

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Proposed Regulations Season length = 153 days Abundance = 60074 Possession Limit = 3, 4, and 5 fish Minimum Size Limit = 16 and 17 inches Landed = A + B1 fish Caught = A + B1 + B2 fish Inshore Regulations = Offshore Regulations

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Numbers of Coast Wide Fish Landed (A + B1) and Caught (A + B1 + B2) (000 of fish) Minimum Size Possession LimitNumbers LandedNumbers Caught (inches)(number of fish) (Type A+B1)(Type A+B1+B2) -------------------------------------------------------------------------------------------------------- 1631585 3715 16417774032 16519414296 -------------------------------------------------------------------------------------------------------- 17316683750 17418703982 17520434530

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Summary This model is a simple application of time proven methods of dealing with imperfect information in a marketplace or natural environment. While the concepts are simple, their actual application is complex. A step by step user guide is provided in the appendix attached. The programs in steps I to VII are used if the existing data set is to be modified for another species of recreationally harvested fish. These steps will update the database needed to estimate a new sets of coefficients for use in a policy analysis of any existing or proposed fishery management regulations.

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