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

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

Summer Flounder Size Class2011

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)) = αi + β’i x i = 1,. . . .,k• • αi = the intercept parameters, and • βi = the vector of the slope parameters.

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 -0.8373 0.0477 308.1836<.0001

FPPI 1 0.0034 0.000272156.1948 <.0001 pr 1 0.0702 0.00567153.3822 <.0001 NP 1 7.46E-09 2.71E-09 7.545

0.006NPd 1 -0.4741 0.048894.5362 <.0001 omega3 1 -0.1824 0.0397 21.0956

<.0001

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

Weight 1 -12.2533 0.041886011.0892 <.0001TotSFL 1 0.000036 6.19E-06 33.7463

<.0001 SSB 1 -8.86E-06 2.03E-0619.0343 <.0001PARTY 1 -0.00268 0.000621 18.646

<.0001

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 -0.0211 0.013 2.61740.1057

minslmi 1 0.0287 0.00497 33.3697<.0001

PosLmt 1 0.00231 0.00153 2.2790.1311

ARecTrgt 1 -0.00214 0.000296 51.966<.0001

Numbers of Summer Flounder LandedMinimum Size = 16Possession Limit = 3

StA Totnszcl nszcl11 nszcl12 nszcl13 nszcl14 nszcl15 nszcl16 nszcl17 nszcl18 nszcl19 nszcl20 nszcl21 nszcl22 nszcl23 nszcl24 nszcl25

CT 61054 0 0 0 0 0 1 9 82 1133 12674 37270 9446 431 8 0

DE 43404 0 0 0 1 9 50 361 2908 19581 17953 2388 147 6 0 0

MA 134979 0 0 0 1 6 37 273 2328 25969 78645 25763 1883 73 1 0

MD 26806 0 0 0 0 4 25 181 1476 11036 12168 1799 113 4 0 0

NC 48039 3 16 103 650 5135 16329 19075 5821 836 64 4 0 0 0 0

NJ 951286 0 0 2 10 91 529 3854 32267 297157 509018 101445 6652 256 5 0

NY 526318 0 0 0 0 0 0 0 2 32 469 8207 154343 341652 20717 891

RI 109727 0 0 0 0 0 1 5 48 668 8825 59137 38639 2357 45 2

VA 266436 0 0 3 17 151 878 6253 44094 151853 57550 5310 315 12 0 0

Coastwide Total 2168049 3 16 108 679 5396 17850 30011 89026 508265 697366 241323 211538 344791 20776 893

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).

M1: Parameters of InterestVariable Parameter

Estimate Standard Error F Value Pr > F

Offshore Minimum Size limit

0.83948 0.01613 2710.07 <.0001

Inshore Minimum Size Limit

-0.25423 0.0080

1003.64 <.0001

Possession Limit Offshore

0.39667 0.01234 1034.15 <.0001

Possession Limit Inshore

-0.31416 0.00784 1604.92 <.0001

Open Season -0.17828 0.00640 776.85 <.0001

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.

Summer flounder recreational management measures by state, 2012.

Estimated Landed and CaughtState Landed Caught

MA 39.116 106.159

RI 213.724 516.305

CT 182.143 273.405

NY 224.219 800.370

NJ 417.604 1034.970

DE 250.582 526.213

MD 51.9624 150.618

VA 230.185 485.789

NC 273.608 354.256

Coast Wide 1883.146 4218.085

Fluke MRIP 2012Number of Fish

STATE 1 2 3 4 5 6Grand Total Sum W1-4

% W1-4 from 2011 Proj Total

MASSACHUSETTS     19717 56503     76,220 76,220 56.47% 134,981

RHODE ISLAND     60299 42987 103,286 103,286 94.13% 109,727

CONNECTICUT     12052 49004 61,056 61,056 100.00% 61,056

NEW YORK   0 196649 291676 488,325 488,325 92.78% 526,319

NEW JERSEY   0 361997 566851 928,848 928,848 97.64% 951,286

DELAWARE   0 7492 28887 36,379 36,379 83.81% 43,404

MARYLAND     887 15995 16,882 16,882 62.98% 26,806

VIRGINIA   42995 77605 132149 252,749 252,749 94.85% 266,473

NORTH CAROLINA 70 1706 19386 10887 32,049 32,049 66.71% 48,039

1,995,794 1,995,794 2,168,092

2,168

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

Numbers of Coast Wide Fish Landed (A + B1) andCaught (A + B1 + B2)

(000 of fish)

MinimumSize Possession Limit Numbers Landed

Numbers Caught (inches) (number of fish) (Type A+B1)

(Type A+B1+B2) --------------------------------------------------------------------------------------------------------16 3

1585 371516 4

1777 403216 5

1941 4296--------------------------------------------------------------------------------------------------------17 3

1668 375017 4

1870 398217 5

2043 4530

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.