05 Schaeffer

05 Schaeffer - + Recruitment (R> ) + Growth (K) -...

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Unformatted text preview: + Recruitment (R> ) + Growth (K) - Natural Mortality (M> ) - Yield or Catch (C> ) and Fishing Mortality (F> ) Fish Stock Stock EXST025 - Biological Population Statistics Schaeffer model development Exponential Growth Model Derivation ˜N ˜t Define = + rN where, ˜ N is the change in N ˜ t is a time unit r is a proportionality constant which can be positive or negative depending on the dominant term of r = (births deaths) N is the number at the start of the time period then; ˜t ˜N = 1 rN integrate over time (one unit, such as one year) t = 1 r ' ˜N N = 1 r ln(N) + c = t ln(N) + ln(cw ) = rt N cw = ert N = cww ert where, solving for cww at t = 0 and adjusting notation accordingly N! = cww ert! = cww er 0 = cww = N! so Nt = cww ert = N! ert and for any 1 time interval from time t to t+1 we can also use Nt+1 = Nt er Logistic Growth Model - a similar derivation with additional considerations Recall that ˜N ˜t = rN for simplicity, let ˜ t = 1 time interval (ie. ˜ t = 1), then ˜ N = rN = (b - d) N = (r7+B - d) N giving by integration N = N! ert Page 2 EXST025 - Biological Population Statistics Page 3 Since no organism follows exponential growth forever, lets invent a function that modifies “r" as the number of organisms increases eg. ˜N ˜t = (rm - cN) N such that ˜N ˜t p 0 this would be true if N p Nmax as rm - cN = 0 when N = Nmax so let c= then ˜N ˜t rm Nmax = rm N ’1 - N Nmax “ = rm N ’ Nmax - N “ = rm N Nmax remember this step for later we can then show (integrating the above over time) a) invert (middle equation above) and integrate t = Nmax rm ' ˜N N (Nmax - N) b) split integrand into partial fractions 1 N(Nmax - N) = A N + B Nmax - N 1 = A(Nmax - N) + BN B= 1 Nmax so 1 N(Nmax - N) = 1 Nmax and 1 ’N A= 1 Nmax 1 Nmax - N “ rm Nmax N# EXST025 - Biological Population Statistics the integral can then be written as t= 1 rm t= ' 1 rm ˜N N 1 rm Page 4 ' ˜N Nmax - N clog(N) - log(Nmax - N) + cd solve for c when t = 0, where all N = N! 0= 1 rm c = 1 rm * log(N! ) so t= and 1 rm log(Nmax - N! ) c * log’ Nmax !- N! “ N ’log(N) log(Nmax - N) log’ Nmax !- N! ““ N 1 rm t= 1 rm N * log’ N! ’ Nmax --N! ““ Nmax N Nmax N N rm t = log’ N! ’ Nmax -- N! ““ c) then solve for N erm t = ’ N! (Nmax - N) N (Nmax - N! ) Nmax - N! “e-rm t N! = (Nmax - N) N 1 ’ Nmax - N! “e-rm t N! N> = 1 +’ = Nmax Nmax - N! “ erm t N! = Nmax N Nmax N 1 EXST025 - Biological Population Statistics N> = 1 +’ Page 5 Nmax Nmax N! “ e-rm t N! Nmax Nt N0 time EXST025 - Biological Population Statistics DERIVATION OF THE SCHAEFFER MODEL used to describe FISH POPULATION DYNAMICS FROM CATCH AND EFFORT DATA this type data is often readily available for a fishery STARTS WITH LOGISTIC GROWTH CURVE - we will redefine some notation Let Nmax = k “carrying capacity" rm = r intrinsic or maximum rate of growth recall “old r" = b - d and was a generic growth rate = rm - cN = rm - rm Nmax N where; k = Nmax c = rm Nmax r k = where cN> is a maximum at N! , and decrease thereafter then, define the Logistic Equation as N> = k 1+ k - N! N! e-rt This is the LOGISTIC GROWTH CURVE Nmax Nt N0 time Page 6 EXST025 - Biological Population Statistics Page 7 SCHAEFFER WAS NOT INTERESTED IN THE WHOLE LOGISTIC GROWTH CURVE, BUT ONLY IN THE PRODUCTION, ie. ˜N - near N! ˜ N is small - near k ˜ N is small - in the middle ˜ N is largest How then, would we maintain the population in order to maximize the harvest? take derivative of logistic w.r.t. time (reversing integration process) ˜N ˜t = rN (1 - N k) r = rN - k N# recall all “r" from now on are rmax then, letting b" be equal to r b# be equal to Y = ˜ N, r K (where our time unit is 1 season) X=N Y = b" X + b# X# the result is a polynomial WITHOUT AN INTERCEPT ΔN 0 Nt K EXST025 - Biological Population Statistics Page 8 for SCHAEFFER's PURPOSES ˜ N was the PRODUCTION for a given population size N and given production data, all Schaeffer needed to describe the fishery was to subtract HARVEST OR CATCH officially he “integrated" across 1 time period (eg. 1 year) so ˜ t = 1 and all N values are means See SCHNUTE (1977) for the mathematical niceties ˜ N = rN r # KN C where C = CATCH or HARVEST unfortunately, in practice we never know N or ˜ N, so we define some well known relationships from fisheries let q = catchability coefficient or that fraction of the population captured by 1 application of the EFFORT f = effort then C = qNf = total catch U = qN = CATCH PER UNIT EFFORT U= C f = qNf f = qN finally, ˜ N = rN – NOTE: all N are N after integration, r # KN qfN EXST025 - Biological Population Statistics Page 9 multiplying both sides by q (recall qN = U) gives r K UN ˜ U = rU multiply coefficient of (UN) by q q qfU = 1, express last U as ˜ U = rU - r Kq U(qN) - qf C f ˜ U = rU - r Kq C f U# - qC – where all U are actually U (annual or seasonal) after integration another common version, take U# - qC ˜ U = rU - r Kq ˜U U U - qf = r- r Kq these versions can be fitted with multiple regression techniques, the problem as we will – see is estimating ˜ U this is a multiple regression model with a polynomial term ˜ U = b" Ui + b# U# + b$ Ci + ei i NOTE that the parameter estimates are “meaningful" biological terms the “i" are generally observations over time, so “t" could also be used as a subscript EXST025 - Biological Population Statistics Page 10 ASSUMPTIONS for the SCHAEFFER MODEL a) all assumption for multiple regression apply when fitted by least squares techniques b) note that the model is based on the logistic growth curve so we must assume this function is adequate - the curve could be derived through other means, perhaps empirically, but the coefficients would not have the same interpretation c) addition assumption may be made on an application by application basis e.g. assume that a “unit of effort" is the same across the years of available data (or correct) - closed population or equal immigration and emigration - stable stock age structure, reproductive rate Note on HOMOGENEITY OF VARIANCE one transformation for non - homogeneous variance is if Yi = b! + b" Xi + ei Xi then Yi Xi 1 = b! Xi + b" + ei which improves the variance properties of the model we saw two versions mentioned ˜ Ui = rUi + ˜Ui Ui = r+ r # Kq Ui r Kq Ui - qCi + ei - qfi + ewi note that the error is not the same, it is likely that one of these will not have homogeneous variance EXST025 - Biological Population Statistics Page 11 THE TWO MODELS ABOVE ARE THE BASIC NON - EQUILIBRIUM VERSIONS ˜U Á 0 where The greatest difficulty comes in getting a value of ˜ Ui or ˜Ui Ui SCHAEFFER - in integrating defines ˜ U = U# - U" where; U" = Ut + Ut-1 2 -- the beginning of the year U# = Ut+1 + Ut 2 -- the end of the year (or season) ˜U= Ut+1 + Ut - Ut - Ut-1 2 = Ut+1 Ut-1 2 so, we don't even have to know this years data to get this years ˜ U The best estimate of ˜ U probably comes from SCHNUTE (1977) one of whose versions describes ˜U U = 1 ˜U U ˜t which after integration from time = t to time t+1 gives Log(Ut+1 ) - Log(Ut ) = Log’ Ut+1 “ Ut Other estimates include a) Schaeffer's b) 2(Ut+1 - Ut ) (Ut+1 + Ut ) ˜U U -- does not do very well from Marchesseault et. al. 1976 c) log’ Ut+1 + Ut “ also from Schnute 1977 Ut + Ut-1 d) and many more, BUT so far I would say SCHNUTE'S or MARCHESSEAULT et. al. is best EXST025 - Biological Population Statistics POLYNOMIALS Yi = "! "" X"i "# X#i ... "k Xk %i # ki NOTE that there is only one Xi value, it is just raised to different powers. There is no doubt about the order in which the variables are entered, the first term in is Xi this is called the LINEAR term the second is X# this is called the QUADRATIC term i $ the third is Xi the CUBIC term X% the QUARTIC term i X& the QUINTIC term, etc. i The types of curves fitted are: LINEAR is just simple linear QUADRATIC CUBIC QUARTIC The first curvature (may) appear with the Quadratic The first inflection (may) appear with the Cubic Each additional term can cause an additional inflection Page 12 EXST025 - Biological Population Statistics Page 13 OBJECTIVES of POLYNOMIAL REGRESSION Population Model: Yi = "! "" X"i "# X#i ... "k Xk %i # ki Objectives: 1) Is there a curvilinear relationship between the Yi and Xi . 2) Is the curvature linear? Quadratic? Cubic? Quartic? ... 3) Obtain the curvilinear predictive equation for Yi on Xi . NOTES on POLYNOMIAL REGRESSION 1) Polynomial regressions are fitted successively starting with the linear term (a first order polynomial). These are tested in order, so Sequential SS are appropriate. 2) When the highest order term is determined, then all lower order terms are also included. If for instance we fit a fifth order polynomial, and only the CUBIC term is significant, then we would OMIT THE HIGHER ORDER NON-SIGNIFICANT TERMS, BUT RETAIN THOSE TERMS OF SMALLER ORDER THAN THE CUBIC. This does not mean that Yi = b! b" Xi ei is not a useful model, only that this is not a “polynomial". 3) If there are s different values of Xi , then s-1 polynomial terms (plus the intercept) will pass through every point (or the mean of every point if there are more than one observation per Xi value. It is often recommended that not more than 1/3 of the total number of points (different Xi values) be tied up in polynomial terms. eg. If we are fitting a polynomial to the 12 months of the year, don't use more than 4 polynomial terms (quartic). 4) All of the assumptions for regression apply to polynomials. 5) Polynomials are WORTHLESS outside the range of observed data, do not try to extend predictions beyond this range. EXST025 - Biological Population Statistics Page 14 INFLECTIONS for Polynomial Regression lines Linear straight line, no curve or inflections Quadratic one parabolic curve, no inflections Cubic two parabolic rates of curvature with the possibility of an inflection point. Each additional term allows for another change in the rate of curvature and allows for an additional inflection. APPLICATIONS of Polynomial Regression lines 1) If enough polynomial terms are used, these curves will fit about anything. However, there is usually no good theoretical reason for using polynomial curves. eg. Suppose we have a model where we expect an exponential type growth curve to result. We could fit this with a quadratic or cubic or quartic polynomial, but the exponential curve would fit with two advantages. a) Good interpretation of the regression coefficient (proportional growth) b) Uses fewer d.f. in a simpler model. 2) Polynomials are useful for testing for the presence of curvature, and the nature of that curvature (inflections or no), and can be used to fit trends with complex curvature where no particular theoretical function is known to be applicable. 3) The successive terms in polynomials are highly correlated. This is not a problem when Sequential SS are used. EXST025 - Biological Population Statistics THE SCHAEFFER MODEL IN SAS -- there is a data set is in XST716.EXST7025.ASSIGN(FOUR) a) To get “t+1", “t", “t-1" we need to use a lag function e.g. X> 17 28 13 42 19 35 . . X>" . 17 28 13 42 19 35 . X># . . 17 28 13 42 19 35 then use as X>" , X> , and X>" respectively In SAS we can LAG to t-n, but can't got “forward", so let the variable as entered be “forward", e.g. suppose we pretend to enter “t+1" as our data using CP1 for Ct+1 , C for Ct , CM1 for Ct-1 INPUT YEARP1 CP1 EP1; YEAR = LAG1 (YEARP1) C = LAG1(CP1); CM1 = LAG2(CP1); E = LAG1(EP1); EM1 = LAG2(CP1); DROP YEARP1; then get CPUE = U by U = C/E; UP1 = CP1 / EP1; UM1 = CM1 / EM1; then proceed to get aU estimate using the appropriate combinations SCHAEFER = (UP1 - UM1) / 2; SCHNUTE = LOG(UP1 / U); MARCH = 2 * (UP1 - U) / (UP1 + U); Page 15 EXST025 - Biological Population Statistics Page 16 EQUILIBRIUM EQUATIONS (basically 2) Recall ΔN 0 Nt K Our equilibrium versions will bare a superficial resemblance to this, but be aware of the transformations undertaken EQUILIBRIUM, for the logistic curve can be achieved whenever we harvest exactly ˜ N> at any level of Nt , thus returning population level to the same Nt VERSION 1 At equilibrium ˜ U = 0 and ˜N r rN - K N# - C = C = rN - r K = 0 N# or, ˜ U = rU r C = qU r qK U# - qC = 0 r # q# K U this is the first equilibrium version EXST025 - Biological Population Statistics Page 17 VERSION 2 - from CLARK (1976) [can also derive from the above by dividing through by C and solving for C ˜ N = rN r # KN r # KN qfN = 0 = rN - qfN N = K- qK r f qfN = C = (qK)f q# K r f# or U = qK qK r f the most commonly used form is from version 2 qEN = C = (qK)f qK r f# or, statistically Ci = b" fi b# fi# ei where; b" = qK b# = qK r notice that we cannot solve for the 3 unknowns with 2 values. Catch This describes the “classic" representation Effort which is a symmetric, polynomial curve EXST025 - Biological Population Statistics Page 18 NOTE that the axes are not the same as the original ˜ N form, even though the curve looks the same also that axes are reversed, lowest effort nearest K and highest effort is nearest 0 - this form can be fitted directly (statistically) from data, or the coefficients can be derived from other sources (Schaeffer's original approach) NOTE: this is an equilibrium curve, This is result of fishing year after year at the same level not what would be observed in a single year with increasing effort for a single year Catch Asymtotic on N0 Effort EXST025 - Biological Population Statistics Page 19 Suppose we wish to fit the NONEQUILIBRIUM VERSION, but wish to graph the equilibrium version To approximate the equilibrium parameters from non - equilibrium fits; either for Schaeffer's version; ˜ U = b! U + b" U# + b# C = 0 0 = b! 1 + b" fC + b# # f 0 = b! f + b " C + b # f # b" C = b! f + b# f # C = b! b" f b# b" f# not that the negatives are independent of the sign of b! , b" and b# , so those signs would also be present. If the model works properly, we expect b! to be positive and " and # to be negative. The equilibrium approximation is then C = b! b" f b# b" f# or, the other transformation (Schnute or Marchesseault) ˜ U = b! + b" U + b# f = 0 0 = b! f + b " C + b # f # b" C = b! f + b# f # C = b! b" f b# b" f# which is the same transformation as above. EXST025 - Biological Population Statistics INTERPRETATIONS and IMPLICATIONS a) fish at low levels of effort high catch rates (UNDER FISHING) b) fish at high levels of effort low catch (OVER FISHING) c) fish at medium effort levels highest catch 1) MSY = MAXIMUM SUSTAINED YIELD 2) in middle due to symmetry DISCUSS UTILITY AS A CONCEPT (MSY) DISCUSS Larkin's epitaph Mark Twain - “Reports of my death are greatly exaggerated" Show LOBSTER Example Was the lobster in equilibrium? Which curve is Better? Notice chronological line. Perhaps the line is not symmetric! Next models address this. Larkin, P. A. 1977. An epitaph for the concept of maximum sustained yield. Transactions of the American Fisheries Society 106(1):1-11. Pamela M Mace. A new role for MSY in single-species and ecosystem approaches to fisheries stock assessment and management. Fish and Fisheries. 2001, 2, 2-32. Page 20 EXST025 - Biological Population Statistics Page 21 OTHER VERSIONS 1) PELLA AND TOMLINSON ˜ U = rU - r qK U# - qC is symmetric r qK UP - qC WHICH IS NOT SYMMETRIC they suggest ˜ U = rU - This is not a linear technique, it requires proc NLIN in SAS with a restriction “p Á 1", otherwise it can be undefined There is also a canned or a canned program from Pat Tomlinson Shape of curve(s) by Pella & Tomlinson EXST025 - Biological Population Statistics Page 22 2) Fox 1970 (See Pitcher and Hart) in above model, as p p 1 the model p GOMPERTZ FUNCTION (which we will see later) Shape of Gompertz (compared to Logistic) Biomass Logistic Gompertz Time Comparison of Schaeffer's and Fox's models Schaeffer's Equilibrium : Fox's Equilibrium : C = b" feb# f Schaeffer Catch Fox C = b" f - b # f # Biomass EXST025 - Biological Population Statistics CPUE Schaeffer: U = U_ - q# k r Page 23 q Fox: U = U_ e- k f f Schaeffer Fox Effort Schaeffer - Equilibrium Schaeffer Catch Fox Fox - Equilibrium Effort EXST025 - Biological Population Statistics Page 24 PROBLEMS 1) applied to many fisheries, some problems in long term results - Note the model is “economic" even before GORDON i.e. maximize the fish (or $) for least amount of effort so there is little biology in the model =n though if the fishery is stable and really maximized, then the biological aspects are probably not adversely affected (it would still be nice to consider then though) 2) ANCHOVY PROBLEMS -- biological assumptions and obvious changes were not considered a) Age structure was never stable b) indications of technological advance effort c) EL NINO - a current effectively reduces K, tremendously at some times MORAL: Don't blindly apply the model, it ignores much biology. 3) Additional variables can be included to improve the model these are not really a part of the derivation of the model, simply added to reduce the variance and improve the fit statistically a) TEMPERATURE - often lagged 1 to 5 years (lobster model, anchovies) b) TECHNOLOGICAL ADVANCE - entered into anchovy model by Segura as a trend line c) ADULT BIRD POPULATION - this is actually an additional form of harvest, so it may be considered as a second “ - C ", and does fit into the theory well =n these variables probably do help since they will contribute to “explaining" (statistically) additional sources of variability in N d) Walter (1973, in Pitcher & Hart) ˜ N does not depend only on N> , but also on N>" , etc. We can add time lags to the model. RECRUITMENT - the next topic, will also include a term which is similar to N, and may also benefit from additional exogenous variables EXST025 - Biological Population Statistics Page 25 GORDON - SCHAEFFER MODEL GORDON AN ECONOMIST -- first thing he sells the fish each pound or fish converts to monetary value $ $ Effort This line now describes INCOME per quantity of effort (sustained) Then consider COST of fishing $ Effort Each unit of effort costs a certain quantity to maintain (including boat, maintenance, gasoline, crew, food, net maintenance, interest on loans, processing, marketing, etc. also, included by economists is an interest rate, so the fishery is not profitable unless we get more income than if we put the original investment in the bank EXST025 - Biological Population Statistics combine cost and income lines $ Effort PROFIT = area under curve when cost is below income LOSS = area under curve when cost is above income MSY = MAXIMUM SUSTAINED YIELD - maximizes difference between the fish income and X axis - maximizes protein MEY (or OSY) = MAXIMUM ECONOMIC YIELD or optimum sustained yield - maximizes difference between income and cost - maximizes profit OSY = optimum sustained yield This is ambiguous. It could be the MSY or the OSY or neither. eg. the best objective in a sport fishery may be to maximize “fun" or fish per person Economic equilibrium point with profit, more people enter fishery, EFFORT goes up with loss, people leave fishery EFFORT GOES DOWN the overall result is that the effort tends to an equilibrium point Page 26 EXST025 - Biological Population Statistics OSY $ Page 27 MSY Loss Profit Effort ee BIOLOGICAL INTERPRETATIONS 1) a number of concepts are depicted in this presentation a) how over fishing arises b) why is it economically feasible to fish whales to extinction 2) MEY and OSY and MSY 3) note that the OSY is “economic" only, it doesn't spell out how to “slice the pie" =n consider a sport fishery, would we want an “economic" optimum? EXST025 - Biological Population Statistics Page 28 CALCULATION OF OSY, essentially a) income (or protein) can be optimized at derivative of $ = b" f - b# f # b) Cost is usually described by direct proportion model $ = b$ f though an intercept is feasible c) Optimize profit by getting maximum of [income - cost] However, economists consider much more in the cost function, the optimum turns out to be for q, K, r = biological parameters as before c = cost per unit of effort p = price per unit biomass X_ = economic equilibrium yield $ = interest rate, The amount that could be made with another investment stock, bonds) Z_ = # = X_ K = c pqK $ r then, MEY = 1 4 1 + Z_ - # + È((1 + Z_ - # )# + 8Z_ # )‘ from CLARK (1977) this evaluates the MEY with economic considerations (eg. bank, EXST025 - Biological Population Statistics Page 29 Summary of the SCHAEFFER MODEL Based on the Logistic Model N> = k 1+ k - N! N! e-rt This is the LOGISTIC GROWTH CURVE Nmax Nt N0 time There are 2 common versions r ˜ Ui = rUi + Kq U# - qCi + ei i ˜Ui Ui = r+ r Kq Ui - qfi + ewi with variations such as Pella & Tomlinson's variable Power term or Fox's version based on the Gompertz growth curve Other variations come from the various estimates of ˜ U or a) Schaeffer's b) 2(Ut+1 - Ut ) (Ut+1 + Ut ) ˜U U ˜U U -- does not do very well from Marchesseault et. al. 1976 c) Log(Ut+1 ) - Log(Ut ) = Log’ Ut+1 “ Ut and log’ Ut+1 + Ut “ Ut + Ut-1 from Schnute 1977 EXST025 - Biological Population Statistics The model is usually presented as an equilibrium curve C = (qK)f qK r f# Ci = b" fi b# fi# ei Which can be modified by selling catch and adding COST considerations to give the GORDON - SCHAEFFER MODEL $ Effort Which introduces the concepts of MEY and OSY in addition to MSY Page 30 EXST7025 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 The Schaefer Model Geaghan Page 1 ***************************************************************; *** Schaeffer Model (Halibut data) ***; *** The data is from Ricker (1975) pg 320-321 ***; *** Halibut yeild (millions of lbs) and effort (thousands ***; *** of skates) ***; ***************************************************************; OPTIONS NOCENTER PS=61 LS=78 NODATE; *data included below - FILENAME INPUT 'C:\SASPROG\E25\HALIBUT.DAT'; DATA ONE; INFILE CARDS MISSOVER FIRSTOBS=4; TITLE1 'Analysis of Catch and Effort data for Pacific Halibut'; INPUT YEARP1 CATCHP1 EFFORTP1 OBSID $; YEAR = LAG1(YEARP1); YR = YEAR - 1909; Y = YEAR - INT(YEAR/10)*10; CATCH = LAG1(CATCHP1); CATCHM1 = LAG2(CATCHP1); EFFORT = LAG1(EFFORTP1); EFFORTM1 = LAG2(EFFORTP1); CPUEP1 = CATCHP1/EFFORTP1; CPUEM1 = CATCHM1/EFFORTM1; CPUE = CATCH / EFFORT; CPUE2 = CPUE*CPUE; EFFORT2 = EFFORT*EFFORT; SCHAE = (CPUEP1 - CPUEM1) / 2; SCHNU = LOG(CPUEP1 / CPUE); MARCH = 2*(CPUEP1 - CPUE) /(CPUE + CPUEM1); IF CATCH EQ . THEN DELETE; DROP YEARP1; CARDS; NOTE: Missing values were generated as a result of performing an operation on missing values. Each place is given by: (Number of times) at (Line):(Column). 1 at 13:47 1 at 14:18 1 at 14:20 1 at 14:28 1 at 14:32 2 at 17:53 1 at 18:24 1 at 19:22 1 at 19:53 2 at 21:25 2 at 21:35 1 at 22:17 1 at 22:28 1 at 23:18 1 at 23:27 2 at 23:35 2 at 23:42 NOTE: The data set WORK.ONE has 44 observations and 18 variables. NOTE: The DATA statement used 4.99 seconds. 26 RUN; 75 ; 76 PROC PRINT; 77 VAR YEAR CATCH EFFORT CPUE CATCHM1 CATCHP1 SCHAE SCHNU MARCH; RUN; NOTE: The PROCEDURE PRINT printed page 1. NOTE: The PROCEDURE PRINT used 1.1 seconds. Section used for preparing predicted lines. 92 DATA TWO; 93 DO EFFORT = 0 TO 700 BY 10; E = EFFORT; E2 = EFFORT * EFFORT; 94 SCHAEP=-(0.413310324/-1.801221992)* E -(-0.000720678/-1.801221992)*E2; 95 SCHNUP=-(0.331461058/-2.075163729)* E -(-0.000442519/-2.075163729)*E2; 96 MARCHP=-(0.412076334/-2.487629266)* E -(-0.000552460/-2.487629266)*E2; 97 EQUILP= (0.1606674819) * E - (0.0002122178)*E2; 98 OUTPUT; END; RUN; EXST7025 The Schaefer Model Geaghan Page 2 Analysis of Catch and Effort data for Pacific Halibut OBS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 YEAR CATCH EFFORT CPUE CATCHM1 CATCHP1 SCHAE SCHNU MARCH 1913 55.4 432 0.12824 . 44.5 . -0.03677 . 1914 44.5 360 0.12361 55.4 44.0 -0.005454 -0.05212 -0.04985 1915 44.0 375 0.11733 44.5 30.3 -0.004636 -0.02585 -0.02485 1916 30.3 265 0.11434 44.0 30.8 -0.018033 -0.34144 -0.28552 1917 30.8 379 0.08127 30.3 26.3 -0.013627 0.06916 0.05950 1918 26.3 302 0.08709 30.8 26.6 0.000290 -0.06206 -0.06225 1919 26.6 325 0.08185 26.3 32.4 -0.001683 0.02265 0.02220 1920 32.4 387 0.08372 26.6 36.6 -0.002718 -0.09139 -0.08832 1921 36.6 479 0.07641 32.4 30.5 -0.010610 -0.20094 -0.17372 1922 30.5 488 0.06250 36.6 28.0 -0.009865 -0.09774 -0.08379 1923 28.0 494 0.05668 30.5 26.2 -0.003554 -0.02300 -0.02163 1924 26.2 473 0.05539 28.0 22.6 -0.002716 -0.07776 -0.07395 1925 22.6 441 0.05125 26.2 24.7 -0.001859 0.00829 0.00800 1926 24.7 478 0.05167 22.6 22.9 -0.001210 -0.05666 -0.05531 1927 22.9 469 0.04883 24.7 25.4 -0.002187 -0.03178 -0.03040 1928 25.4 537 0.04730 22.9 24.6 -0.004478 -0.17087 -0.15458 1929 24.6 617 0.03987 25.4 21.4 -0.006280 -0.13773 -0.11770 1930 21.4 616 0.03474 24.6 21.6 0.000290 0.15215 0.15304 1931 21.6 534 0.04045 21.4 22.0 0.007349 0.20067 0.23910 1932 22.0 445 0.04944 21.6 22.5 0.005460 0.03833 0.04298 1933 22.5 438 0.05137 22.0 22.6 0.002775 0.06806 0.07178 1934 22.6 411 0.05499 22.5 22.8 0.005463 0.12477 0.13741 1935 22.8 366 0.06230 22.6 24.9 -0.000370 -0.13831 -0.13722 1936 24.9 459 0.05425 22.8 26.0 -0.000985 0.10617 0.10428 1937 26.0 431 0.06032 24.9 25.0 0.007311 0.13248 0.14917 1938 25.0 363 0.06887 26.0 27.4 0.000147 -0.12761 -0.12773 1939 27.4 452 0.06062 25.0 27.6 -0.003072 0.03418 0.03256 1940 27.6 440 0.06273 27.4 26.0 0.000207 -0.02738 -0.02747 1941 26.0 426 0.06103 27.6 24.3 0.000779 0.05192 0.05257 1942 24.3 378 0.06429 26.0 25.3 0.006044 0.12878 0.14101 1943 25.3 346 0.07312 24.3 26.5 0.010055 0.14339 0.16409 1944 26.5 314 0.08439 25.3 24.4 0.003703 -0.04690 -0.04910 1945 24.4 303 0.08053 26.5 29.7 0.000110 0.04951 0.04957 1946 29.7 351 0.08462 24.4 28.7 0.002700 0.01540 0.01590 1947 28.7 334 0.08593 29.7 28.4 0.003205 0.05763 0.05978 1948 28.4 312 0.09103 28.7 26.9 0.002019 -0.01170 -0.01197 1949 26.9 299 0.08997 28.4 27.0 0.002360 0.06225 0.06385 1950 27.0 282 0.09574 26.9 30.6 0.002680 -0.00437 -0.00450 1951 30.6 321 0.09533 27.0 30.8 0.013239 0.24853 0.28152 1952 30.8 252 0.12222 30.6 33.0 0.024389 0.16470 0.20117 1953 33.0 229 0.14410 30.8 36.7 0.005860 -0.07314 -0.07632 1954 36.7 274 0.13394 33.0 28.7 -0.010728 -0.08807 -0.08122 1955 28.7 234 0.12265 36.7 35.4 -0.001897 0.05933 0.05844 1956 35.4 272 0.13015 28.7 31.3 -0.009504 -0.22772 -0.20969 1 EXST7025 78 79 80 The Schaefer Model Geaghan Page 3 PROC REG; TITLE2 'Schaeffer model using Schaeffer''s version of change in CPUE'; MODEL SCHAE = CPUE CPUE2 CATCH / NOINT; RUN; Analysis of Catch and Effort data for Pacific Halibut Schaeffer model using Schaeffer's version of change in CPUE 2 Model: MODEL1 NOTE: No intercept in model. R-square is redefined. Dependent Variable: SCHAE Analysis of Variance Source DF Sum of Squares Mean Square Model Error U Total 0.00036 0.00190 0.00226 0.00012 0.00005 3 40 43 Root MSE Dep Mean C.V. 0.00689 -0.00021 -3281.87928 Parameter Estimates Parameter Variable DF Estimate CPUE 1 0.413310 CPUE2 1 -1.801222 CATCH 1 -0.000721 81 82 83 F Value Prob>F 2.500 0.0733 R-square Adj R-sq 0.1579 0.0947 Standard Error 0.15547588 0.74785726 0.00026744 T for H0: Parameter=0 2.658 -2.409 -2.695 Prob > |T| 0.0112 0.0207 0.0102 PROC REG; TITLE2 'Schaeffer model using Schnute''s version of change in CPUE'; MODEL SCHNU = CPUE EFFORT; RUN; Analysis of Catch and Effort data for Pacific Halibut Schaeffer model using Schnute's version of change in CPUE 3 Model: MODEL1 Dependent Variable: SCHNU Analysis of Variance Source DF Model 2 Error 41 C Total 43 Root MSE Dep Mean C.V. Sum of Squares 0.05797 0.54948 0.60745 0.11577 -0.00484 -2391.83386 Parameter Estimates Parameter Variable DF Estimate INTERCEP 1 0.331461 CPUE 1 -2.075164 EFFORT 1 -0.000443 Mean Square 0.02899 0.01340 F Value 2.163 R-square Adj R-sq 0.0954 0.0513 Standard Error 0.18985752 1.00985201 0.00030563 T for H0: Parameter=0 1.746 -2.055 -1.448 Prob>F 0.1279 Prob > |T| 0.0883 0.0463 0.1552 EXST7025 84 85 86 The Schaefer Model Geaghan Page 4 PROC REG; TITLE2 'Schaeffer model using Marchesseault''s version of change in CPUE'; MODEL MARCH = CPUE EFFORT; RUN; Analysis of Catch and Effort data for Pacific Halibut Schaeffer model using Marchesseault's version of change in CPUE 4 Model: MODEL1 Dependent Variable: MARCH Analysis of Variance Source DF Sum of Squares Mean Square Model Error C Total 0.06047 0.54278 0.60326 0.03024 0.01357 2 40 42 Root MSE Dep Mean C.V. 0.11649 0.00374 3115.13569 Parameter Estimates Parameter Variable DF Estimate INTERCEP 1 0.412076 CPUE 1 -2.487629 EFFORT 1 -0.000552 87 88 89 F Value Prob>F 2.228 0.1209 R-square Adj R-sq 0.1002 0.0553 Standard Error 0.22113203 1.19483292 0.00034969 T for H0: Parameter=0 1.863 -2.082 -1.580 Prob > |T| 0.0697 0.0438 0.1220 PROC REG; TITLE2 'Equilibrium version of the Schaeffer model'; MODEL CATCH = EFFORT EFFORT2 / NOINT; RUN; Analysis of Catch and Effort data for Pacific Halibut Equilibrium version of the Schaeffer model 5 Model: MODEL1 NOTE: No intercept in model. R-square is redefined. Dependent Variable: CATCH Analysis of Variance Source DF Model Error U Total Root MSE Dep Mean C.V. 2 42 44 Sum of Squares Mean Square 35960.15274 1922.60726 37882.76000 17980.07637 45.77636 6.76582 28.59091 23.66425 Parameter Estimates Parameter Variable DF Estimate EFFORT 1 0.160667 EFFORT2 1 -0.000212 F Value Prob>F 392.781 0.0001 R-square Adj R-sq 0.9492 0.9468 Standard Error 0.01178765 0.00002640 T for H0: Parameter=0 13.630 -8.037 Prob > |T| 0.0001 0.0001 EXST7025 The Schaefer Model Geaghan Page 5 1 **************************************************************; 2 *** Schaeffer Model (Lobster data) - EXST7025 Example ****; 3 **************************************************************; 4 OPTIONS NOCENTER PS=61 LS=78 NODATE; 5 FILENAME INPUT 'C:\SHORTREG\LOBSTER.DAT'; 6 7 DATA ONE; INFILE INPUT MISSOVER; 8 TITLE1 'Analysis of Catch and Effort data for Homarus americanus'; 9 INPUT YEARP1 CATCHP1 EFFORTP1 OBSID $; 10 YEAR = LAG1(YEARP1); YR = YEAR - 1927; 11 Y = YEAR - INT(YEAR/10)*10; 12 CATCH = LAG1(CATCHP1); CATCHM1 = LAG2(CATCHP1); 13 EFFORT = LAG1(EFFORTP1); EFFORTM1 = LAG2(EFFORTP1); 14 CPUEP1 = CATCHP1/EFFORTP1; CPUEM1 = CATCHM1/EFFORTM1; 15 CPUE = CATCH / EFFORT; 16 CPUE2 = CPUE*CPUE; EFFORT2 = EFFORT*EFFORT; 17 18 SCHAE = (CPUEP1 - CPUEM1) / 2; 19 SCHNU = LOG(CPUEP1 / CPUE); 20 MARCH = 2*(CPUEP1 - CPUE) /(CPUE + CPUEM1); 21 22 IF CATCH EQ . THEN DELETE; 23 DROP YEARP1; RUN; NOTE: The infile INPUT is: FILENAME=C:\SHORTREG\LOBSTER.DAT, RECFM=V,LRECL=132 NOTE: 49 records were read from the infile INPUT. The minimum record length was 21. The maximum record length was 21. NOTE: Missing values were generated as a result of performing an operation on missing values. Each place is given by: (Number of times) at (Line):(Column). 1 at 10:47 1 at 11:18 1 at 11:20 1 at 11:28 1 at 11:32 2 at 14:53 1 at 15:24 1 at 16:21 1 at 16:53 2 at 18:25 2 at 18:35 1 at 19:17 1 at 19:28 1 at 20:18 1 at 20:27 2 at 20:35 2 at 20:42 NOTE: The data set WORK.ONE has 48 observations and 18 variables. NOTE: The DATA statement used 8.17 seconds. 24 25 PROC PRINT; 26 VAR YEAR CATCH EFFORT CPUE CATCHM1 CATCHP1 SCHAE SCHNU MARCH; RUN; NOTE: The PROCEDURE PRINT printed page 1. NOTE: The PROCEDURE PRINT used 2.25 seconds. EXST7025 The Schaefer Model Geaghan Page 6 Analysis of Catch and Effort data for Homarus americanus OBS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 YEAR 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 CATCH EFFORT CPUE CATCHM1 CATCHP1 7100 211 33.6493 . 6600 6600 208 31.7308 7100 7800 7800 205 38.0488 6600 5400 5400 168 32.1429 7800 6100 6100 208 29.3269 5400 5900 5900 180 32.7778 6100 5400 5400 183 29.5082 5900 7700 7700 185 41.6216 5400 5100 5100 185 27.5676 7700 7300 7300 186 39.2473 5100 7700 7700 258 29.8450 7300 6600 6600 260 25.3846 7700 7600 7600 222 34.2342 6600 8900 8900 194 45.8763 7600 8400 8400 187 44.9198 8900 11500 11500 209 55.0239 8400 14100 14100 252 55.9524 11500 19100 19100 378 50.5291 14100 18800 18800 473 39.7463 19100 18300 18300 516 35.4651 18800 15900 15900 439 36.2187 18300 19300 19300 462 41.7749 15900 18400 18400 430 42.7907 19300 20800 20800 383 54.3081 18400 20000 20000 417 47.9616 20800 22300 22300 490 45.5102 20000 21700 21700 488 44.4672 22300 22700 22700 532 42.6692 21700 20600 20600 533 38.6492 22700 24400 24400 565 43.1858 20600 21300 21300 609 34.9754 24400 22300 22300 717 31.1018 21300 24000 24000 745 32.2148 22300 20900 20900 752 27.7926 24000 22100 22100 767 28.8136 20900 22800 22800 731 31.1902 22100 21400 21400 754 28.3820 22800 18900 18900 789 23.9544 21400 19900 19900 776 25.6443 18900 16500 16500 705 23.4043 19900 20500 20500 733 27.9673 16500 19800 19800 805 24.5963 20500 18200 18200 1166 15.6089 19800 17600 17600 1264 13.9241 18200 16300 16300 1448 11.2569 17600 18200 18200 1825 9.9726 16300 16500 16500 1810 9.1160 18200 17000 17000 1900 8.9474 16500 19000 SCHAE . 2.1997 0.2060 -4.3609 0.3175 0.0906 4.4219 -0.9703 -1.1872 1.1387 -6.9313 2.1946 10.2458 5.3428 4.5738 5.5163 -2.2474 -8.1030 -7.5320 -1.7638 3.1549 3.2860 6.2666 2.5855 -4.3989 -1.7472 -1.4205 -2.9090 0.2583 -1.8369 -6.0420 -1.3803 -1.6546 -1.7006 1.6988 -0.2158 -3.6179 -1.3688 -0.2751 1.1615 0.5960 -6.1792 -5.3361 -2.1760 -1.9757 -1.0704 -0.5126 0.8397 SCHNU -0.05871 0.18158 -0.16868 -0.09168 0.11124 -0.10508 0.34395 -0.41198 0.35324 -0.27387 -0.16187 0.29908 0.29272 -0.02107 0.20289 0.01673 -0.10195 -0.24003 -0.11397 0.02103 0.14272 0.02403 0.23835 -0.12427 -0.05246 -0.02318 -0.04128 -0.09895 0.11099 -0.21087 -0.11738 0.03516 -0.14766 0.03608 0.07926 -0.09435 -0.16960 0.06817 -0.09140 0.17812 -0.12844 -0.45475 -0.11422 -0.21264 -0.12114 -0.08981 -0.01867 0.18777 1 MARCH . 0.19327 -0.16927 -0.08024 0.11228 -0.10529 0.38896 -0.39517 0.33762 -0.28144 -0.12911 0.32047 0.39055 -0.02388 0.22257 0.01858 -0.09774 -0.20253 -0.09485 0.02004 0.15502 0.02605 0.27239 -0.13072 -0.04794 -0.02232 -0.03997 -0.09227 0.11158 -0.20066 -0.09912 0.03369 -0.13969 0.03403 0.08397 -0.09360 -0.14865 0.06458 -0.09033 0.18606 -0.13124 -0.34196 -0.08381 -0.18062 -0.10201 -0.08070 -0.01767 0.20462 EXST7025 27 28 29 The Schaefer Model Geaghan Page 7 PROC REG; TITLE2 'Schaeffer model using Schaeffer''s version of change in CPUE'; MODEL SCHAE = CPUE CPUE2 CATCH / NOINT; RUN; Analysis of Catch and Effort data for Homarus americanus Schaeffer model using Schaeffer's version of change in CPUE 2 Model: MODEL1 NOTE: No intercept in model. R-square is redefined. Dependent Variable: SCHAE Analysis of Variance Source DF Model Error U Total 3 44 47 Root MSE Dep Mean C.V. Sum of Squares Mean Square 91.33956 568.30857 659.64814 30.44652 12.91610 3.59390 -0.48550 -740.24297 Parameter Estimates Parameter Variable DF Estimate CPUE 1 0.088675 CPUE2 1 -0.000556 CATCH 1 -0.000178 30 31 32 F Value Prob>F 2.357 0.0846 R-square Adj R-sq 0.1385 0.0797 Standard Error 0.09232656 0.00176936 0.00007422 T for H0: Parameter=0 0.960 -0.314 -2.393 Prob > |T| 0.3421 0.7546 0.0210 PROC REG; TITLE2 'Schaeffer model using Schnute''s version of change in CPUE'; MODEL SCHNU = CPUE EFFORT; RUN; Analysis of Catch and Effort data for Homarus americanus Schaeffer model using Schnute's version of change in CPUE 3 Model: MODEL1 Dependent Variable: SCHNU Analysis of Variance Source DF Model 2 Error 45 C Total 47 Root MSE Dep Mean C.V. Sum of Squares 0.13960 1.37412 1.51372 0.17475 -0.02368 -737.79797 Parameter Estimates Parameter Variable DF Estimate INTERCEP 1 0.289744 CPUE 1 -0.006364 EFFORT 1 -0.000174 Mean Square 0.06980 0.03054 F Value 2.286 R-square Adj R-sq 0.0922 0.0519 Standard Error 0.15119121 0.00324288 0.00008600 T for H0: Parameter=0 1.916 -1.962 -2.029 Prob>F 0.1134 Prob > |T| 0.0617 0.0559 0.0484 EXST7025 33 34 35 The Schaefer Model Geaghan Page 8 PROC REG; TITLE2 'Schaeffer model using Marchesseault''s version of change in CPUE'; MODEL MARCH = CPUE EFFORT; RUN; Analysis of Catch and Effort data for Homarus americanus Schaeffer model using Marchesseault's version of change in CPUE 4 Model: MODEL1 Dependent Variable: MARCH Analysis of Variance Source DF Sum of Squares Mean Square Model Error C Total 0.17008 1.33579 1.50587 0.08504 0.03036 2 44 46 Root MSE Dep Mean C.V. 0.17424 -0.00950 -1834.22320 Parameter Estimates Parameter Variable DF Estimate INTERCEP 1 0.344371 CPUE 1 -0.007199 EFFORT 1 -0.000194 36 37 38 F Value Prob>F 2.801 0.0716 R-square Adj R-sq 0.1129 0.0726 Standard Error 0.15318030 0.00326201 0.00008717 T for H0: Parameter=0 2.248 -2.207 -2.222 Prob > |T| 0.0296 0.0326 0.0315 PROC REG; TITLE2 'Equilibrium version of the Schaeffer model'; MODEL CATCH = EFFORT EFFORT2 / NOINT; RUN; QUIT; Analysis of Catch and Effort data for Homarus americanus Equilibrium version of the Schaeffer model 5 Model: MODEL1 NOTE: No intercept in model. R-square is redefined. Dependent Variable: CATCH Analysis of Variance Source DF Model Error U Total Root MSE Dep Mean C.V. Sum of Squares Mean Square 2 12952522021 46 532427978.92 48 13484950000 6476261010.5 11574521.281 3402.13481 15535.41667 21.89922 Parameter Estimates Parameter Variable DF Estimate EFFORT 1 44.723794 F Value Prob>F 559.527 0.0001 R-square Adj R-sq 0.9605 0.9588 Standard Error 1.65676360 T for H0: Parameter=0 26.995 Prob > |T| 0.0001 EXST7025 EFFORT2 41 42 43 44 45 46 47 NOTE: NOTE: 48 49 50 51 NOTE: NOTE: 52 53 The Schaefer Model 1 -0.020077 DATA TWO; 0.00120713 Geaghan Page 9 -16.632 0.0001 DO EFFORT = 0 TO 2300 BY 20; E = EFFORT; E2 = EFFORT * EFFORT; SCHAEP=-(0.0886747/-0.000556446)*E -(-0.000177626/-0.000556446)*E2; SCHNUP=-(0.289744/-0.00636414) * E -(-0.000174475/-0.00636414) *E2; MARCHP=-(0.344371/-0.00719866) * E -(-0.000193685/-0.00719866) *E2; EQUILP = (44.72379431) * E - (0.02007692)*E2; OUTPUT; END; RUN; The data set WORK.TWO has 116 observations and 7 variables. The DATA statement used 1.15 seconds. DATA three; SET ONE TWO; IF SCHAEP LT 0 THEN SCHAEP=.; IF SCHNUP LT 0 THEN SCHNUP=.; IF MARCHP LT 0 THEN MARCHP=.; IF EQUILP LT 0 THEN EQUILP=.; RUN; The data set WORK.THREE has 164 observations and 24 variables. The DATA statement used 1.27 seconds. OPTIONS LS=99 PS=61; 60 GOPTIONS DEVICE=CGM GSFMODE=REPLACE GSFNAME=OUT VSIZE=8 HSIZE=10 NOTE: No units specified for the VSIZE option. INCHES will be used. 61 NOPROMPT NOROTATE; NOTE: No units specified for the HSIZE option. INCHES will be used. 62 63 FILENAME OUT 'C:\SHORTREG\LOBSTER.CGM'; NOTE: The PROCEDURE PLOT printed page 7. NOTE: The PROCEDURE PLOT used 3.95 seconds. 64 PROC GPLOT; 65 TITLE1 H=1.7 F=SWISSB 'Schaefer Model (Equilibrium)'; 66 TITLE2 H=1.4 F=SWISS 'Maine lobster (Homarus americanus)'; 67 PLOT CATCH*EFFORT=1 SCHAEP*EFFORT=2 SCHNUP*EFFORT=3 68 MARCHP*EFFORT=4 EQUILP*EFFORT=5 / 69 CAXIS=BLACK CTEXT=BLACK OVERLAY HAXIS=AXIS1 VAXIS=AXIS2; 70 AXIS1 LABEL=(F=SWISS H=1.6 'Effort (pots)') 71 VALUE=(F=SWISSL H=1.1) WIDTH=2 ORDER=0 TO 2500 BY 500; 72 AXIS2 LABEL=(F=SWISS H=1.6 'Catch') 73 VALUE=(F=SWISSL H=1.1) WIDTH=2 ORDER=0 TO 30000 BY 5000; 74 SYMBOL1 V=STAR I=JOIN C=RED L=1 W=2; 75 SYMBOL2 V=NONE I=JOIN C=BLUE L=1 W=2; 76 SYMBOL3 V=NONE I=JOIN C=MAGENTA L=1 W=2; 77 SYMBOL4 V=NONE I=JOIN C=YELLOW L=1 W=2; 78 SYMBOL5 V=NONE I=JOIN C=ORANGE L=1 W=2; 79 RUN; WARNING: The specified value of 10.00 inches for HSIZE= is larger than 8.50 inches which is the maximum for the device CGM. HSIZE is ignored. NOTE: You specified GOPTIONS HSIZE or VSIZE and did not specify a GOPTIONS HPOS or VPOS. The current HPOS=85 and VPOS=72 values differ from the values of HPOS=85 and VPOS=100 which would have been used by version 6.06 NOTE: NOTE: NOTE: NOTE: NOTE: 116 observation(s) contained a MISSING value for the CATCH * EFFORT request. 139 observation(s) contained a MISSING value for the SCHAEP * EFFORT request. 80 observation(s) contained a MISSING value for the SCHNUP * EFFORT request. 75 observation(s) contained a MISSING value for the MARCHP * EFFORT request. 52 observation(s) contained a MISSING value for the EQUILP * EFFORT request. NOTE: 113 RECORDS WRITTEN TO OUT. NOTE: The PROCEDURE GPLOT used 22.85 seconds. EXST7025 The Schaefer Model Geaghan Page 10 60 Schaefer Model (Equilibrium) Catch (millions of lbs) Halibut (Hippoglossus stenolepis) 50 40 30 20 Equilibrium Schnute 10 Schaeffer Marchesseault 0 0 100 200 300 400 500 600 700 Effort (1000 skates) Equilibrium Model Parameter Estimates Maximum Sustained Yield Model bo b1 Effort Catch Schaeffer 0.238019 -0.00043080 276.25 32.8766 Schnute 0.165196 -0.00022937 360.11 29.7442 -0.00021338 382.39 31.2002 Marchesseault 0.163186 0.185606 -0.00026287 353.04 32.7629 Equilibrium 800 EXST7025 The Schaefer Model Catch 30000 Geaghan Page 11 Schaefer Model (Equilibrium) Maine lobster (Homarus americanus) 25000 20000 15000 Equilibrium 10000 5000 Schaeffer Schnute 0 0 500 1000 1500 Effort (pots) Marchesseault 2000 2500 EXST7025 The Schaefer Model Geaghan Page 12 For the Cod the SAS program was; 1 2 3 4 5 6 7 8 9 10 11 12 13 NOTE: NOTE: 14 15 16 NOTE: 17 18 19 20 21 22 23 24 25 26 27 28 NOTE: NOTE: 29 30 31 32 33 NOTE: NOTE: OPTIONS LINESIZE=76 NODATE NONUMBER; GOPTIONS DEVICE=LQ1000 HSIZE=8 VSIZE=6; DATA ONE; N0 = 1000; M = 0.20; K = 0.14; WINF = 11.41; T0 = 0.070; TLAMBDA = 13; DO F = 0 TO 2 BY 0.1; DO R = 0 TO 13 BY 0.50; Z = F + M; YIELD = F* N0* EXP(-M*R) * WINF *((1/Z)-(3*EXP(-K*R)/(Z+K)) + (3*EXP(-2*K*R)/(Z+2*K)) - (EXP(-3*K*R)/(Z+3*K))); OUTPUT; END; END; run; The data set WORK.ONE has 567 observations and 10 variables. The DATA statement used 5.66 seconds. GOPTIONS DEVICE=CGM GSFMODE=REPLACE GSFNAME=OUT VSIZE=7.5 HSIZE=8 NOPROMPT NOROTATE VORIGIN=0.00 HORIGIN=0.00; No units specified for the HORIGIN option. INCHES will be used. GOPTIONS GSFNAME=OUT1; FILENAME OUT1 'C:\SAS\bhcont2.CGM'; PROC GCONTOUR; TITLE1 'Beverton - Holt Model fitted to Cod'; PLOT R*F=YIELD / JOIN VREF=4.2 LEVELS = 200 TO 700 BY 50 LLEVELS= 1 1 1 1 1 1 1 1 3 1 1 CLEVELS= red red red orange orange orange green cyan blue magenta brown HAXIS=AXIS1 VAXIS=AXIS2; AXIS1 LABEL=(F=SWISS H=1 'Fishing mortality') WIDTH=5 VALUE=(F=SWISS H=1) ORDER=0 to 2 by 0.4; AXIS2 LABEL=(F=SWISS H=1 A=90 R=-90 'Age at recruitment') WIDTH=5 VALUE=(F=SWISS H=1) ORDER=0 to 12 by 2; run; 35 RECORDS WRITTEN TO OUT1. The PROCEDURE GCONTOUR used 12.25 seconds. GOPTIONS GSFNAME=OUT2; FILENAME OUT2 'C:\SAS\bh3d2.CGM'; PROC G3D; PLOT R*F=YIELD / TILT=55 ROTATE=55; run; 27 RECORDS WRITTEN TO OUT2. The PROCEDURE G3D used 10.27 seconds. The major differences for the NORTH SEA HADDOCK were in the parameters which were; 4 DATA ONE; 5 N0 = 1.5; M = 0.20; K = 0.20; 6 WINF = 1209; T0 = -1.066; TLAMBDA = 10; 7 DO F = 0 TO 2 BY 0.1; 8 DO R = 0 TO 10 BY 0.50; 9 Z = F + M; 10 YIELD = F* N0* EXP(-M*R)* WINF* ((1/Z)-(3*EXP(-K*R)/(Z+K)) 11 + (3*EXP(-2*K*R)/(Z+2*K)) - (EXP(-3*K*R)/(Z+3*K))); 12 OUTPUT; END; END; Note that TILT and ROTATE for this species were 45 and 45 respectively. ...
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This note was uploaded on 12/29/2011 for the course EXST 7025 taught by Professor Geaghan,j during the Spring '08 term at LSU.

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