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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!
“erm t
N! = (Nmax  N)
N 1 ’ Nmax  N!
“erm 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!
“ erm 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! ert 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 + Ut1
2  the beginning of the year U# = Ut+1 + Ut
2  the end of the year (or season) ˜U= Ut+1 + Ut  Ut  Ut1
2 = Ut+1 Ut1
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 + Ut1
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 NONSIGNIFICANT 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 s1 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", “t1" 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 tn, 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 Ct1
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):111.
Pamela M Mace. A new role for MSY in
singlespecies and ecosystem approaches
to fisheries stock assessment and management.
Fish and Fisheries. 2001, 2, 232. 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! ert 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 + Ut1 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
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26 The Schaefer Model Geaghan Page 1 ***************************************************************;
*** Schaeffer Model (Halibut data)
***;
*** The data is from Ricker (1975) pg 320321
***;
*** 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. Rsquare 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 Rsquare
Adj Rsq 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 Rsquare
Adj Rsq 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 Rsquare
Adj Rsq 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. Rsquare 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 Rsquare
Adj Rsq 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. Rsquare 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 Rsquare
Adj Rsq 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 Rsquare
Adj Rsq 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 Rsquare
Adj Rsq 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. Rsquare 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 Rsquare
Adj Rsq 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;
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AXIS2 LABEL=(F=SWISS H=1.6 'Catch')
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VALUE=(F=SWISSL H=1.1) WIDTH=2 ORDER=0 TO 30000 BY 5000;
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SYMBOL1 V=STAR I=JOIN C=RED
L=1 W=2;
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SYMBOL2 V=NONE I=JOIN C=BLUE
L=1 W=2;
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SYMBOL3 V=NONE I=JOIN C=MAGENTA L=1 W=2;
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SYMBOL4 V=NONE I=JOIN C=YELLOW L=1 W=2;
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SYMBOL5 V=NONE I=JOIN C=ORANGE L=1 W=2;
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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;
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NOTE:
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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.
 Spring '08
 Geaghan,J

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