Reading the data
Data <- read.csv("DeLury_R.csv", header=T)
Data
## Period Catch Effort CPUE CumCatch CumEffort
## 1 1 60 170.6 0.352 0 0.0
## 2 2 274 453.8 0.604 60 170.6
## 3 3 240 513.4 0.467 334 624.4
## 4 4 244 714.4 0.342 574 1137.8
## 5 5 301 679.1 0.443 818 1852.2
## 6 6 151 419.9 0.360 1119 2531.3
## 7 7 127 470.3 0.270 1270 2951.2
## 8 8 90 318.4 0.283 1397 3421.5
## 9 9 31 136.8 0.227 1487 3739.9
## 10 10 7 177.6 0.039 1518 3876.7
CPUE <- Data$CPUE
CumCatch <- Data$CumCatch
CumEffort <- Data$CumEffort
plot(CumCatch, CPUE, pch=19, col="red",
main="CPUE against cumulative catch")

Analyzing data by De Lury method 1
Res.DeLury1 <- lm(CPUE~CumCatch)
summary(Res.DeLury1)
##
## Call:
## lm(formula = CPUE ~ CumCatch)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.16798 -0.03658 0.01883 0.06804 0.10617
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.098e-01 6.013e-02 8.478 2.87e-05 ***
## CumCatch -1.995e-04 5.883e-05 -3.391 0.00949 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1034 on 8 degrees of freedom
## Multiple R-squared: 0.5897, Adjusted R-squared: 0.5384
## F-statistic: 11.5 on 1 and 8 DF, p-value: 0.00949
plot(CumCatch, CPUE, pch=19, col="red",
main="CPUE against cumulative catch")
abline(Res.DeLury1, col="purple", lwd=2, lty=2)

Para1 <- coef(Res.DeLury1)
Para1
## (Intercept) CumCatch
## 0.509796545 -0.000199483
q.est1 <- (-1)*Para1[2]
N.est1 <- Para1[1]/q.est1
data.frame(q.est1, N.est1)
## q.est1 N.est1
## CumCatch 0.000199483 2555.589
Analyzing data by De Lury method 2
Ignoring M (M=0)
Res.DeLury2 <- lm(log(CPUE)~CumEffort)
summary(Res.DeLury2)
##
## Call:
## lm(formula = log(CPUE) ~ CumEffort)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.36018 -0.09308 0.18410 0.37092 0.46580
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5562541 0.3303927 -1.684 0.1308
## CumEffort -0.0003425 0.0001338 -2.560 0.0336 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5946 on 8 degrees of freedom
## Multiple R-squared: 0.4503, Adjusted R-squared: 0.3816
## F-statistic: 6.553 on 1 and 8 DF, p-value: 0.03365
plot(CumEffort, log(CPUE), pch=19, col="red",
main="log CPUE against cumulative effort")
abline(Res.DeLury2, col="blue", lwd=2, lty=3)

Para2 <- coef(Res.DeLury2)
Para2
## (Intercept) CumEffort
## -0.5562540837 -0.0003424973
q.est2 <- (-1)*Para2[2]
N.est2 <- exp(Para2[1])/q.est2
data.frame(q.est2, N.est2)
## q.est2 N.est2
## CumEffort 0.0003424973 1674.036
Try to estimate unknown M
Period1 <- Data$Period-1
Res.DeLury3 <- lm(log(CPUE) ~ CumEffort + Period1)
summary(Res.DeLury3)
##
## Call:
## lm(formula = log(CPUE) ~ CumEffort + Period1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.82722 -0.05662 0.16564 0.29739 0.38859
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2169073 0.3107284 -0.698 0.5077
## CumEffort 0.0014243 0.0008032 1.773 0.1195
## Period1 -0.8726329 0.3929920 -2.220 0.0618 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4869 on 7 degrees of freedom
## Multiple R-squared: 0.6775, Adjusted R-squared: 0.5853
## F-statistic: 7.352 on 2 and 7 DF, p-value: 0.01905
Para3 <- coef(Res.DeLury3)
Para3
## (Intercept) CumEffort Period1
## -0.216907302 0.001424257 -0.872632934
q.est3 <- (-1)*Para3[2]
N.est3 <- exp(Para3[1])/q.est3
M.est3 <- (-1)*Para3[3]
data.frame(q.est3, N.est3, M.est3)
## q.est3 N.est3 M.est3
## CumEffort -0.001424257 -565.21 0.8726329
With M (known, fixed at 0.1)
Res.DeLury4 <-
lm(log(CPUE)~CumEffort+offset(-Period1*0.1))
summary(Res.DeLury4)
##
## Call:
## lm(formula = log(CPUE) ~ CumEffort + offset(-Period1 * 0.1))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.28395 -0.06134 0.17919 0.35625 0.43419
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5173664 0.3152973 -1.641 0.139
## CumEffort -0.0001400 0.0001277 -1.097 0.305
##
## Residual standard error: 0.5674 on 8 degrees of freedom
## Multiple R-squared: 0.4752, Adjusted R-squared: 0.4096
## F-statistic: 7.244 on 1 and 8 DF, p-value: 0.02744
Para4 <- coef(Res.DeLury4)
Para4
## (Intercept) CumEffort
## -0.5173663947 -0.0001400347
q.est4 <- (-1)*Para4[2]
N.est4 <- exp(Para4[1])/q.est4
data.frame(q.est4, N.est4)
## q.est4 N.est4
## CumEffort 0.0001400347 4256.718
With M (known, fixed at 0.01)
Res.DeLury5 <-
lm(log(CPUE)~CumEffort+offset(-Period1*0.01))
summary(Res.DeLury5)
##
## Call:
## lm(formula = log(CPUE) ~ CumEffort + offset(-Period1 * 0.01))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3526 -0.0899 0.1836 0.3700 0.4626
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5523653 0.3288333 -1.68 0.1315
## CumEffort -0.0003223 0.0001332 -2.42 0.0418 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5918 on 8 degrees of freedom
## Multiple R-squared: 0.4527, Adjusted R-squared: 0.3842
## F-statistic: 6.616 on 1 and 8 DF, p-value: 0.03302
Para5 <- coef(Res.DeLury5)
Para5
## (Intercept) CumEffort
## -0.552365315 -0.000322251
q.est5 <- (-1)*Para5[2]
N.est5 <- exp(Para5[1])/q.est5
data.frame(q.est5, N.est5)
## q.est5 N.est5
## CumEffort 0.000322251 1786.144
Method <- 1:5
M <- c("NA", 0, round(M.est3,4), 0.1, 0.01)
N.est <- c(N.est1,N.est2,N.est3,N.est4,N.est5)
data.frame(Method, M, N.est)
## Method M N.est
## 1 1 NA 2555.589
## 2 2 0 1674.036
## 3 3 0.8726 -565.210
## 4 4 0.1 4256.718
## 5 5 0.01 1786.144