Data preparation

Data <- read.csv("Covernet.csv", header=T)
Length <- Data$Length
Codend <- Data[,seq(2,12,2)]
Cover <- Data[,seq(3,13,2)]
Encounter <- Codend + Cover

NN <- Codend + Cover
Selectivity <- Codend/Encounter
Duration <- c(20,20,20,60,60,60)
Repeat <- c(1,2,3,4,5,6)
Text <- c("20min(1)","20min(2)","20min(3)","60min(1)","60min(2)","60min(3)")

par(mfcol=c(3,2))
Ntrial <- 6
for(i in 1:Ntrial)
{
 par(mar=c(4,4,4,5))
 plot(Length, Selectivity[,i], ylim=c(0,1), ylab="Selectivity", main=Text[i])
 par(new=T)
 plot(Length, NN[,i], type="h", axes=F, ylab="", ylim=c(1,max(NN)))
 axis(4); mtext("#Encounters", side=4, line=2, cex=0.7)
}

GLM analysis by haul

Res.glm0 <- NULL
Para0 <- array(NA, c(Ntrial, 2))
colnames(Para0) <- c("a","b")

Retention <- function(x,para){ 1/(1+exp(-para[1]-para[2]*x)) }

par(mfcol=c(3,2))

for(i in 1:Ntrial){
 Res.glm0[[i]] <- glm(cbind(Codend[,i],Cover[,i])~Length, family=binomial)
 Para0[i,] <- Res.glm0[[i]]$coefficients
 plot(Length, Selectivity[,i], ylim=c(0,1), ylab="Selectivity", main=Text[i])
 curve(Retention(x,Para0[i,]), add=TRUE)
}

Para0
##               a         b
## [1,] -26.361227 0.7347294
## [2,] -14.946438 0.4126321
## [3,]  -9.819376 0.2785152
## [4,]  -7.204277 0.1938873
## [5,] -11.980199 0.3407501
## [6,] -10.661597 0.2901800
sum(as.numeric(lapply(Res.glm0, AIC)))
## [1] 385.9945

Combined GLM analysis over hauls

Codend.vec <- as.vector(as.matrix(Codend))
Cover.vec <- as.vector(as.matrix(Cover))
Length.vec <- rep(Length, Ntrial)
Repeat.vec <- factor(rep(Repeat, each=length(Length)))

CC <- cbind(Codend.vec,Cover.vec)
Res.glm1 <- glm(CC ~ -1+Repeat.vec+Length.vec*Repeat.vec, family=binomial)
Res.glm1
## 
## Call:  glm(formula = CC ~ -1 + Repeat.vec + Length.vec * Repeat.vec, 
##     family = binomial)
## 
## Coefficients:
##            Repeat.vec1             Repeat.vec2             Repeat.vec3  
##               -26.3612                -14.9464                 -9.8194  
##            Repeat.vec4             Repeat.vec5             Repeat.vec6  
##                -7.2043                -11.9802                -10.6616  
##             Length.vec  Repeat.vec2:Length.vec  Repeat.vec3:Length.vec  
##                 0.7347                 -0.3221                 -0.4562  
## Repeat.vec4:Length.vec  Repeat.vec5:Length.vec  Repeat.vec6:Length.vec  
##                -0.5408                 -0.3940                 -0.4445  
## 
## Degrees of Freedom: 173 Total (i.e. Null);  161 Residual
## Null Deviance:       1776 
## Residual Deviance: 149   AIC: 386
Duration.vec <- factor(rep(Duration, each=length(Length)))

Res.glm2 <- glm(CC ~ -1+Duration.vec+Length.vec*Duration.vec, family=binomial)
Res.glm2
## 
## Call:  glm(formula = CC ~ -1 + Duration.vec + Length.vec * Duration.vec, 
##     family = binomial)
## 
## Coefficients:
##            Duration.vec20             Duration.vec60  
##                 -10.86003                   -8.95278  
##                Length.vec  Duration.vec60:Length.vec  
##                   0.30982                   -0.06467  
## 
## Degrees of Freedom: 173 Total (i.e. Null);  169 Residual
## Null Deviance:       1776 
## Residual Deviance: 189.8     AIC: 410.8
Res.glm3 <- glm(CC ~ -1+Duration.vec+Length.vec, family=binomial)
Res.glm3
## 
## Call:  glm(formula = CC ~ -1 + Duration.vec + Length.vec, family = binomial)
## 
## Coefficients:
## Duration.vec20  Duration.vec60      Length.vec  
##        -9.0478         -9.4523          0.2596  
## 
## Degrees of Freedom: 173 Total (i.e. Null);  170 Residual
## Null Deviance:       1776 
## Residual Deviance: 196.3     AIC: 415.3
Res.glm4 <- glm(CC ~ Length.vec*Duration.vec, family=binomial)
Res.glm4
## 
## Call:  glm(formula = CC ~ Length.vec * Duration.vec, family = binomial)
## 
## Coefficients:
##               (Intercept)                 Length.vec  
##                 -10.86003                    0.30982  
##            Duration.vec60  Length.vec:Duration.vec60  
##                   1.90725                   -0.06467  
## 
## Degrees of Freedom: 172 Total (i.e. Null);  169 Residual
## Null Deviance:       1513 
## Residual Deviance: 189.8     AIC: 410.8
Res.glm5 <- glm(CC ~ Length.vec, family=binomial)
Res.glm5
## 
## Call:  glm(formula = CC ~ Length.vec, family = binomial)
## 
## Coefficients:
## (Intercept)   Length.vec  
##     -9.4615       0.2632  
## 
## Degrees of Freedom: 172 Total (i.e. Null);  171 Residual
## Null Deviance:       1513 
## Residual Deviance: 204.7     AIC: 421.7
Res.glm6 <- glm(CC ~ -1+Repeat.vec+Length.vec*Duration.vec, family=binomial)
Res.glm6
## 
## Call:  glm(formula = CC ~ -1 + Repeat.vec + Length.vec * Duration.vec, 
##     family = binomial)
## 
## Coefficients:
##               Repeat.vec1                Repeat.vec2  
##                 -10.23583                  -10.87205  
##               Repeat.vec3                Repeat.vec4  
##                 -10.73100                   -8.99041  
##               Repeat.vec5                Repeat.vec6  
##                  -8.75276                   -9.09720  
##                Length.vec             Duration.vec60  
##                   0.30420                         NA  
## Length.vec:Duration.vec60  
##                  -0.05818  
## 
## Degrees of Freedom: 173 Total (i.e. Null);  165 Residual
## Null Deviance:       1776 
## Residual Deviance: 184.3     AIC: 413.3
Res.glm7 <- glm(CC ~ -1+Duration.vec+Length.vec:Repeat.vec, family=binomial)
Res.glm7
## 
## Call:  glm(formula = CC ~ -1 + Duration.vec + Length.vec:Repeat.vec, 
##     family = binomial)
## 
## Coefficients:
##         Duration.vec20          Duration.vec60  Length.vec:Repeat.vec1  
##               -10.6943                 -8.9828                  0.3176  
## Length.vec:Repeat.vec2  Length.vec:Repeat.vec3  Length.vec:Repeat.vec4  
##                 0.3005                  0.3025                  0.2439  
## Length.vec:Repeat.vec5  Length.vec:Repeat.vec6  
##                 0.2555                  0.2441  
## 
## Degrees of Freedom: 173 Total (i.e. Null);  165 Residual
## Null Deviance:       1776 
## Residual Deviance: 182.1     AIC: 411.1
lapply(list(Res.glm1,Res.glm2,Res.glm3,Res.glm4,Res.glm5,Res.glm6,Res.glm7), AIC)
## [[1]]
## [1] 385.9945
## 
## [[2]]
## [1] 410.8121
## 
## [[3]]
## [1] 415.3129
## 
## [[4]]
## [1] 410.8121
## 
## [[5]]
## [1] 421.7207
## 
## [[6]]
## [1] 413.3131
## 
## [[7]]
## [1] 411.0692