AIFFD Box 6.3 Vignette

I have provided a more thorough analysis of the Chapman-Robson method for estimating mortality here.

Required Packages and Setting Options

> library(FSA)      # chapman.robson

Preparing Data

The data for this box is very simple — number of fish in ten age-classes — and could have been entered directly into R as shown in the Box6.2 vignette. However, I have entered these data into an external tab-delimited text file which is read into R as follows:

> setwd("c://aaaWork//web//fishR//bookex//AIFFD//Box6_3")
> d <- read.table("box6_3.txt",header=TRUE)
> d
   age catch
1    1    90
2    2   164
3    3   162
4    4   110
5    5    55
6    6    41
7    7    20
8    8    14
9    9     7
10  10     5

Chapman-Robson’s Method

The maximum-likelihood method for estimating the rate of survival proposed by Chapman and Robson (1960) and Robson and Chapman (1961) is implemented with chapman.robson() from the FSA package. This function requires the vector of ages as the first argument, the vector of catches as the second argument, and a third argument that indicates which ages represent fully recruited fish. The ages of fully recruited fish can be identified with a full range (i.e., 3:10) or a concatenated list of ages (i.e., c(3,4,5,6,7,8,9,10)). The results of this constructor function should be saved to an object so that specific information can be extracted from it. Thus, the Chapman-Robson method for these data, assuming that all fish age-3 and older are fully recruited, is computed with,

> cr1 <- chapman.robson(d$age, d$catch, 3:10)

The best estimates (with SEs) of the rate of survival (S) and instantaneous mortality rate (Z) are extracted with,

> summary(cr1)
Intermediate Statistics
n=414; T=570

Estimates with Standard Errors
    Estimate  Std. Err.
S 57.9857579 1.57508209
Z  0.5449728 0.02716326

Note here that the SE results are somewhat different from what is presented in Box 6.3 because the R function maintains more decimal places throughout the calculation. The 95% confidence intervals for the two parameters are extracted with,

> confint(cr1)
     95% LCI    95% UCI
S 54.8986537 61.0728620
Z  0.4917338  0.5982118

Again, the difference (from the book results) in the endpoints is due to the difference in SE. Finally, a plot depicting the calcualtions is obtained with,

> plot(cr1)