// library(ascii)
// setwd("c://aaaWork//web//fishR//bookex//AIFFD//Box6_3")
// Sweave("Box6_3a.Rnw",driver=RweaveAsciidoc)









AIFFD Box 6.3  Vignette
=======================
:Author:    Derek H. Ogle
:Email:     dogle@northland.edu
:Date:      10-June-2010
:Revision:  2

.Author Comment
****
I have provided a more thorough analysis of the Chapman-Robson method for estimating mortality link:../../../gnrlex/CatchCurve/CatchCurve.pdf[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 link:../Box6_2/box6_2a.html[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 +*[red]#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., +*[red]#3:10#*+) or a concatenated list of ages (i.e., +*[red]#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)
----
image::Box6_3a-007.png[]