Mean Values-at-age from an age-length key

Computes the mean value-at-age in a larger sample based on an age-length-key created from a subsample of ages through a two-stage random sampling design. The mean values could be mean length-, weight-, or fecundity-at-age, for example. The methods of Bettoli and Miranda (2001) or Quinn and Deriso (1999) are used. A standard deviation is computed for the Bettoli and Miranda (2001) method and standard error for the Quinn and Deriso (1999) method. See the testing section notes.

Usage

alkMeanVar(
  key,
  formula,
  data,
  len.n,
  method = c("BettoliMiranda", "QuinnDeriso")
)

Arguments

key: A numeric matrix that contains the age-length key. See details.
formula: A formula of the form var~lencat+age where var generically represents the variable to be summarized (e.g., length, weight, fecundity), lencat generically represents the variable that contains the length intervals, and age generically represents the variable that contains the assigned ages.
data: A data.frame that minimally contains the length intervals, assessed ages, and the variable to be summarized (i.e., this should be the aged sample) as given in formula.
len.n: A vector of sample sizes for each length interval in the complete sample (i.e., all fish regardless of whether they were aged or not).
method: A string that indicates which method of calculation should be used. See details.

Value

A data.frame with as many rows as ages (columns) present in key and the following three variables:

age The ages.
mean The mean value at each age.
sd,se The SD if method="BettoliMiranda" or SE of the mean if method="QuinnDeriso" for the value at each age.

Details

The age-length key key must have length intervals as rows and ages as columns. The row names of key (i.e., rownames(key)) must contain the minimum values of each length interval (e.g., if an interval is 100-109, then the corresponding row name must be 100). The column names of key (i.e., colnames(key)) must contain the age values (e.g., the columns can NOT be named with “age.1”, for example).

The length intervals in the rows of key must contain all of the length intervals present in the larger sample. Thus, the length of len.n must, at least, equal the number of rows in key. If this constraint is not met, then the function will stop with an error message.

Note that the function will stop with an error if the formula in formula does not meet the specific criteria outlined in the parameter list above.

Testing

The results of these functions have not yet been rigorously tested. The Bettoli and Miranda (2001) results appear, at least, approximately correct when compared to the results from alkIndivAge. The Quinn and Deriso (1999) results appear at least approximately correct for the mean values, but do not appear to be correct for the SE values. Thus, a note is returned with the Quinn and Deriso (1999) results that the SE should not be trusted.

IFAR Chapter

5-Age-Length Key.

References

Ogle, D.H. 2016. Introductory Fisheries Analyses with R. Chapman & Hall/CRC, Boca Raton, FL.

Bettoli, P. W. and Miranda, L. E. 2001. A cautionary note about estimating mean length at age with subsampled data. North American Journal of Fisheries Management, 21:425-428.

Quinn, T. J. and R. B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York, New York. 542 pages

Author

Derek H. Ogle, DerekOgle51@gmail.com

Examples

## Example -- Even breaks for length categories
WR1 <- WR79
# add length intervals (width=5)
WR1$LCat <- lencat(WR1$len,w=5)
# get number of fish in each length interval in the entire sample
len.n <- xtabs(~LCat,data=WR1)
# isolate aged sample
WR1.age <- subset(WR1, !is.na(age))
# create age-length key
raw <- xtabs(~LCat+age,data=WR1.age)
( WR1.key <- prop.table(raw, margin=1) )
#>      age
#> LCat           4          5          6          7          8          9
#>   35  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   40  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   45  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   50  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   55  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   60  0.60000000 0.40000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   65  0.00000000 1.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   70  0.00000000 1.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>   75  0.00000000 0.88888889 0.11111111 0.00000000 0.00000000 0.00000000
#>   80  0.00000000 0.25000000 0.75000000 0.00000000 0.00000000 0.00000000
#>   85  0.00000000 0.00000000 0.90909091 0.09090909 0.00000000 0.00000000
#>   90  0.00000000 0.00000000 0.26315789 0.63157895 0.10526316 0.00000000
#>   95  0.00000000 0.00000000 0.05882353 0.70588235 0.17647059 0.00000000
#>   100 0.00000000 0.00000000 0.00000000 0.55555556 0.16666667 0.27777778
#>   105 0.00000000 0.00000000 0.00000000 0.28571429 0.42857143 0.14285714
#>   110 0.00000000 0.00000000 0.00000000 0.20000000 0.20000000 0.20000000
#>   115 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>      age
#> LCat          10         11
#>   35  0.00000000 0.00000000
#>   40  0.00000000 0.00000000
#>   45  0.00000000 0.00000000
#>   50  0.00000000 0.00000000
#>   55  0.00000000 0.00000000
#>   60  0.00000000 0.00000000
#>   65  0.00000000 0.00000000
#>   70  0.00000000 0.00000000
#>   75  0.00000000 0.00000000
#>   80  0.00000000 0.00000000
#>   85  0.00000000 0.00000000
#>   90  0.00000000 0.00000000
#>   95  0.05882353 0.00000000
#>   100 0.00000000 0.00000000
#>   105 0.14285714 0.00000000
#>   110 0.20000000 0.20000000
#>   115 1.00000000 0.00000000

## use age-length key to estimate mean length-at-age of all fish
# Bettoli-Miranda method
alkMeanVar(WR1.key,len~LCat+age,WR1.age,len.n)
#>   age      mean       sd
#> 1   4  51.95492 5.050430
#> 2   5  72.01342 5.519135
#> 3   6  86.59311 4.714664
#> 4   7  97.45567 5.247117
#> 5   8 101.38084 5.576238
#> 6   9 103.65599 2.312767
#> 7  10 104.86056 7.497515
#> 8  11 113.00000 0.000000

# Quinn-Deriso method
alkMeanVar(WR1.key,len~LCat+age,WR1.age,len.n,method="QuinnDeriso")
#> The 'se' values should not be trusted!
#>   age      mean        se
#> 1   4  51.95492 0.3031374
#> 2   5  72.01342 0.5018225
#> 3   6  86.59311 0.5977608
#> 4   7  97.45567 0.4823013
#> 5   8 101.38084 1.4384950
#> 6   9 103.65599 0.9653842
#> 7  10 104.86056 0.6696853
#> 8  11 113.00000 0.0000000