Computes the proportions-at-age (with standard errors) in a larger sample based on an age-length-key created from a subsample of ages through a two-stage random sampling design. Follows the methods in Quinn and Deriso (1999).
Arguments
- key
A numeric matrix that contains the age-length key. See details.
- lenA.n
A numeric vector of sample sizes for each length interval in the aged sample.
- len.n
A numeric vector of sample sizes for each length interval in the complete sample (i.e., all fish regardless of whether they were aged or not).
Value
A data.frame with as many rows as ages (columns) present in key and the following three variables:
age The ages.
prop The proportion of fish at each age.
se The SE for the proportion of fish at each age.
Details
The age-length key in 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.
The values in lenA.n are equal to what the row sums of key would have been before key was converted to a row proportions table. Thus, the length of lenA.n must also be equal to the number of rows in key. If this constraint is not met, then the function will stop with an error message.
Testing
The results from this function perfectly match the results in Table 8.4 (left) of Quinn and Deriso (1999) using SnapperHG2 from FSAdata. The results also perfectly match the results from using alkprop in fishmethods.
References
Ogle, D.H. 2016. Introductory Fisheries Analyses with R. Chapman & Hall/CRC, Boca Raton, FL.
Lai, H.-L. 1987. Optimum allocation for estimating age composition using age-length key. Fishery Bulletin, 85:179-185.
Lai, H.-L. 1993. Optimum sampling design for using the age-length key to estimate age composition of a fish population. Fishery Bulletin, 92:382-388.
Quinn, T. J. and R. B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York, New York. 542 pages.
See also
See alkIndivAge and related functions for a completely different methodology. See alkprop from fishmethods for the exact same methodology but with a different format for the inputs.
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 and get number in each length interval
WR1.age <- subset(WR1, !is.na(age))
lenA.n <- xtabs(~LCat,data=WR1.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 age distribution of all fish
alkAgeDist(WR1.key,lenA.n,len.n)
#> age prop se
#> 1 4 0.416378219 0.013206893
#> 2 5 0.167201351 0.013907259
#> 3 6 0.113882857 0.014938965
#> 4 7 0.189170701 0.021247383
#> 5 8 0.061572157 0.016537338
#> 6 9 0.032955436 0.011718417
#> 7 10 0.016306565 0.008988814
#> 8 11 0.002532714 0.002574054