Working with Multiple Age-Length Keys

Introduction

An age-length key (ALK) describes the relationship between length (category) and age of fish. An estimated age may be assigned to unaged fish in a sample based on the ALK derived from aged fish from the same (or very closely related) sample as described by Isermann and Knight (2005) and implemented in FSA (Ogle 2016). It is critical to this process that the ALK is representative of the fish to which ages will be assigned. Thus, for example, it is not recommended to use an ALK developed from fish collected in one year to assign age to fish collected in another year.¹

¹ The same argument can be made for fish from different areas.

This recommendation can lead to cumbersome data wrangling during analysis. For example, suppose that samples of fish were collected from two different areas over a five year period. In this case separate age-length keys would be required to be developed and applied for the ten combinations of locations and years. For each location-year the specific data would need to be isolated and for that data the ALK developed and applied, which has several steps as was shown in Ogle (2016) and will be outlined below. The final data produced for each location-year would then need to be combined back together to make an overall data set. In other words, using the Isermann and Knight (2005) method to assign estimated ages to unaged fish for multiple groups of fish is quite a bit of work. The goal of this post is to provide a more efficient method to accomplish this task.

The following packages are loaded for use below.

library(tidyverse)  # for dplyr, tidyr, purr packages
library(FSA)        # for ALK functionality

The random number seed was set to ensure repeatability for the random components of alkIndivAge() below.

set.seed(14354454)

 

Age-Length Keys in FSA

Original Example from Ogle (2016)

Ogle (2016) demonstrated the Isermann and Knight (2005) method for assigning ages to unaged Creek Chubs (Semotilus atromaculatus). The portion of the script used there to produce a final data frame with ages for all sampled fish is shown below.²

² This code was extracted from the script provided here. It is slightly modified here to maintain the original unaltered data frame in cc.

## Load data
cc <- read.csv("https://derekogle.com/IFAR/scripts/CreekChub.csv")
## Add length category variable
cc1 <- cc |> mutate(lcat10=lencat(len,w=10))
## Separate aged and unaged fish
cc1.unaged <- filter(cc1,is.na(age))
cc1.aged <- filter(cc1,!is.na(age))
## Develop ALK from aged fish
alk.freq <- xtabs(~lcat10+age,data=cc1.aged)
alk <- prop.table(alk.freq,margin=1)
## Use I-K method to assign ages to unaged fish
cc1.unaged.mod <- alkIndivAge(alk,age~len,data=cc1.unaged)
## Create overall data frame with ages for all fish
cc1.fnl <- rbind(cc1.aged,cc1.unaged.mod)

The lengths-at-age in this final data frame may be summarized as follows.

cc1.fnl |>
  group_by(age) |>
  summarize(n=n(),
            mn=mean(len,na.rm=TRUE),
            sd=sd(len,na.rm=TRUE)) |>
  as.data.frame()

#R|    age   n        mn       sd
#R|  1   0  20  48.65000  5.62209
#R|  2   1 142  74.64789 16.82163
#R|  3   2  43 113.41860 15.77405
#R|  4   3   8 151.87500 11.17954
#R|  5   4   5 183.20000 17.25399

Simplifying Function

I have resisted writing a function that would combine all the steps above, as I did not want to create a “black-box” function for this analysis that could be implemented without much thought. However, such a function would be useful for efficiently applying ALKs to multiple groups of fish. Thus, I create such a function and demonstrate how it can be used to produce the same results as those shown for Creek Chub in Ogle (2016).³ In the next section, I demonstrate how this new function can then be used to efficiently apply ALKs for multiple groups of fish.

³ he same at least within rounding because of the inherent randomization in the Isermann and Knight (2005) method.

⁴ This allows the variable names to be supplied by user in the function call, rather than hard-coded in the function.

The applyALK() function created below performs the code shown above to create a “final” data frame that has ages assigned to the unaged fish based on the ALK. The function largely repeats the code above but uses some “advanced” code (e.g., deparse(substitute()) and {{}}) to handle the use of unquoted variables names.⁴

## Computes and applies an ALK
##   data: The data frame with, at least, the age & length variables
##   avar: The name (without quotes) of the age variable in data
##   lvar: The name (without quotes) of the length variable in data
##   w: The width of length categories/bins for use in the ALK
## Returns the data data frame with ages in avar assigned from the ALK for
##   unaged fish and a new length category (lcat) variable derived from w

applyALK <- function(data,avar,lvar,w) {
  ## Get avar variable name as character for non-tidyverse functions below
  avarn <- deparse(substitute(avar))
  ## Add length category variable
  data <- data |> dplyr::mutate(lcat=FSA::lencat({{lvar}},w=w))
  ## Separate into aged and unaged dataframes
  aged <- data |> dplyr::filter(!is.na({{avar}}))
  unaged <- data |> dplyr::filter(is.na({{avar}}))
  ## Make ALK (find frequencies, convert to row proportions)
  ALK <- prop.table(xtabs(as.formula(paste0("~lcat+",avarn)),data=aged),margin=1)
  ## Apply ALK according to Isermann-Knight method
  tmp <- FSA::alkIndivAge(ALK,as.formula(paste0(avarn,"~lcat")),data=unaged)
  ## Put aged and newly assigned age data frames together to return
  dplyr::bind_rows(aged,tmp)
}

With this new function the final data frame can be created by supplying the original data frame (with aged and unaged fish) as the first argument, the names of the age and length variables in avar= and lvar= respectively, and the width for the length categories/bins in w=. For example, the final data frame for the Creek Chub case study can be created as follows.⁵

⁵ Note the use the original cc data frame without the length categorization variable.

cc.fnl <- applyALK(cc,avar=age,lvar=len,w=10)

The lengths-at-age summary for this final data frame is similar to that from above.⁶

⁶ Again, not exact because of the inherent randomization in the Isermann and Knight (2005) method.

cc.fnl |>
  group_by(age) |>
  summarize(n=n(),
            mn=mean(len,na.rm=TRUE),
            sd=sd(len,na.rm=TRUE)) |>
  as.data.frame()

#R|    age   n        mn        sd
#R|  1   0  20  48.95000  6.012925
#R|  2   1 142  74.66197 16.955046
#R|  3   2  43 113.23256 15.929663
#R|  4   3   8 151.87500 11.179541
#R|  5   4   5 183.20000 17.253985

Important

One still needs to carefully consider the application of ALKs for each of the groups. For example, if the minimum length of unaged fish is less than the minimum length of aged fish (i.e., smaller than that which the ALK is based on) for any one group then this process will fail for ALL groups. In other words a complete fail will occur if there is a fail for any one group in the analysis.

 

Efficiently Applying ALKs to Multiple Groups

Example Data

Schall et al. (2020) examined the effect of season (Spring and Fall) on the vital statistics of Channel Catfish (Ictalurus punctatus) and Walleye (Sander vitreus) in a large Nebraska reservoir. One part of their analysis required computing mortality rates from catch curves for each species and season combination. Prior to constructing the catch curve they used the Isermann and Knight (2005) method to assign estimated ages to unaged fish. Schall et al. (2020) provided the raw data as a CSV file in their Supplement Material Data S1. Note that I removed some variables here for simplicity of presentation in this post, and that their Month completely defined Season.

dat <- read.csv("JFWM-20-027.S1.csv") |>
  select(-Year,-Weight,-Sex,-BCAge,-BCLength) |>
  mutate(Season=case_when(
    Month=="May" ~ "Spring",
    Month=="September" ~ "Fall"
  ))
headtail(dat)

#R|       Spp Length     Month Age Season
#R|  1    CCF    279       May   3 Spring
#R|  2    CCF    334       May   4 Spring
#R|  3    CCF    351       May   4 Spring
#R|  2377 WAE     NA September  NA   Fall
#R|  2378 WAE     NA September  NA   Fall
#R|  2379 WAE     NA September  NA   Fall

A common “issue” with using the ALK to assign ages to unaged fish is that the lengths of some unaged fish are not represented within the lengths of aged fish used to derive the ALK. In other words, the ALK does not contain information for fish of those lengths. The summary below is used to find the sample size and valid sample size (i.e., after excluding fish with no length measurement) and minimum and maximum length for each combination of species, season, and whether an age was assigned or not.

dat |>
  mutate(Aged=!is.na(Age)) |>
  group_by(Spp,Season,Aged) |>
  summarize(n=n(),
            validn=FSA::validn(Length),
            minL=min(Length,na.rm=TRUE),
            maxL=max(Length,na.rm=TRUE))

#R|  # A tibble: 8 × 7
#R|  # Groups:   Spp, Season [4]
#R|    Spp   Season Aged      n validn  minL  maxL
#R|    <chr> <chr>  <lgl> <int>  <int> <int> <int>
#R|  1 CCF   Fall   FALSE   105    104   197   674
#R|  2 CCF   Fall   TRUE     97     97   200   724
#R|  3 CCF   Spring FALSE   394    393   260   733
#R|  4 CCF   Spring TRUE    104    104   279   769
#R|  5 WAE   Fall   FALSE   883    870   181   634
#R|  6 WAE   Fall   TRUE    466    466   157   676
#R|  7 WAE   Spring FALSE   117    116   332   724
#R|  8 WAE   Spring TRUE    213    213   191   753

It is seen from this that there are some missing length measurements (n does not equal validn in all cases) and that the minimum length of unaged fish is less than the minimum length of aged fish for Channel Catfish in both the Spring and Fall. Thus, to appropriately use the Isermann and Knight (2005) method as implemented in alkIndivAge() of FSA, those records with missing lengths must be removed, as well as those records for Channel Catfish that are less than the minimum length for aged Channel Catfish in their respective season.⁷

⁷ It is not clear that Schall et al. (2020) did this, but it is required when using alkIndivAge().

dat <- dat |>
  filter(!is.na(Length)) |>
  filter(!(Spp=="CCF" & Season=="Spring" & Length<279)) |>
  filter(!(Spp=="CCF" & Season=="Fall" & Length<200))

Method-Specific Data Wrangling

The first step in efficiently applying the ALK to all groups is to “split” the original data frame based on the “groups” with split(). Below dat is split by the combination of Spp (species) and Season.

dat2 <- split(dat,~Spp+Season)

The result, in dat2, is a list with four items. Each item in the list is a data frame with the same structure as the original dat but reduced to a specific group defined by Spp and Season. Below names() is used to show that the names of the four items in dat2 are combinations of the “levels” in Spp and Season.

names(dat2)

#R|  [1] "CCF.Fall"   "WAE.Fall"   "CCF.Spring" "WAE.Spring"

The specifics of one of these items is examined by appending the item name to dat2, separated by a $. Below, as an example, are a few rows from the beginning and end of the data frame in CCF.Spring (Channel Catfish in Spring).⁸

⁸ Note here that it appears that all Spp values are “CCF”, all Season values are “Spring”, and that some fish have ages (the top three) and some do not (the bottom three).

headtail(dat2$CCF.Spring)

#R|      Spp Length Month Age Season
#R|  1   CCF    279   May   3 Spring
#R|  2   CCF    334   May   4 Spring
#R|  3   CCF    351   May   4 Spring
#R|  491 CCF    701   May  NA Spring
#R|  492 CCF    730   May  NA Spring
#R|  493 CCF    733   May  NA Spring

Applying ALK

The idea now is to “apply” applyALK() to each data frame in each item of the list in dat2. This can be done with lapply() where the list of data frames is the first argument, the function to apply is the second argument, and the remaining arguments are further arguments to the function being applied. The result is a list with data frames in the items as before, but now with ages for all fish.

dat3 <- lapply(dat2,applyALK,avar=Age,lvar=Length,w=10)
names(dat3)

#R|  [1] "CCF.Fall"   "WAE.Fall"   "CCF.Spring" "WAE.Spring"

headtail(dat3$CCF.Spring)

#R|      Spp Length Month Age Season lcat
#R|  1   CCF    279   May   3 Spring  270
#R|  2   CCF    334   May   4 Spring  330
#R|  3   CCF    351   May   4 Spring  350
#R|  491 CCF    701   May  17 Spring  700
#R|  492 CCF    730   May  17 Spring  730
#R|  493 CCF    733   May  17 Spring  730

The exact same result⁹ is also obtained with map() from the purr package, which was loaded with library(tidyverse). The arguments to map() and the resulting list are the same as those for lapply().

⁹ Disregarding the randomization inherent in alkIndivAge().

dat3 <- map(dat2,applyALK,avar=Age,lvar=Length,w=10)
names(dat3)

#R|  [1] "CCF.Fall"   "WAE.Fall"   "CCF.Spring" "WAE.Spring"

headtail(dat3$CCF.Spring)

#R|      Spp Length Month Age Season lcat
#R|  1   CCF    279   May   3 Spring  270
#R|  2   CCF    334   May   4 Spring  330
#R|  3   CCF    351   May   4 Spring  350
#R|  491 CCF    701   May  17 Spring  700
#R|  492 CCF    730   May  17 Spring  730
#R|  493 CCF    733   May  17 Spring  730

The reason for introducing map() from purr() is that ultimately the four data frames in dat3 need to be “row-bound” together to form a single data frame. There are multiple ways to do this, but the simplest is to use map_df() from purr. map_df() has the same arguments as map() and lapply() but it returns a single combined data frame, rather than a list with multiple data frames.

dat3 <- map_df(dat2,applyALK,avar=Age,lvar=Length,w=10)
names(dat3)  # now column names of the single data frame

#R|  [1] "Spp"    "Length" "Month"  "Age"    "Season" "lcat"

headtail(dat3)

#R|       Spp Length     Month Age Season lcat
#R|  1    CCF    232 September   1   Fall  230
#R|  2    CCF    216 September   1   Fall  210
#R|  3    CCF    238 September   1   Fall  230
#R|  2355 WAE    632       May  10 Spring  630
#R|  2356 WAE    653       May  10 Spring  650
#R|  2357 WAE    720       May  13 Spring  720

Warning

The process, as shown above, will not handle situations where the length category bin width required differs among the groups.

 

Preview - Summaries

While there are still some issues to deal with before the mortality rate can be estimated via catch curve with these data, the summary table and graphic below provide an indication of how the final result from above can be visualized. The issue of estimating mortality rate from these data will be taken up in the next post.

sumdat1 <- dat3 |>
  group_by(Spp,Season,Age) |>
  summarize(Catch=n(),
            meanL=mean(Length),
            sdL=sd(Length))
sumdat1

#R|  # A tibble: 53 × 6
#R|  # Groups:   Spp, Season [4]
#R|     Spp   Season   Age Catch meanL   sdL
#R|     <chr> <chr>  <dbl> <int> <dbl> <dbl>
#R|   1 CCF   Fall       1    15  227.  14.7
#R|   2 CCF   Fall       2    22  262.  37.7
#R|   3 CCF   Fall       3     3  309   27.7
#R|   4 CCF   Fall       4    16  359.  15.4
#R|   5 CCF   Fall       5    30  384.  37.5
#R|   6 CCF   Fall       6    21  405.  23.4
#R|   7 CCF   Fall       7    22  430.  25.1
#R|   8 CCF   Fall       8    29  449.  40.6
#R|   9 CCF   Fall       9    22  488.  40.3
#R|  10 CCF   Fall      10    11  495.  29.5
#R|  # … with 43 more rows

ggplot(dat=sumdat1,mapping=aes(x=Age,y=Catch,color=Season)) +
  geom_point(size=2) +
  geom_line(alpha=0.1,linewidth=1.5) +
  scale_x_continuous(name="Age (yrs)",expand=expansion(mult=0.02)) +
  scale_y_continuous(name="Total Catch",expand=expansion(mult=0.02),
                     trans="log",breaks=c(1,2,5,10,20,50,100,200,500)) +
  facet_wrap(vars(Spp)) +
  theme_bw() +
  theme(panel.grid.major=element_blank(),
        legend.position=c(1,1),
        legend.justification=c(1.1,1.1),
        legend.title=element_blank(),
        legend.background=element_blank())

References

Isermann, D., and C. Knight. 2005. A computer program for age–length keys incorporating age assignment to individual fish. North American Journal of Fisheries Management 25:1153–1160.

Ogle, D. H. 2016. Introductory Fisheries Analyses with R. CRC Press, Boca Raton, FL.

Schall, B. J., C. W. Schoenebeck, and K. D. Koupal. 2020. Seasonal sampling influence on population dynamics and yield of Channel Catfish and Walleye in a large Great Plains reservoir. Journal of Fish and Wildlife Management 12(1):223–233.