# Background

Bur (1984) examined the population dynamics of Freshwater Drum (*Aplodinotus grunniens*) in Lake Erie in the late 1970s. In one part of his study, he measured the total length (TL) of all 1577 drum sampled and extracted scales for age estimation from a proportionate sample from each 10 mm length interval. The length and age data are recorded in FWDrumLE2.^{1}

^{1} See “CSV file” link in “Source” section of linked page.

# Construct an ALK

- Add a variable to the data frame that contains the 10 mm TL categories and then separate the observed data into age- and length-samples. How many fish are in each sample?
- Construct a table of the
**number**(not proportion) of fish in each age and 10 mm TL category in the age-sample. From these results, compute each of the following*by hand*(i.e., not using R, but you can use a calculator).- How many Freshwater Drum are in the 230 mm TL category?
- How many Freshwater Drum are age 5?
- What proportion of Freshwater Drum in the 300 mm TL category are age 5?
- What proportion of Freshwater Drum in the 200 mm TL category are age 4?

- Construct an
**observed**age-length key from the table above (using R). From these results answer the following questions.- What proportion of Freshwater Drum in the 210 mm TL category should be assigned age 5?
- How many of thirty Rock Bass in the 250 mm TL category should be assigned age 4?
- Construct a plot of the
**observed**age-length key. Are there any potential anomalies in the plot that would suggest that a smoothed age-length key could be appropriate?

- Construct a
**smoothed**age-length key. From these results answer the following questions.- What proportion of Freshwater Drum in the 210 mm TL category should be assigned age 5?
- How many of thirty Rock Bass in the 250 mm TL category should be assigned age 4?

# Apply an ALK I

Continue with the age- and length-sample data frames and the **observed** age-length key from the previous section.

- Use the semi-random age assignment technique from Isermann and Knight (2005) and the
**observed**age-length key to assign ages to the unaged fish in the length-sample. Combine the age-sample and the age-assigned length-sample into a single data frame to answer the following questions.- How many fish are estimated to be age 3?
- How many fish are estimated to be age 8?
- Plot the age distribution for all fish.
- How many fish are in the 150 mm TL interval?
- What is the mean TL of age-4 fish?
- Plot the length-at-age with the mean length-at-age superimposed for all fish.

- Compare your results from the previous question to someone else’s results (or repeat the previous question). Did you both get the
*exact*same results? Why or why not? If not, how different were they?

# Apply an ALK II

Continue with the age- and length-sample data frames and the **observed** age-length key from the first section.

- Use the “classical” method to estimate the age distribution (with standard errors) for all sampled fish.
- How many fish are estimated to be age 3?
- How many fish are estimated to be age 8?
- Plot the age distribution for all fish.

- Use the “classical” method to estimate the mean length-at-age (with standard deviations) for all sampled fish.
- What is the mean TL of age-4 fish?
- Plot the length-at-age with the mean length-at-age superimposed for all fish.

- Compare your results to someone else’s results (or repeat the steps above). Did you both get the
*exact*same results? Why or why not? If not, how different were they? - Compare your results using the “classical” method here to your results from using the Isermann and Knight (2005) method in the previous section.

## References

Bur, M. T. 1984. Growth, reproduction, mortality, distribution, and biomass of Freshwater Drum in Lake Erie. Journal of Great Lakes Research 10:48–58.

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.