# Background

Hansen et al. (1998) modeled recruitment variation of age-0 Walleye (*Sander vitreus*) in Escanaba Lake (Wisconsin) to determine factors regulating their abundance. Specifically, they examined the abundance of age-5 and older Walleye (spawning population), variation in May water temperatures, and abundance of 152.4 mm total length and longer Yellow Perch (*Perca flavescens*) on the abundance of age-0 Walleye. These data are available in WalleyeEL.^{1}

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

If you want to compare your results below to those in Hansen et al. (1998), note that they used what is called the second parameterization of the Ricker function in `FSA`

and that they restricted their data to the year-classes prior to 1992 for “model construction.”

# Basic Analysis

- Which variable should be considered the “recruits” and which variable should be considered the “spawning stock?” Explain.
- From an appropriate plot, describe the relationship between “recruits” and “stock.” Do you expect a stock-recruitment model to fit these data well?
- Fit the density-independent recruitment function to these data, assuming a multiplicative error structure. Show your results by expressing the equation of the recruitment function with the parameters replaced by their estimated values.
- Repeat the previous question but using the Ricker recruitment function.
- Determine if the density-dependent parameter is statistically significant in the Ricker model.
- Describe what proportion of variability in recruitment is explained by the Ricker model.
- Construct a single plot that shows how well each recruitment function fits these data. Show confidence bands for the Ricker recruitment function.
^{2} - Estimate recruitment for the mean stock level with each recruitment function. How variable are the results among models?

^{2} This may be useful.

# Extended Analysis

- Determine if adding the variation in May water temperatures or the abundance of Yellow Perch significantly improves the predictive power of the Ricker model.
- If either of these two variables improved the predictive power of the model then ….
- Express the best model by replacing parameters with their estimated values.
- Specifically describe the effect of the other variables on the recruitment of age-0 Walleye.
- Do you feel that this model provides a clear explanation for the variability in recruitment of age-0 Walleye in Escanaba Lake? Explain.

Available upon request to students not in a class. Contact fishR maintainers.