# 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.

# 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.

## References

Hansen, M., M. Bozek, R. Justine, S. Newman, and M. Staggs. 1998. Factors affecting recruitment of Walleyes in Escanaba Lake, Wisconsin, 1958–1996. North American Journal of Fisheries Management 18:764–774.