# Background

Wolfert (1980) measured the total length (TL) of 1288 Rock Bass (*Ambloplites rupestris*) from Eastern Lake Ontario in the late 1970s. In addition, scales were removed for age estimation from as many as 10 specimens from each 10 mm length interval. All data are recorded in RockBassLO2.^{1}

^{1} See “CSV file” link in “Source” section of linked page. Also note that the filename contains an “oh” not a “zero.”

This exercise requires the data frame that contains length and ages, both estimated and assigned from an age-length-key, for all sampled fish. This data frame was constructed in this age-length key exercise. Please load/run your script from that exercise that produces the data frame with ages for all sampled fish.

# Fit Traditional VBGF

- Examine the plot of TL versus age.
^{2}Make observations regarding the “shape” of the data (do the results look linear or like a von Bertalanffy growth curve, is there an obvious asymptote, are young fish well represented, how variable are lengths within ages). - Fit the typical parameterization of the von Bertalanffy growth function (VBGF).
- How realistic do the point estimates of \(L_{\infty}\), \(K\), and \(t_{0}\) seem?
- Write the typical VBGF with parameters replaced by their estimated values.
- Carefully interpret the meaning of each parameter.
- Construct 95% bootstrapped confidence intervals for each parameter. Comment on the widths of these confidence intervals. What explains this?
- Predict the mean TL, with 95% confidence interval, for an age-6 Rock Bass. Comment on the width of this confidence interval. What explains this?
- Plot TL versus age and superimpose the best-fit VBGF.
^{3}Comment on model fit. - Construct a residual plot. Comment on model fit.
- Compute the correlation between parameter values. Comment.

^{2} This plot was made in this exercise.

^{3} This post may be useful.

# Alternative Parameterization

- Fit the Gallucci and Quinn (1979) parameterization.
^{4}- Interpret the interval estimate for the \(\omega\) parameter.
- Write the Gallucci and Quinn VBGF with parameters replaced by their estimated values.
- Construct 95% bootstrapped confidence intervals for each parameter. Comment on the widths of these confidence intervals. What explains this?
- Predict the mean TL, with 95% confidence interval, for an age-6 Rock Bass. Comment on the width of this confidence interval. What explains this?
- Plot TL versus age and superimpose the best-fit VBGF. Comment on model fit.
- Compute the correlation between parameter values. Comment
- How does the estimate of \(K\) from fitting this parameterization compare to that from the typical VBGF fit above. Explain your observation.

^{4} See `growthFunShow("vonBertalanffy",param="GQ",plot=TRUE)`

) and this.

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