Zoo 511
Age and Growth Lab
Understanding age and growth is a critical component of fisheries science. Understanding how to calculate
age and growth can be a crucial component of many fish related studies including general population
dynamics, survivorship, behavior, the impacts of a fisheries regulation, and questions about temperature
such as the impacts of global warming.
The goal of today is to learn all of the critical components and steps involved in aging a fish and calculating
growth. We are going to remove an essential aging structure, an otolith, from white perch, age fish using
both scales and otoliths, calculate growth rate (mm year -1) using Fraiser-Lee back-calculation from scales,
and experiment with one way to look at growth data: the von Bertalanffy growth curve.
Otolith extraction
Follow procedures outlined in lecture for otolith extraction
Scale Reading
Get one scale slide from Little Rock Lake and one scale slide with its accompanying otolith slide from
Crampton Lake. Starting with the Crampton Lake set, use the otolith to help determine your fish’s age.
Identify the annuli on the scale image on your handout.
Fraiser-Lee back-calculation
Using the simple conversion on your handout (actual radius length = (measured radius length X actual micrometer
length) / measured micrometer line length), calculate the length of each annuli radius (the distance from the
origin to the edge of the annuli) and the total scale radius length. Enter these data into your Excel
template to perform Fraiser-Lee back-calculation to determine length at age (length at each annuli):
Lt= c + (LT –c)(St/ST)
Length at age t
Total fish length
Scale radius length at age t
Total scale radius
Carlander’s constant
Largemouth bass
Black crappie
Yellow perch
c (mm)
Von Bertalanffy model
Open two growth templates, one for each lake. Insert data from all 6 fish from each lake in the “FraiserLee” worksheet. Enter the correct Carlander intercept value for your species.
Von Bertalanffy growth model: Lt = Linf - (Linf - Lzero)exp(-kt)
Length at age t
Length at time infinity
Length at birth
“Curvature” parameter
Time or age
Select the “von Bertalanffy” worksheet. It is now time to fit the model by minimizing the sum of squared
differences i.e. making the model estimations as close to the real data as possible.
1. To sum all of the sum of squared differences, in cell I10 type “=SUM(highlight all E cells with a value in
2. Enter an arbitrary set of model estimates in the blue box to initiate the model (Linf=450mm; Lzero=20mm;
3. Fit the model using excel solver:
Data> Analysis>solver> set target cell (to the sum of squared difference) “I10”
> by changing cells “H4:H6”
> Solve > keep solver solution > ok
4. Plot the data
>Highlight annuli data and back calculated data
> Insert> plot > XYScatter
>Right click on plot > select data > Series > Add > Highlight the oldest fish’s annuli for “X values”
and the respective model predictions for “Y” > ok
> Right click on a data point from series 2 (make sure it is not series one) > Chart Type > Scatter w/
smooth line w/out points > ok.
5. Repeat for the other lake.
You now have a plot of your raw data for each lake as well as a von Bertalanffy estimate of growth for the
total sampled population of each lake.
How does growth differ between these lakes?
Which lake has faster growth at age one? Age 3? Age 7?
Is growth in one lake always higher than the other?
Do they shift across age?
Create a scenario based on your knowledge of fish ecology explaining how these trends could be observed: