Talk provided by Martin Hughes (Glasgow University) on 26th March 2015.

1. March 2015
IFM, The Tweed Foundation
& SFCC
A project supported by the European Union's INTERREG IVA Programme managed by the Special EU Programmes Body
Ferox Trout Scale
Analysis
Martin Hughes

3. Growth rates
37
47
60
66.5
+8
4
10
16
25
30
1. Age the fish
2. Back Calculation
3. Von Bertalanffy Growth
Function (VBGF)
4. Calculate growth
curves
5. Likelihood ratio tests

4. 1. Aging the Scale

5. 2. Back Calculation
Measurements were made from the focus along the longest
axis to the edge of the scale (St) and to the annulus being
examined (Sf). The length of the fish at the time a feature
was laid down (LF) is estimated by:
LF = Lt (Sf /St);
LF = back-calculated fish length at annulus f;
Lt = fish length at capture;
Sf = scale length to annulus f;
St = total scale length t;

6. 3. Von Bertalanffy Growth Equation
Von Bertalanffy derived this equation in 1938 from simple physiological
arguments. It is the most widely used growth curve and is especially
important in fisheries studies.
L(t) = Linf *(1 - exp(-K*(t-t0)))
L(t) = Von Bertalanffy growth curve for size (t)
Linf = asymptotic length growth is zero;
K= growth rate;
St = theoretical age at size zero.

7. 4. Growth Curves
The parameter t0 is included to adjust the equation for the initial size of
the organism and is defined as age at which the organisms would have had
zero size. Thus to fit this equation you need to fit 3 parameters (L∞, K and
t0 ) by nonlinear regression.
To fit this curve we must therefore estimate 3 parameters, L∞, K and t0.

8. 5. Compare Growth Curves
Likelihood ratio tests
Curves are non-linear and therefore you cannot use any linear models.
While several techniques can provide reasonable results, a likelihood ratio
test will always equal or surpass other methods in accuracy and reliability
and should be used to determine whether significant differences exists
between growth curves, such as to see if growth parameters estimates are
significantly different or if a single set of growth parameters better
describe the data.
Great package to use on R statistical software (fishmethods)
http://cran.r-project.org/web/packages/fishmethods/fishmethods.pdf

9. Ferox Study
H0- We would find no differences between sympatric brown trout and
ferox trout populations.
Followed the process described.
As growth is genetically determined (selective breeding) larger parents
pass on genes to produce larger offspring, it may give insight into the
number of populations present.

10. 1. Age Scales
1. Pressed the scales on to acetate using a jewellers press.
2. Allows for easier scale reading and provides a permanent copy of the
scale impression
3. Scale ages were recorded in a database then used for step 3 (Back
calculation of length at age)

11. 2. Back Calculations
LF = Lt (Sf /St);

12. 3. Von Bertalanffy Growth Equation
L(t) = Linf *(1 - exp(-K*(t-t0)))

13. 4. Growth Curves

14. 5. Likelihood ratio test
Likelihood ratio test
Location Parameter Chi sq df P
Loch Awe Linf 14.49 1 <0.001
K 11.69 1 0.001
t0 3.76 1 0.052
Loch Rannoch Linf 5.74 1 0.017
K 2.8 1 0.094
t0 0.52 1 0.471
Likelihood ratios tests between sympatric ferox and brown trout. Significant
differences (P<0.05) are highlighted in bold.

15. Limitations of scales
• Criticisms of accuracy of scale reading
 Scales may fall off i.e. replacement scales
 Scales are laid down over time not from hatch
 Can be quite subjective depending on the reader
• Alternatives to scale reading
 Otoliths is a structure in the saccule or utricle of the inner ear
 Fish otoliths accrete layers of calcium carbonate
 Accretion related to growth (summer & winter)
 Most species accretion is daily (determine age in terms of days)
Baumen et al 2013: “Otolith verus Otolith 95% agreement
Scale versus Scale 71% agreement
Otolith versus Scale 72% agreement.”

16. Otolith versus Scales

17. Why stick to scales?
The primary reason is not to sacrifice the fish, especially in the
cause of rare ferox trout.
Otoliths require quite sophisticated methods when compared
with scale analysis
Acknowledge a certain amount of error surrounding scale sizes
and accommodate as such (larger sample sizes when comparing
populations)

18. Thanks
• Colin Adams , Aya Thorne, Alan Kettle-White & Andy Ferguson
• Travis Van Leeuwen, James Barry, Madeleine Carruthers
• Jennifer Dodd, Oliver Hooker & Kyle McFarlane
• Peter Cunningham, Marcus Walters & Kenny Galt
• All IBIS admin and tech support

19. A project supported by the European Union's INTERREG IVA Programme managed by the Special EU Programmes Body
Questions