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

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

1. Aging the Scale

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;

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.

4. Growth CurvesThe 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.

5. Compare Growth CurvesLikelihood 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

Ferox StudyH0- 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.

1. Age Scales1. 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)

2. Back Calculations

LF = Lt (Sf /St);

3. Von Bertalanffy Growth Equation

L(t) = Linf *(1 - exp(-K*(t-t0)))

4. Growth Curves

5. Likelihood ratio testLikelihood 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.

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% agreementScale versus Scale 71% agreementOtolith versus Scale 72% agreement.”

Otolith versus Scales

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)

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

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

Questions