Reza Hakimimofrad-Fish Age and Growth

7/31/2019 Reza Hakimimofrad-Fish Age and Growth

1/17

Age & GrowthReading: Chapter 9 (9.3)

Types of growth Aging structures Backcalculation methods Growth equations Parameter estimation

Individual processes

Important in understanding population dynamicsof fish Fish are poikilotherms Metabolic rate (and growth rate) affected by

temperatureImplications:

Age and growth analyses Timing of life history events (migration, spawning)Seasonal patterns are often the rule

Individual processes

Fish seek out preferred environments(determined by temperature, dissolvedoxygen, salinity) Affects sampling and harvesting locations

Early life history stages are less mobile;suffer high mortality in poor conditions Evolution of high fecundity


2/17

Age & GrowthHow is growth

described?

changes in length,width, or weight

length is easiest

Age & Growth

Age & GrowthLength and age

Variety of methods to measure age number and spacing of annual marks on a

part of the animal that is retainedthroughout its life

scale, otolith, fin ray, vertebrae, spine, or shell

vertebrae

fin rays operclesotoliths


3/17

Age & GrowthRequirements of body structures to be used for

aging:

1) structure must grow in constant proportion tothe size of the fish

2) structure must exhibit easily-read periodicmarks that can related to time

3) marks must be evident for all members of thepopulation

4) marks must be constant across age groups andacross years

Ctenoid scale


4/17

Cycloid scale

regenerated scale

otolith-daily rings


5/17

Surf clam growth rings

Age & Growth

Backcalculation: Fraser-Lee Method Proportional spacing of marks reflective of

historical growth patterns

Fish size related to scale size by:

L = a + bS

where L = fish length, S = scale radius, and

a = length at which scales start to form

Age & GrowthFraser-Lee method

Lengths at earlier ages can be backcalculated:

Li = length of fish at age iLc = current length of the fishS i = length of the scale at age iS c = current length of the scalea = correction factor (start of scale formation)

+=

=

c

ici

c

i

c

i

SSa)(LaL

SS

aLaL


6/17

Otolith size vs. body size

y = 20.1x - 9.4

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70Body size (cm)

O t o l i t h s

i z e

( m i c r o n s )

Body size vs. Otolith size

y = 0.05x + 0.81

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400

Otolith size (microns)

B o

d y s

i z e

( c m

Data for spottedseatrout

Age & GrowthProportional methods

Structure proportional method:

Otolith size = 20.1(Body size) 9.4

If: body size current = 50cmotolith size current = 900 micronsotolith size age1 = 180 microns

Then, use 4 steps to calculate body size age1


7/17

Age & GrowthProportional methods

Otolith size = 20.1(Body size) 9.4(body size current = 50cm; otolith size current = 900 microns; otolith size age1 = 180 microns)

1. Calculate mean otolith size for a 50cm fish:

20.1(50) 9.4 = 995.6 microns2. Calculate the ratio of observed otolith size to predicted mean otolith size:

900/995.6 = 0.9043. Adjust the observed otolith size at age 1 by this ratio to calculate the

expected otolith size for an age 1 sized fish:

180/0.904 = 199.14. Calculate the body size for which 199.1 is the expected otolith size:

199.1 = 20.1 (Body size) 9.4 = 10.4cm

Age & GrowthFraser-Lee method

Lees phenomenon: tendency of back-calculated lengths from older

fish to be smaller at early ages (age 1,2,etc.) thanback-calculated lengths from younger fish in thepopulation

Why?.....Greater proportion of the larger fish in anage group die

other potential back-calculation errors (see p.195)

Age & GrowthLength & weight

Related by:W = a L b

Above can be transformed :

lnW = lna + b*lnL

a and b can be derived from a ln/ln plot of weight asa function of length


8/17

Age & Growth:Length & weight

Data for a Lutjanus spp.

ln W = -11.11 + 3.04ln L

W = 1.5x10 -6L3.04

Age & GrowthLength & weight

Related by:W = aL b

Value of a often used as an index of fishcondition :

a = W / L b

Not recommended; use ANCOVA instead to

compare regressions

Age & GrowthGrowth

Expressed as the change in weight or lengthover time ( Size/ t)

Growth in fish often described by a logistic (or sigmoid) curve

Same shape describes many biologicalfunctions in fish populations (individual andpopulation growth, recruitment, size-selectivityof fisheries and predators, etc.)


9/17


10/17

Lt = length at time tL = asymptotic lengthK = rate at which curve approaches L t0 = hypothetical time when length equals zero

von Bertalanffy growth model

[ ])( 01 t t K t e L L =




11/17

Effects of variation in K


K and L are species-specific (based on lifehistory strategy)


So, what is t 0? scaling factor related to juvenile growth



12/17


13/17

From the plot of L t+1 vs. L t

1. Calculate the slope (b) = e -K (so, K= -lnb)

2. Y-intercept =

3. After re-arranging :

von Bertalanffy growth modelWalford plot

)( K e La = 1

b

a L

=

1

von Bertalanffy growth modelWalford plot

First plot Lt which is (L t+1 - Lt) vs. L t

Then, the slope (b) = 1-e -K

Where the plotted line crosses the x-axis(x-intercept) = L

von Bertalanffy growth modelChapman plot


14/17

von Bertalanffy growth modelChapman method

Slope = 1 - e -K L

L t + 1

- L

t

Lt

von Bertalanffy growth modelWalford and Chapman methods

t0 can then be estimated by substituting L andK into the von Bertalanffy equation

+= L

l L

K t t t ln

10

von Bertalanffy growth modelWalford and Chapman methods

Estimates of t 0 will not be equally good for all lengthsGrowth curve will rarely pass thru originRemember, t 0 is a scaling factor: With negative t 0 juveniles grow more quickly

than predicted growth for adults With positive t 0 juveniles grow more slowly than

predicted growth for adults


15/17

von Bertalanffygrowth model:

summary

Growth parameters from length-frequency plots

Some species are difficult to age

We can separate length-frequencydistributions into cohorts and assign ages

However, age-length relationships may notbe valid if cohort separation is not clear

Length-frequencydistribution

Assigned age cohorts1

2

34

5


16/17

Short spawning season

fast growth rate

protracted spawning season

slow growth rate

+

+

Bhattacharya method

Separates the length-frequency distributioninto a series of normal distributions

Identifies the youngest cohort andremoves them from the distribution

Approach is repeated

Ages are assigned to each cohort andmean length at age calculated

overall length-frequency

first cohort identified

next cohort identified


17/17

ELEFAN method

Electronic length frequency analysis No distributional assumptions Length data are smoothed by taking

running averages and best fitting growthcurve is determined

MULTIFAN-a more objective alternativemethod

Data for Chilean sea scallop

Documents

Reza Hakimimofrad-Fish Age and Growth