Age & Growth - UNCW Faculty and Staff Web Pagespeople.uncw.edu/scharff/courses/458/Lecture 6 - age and growth.pdf · 2 Age & Growth How is growth described? – changes in length,

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Age & GrowthReading: Chapter 9 (9.3)

Types of growthAging structuresBackcalculation methodsGrowth equationsParameter estimation

Individual processesImportant in understanding population dynamics

of 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, dissolved oxygen, salinity)

Affects sampling and harvesting locations

• Early life history stages are less mobile; suffer high mortality in poor conditions

Evolution of high fecundity

2

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 retained throughout its life

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

vertebrae

fin rays operclesotoliths

3

Age & GrowthRequirements of body structures to be used for

aging:1) structure must grow in constant proportion to

the size of the fish2) structure must exhibit easily-read periodic

marks that can related to time3) marks must be evident for all members of the

population4) marks must be constant across age groups and

across years

Ctenoid scale

4

Cycloid scale

regenerated scale

otolith-daily rings

5

Surf clam growth rings

Age & GrowthBackcalculation: 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 fishSi = length of the scale at age iSc = current length of the scalea = correction factor (start of scale formation)

⎟⎟⎠

⎞⎜⎜⎝

⎛•−+=

=−−

c

ici

c

i

c

i

SSa)(LaL

SS

aLaL

6

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)

Oto

lith

size

(mic

rons

)

Body size vs. Otolith sizey = 0.05x + 0.81

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400

Otolith size (microns)

Body

siz

e (c

m)

Data for spotted seatrout

Age & GrowthProportional methods

Structure proportional method:

Otolith size = 20.1(Body size) – 9.4

If: body sizecurrent = 50cmotolith sizecurrent = 900 micronsotolith sizeage1 = 180 microns

Then, use 4 steps to calculate body sizeage1

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Age & GrowthProportional methods

Otolith size = 20.1(Body size) – 9.4(body sizecurrent = 50cm; otolith sizecurrent = 900 microns; otolith sizeage1 = 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

Lee’s phenomenon:tendency of back-calculated lengths from older fish to be smaller at early ages (age 1,2,etc.) than back-calculated lengths from younger fish in the populationWhy?.....Greater proportion of the larger fish in an age group dieother potential back-calculation errors (see p.195)

Age & GrowthLength & weight

Related by:W = a Lb

Above can be transformed:

lnW = lna + b*lnL

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

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Age & Growth:Length & weight

Data for a Lutjanus spp.

lnW = -11.11 + 3.04lnL

W = 1.5x10-6L3.04

Age & GrowthLength & weight

Related by:

W = aLb

Value of ‘a’ often used as an index of fish ‘condition’:

a = W / Lb

Not recommended; use ANCOVA instead to compare regressions

Age & GrowthGrowth

Expressed as the change in weight or length over time (ΔSize/Δt)Growth in fish often described by a logistic (or sigmoid) curve Same shape describes many biological functions in fish populations (individual and population growth, recruitment, size-selectivity of fisheries and predators, etc.)

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Age

Len

gth

Hypothetical growth curve for fish

Age & GrowthCalculating growth

Absolute growth W2 - W1 / (t2 - t1)

Relative growth (W2 - W1) / W1

Instantaneous (lnW2 - lnW1) / (t2 - t1)growth

Age & GrowthGrowth curves

Describing size at age patterns:• underlying model must be biologically meaningful• von Bertalanffy model is most commonly applied• other models include linear, simple exponential,

Gompertz• parameters from von Bertalanffy model used in many

fishery yield models (to predict response to harvest)

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Lt = length at time tL∞ = asymptotic length K = rate at which curve approaches L∞

t0 = hypothetical time when length equals zero

von Bertalanffy growth model

[ ]{ })( 01 ttKt eLL −−

∞ −=



11

Effects of variation in K


K and L∞ are species-specific (based on life history strategy)


So, what is t0?scaling factor related to juvenile growth


12


To convert from length to weight: -assume that W varies as a function of L3

[ ]{ }301 )( ttKt eWW −−

∞ −=

von Bertalanffy growth modelHow can we estimate the parameters?

Walford and Chapman plots, nonlinear models

[ ]{ })( 01 ttKt eLL −−

∞ −=

First step: Plot Lt+1 vs. Lt

von Bertalanffy growth modelWalford plot

Lt

L t+

1

1 to 1 line

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From the plot of Lt+1 vs. Lt

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

2. Y-intercept =

3. After re-arranging:


)( KeLa −∞ −= 1

baL−

=∞ 1


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

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

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

von Bertalanffy growth modelChapman plot

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von Bertalanffy growth modelChapman method

Slope = 1 - e-K L∞

L t+1

-Lt

Lt

von Bertalanffy growth modelWalford and Chapman methods

t0 can then be estimated by substituting L∞ and K into the von Bertalanffy equation

∞

∞ −+=L

lLK

tt tln10

von Bertalanffy growth modelWalford and Chapman methods

Estimates of t0 will not be equally good for all lengthsGrowth curve will rarely pass thru originRemember, t0 is a scaling factor:– With negative t0 juveniles grow more quickly

than predicted growth for adults– With positive t0 juveniles grow more slowly than

predicted growth for adults

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von Bertalanffygrowth model:

summary

Growth parameters from length-frequency plots

• Some species are difficult to age

• We can separate length-frequency distributions into cohorts and assign ages

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

Length-frequencydistribution

Assigned age cohorts1

2

34 5

16

Short spawning season

fast growth rate

protracted spawning season

slow growth rate

+

+

Bhattacharya method

• Separates the length-frequency distribution into a series of normal distributions

• Identifies the youngest cohort and removes them from the distribution

• Approach is repeated

• Ages are assigned to each cohort and mean length at age calculated

overall length-frequency

first cohort identified

next cohort identified

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ELEFAN method

Electronic length frequency analysisNo distributional assumptionsLength data are smoothed by taking running averages and best fitting growth curve is determinedMULTIFAN-a more objective alternative method

Data forChilean sea scallop

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Age & Growth - UNCW Faculty and Staff Web Pagespeople.uncw.edu/scharff/courses/458/Lecture 6 - age and growth.pdf · 2 Age & Growth How is growth described? – changes in length,