Age, Size and Growth

ZOO 511 week 3 slides

Metrics of Size and Growth

• Length– PROS: easy, intuitive, history in angling, length

rarely shrinks, nonlethal – CONS: lots of change in biomass not related to

length

• Wet Weight (i.e., weighing a live fish)– PROS: nonlethal, quick, useful for large calculations

(ie population biomass)– CONS: can be difficult in the field if conditions are

bad

• Dry Weight (i.e., weighing a dehydrated fish)– PROS: accurate description of individual's mass– CONS: time intensive and lethal to fish

3 ways to estimate growth in natural populations• Recaptures of marked individuals

• Length-Frequency Analysis

• Back calculation from calcified structures

#C

augh

t

0

10

20

30

10 40 70 100 130 160 190 220 250 280

Recaptures of marked individuals

METHOD: measure individuals and give them unique marks; recapture and measure again later

PROS: nonlethal, accurate individual data

CONS: high effort - have to catch & mark A LOT of fish

Length-Frequency AnalysisMETHOD: measure population at least once; plot

length vs. frequency to find age classes; compare across age classes to estimate growth

0

10

20

30

10 40 70 100 130 160 190 220 250 280

#C

augh

t

Length (mm)

Age class 3

Age class 4

Age class 5

Age class 2Age

class 1

Length-Frequency AnalysisMETHOD: measure population at least once; plot

length vs. frequency to find age classes; compare across age classes to estimate growth

PROS: nonlethal; can use historic data; can do with 1 sample

CONS: “snap shot” of growth; assumes constant conditions; easy to bias sample with gear, time or location; requires lots of fish

0

10

20

30

10 40 70 100 130 160 190 220 250 280

#C

augh

t

Length (mm)

Back CalculationMETHOD: Examine hard structures from individuals

for age and evidence of past growth rate

Periods of rapid and slow growth show up as rings

Back CalculationMETHOD: Examine hard structures from individuals

for evidence of past growth rate

PROS: sometimes nonlethal; accurate individual data; no repeated sampling; does not assume constant conditions; can used archived structures; can estimate over small size/time changes;

CONS: sometimes lethal; can be technically challenging

Vertebrae (sharks)

Fin RaysOpercula

Cleithra (pikes & relatives)

Hard structures to estimate age & growth

Otoliths (lethal)Scales (non-lethal)

Hard structures to estimate age & growth

HOW TOestimate age & growth with

scales or otoliths

Otoliths work the same way

Plus they are useful for many other things

But you have to kill the fish to retrieve them

And they are more work to process

Otoliths• What is an otolith?• Where exactly is an otolith?

harvestsection & polish analyze

Otoliths and fishery science

• Unique properties:– Otolith growth is continual– Lack of resorption

• Complete growth and environmental record– Crystalline structure

• Holds trace metals

• Scientists use otolith composition to:– Estimate what temperatures the fish

experienced in the past– Determine where the fish traveled (e.g.,

ocean vs. freshwater)

How do we get from age to

growth?

Frasier-Lee Equation

Lt= c + (LT – c)(St/ST)

big T means now

little t means some time in

the past

L means fish length

S means scale radius

Frasier-Lee Equation

Lt= c + (LT – c)(St/ST)

c is “Carlander’s constant” -- it will have a different value for

different species

Now we have a lot of length-at-age points.

0

100

200

300

400

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Age

Leng

th (

mm

)

How do we summarize growth patterns from this?

How do we compare growth between 2 populations?

Insert real data here?

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20

Age

Fis

h L

en

gth

AL

WS

Von Bertalanffy Growth Model

Lt = L∞ - (L∞ - L0) –kt

– Lt = length at time “t” (of an avg. fish in the population)

– L∞ = length at infinity

– L0 = length at time zero (birth)– K = constant (shape of growth line)

Von Bertalanffy Growth Model

Lt = L∞ - (L∞ - L0) –kt

If you give the model

this

It will give you these

Lt = L∞ - (L∞ - L0)-kt

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20

Age

Length AL Model

WS Model

Linf = 523.4

Lzero = 57.54

k = 0.081

Linf = 500.6

Lzero = 28.34

k = 0.080AL WS