Age Analysis 2 Importance Many stock parameters are annual rates eg growth amp mortality components of yield time must be recorded Usually as the age of the fish Age ID: 569214
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Slide1
Age Length KeySlide2
Age Analysis
2
Importance
Many stock parameters are
annual
rates
.
e.g., growth & mortality (components of yield)
“
time” must be recorded.
Usually as
the age of the fish.
Age
assessment is vitally
important.
It is also
EXPENSIVE!Slide3
Age Length Key
3
Concept – Overall
Have a
large
sample of
fish.
Measure length on all fish.
Choose a portion of sample to assign age.
Called the
age sample
.
Fish chosen either
in proportion to the number of fish in each length category
as a fixed number per each length category (more common)
Fish that are not aged are called the
length sample.
Develop relationship between age and length from fish in age sample.
two-way contingency table called an
age-length key
“Assign” age to
fish in length sample with age-length key .Slide4
Age Length Key
4
Concept – Age-Length Key
Age Sample
len age
22 1
24 1
26 2
27 2
30 1
32 2
34 2
39 3 40 1 44 2 46 3 49 3 52 2 53 2 55 3 56 3
Use 10-cm intervals for length categoriesMake raw contingency table AgeLCat 1 2 3 20 30 40 50 Convert to row-proportions table AgeLCat 1 2 3 20 30 40 50
LCat 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50
2
2
2
2
2
2
0
0
1
1
1
1
0.00
0.00
0.50
0.50
0.50
0.50
0.50
0.50
0.25
0.25
0.25
0.25Slide5
Age Length Key
5
Concept – Age-Length Key
Length Sample
len age
23
25
26
28
32
33
36
40 43 44 48 49 51 54
Age-Length Key (as a reminder) Age LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50Use 10-cm intervals for length categoriesCreate length distributionLCat 20 30 40 50Freq 4 3 5 2
LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50Slide6
Age Length Key
6
Concept – Age-Length Key
Length Sample
len age
23
25
26
28
32
33
36
40 43 44 48 49 51 54
Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50Length distribution (as a reminder)LCat 20 30 40 50Freq 4 3 5 2Identify number in each length category to be assigned each age20-cm 4*0.5 = 2 age-1 4*0.5 = 2 age-2 4*0 = 0 age-3
Randomly determine which fish are assigned these ages.LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50
2
2
1
1Slide7
Age Length Key
7
Concept – Age-Length Key
Length Sample
len age
23
25
26
28
32
33
36
40 43 44 48 49 51 54
Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50Length distribution (as a reminder)LCat 20 30 40 50Freq 4 3 5 2Identify number in each length category to be assigned each age30-cm 3*0.25 = 0.75 age-1 3*0.5 =
1.5 age-2 3*0.25 = 0.75 age-3What to do now?LCat 20 20 20 20 30 30 30 40 40 40 40
40 50
50
2
2
1
1Slide8
Age Length Key
8
Age-Length Key – Fractionation
Fractionation
When
a
fraction of a fish
should
be assigned a given age.
Handling fractionation
Round all values
down
to integers.For remaining number of fish, choose random ages in proportion to the proportion in each age.Slide9
Age Length Key
9
Age-Length Key – Fractionation
Handling fractionation
Round all values down to integers.
30-cm
3*0.25 =
0.75
=
0
age-1
3*0.5 =
1.5 = 1 age-2 3*0.25 = 0.75 = 0 age-3For remaining number of fish ...two ages must be chosen such that age-1 has 25% chance, age-2 has 50% chance, and age-3 has 25% chance of being selected.e.g., 2, 1 was chosenthus, randomly assign 1 age-1, 2 age-2, & 0 age-3 for fish in the 30-cm length intervalSlide10
Age Length Key
10
Concept – Age-Length Key
Length Sample
len age
23
25
26
28
32
33
36
40 43 44 48 49 51 54
Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50Length distribution (as a reminder)LCat 20 30 40 50Freq 4 3 5 2Identify number in each length category to be assigned each age30-cm 3*0.25 = 0.75 age-1 3*0.5 =
1.5 age-2 3*0.25 = 0.75 age-3Randomly determine which fish are assigned these ages.LCat 20 20 20 20 30 30 30 40 40 40 40
40 50
50
2
2
1
1
1
2
0
1
2
2Slide11
Age Length Key
11
Concept – Age-Length Key
Length Sample
len age
23
25
26
28
32
33
36
40 43 44 48 49 51 54
Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50Length distribution (as a reminder)LCat 20 30 40 50Freq 4 3 5 2Identify number in each length category to be assigned each age40-cm 5*0.25 = 1.25 = 1 age-1 5*0.25 = 1.25 = 1 age-2 5*0.5 = 2.5 = 2 age-3
Extra fish was chosen to be age-3.Randomize age assignments.LCat 20 20 20 20 30 30 30 40 40 40 40 40 50
50
2
2
1
1
1
1
3
1
2
2
1
3
2
3
3Slide12
Age Length Key
12
Concept – Age-Length Key
Length Sample
len age
23
25
26
28
32
33
36
40 43 44 48 49 51 54
Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50Length distribution (as a reminder)LCat 20 30 40 50Freq 4 3 5 2Identify number in each length category to be assigned each age50-cm 2*0.5 = 1 age-2 2*0.5 =
1 age-3Randomize age assignments.LCat 20 20 20 20 30 30 30 40 40 40 40 40 50
50
2
2
1
1
1
2
2
1
3
2
3
3
3
2Slide13
Age Length Key
13
Utility
Lengths in age sample should cover range of lengths in length sample.
Age sample and length sample must be from the same population.
typically age sample is a subsample
“Extra” effort should be put in age, not length, sample.
Combine age sample and age-assigned length sample for further analysis.Slide14
Age Length Key
14
How – Apply the A-L Key
Use the
age.key()
function to assign ages to fish in a length sample given an A-L Key.
required arguments:
age-length key row proportions table as first argument.
data frame with length sample as second argument.
cl=
(name or number of column containing the measured lengths)
optional arguments: ca= (name or number of column that should receive the assigned ages)if this column does not exist it will be created & called “Age”. type= (A string indicating the type of randomization) type=“SR” semi-random (default, method described here) type=“CR” completely randomSlide15
Age Length Key
15
How – Apply the A-L Key
Demonstration with the age and lengths of spot (
Leiostomus
xanthurus
) from Virginia.
403 fish were collected
as many as 10 per 1-inch length category were aged from
otolith
thin sections.
72 fish were agedinterested in mean length-at-age and age distribution.Examine HandoutSummarize()lencat()table()prop.table()ageKey()