catchability coefficient, raising factor

1. Geronimo R. Rosario

2.  Fish Biomass is affected by the different factors
such as Recruitment, Growth, Natural mortality
and Fishing mortality.
 Mortality caused by fishing is dependent on the
catchability and selectivity of the gear.

3. 1. Size of the population (biomass) is determined by balance
between Growth, Recruitment, Natural mortality and Fishing
mortality (and movement)
 2. Population (biomass) will vary over time proportionately
with the catch rates taken in the fishery, because as biomass
increases or decreases the gear will catch proportionately
more or less fish per unit effort. Therefore catch rates are
effectively an index of abundance (biomass) and can be
used to help the model realistically track biomass over time.
Biomas
s
CPUE
Time
CPUE
Biomas
s

4.  To remind us of how this theory works, consider the following example:
1. A longliner sets 35 hooks in the water.
2. Fish population = 10 fish, each weighs 1 kg, evenly distributed (below 50 meters)
3. Fish caught by gear = blue, fish not caught = pink

5.  Noting that CPUE = Catch/Effort, and the fisher catches 2 fish using 35
hooks, the fishers catch rate is = 2 / 35 = 0.057 kg/hook
 Assuming that the fish are evenly distributed (spatially), what will happen to
the catch rate if we double the biomass (number of fish, each 1kg) to 20 fish
(20 kg)?

6.  Catch per unit effort also doubles (catch/effort = 4/35 = 0.114)
 If we were to double the biomass again, catch rates would double
again, and so on…
 ……This illustrates why catch rates are assumed to vary
proportionately with population size (biomass) and is used as an
index of biomass.

7.  This assumption however has been shown to be often
WRONG!
 And to understand why, we need to understand the
concept of CATCHABILITY!
Biomass
CPUE
Time
CPUE
Biomass

8. ◦ Catchability is defined as the average proportion of
a stock that is taken by each unit of fishing effort.
◦ q = C/EB
◦ Where q = catchability, C = catch, E = effort, and B =
biomass
◦ It will be a value between 0-1 (0 being no catch and 1
being the entire stock), and typically will be very
small….e.g.; 0.000001
◦ As noted before “q” is critical in relating fishing mortality to
fishing effort and relating the index of abundance (catch
rates) to stock biomass

9.  Catchability (q) is defined as the relationship
between the catch rate (CpUE) and the true
population size (B).
 So the unit of catchability is fish caught per fish
available per effort unit and per time unit.
 Catchability is also called gear efficiency or
sometimes fishing power, and is strongly related to
gear selectivity because it is species and size
dependent.
 Catchability can be taken as the mean proportion
of the stock taken by one unit of fishing effort

10.  The probability of a fish being caught at any time
depends on several factors, which are not only
man-made, and can broadly be grouped as
biological or technological:
 Biological factors include:
 fish availability on the fishing ground
 fish behaviour towards the fishing gear
 the size, shape, and external features of the fish
 where some of these factors again are depending
on season, age, environment and other species.

11.  Technological factors include:
 gear type, design, size, colour and material
 gear position, duration and handling
 experience of the fishermen
 where again these factors are depending on
biological changes.

12.  So, in our first example, the catchability (proportion
of stock caught CPUE) was:
 q = C/EB = 2/(35*10) = 0.0057 = each hook
caught 0.57% of the stock
 In our second example, biomass was doubled, and
catchability was:
 q = C/EB = 4/(35*20) = 0.0057 = each hook
caught 0.57% of the stock
 SO, biomass doubled, catch rates doubled, but
catchability remained the same!

13.  q = C/EB
 q = 2/30x28
 =0.00238

14.  What happens to catchability when the depth of the gear is
increased into the habitat of the target fish?
 q = C/EB
 q = 7/30x28
 =0.00833

15.  Where catchability remains the same over time, CPUE
does vary with biomass, and is a good
index…however….
 There's a Problem!
 Catchability can change (increase or decrease) over
time, meaning that our key assumption in stock
assessment, that catch per unit effort will vary
proportionally with stock size, is no longer true.
 What can cause changes in catchability, ie. Changes in
the mean proportion of the stock caught by one unit of
effort?

16. 1. Changes in fishing methods
e.g. Change in depth of setting by Japanese longliners
in early 1970s
2. Changes in fishing technology
e.g. Improved fish finding technologies
3. Experience and skill increases over time.
 These are reasons why we collect information on
methods and gears from fishermen, so we can account
for changes in fishing over time that might impact
catchability.

17.  4. Environmental factors
 e.g. Sea surface temperatures – fish aggregate to
preferred temperatures (and “habitats”)
 5. Behaviour
 some fish show vertical migration habits each day and
night;
 e.g. Bigeye tuna migrate to surface at night and deep
during the day

18.  5. Contraction of species to prime habitats
when biomass declines
 (e.g. due to fishing, especially in schooling fish).
“McCall basin theory”
Prime habitat

19. 1. It relates catch rates to the stock biomass, via:
 C/E = qB
 Stock assessment model rely on the assumption
that catch per unit effort will vary over time
proportionately with biomass, so CPUE acts as an index
of abundance. Having such an index is critical to the
estimation of biomass.
Biomass
CPUE
e.g.
Time
CPUE
Biomass

20.  2. It relates fishing mortality rates to fishing effort,
via:
 C/B = F = qE
 F= C/B=qf
 CPUE=C/f=qB
 C=q f B
 C= catch
 q= catchability coefficient
 F= effort
 B= Biomass

21. Catch (C)
(kg)
Effort (f)
(hr)
Catchability
Coefficient
(q)
Biomass
(B)
(kg)
1 7500 10 0.5 1500
2 10,500 15 0.7 1000
3 5,670 12 0.4 1200
4 25,780 2.32 0.9 12,340
5 45888 8 0.6 9,560

22. Implications of catchability for biomass estimation
Example:
Fish species X is targetted in a
longline fishery. If CPUE varies
proportionately with Biomass, as
in graph, what is the value of q
for different CPUE and biomass values…
Rearranging the equation C=qEB to estimate q:
q=(C/E)/B
Using the graphed relationship, q is constant!
e.g. 1 Biomass = 10000 MT
Catch = 10 q = (10/1000)/10000 = 0.000001
Effort = 1000 hooks
e.g. 2 Biomass = 3000 MT
Catch = 3 q = (3/1000)/3000 = 0.000001
Effort = 1000 hooks
Biomass
CPUE(mt/1000hooks)
0 1000 2000 3000 4000 5000 6000 7000
0123456

23. Lets now consider a situation where
fishermen, after fishing for a long time
with the same method, develop a new
technology at time “a” and then another
technology at time “b”, and both of
these technologies result in higher
mean catch rates.
To simplify the example, lets say the fish
biomass has been held constant at
3000 MT for the period of interest. The
relationship above says that catch rates
would also be proportionally constant at
3 mt/1000 hooks.
However at time a, the mean catch rate
increases to 4 mt/1000 hooks due to
the new technology, and at time b it
increases to 5 mt/1000 hooks due to
the second technological advance.
The stock biomass has still not changed, yet
the index in increasing!
Biomass
Biomass(MT)
0 1 2 3 4 5 6 7
6000
5000
4000
3000
2000
1000
0
5
4
3
2
1
0
a
b
CPUE(mt/1000hooks)
Time (years)
Implications of catchability for biomass estimation

24. If we now calculate q based on the
new C/E-Biomass relationship:
e.g. 2 Biomass = 3000 MT
Catch = 4
Effort = 1000 hooks
q = (4/1000)/3000 = 0.0000013
e.g. 2 Biomass = 3000 MT
Catch = 5
Effort = 1000 hooks
q = (5/1000)/3000 = 0.0000017
Here, increasing q is indicating to us that the proportion of the stock removed by
each unit of fishing effort is increasing over time. Because q tracks
deviations from the proportional relationship between CPUE and Biomass it
allows us to account for such deviations to ensure that estimates of biomass
derived in part from CPUE series are not biased.
Biomass
Biomass(MT)
0 1 2 3 4 5 6 7
6000
5000
4000
3000
2000
1000
0
5
4
3
2
1
0
a
b
CPUE(mt/1000hooks)
Time (years)
q = C/EB
Implications of catchability for biomass estimation

25. To show how q does this, lets estimate biomass at times 1,2,3,5……
T1 - Biomass = ? MT
Catch = 3 B = (3/1000)/0.00000100 = 3000
Effort = 1000 hooks
q = 0.000001
T2 - Biomass = ? MT
Catch = 3 B = (3/1000)/0.00000100 = 3000
Effort = 1000 hooks
q = 0.000001
T3 - Biomass = ? MT
Catch = 4 B = (4/1000)/0.00000133 = 3000
Effort = 1000 hooks
q = 0.00000133
T5 - Biomass = ? MT
Catch = 5 B = (5/1000)/0.00000166 = 3000
Effort = 1000 hooks
q = 0.00000166
Because we know the value of q at each time step, we can still
accurately estimate biomass using our catch rate data, despite the
change in proportional relationship between CPUE and biomass!
Implications of catchability for biomass estimation

26. To emphasise the importance of understanding changes in q over time, lets
see what would happen if we assumed that q was constant……..
T3 - Biomass = ? MT
Catch = 4
Effort = 1000 hooks
q = 0.000001
B = (4/1000)/0.000001 = 4000
T5 - Biomass = ? MT
Catch = 5
Effort = 1000 hooks
q = 0.000001
B = (5/1000)/0.000001 = 5000
RESULT: We would be overestimating
biomass well above what it actually is!
Biomass
Biomass(MT)
0 1 2 3 4 5 6 7
6000
5000
4000
3000
2000
1000
0
5
4
3
2
1
0
a
b
CPUE(fish/1000hooks)
Time (years)
Implications of catchability for biomass estimation

27.  Raising Factor- is the factor by which the numbers in the
sample have to be multiplied to give the total numbers in
the population sampled.
 Raising Factor = No. of days in month
 No. of sampling days
 Raising factor is used for production estimates
 Production Estimates
 Estimated production per boat of the different gears per site
can be computed from the monthly total catch of each gear
per site divided by the total number of boat landings.
 The result will be multiplied by the raising factor to
determine the raised catch per boat per month.

28. Example:
Determine days in a month and samplings days(January – 31/7)
RF = 4.43, Feb (28/6), 4.67, March (31/5), 6.2, Apr (30/4) 7.5
January February March April
1 20 23 27 35
2 15 30 30
3 25 21
4 30 25 22 18
5 35 26 15 16
6 18 30
7 20 18 23
Total (kg) 163 143 117 99

29.  The raised catch per boat per month can be computed
by the formula:
 Raised catch = Total Catch x raising factor ;
 No. of boat landed
 If there are 3 boats then RC = (163/3) * 4.43= 240.7 kg for January
January February March April
1 20 23 27 35
2 15 30 30
3 25 21
4 30 25 22 18
5 35 26 15 16
6 18 30
7 20 18 23
Total (kg) 163 143 117 99
240.70

30.  The raised catch per boat per month can be computed by the
formula:
 Raised catch = Total Catch x raising factor ;
 No. of boat landed
 If there are 5 boats then RC = (143/5) * 4.67= 133.56 kg for February
January February March April
1 20 23 27 35
2 15 30 30
3 25 21
4 30 25 22 18
5 35 26 15 16
6 18 30
7 20 18 23
Total (kg) 163 143 117 99
240.70

31.  The length frequencies can be raised to the
corresponding raise in weight with the following
formula:
 Raised length = Frequency x raising factor;
 Raising factor = Total weight
 sampled weight