Transcript Natural mortality and fishing mortality estimation

Stock Assessment Workshop
19th June -25th June 2008
SPC Headquarters
Noumea
New Caledonia
Day 3 Session 1
Parameter Estimation – Natural Mortality
and Fishing Mortality
Overview
• What is mortality?
• What is natural mortality?
• How and why does it vary with age and size?
• Why do we estimate it in stock assessments
• How is M estimated (outside assessment models)
• How is M used and estimated inside assessment models
• What is fishing mortality and why is it important to assessment
models?
• How and why does it vary with size and age?
• How is F estimated outside and inside models, and in
MULTIFAN-CL
• How can F estimates be used to provide information to
fishery managers
• Summary
Our model
Bt+1=Bt+R+G-M-C
Death
(Natural mortality - M)
Recruitment
(+)
Whole population
(-)
(-)
Growth
(+)
Movement
Catch
(Fishing mortality - F)
= Z (Total
Mortality)
Introduction – Age/size structured models
RECRUITMENT BIOMASS
1 year olds
+
(+) Growth
(-) Natural mortality
Whole population
(-) Fishing mortality
2 year olds
(+) Growth
(-) Natural mortality
(-) Fishing mortality
3 year olds
(+) Growth
(-) Natural mortality
(-) Fishing mortality
What is mortality (Z)?
• Simply, the process of mortality (death) of fish
Total mortality = fishing mortality + natural mortality
Z= F+M
• Think of it as the removal of fish from a population from
all causes
• Reduces the number of fish in subsequent age classes
• F and M are generally treated separately in stock
assessment models, as the implications for management
of high F or high M can be very different
•F can be managed
•M generally cant be controlled.
How are mortality estimates incorporated
into age based models?
Bt+1=Bt+R+G-M-C
Age/size-specific growth
Age/size-specific natural mortality
Age/size-specific maturity
Age/size-specific movement
Age/size-specific habitat
Age/size-specific fishing mortality
Age/size-specific selectivity
Ba+1,t+1 = Ba,t + Ra,t + Ga,t - Ma,t - Ca,t
Bt =  Bt,axwa
Natural Mortality
What is natural mortality (M)?
• The process of mortality (death) of fish due to
natural causes;
• predation
• disease
• senescence
• Starvation
• other
•
Would occur with or without fishing
How and why does M vary with age and size?
BET
• M tends to decrease with age
[Fish ‘out-grow’ predators]
• May increase again in older fish
[‘Stress’ associated with reproduction, old
age?]
SKJ
YFT
How and why does M vary with age and size?
• Natural mortality varies throughout the life-cycle of a species
•Lower condition factor and reduced capacity to survive periods
without food
• Size/age – fish may “out-grow” predators (e.g. range of
predators of larval v juvenile v adult marlin, plus cannabalism factor)
• Senescence processes
• Reproductive stresses
• Movement away from areas of high mortality
• Behavioural changes (e.g. formation of schools)
• Changes in ecosystem status (e.g. prey availability, habitat
availability)
• Changes in abundance (e.g. density-dependence influences, like
cannibalism, prey limitations, older fish outcompeting younger fish)
Why do we estimate M in stock
assessment models?
• Natural mortality rates are critical in understanding
stock dynamics of fishery species
Bt+1=Bt+R+G-M-C
• Allows an understanding of the relative impacts of
fishing (e.g. compare natural v fishing mortality rates)
Zt=Mt+Ft
• Permits an understanding of the “robustness” of a
stock to fishing
• Allows an understanding of the impacts of fishing of
a stock (overall and by age/size class)
Why do we estimate M in stock
assessment models?
M has direct and indirect impacts on populations
and fisheries which are important to be able to
understand and account for within models
Direct
• M will affect the number of fish surviving to a
given size/age that become available to a fishery
• Thus M may influence the abundance of fish
available to fisheries
Why do we estimate M in stock
assessment models?
Indirect impacts
• Need to ensure that an adequate number/proportion
of each size class survive through to the next age
class (and ultimately to contribute to reproduction of a
stock)
• If M is very high then F may need to be relatively
low (as you cannot control M)
• M may limit/restrict total fishing mortality rate (F) of
an age/size-class or stock if M is extremely high
• This could potentially mean that fishing on a certain
component of the stock may be restricted
How is M estimated?
• One of the more difficult parameters to estimate
• Confounded with the effects of recruitment and
fishing mortality
• Measuring the ‘disappearance’ of fish that
can’t be attributed to other sources - fishing
mortality, movements
• Often, total mortality (Z) and fishing mortality
(F) are estimated first;
Z = F + M,
M=Z–F
then
How is M estimated (outside the assessment
models)?
1. Maximum age (Hoenig)
• There is a relationship between the maximum age of
a species and total mortality
• The higher the estimated maximum age, the lower
the mortality must be
• ln(Z) = 1.44 - 0.984 ln tmax
2. Length- based (Beverton and Holt)
• Extends the relationship between growth rate (K)
and size, incorporating the mean size and smallest
size of captured fish
Z = K* [(Linf- Lmean)/(Lmean - Lsmallest in catch)]
How is M estimated (outside the assessment
models)?
3. Application of the relationship between M and K
• Ratio of M:K has been tested and shown to be between
1.5 and 1.6, (with a standard error of 0.58)
• [A result of biological ‘trade-offs’ between growth and
mortality, due to the influences on reproduction and
survival].
• Therefore, if you have an estimate of K (from growth),
then you also have a starting point for M
• e.g. K = 0.4, M = 0.6
• [Can incorporate variations between M and K by using the
SE to define a prior distribution]
How is M estimated (outside the assessment
models)?
4. Length frequency analyses (catch-curves for Z)
• develop length/age-frequency plots
• look for declines in frequency of older age/size classes
• Estimate regression parameters for the decline in
frequency in older age classes
•
-1 * slope= mortality rate
• in the absence of fishing this would equate to natural
mortality [rare for the WCPO tuna species]
• in the presence of fishing this would equate to total
mortality (Z)
How is M estimated (outside the assessment
models)?
5. Otolith based studies
• Calculations to similar to length-frequency estimates
of M except that age classes are used.
• Labour intense in order to generate enough
ageing data
• Usually rely on a (much) smaller sample size
than length-frequency analyses.
• Used widely on non-fishery species
How is M estimated (outside the assessment
models)?
6. Tagging studies
• Known number of returns of tagged fish (from fishers)
• [Estimated return rate from fishers can be included]
• Reduction in the number of returns through time
• Estimate slope of regression: Z if fished; M if unfished
More tagged fish = higher number of returns = better
estimates of mortality
(and other parameters – movement, biomass, growth)
How is M estimated (outside the assessment
models)?
• Many estimates of mortality on fished stocks result in
estimates of total mortality (Z)
• i.e. Fishing mortality (F) + Natural mortality (M)
Z = M+ F
• Need to split into estimates of M and F
• Splitting can be done if contrasting effort levels are
available
• Plot Z estimates (from length-based) against effort
• Estimate slope
• Intercept on y-axis gives and estimate of M
How is M used in stock assessments?
• Simply, to remove fish from a stock due to natural
sources of mortality
• Allows for the “removal” of fish in the model not
related to fishing
Nt+1= Nt+ (Rt+ Gt) – (Zt+ Et);
Zt=Mt+Ft
‘Removes’ an age/size specific proportion of fish from
each age/size class at each time step in age/size
structured models (i.e. incorporated into a rate)
Provides for more realistic population dynamics
• M can be fixed or size/age dependant
How is M incorporated into assessments?
1. Estimates of M (e.g. from previous studies) can be
used and fixed for all age classes
• An estimate of M is fixed in the model for all age-classes
• At each time step, M-proportion of fish from each ageclass are “removed” from further calculations
• This allows the model to incorporate total mortality for
each age-class at each time-step
• [Can also test the sensitivity of the analyses to M by
changing the value of M]
How is M incorporated into assessments?
2. Age/size specific estimates of M-at-age can
be used for each age-class
• Mortality estimates for some ages/stages of fish for
a species may be available
• These are also applied at each time step to the
appropriate age-classes of fish, to remove fish from
the model
• Biomass estimates and other outputs incorporate
age-specific M
Age-specific estimates of M from MFCL
BET
(SC-s SAWP-2)
YFT
(SC-1 SAWP-1)
SKJ
(SC-1 SAWP-4)
How is M incorporated into assessments?
3. M can be estimated by MFCL
• Still require a starting value (seed-value) and range
(prior distribution) [usually from previous studies]
• Seed values are usually available from published
literature and/or from previous assessments;
constrain possible values by limiting range (priors)
• MFCL can calculate average overall M
• Age-specific deviations from average M can also be
calculated by MFCL, allowing identification of ageclasses that may be more or less susceptible to
fishing
Fishing Mortality
What is Fishing mortality (F)?
• The process of mortality (death) of fish due to fishing;
• Catch
• Discard mortalities
• Think of it as the removal of fish from a population
due to fishing activities only
Why is F important to stock assessment
models?
• Fishing mortality (or catch) is the entire reason you are
here today! It is the primary reason that we undertake
stock assessments!
•We wish to understand the past, present and future
probable impacts of fishing upon the fish stocks that we
exploit.
• With age structured models we go one step further,
identifying which components (age classes) within the
stock are the most impacted.
• In situations where the resource is being
overexploited, we can simulate different management
options to help the stock to recover, by simulating
different fishing mortality rates by different gears on
different age classes within the stock.
How and why does fishing mortality vary
with age and size?
• Fishing mortality often varies by size or age class for one main
reason….fishing gears tend to be size selective, that is, more likely to catch
fish of a certain size and less likely to catch fish of other sizes
•For example, small bigeye tuna tend to be caught by purse seine sets on
floating objects, but large (adult) bigeye tuna are much less frequently
caught. In contrast, adult bigeye are caught on longline, but very small
juvenile bigeye are not often caught …**More on Selectivity this afternoon!
YFT (SC-1 SAWP-1)
Proportion at Age
BET (SC-1 SAWP-2)
F at Age
Proportion at Age
F at Age
How is F estimated outside and inside
the models?
• Estimating F is different to estimating M as you
have the data  CATCH
• Observer data, port sampling data (size data)
• Can estimate the proportion of fish in each
size/ age class in the catch (selectivity,
catchability) and then the impact on each size
class
How is F estimated?
• So where does F fit in stock assessment models?
• Schaefer model:
dB/dt = rB(1-B/k)-C
…….or as a differential equation…..
Bt+1 = Bt + rB(1-Bt/k)-Ct
• Fishing mortality rate is the proportion of the
population killed by fishing each time step
(e.g. year, quarter)
How is F estimated?
1.Schaefer model:
dB/dt = rB(1-B/k)-C
There is an assumption that catch rate C is proportional to
biomass and to fishing effort;
C=qEB
Catch rate* = Catchability x Effort x Biomass
(*per unit time)
How is F estimated?
Firstly, lets consider what are the main factors that will effect
catch?
What happens to catch if we increase the number of hooks (effort)?(E)
What happens to catch if biomass (B) decreases?
What happens to catch if the fish swim deeper? Catchability (q) decreases.
How is F estimated?
What happens to catch if we increase the depth of our hooks to target the
deep swimming fish?
How is F estimated?
We can rearrange this equation to show that CPUE is
proportional to biomass (abundance)
C/E = qB
And Catchability is the proportion of the stock caught by
one unit fishing effort (e.g. one set, 100 hooks etc)….
q = C/EB
And fishing mortality rate is the proportion of the
population removed by fishing over time, (e.g. a year’ a
quarter)
F = C/B
How is F estimated?
Then using the previous equations, fishing mortality rate will be
the product of catchability and fishing effort
F = qE = C/B
Therefore, we can also state a relationship between catch and
fishing mortality rate:
C = FB
In age-structured models we calculate F at age, and this
requires an additional parameter, Selectivity:
Fa = qEsa
How is F estimated?
Fishing mortality rate can be estimated within a
model or outside of it
[Can be confounded with the effects of (and variations in)
recruitment and natural mortality]
Outside of model
1. Tagging studies
2. Effort based series (remember back to natural
mortality?]:
•
Plot Z estimates (from length-based data) against effort
•
Estimate slope
•
Intercept on y-axis gives an estimate of M. Difference is F
F estimation in age structured models
In age/length structured models, F is critical for the estimation of C
(catch).
Number of fish
(Number of fish
Survival
in age class a in =
x rate)
of age a now
one years time
Nt+1,a+1 = Nt,a(1-m) – Ct,a
Biomass being the
sum of products of
age specific numbers
and mean weights
Ct,a = Nt,aftva
Bt = ∑aNt,awa
Nt+1,1 = (aEt)/(b+Et)
Catch of fish
age a now
Catch at age being the product
of numbers, fishing mortality
and age specific vulnerability to
gear
Recruitment as estimated
by the Beverton and Holt
SRR
F is critical to estimation of catch, which is required in
predicting biomass in the future.
Fishing mortality and age distributions
• Estimating age specific mortality also yields key
information for managers, e.g. ;
• which parts of the stock are being fished hardest
• in the identification of growth and recruitment
overfishing
YFT
(SC-1 SAWP-1)
BET
(SC-1 SAWP-2)
F in MULTIFAN-CL
“Catch by age, time period, and fishery is determined by
fishing mortality at age, time period and fishery applied to
estimated abundance by age and region....”
i.e. C = F x B for each age, time period and fishery
Fishing mortality is a product of;
1. Fishery and time specific effort
2. A fishery specific catchability that can vary with time
3. A fishery and age specific selectivity that does not
vary with time.
[Problem: In many fisheries, discarding is not well recorded and recorded retained
catch is considered to equate to F]
F adults; F juveniles
F – BET SC-2 2006
Initial F is high for older age classes,
due to the predominance of the
longline fishery. However the purse
seine fishery on floating objects, and
particularly drifting FADs since 1995,
has led to high F on juvenile age
classes also (Note: age classes are
quarters)
10 15 20 25
0
1960
1970
1980
1990
2000
1960
1970
1980
1990
2000
Region 4
40
20
40
0
20
0
1960
1970
1980
1990
2000
1950
10 20 30 40 50
1950
Region 5
1960
1970
1980
1990
2000
1980
1990
2000
Region 6
0
0
10
30
50
1950
60
Region 3
60
80
1950
1950
1960
1970
1980
1990
2000
20
1950
1960
1950
1960
1970
PH/ID
PS assoc
PS unassoc
LL
40
60
WCPO
0
Impact %
Region 2
5
Region 1
0
10 20 30 40 50 60
F – BET SC-2 2006
1970
1980
1990
2000
Impacts of
fishing on
total biomass
x gear
F – BET SC-2 2006
Comparing (current) F to
F required to achieve
maximum sustainable
yield (MSY)
Calculating unfished biomass
• MFCL models can be used to estimate biomass
that would have occurred in the absence of
fishing
• i.e. fishing mortality (effort) can be ‘turned-off’
• i.e. Z = M + 0  Z = M
• Allows the assessment of biomass trajectories in
the absence of fishing
• Can be used to estimate the reduction in
biomass as a result of fishing
 Impacts of fishing
F – BET SC-2 2006
- Z (F + M)
- M only
Impacts of fishing
Summary – Natural Mortality (M)
• M is a critical variable in describing population
dynamics
• Likely to vary with size/age of fish
• M can be estimated using a variety of techniques.
• Critical in producing ‘realistic’ models
• Difficult to estimate (confounded with F, R)
• As a result, the impacts of different rates of M are
often examined in sensitivity analyses
Summary – Natural Mortality (M)
• Age-structured models (like MFCL) can incorporate M in a
variety of ways
• Fixed estimate of M
• Age-specific estimates of M
• Can also estimate M
• Incorporated in reference points, relative impacts of fishing,
relative impacts of fishing methods etc
• Solid biological data is required to provide at least seed
estimates
• Tagging studies are most likely to produce better estimates
of Z, F and M (and other parameters)
Summary – Fishing Mortality (F)
1. Is the whole reason you are here!
2. F can be estimated within stock assessments and by other
methods (e.g. tagging, effort series analyses etc)
3. In age structured stock assessment models, F is
calculated for each time, age and fishery as a function of
selectivity, catchability, and fishing effort
4. F estimation is critical in the calculation and interpretation
of biological reference points - Fcurrent /Fmsy.
5. Estimating F-at-age is also important in the identification
and type of overfishing (e.g. growth or recruitment
overfishing).
6. F can be “switched off” within a model to estimate the
impacts of fishing