2. Overview of fish population model dynamics
What is fish stock assessment
Stock assessment process
Assumptions
Approach
Holistic models
Yield or yield per recruit model
VPA(Cohort analysis)
Length Cohort Analysis
Time series analysis
Ecological modeling
Simulation modeling
Worked examples of models
Marine Fish Stock AssessmentMarine Fish Stock Assessment
Models & AnalysisModels & Analysis
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Stock assessmentStock assessment
What is stock assessment ?
– Quantitative evaluation of status of the exploited
stock
– Functional relationship of stock size or yield with the
factors that affect the dynamics of the stock
Stock assessment and management
– Evaluation of the fishery under different management
regimes
– Development of management reference points
– Socio-economic objectives
8. Summary of models & methods commonly used
Holistic or macro or surplus production models
This approach involves methods of estimation of the past
and current level of biomass and the state of the stock,
from the analysis of the relationship between effort and
catch. It is based on a biomass growth equation, the
relationship F=q·E and the catch equation C=F· B, where
F is the fishing mortality, E is the fishing effort and q the
coefficient of catchability
Holistic or macro models do not consider events within
the population and ignore growth and mortality of
individuals and the effect of mesh size on age of fish
capture
These models consider mainly the four basic quantities
namely, population biomass (B), the catch (Y), fishing
effort (f) and net natural rate of increase
9. Summary of models & methods commonly used
Holistic or macro or surplus production models
The Schaefer & Fox models are the popular models of this
approach
These models are also termed as surplus production models
There are a number of equilibrium & dynamic (non-
equilibrium) models
The data required are the historical series of catch-effort data
(usually on an annual basis) of one species
The three parameters of the production model are obtained:
Carrying capacity (equivalent to Virgin Biomass), catchability
and growth rate. These three parameters allow drawing the
equilibrium curve in the catch-effort plane. If the observed path
of the fishery is also drawn on the same graph, a very general
and useful view of the fishery’s history is obtained MSY and
EMSY
10. Summary of models & methods commonly usedSummary of models & methods commonly used
Holistic or macro or surplus production models (contd)
The output gives a very general view of the current state of the
fishery and its history. Easy to relate to management reference points
Inapplicable to multi-species fisheries, mainly due to the difficulties
of effort allocation
Not suitable when there are clear changes in catchability (although
this parameter can also be modeled) or changes in selectivity
Bayesian approaches in surplus production models can also be used
that enable risk assessment & uncertainity and facilitates participatory
approach
The only control parameter is the effort
11. Summary of models & methods commonly used
Yield or Yield per Recruit Model
Computes the yield that produces one recruit given particular exploitation
pattern (F vector) at different intensities of effort
Fishing mortality vector (F), natural mortality vector (M), Age-length key or
parameters of the growth model form the essential inputs
Equilibrium surface of yield as function of overall F (or effort) and
exploitation pattern (selectivity), Y/Rmax, Ymax, Fmax, biomass per recruit
are outputs
All these results are relative (it means “by recruit”) or absolute if recruitment
is known
The output is very synthetic and gives a general overview of the state of the
fishery. Easy to relate to reference points (maxima, current stock vs. virgin
stock, etc.). With this method it is easy to detect growth overfishing and get
the clues of management alternatives.
Assumes steady state
12. Summary of models & methods commonly used
VPA (Virtual Population Analysis).
Cohort Analysis
From catch-at-age data and some parameters, VPA reconstructs the past
history of stock in terms of number of individuals and fishing mortalities.
The VPA and its variants is the most standard and reliable method of stock
assessment
Catch-at-age of several years by operational unit (this implies previous age
estimations and length composition of catches), M vector, Terminal Fs (this
implies tuning, through surveys or CPUEs) and length-weight relationship (if
biomasses are wanted in the output) are the inputs required
Numbers of individuals and biomass at sea by year and age (thus series of
recruitment, total biomass at sea etc.), Fishing mortality by year, age and
operational unit are the outputs
The most efficient standard assessment method requiring many parameters,
some of them assumed (M) and tuning of fishing effort
Summary of models & methods commonly usedSummary of models & methods commonly used
13. Summary of models & methods commonly used
LCA (Length Cohort Analysis)
A modification of VPA, essentially is a VPA on a pseudo-
cohort that can be run also on the length frequency distribution
of the catch.
Steady state is assumed
A length or age frequency distribution of the catch representing
the pseudocohort, M vector, terminal Fs (this implies tuning,
through surveys or CPUEs), length-weight relationship (if
biomasses are wanted in the output), total catch in biomass by
operational unit are the inputs
Numbers of individuals and biomass at sea by age or length
(recruitment, total biomass at sea etc.), fishing mortality by age
or length and operational unit
With short data series (even one year) something can be said
about the state of the stock. Since the steady state is assumed
(pseudo-cohort), important biases can be estimated if this
hypothesis is far from reality.
14. Summary of models & methods commonly used
Time series analysis
The standard ARIMA method is the analysis of a time series (usually
monthly structured) which is split off into trend (including cycles),
seasonality and noise. Some further developments, as transfer functions,
allow to associate these outputs with environmental or other external
variables, or intervention analysis to detect anomalous events
Time series of data, usually catch, CPUE, effort, data on vessel
characteristics, environmental etc
Most frequently the trend and seasonality of the variable analysed are
obtained. When additional information (i.e. environmental) is added, it is
possible to relate the behaviour of the dependent variable to other variables,
such as effects of environment and also enables short term forecasting
Absence of underlying biological hypotheses has both pros and cons. It is a
powerful method to reveal hidden structures in the data. Useful for short term
forecasting, with due caution in its interpretation
15. Summary of models & methods commonly used
Ecological modeling
Multispecies modeling
Some approaches are extensions of the indirect assessment methods taking into
account the biological interaction between species (technical, or technological
interaction can be studied by the classical methods)
Multispecies VPA or MSVPA belong to this group
Ecological modeling based on mass balance and food webs approach –
ECOPATH & ECOSIM
In addition to the single species analysis data needs, it requires the interaction
factors, particularly the quantification of the predator-prey relationships, diet
composition data etc
Quantified pathways of matter and energy between the different species (in
steady state) and other parameters such as predation, technological and
biological interactions and indicators of health of fisheries ecosystem
It approaches much better the real ecological system than the single species does
Huge amount of biological information is required and so also the generated
outputs
The number of interaction parameters to be estimated grows with the square of
species considered
16. Summary of models & methods commonly used
Simulation modeling
Indirect (population dynamics) methods that reproduce in the computer aided
dynamics of a stock and a fishery
Often with the aim to test the effects of different environmental situations or
alternative management actions
All population dynamics parameters and stock-recruitment relationship
Projection to the future of different variables (biomass, catch) and trends at
short and medium term
In the case of stochastic models confidence intervals are provided
Several management scenarios are created and depicted
Very useful to analyse and compare the possible results of alternative
management measures at short and medium term
Uncertainties in the projection, particularly because of the stock-recruitment
relationship are also quantified
Useful to understand complex natural systems
17. INPUT
Effort Catch(t) c/f
623 50 0.0803
628 49 0.0780
520 47.5 0.0913
513 45 0.0877
661 51 0.0772
919 56 0.0609
1158 66 0.0570
1970 58 0.0294
1327 52 0.0392
Holistic or surplus production models
Schaefer model
c/f = a + b*f
a= 0.1065 ; b=-0.00004312; R2
= 92.1%
MSY = -0.25*a2
/b = 65.8 tonnes
fMSY = -0.5*a/b = 1235 units
Fox model
Ln(c/f) =c + d *f
c= 0.1065 ; d=-0.00004312; R2
= 92.1%
MSY = -(1/d)*e(c-1)
= 60.9 tonnes
fMSY = -(1/d) = 1274 units
18. Beverton & Holt yield per recruit model
INPUT
L∞ 28.4cm
W∞ 286gm
K 0.37
M 1.1
Lc 10.2
Lr 2.03
tc 1
tr 0
tzero -0.2
a 0.0125
b 3
a & b denote length-
weight relationship
parameters
Y/R = F*exp(-M*(tc-tr))*W∞*[1/Z – 3S/(Z+K)+ 3S2
/(Z+2K) – S3
/(Z+3K)]
Where S= exp[-K*(tc-tzero)]
Yield per recruit model
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
F
Y/R
Biomass per recruit curve
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0 0.5 1 1.5 2 2.5
F
B/R
19. Length Cohort Analysis(LCA)
INPUT
Length frequency data (preferably, averaged over a period of time. Say,
over 3 to 5 years)
Estimates of VBGF Growth in length parameters L∞ and K.
Instantaneous rate of natural mortality M
Estimates of parameters a and b of the l-w relationship w = a. Lb
Formulation
Let
C(L1,L2) be the numbers caught between lengths L1 and L2
N(L1) be the numbers in sea that attain length L1
N(L2) be the numbers in sea that attain length L2
H(L1,L2) = [(L∞ - L1)/(L∞ - L2) ] (M/2K)
20. Length Cohort analysis(LCA)
Formulae used in the analysis
N(L1) = [N(L2)*H(L1,L2) + C(L1,L2)]*H(L1,L2)
C(L1,L2) = N(L1) *(F/Z)* [ 1 – exp(-z* Δt) ]
Where Δt = (1/K) * ln [(L∞ - L1)/(L∞ - L2) ]
Calculations
Start with the last length group
Compute H for each length group H(L1,L2) = [(L∞ - L1)/(L∞ - L2) ] (M/2K)
Compute average weight for each length group as w(L1,L2)= a*[(L1+L2)/2]b
Assume a value F/Z for the last length group ( how to choose terminal F/Z ?)
Compute the numbers in sea for the last length group by dividing the catch in numbers by the terminal
F/Z
Compute, recursively, N(L1) for each length group
Compute F(L1,L2)/(Z(L1,L2) = C(L1,L2)/(N(L1) – N(L2))
Compute F(L1,L2) = M*(F(L1,L2)(/Z(L1,L2)) / (1 – (F(L1,L2)/Z(L1,L2)))
Compute Z(L1,L2) = F(L1,L2)+M
Compute average annual numbers in the sea = [N(L1) – N(L2)]/Z(L1,l2)= avg.N(L1,L2)
Catch(yield) in weight = C(L1,L2)*w(L1,L2)
Mean biomass = avg.N(L1,L2)*w(L1,L2)
Caution:: Approximation valid only when F* Δt is upto 1.2 and M* Δt upto 0.3
Output from LCA
Total mortality in each length group
Fishing mortality in each length group
Numbers in sea at the beginning of length group
Mean numbers in sea in each length group
Mean biomass(in weight) of each length group
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Stock assessment involves understanding and making predictions
about the response of fishery systems to alternative management
actions.
Must help managers make choices about dynamic fishery systems
in the face of uncertainity
The output of a stock assessment should not be recommended
quotas or fishing effort – it should be biological consequences of
different actions.
The people doing stock assessment are not likely to be the right
people to weigh the risks of alternative management actions.
……. Ray Hilborn & Carl Walters
…………… thus spake wise