Cohort models

1
Cohort models

• VPA
• Gullands method
• Popes method
• Catch-at-age
• Multispecies, ecosystem models

2
Cohort models

• relies on tracing the declining abundance of a
  cohort as it ages and passes through the fishery
• In simplest form, estimates abundance of an age
  group over a series of years and calculates
  survival from mortality
• If we assume that mortality is constant across
  ages and through time the age structure from one
  year can be used across years

3
Cohort models

• Now used to estimate F, abundance and recruitment
• Originated with Derzhavin (1922) with this work
  on sturgeon
• Cohort size when entry to fishery can be
  approximated by summing catches of that cohort
  the years it is in fishery
• The sum of the catches is the population that
  must have been alive to generate those catches
  (virtual population)

4
Virtual Population Analysis

• Uses the numbers of fish caught during fishing
  operations to estimate historic F and stock
  numbers in a cohort
• Called cohort analysis because each cohort is
  analyzed separately
• Simple relationship

5
Virtual Population Analysis

• No recruitment since a single cohort
• If we knew initial cohort size and M, we could
  calculate N each year
• But we dont, so VPA tells us

6
Virtual Population Analysis

• Fry (1949) applied Derzhavins model and called
  the minimum population estimate the virtual
  population, but
• assumed no M
• Ricker, Beverton Holt, and Paloheimo
  incorporated M, and estimated F as a function of
  effort (fe) and catchability (q)
• Fqfe

7
Virtual Population Analysis

• Gulland (1965) started with an F for oldest age
  group and worked backwards to link successive age
  classes
• there are essentially no fish older than the
  oldest ever caught
• use this (knowing M) to iteratively calculate the
  number alive each year starting from the oldest

8
Virtual Population Analysis
9
Virtual Population Analysis

• Starting value of F is called terminal F
• Subsequent tests showed backwards technique was
  superior

10
Virtual Population Analysis

• Survivors in year t-1 M catch survivors in
  previous year

7.9
11
Virtual Population Analysis

• How to estimate M? ZMqfe

9.25
12
Virtual Population Analysismethodology

• Start with exponential decay equation

(7.7)
13
Virtual Population Analysismethodology

• Start with exponential decay equation
• and the catch equation (derived in Box 7.2)

(7.7)
(7.8)
14
Virtual Population Analysismethodology

• Step 1 calculate the terminal abundance by
  re-arranging 7.8 to give Nt

(7.9)
15
Virtual Population Analysismethodology

• Step 1 calculate the terminal abundance by
  re-arranging 7.8 to give Nt
• Step 2 substitute 7.7 into 7.8 to obtain Ft-1

(7.9)
(7.11)
16
Virtual Population Analysismethodology

• Step 3 calculate Nt-1 by inserting Ft-1 from
  step 2 into equation 7.7

(7.12)
17
Virtual Population Analysismethodology

• Step 3 calculate Nt-1 by inserting Ft-1 from
  step 2 into equation 7.7
• Repeat steps 2 and 3 to work backwards through
  time

(7.12)
18
Virtual Population Analysisexample

• Age 3, C3 80, Fterminal 0.6
• Step 1, calculate N3

(7.9)
19
Virtual Population Analysisexample

• Age 2, C2 90, N3194
• Step 2, calculate F2

(7.11)
20
Virtual Population Analysisexample

• Age 2, N3 194, F20.349
• Step 3, calculate N2

(7.12)
21
Virtual Population Analysis Popes method

• Non-linear cohort analysis is cumbersome
• Pope (1972) proposed a step function that
  approximates the non-linear form
• Principal assumption is all fish caught exactly
  half-way through time period
• Catch occurs instantaneously
• Using this method, first calculate N, then F

22
Virtual Population Analysis Popes method

• Number of fish alive just before fishing number
  alive a start -reduction due to half M

7.13
23
Virtual Population Analysis Popes method

• Number of fish alive just before fishing number
  alive a start -reduction due to half M
• Start fishing instantaneously

7.13
7.14
24
Virtual Population Analysis Popes method

• Remaining fish suffer M leaving number of fish
  alive at the end of year

7.15
25
Virtual Population Analysis Popes method

• Remaining fish suffer M leaving number of fish
  alive at the end of year
• Re-arrange to solve for Nt

7.15
7.16
26
Virtual Population Analysis Popes
methodexample (Box 7.4)

• Step 1 identical to VPA. Find N3 from catch
  equation (7.9)

27
Virtual Population Analysis Popes
methodexample (Box 7.4)

• Step 1 identical to VPA. Find N3 from catch
  equation (7.9)
• Step 2 substitute N3 into 7.16 as Nt1

28
Virtual Population Analysis Popes
methodexample

• Step 3 solve for F2 from re-arranged exponential
  decay equation (7.7)

29
Virtual Population Analysis Popes
methodexample

• Popes method gives identical result to VPA
• Method gets around iterative calculation for F
• Can also be length-based when species cannot be
  aged
• Animals are separated into length classes rather
  than age-classes
• See section 7.5.2 and Box 7.5

30
Virtual Population Analysis Popes
methodexample
31
Virtual Population Analysisassumptions

• No fish alive at some age
• Cohorts must have all passed thru fishery
• M is known, constant, and not very large
• Oldest cohorts?
• Best when M lt F and F/Z0.5-1
• Terminal F
• source of bias and model sensitivity, tuning
• No error in catch/age data
• Oldest cohorts? bycatch, discards
• No net immigration or emigration

32
Virtual Population Analysisconsequences of
assumptions

• Using discrete approximation of survival model
  (Pope)
• If F is evenly distributed thru year, N will be
  overestimated
• M is known, constant, and not very large
• If M used is lower, N will be underestimated
• If M used is higher, overestimation
• M is likely to vary by age and year
• Terminal F is known
• If F is underestimated, N will be overestimated
• If F is overestimated, N will be underestimated

33
Virtual Population Analysisconsequences of
assumptions

• No error in catch/age data
• If harvest are under-reported, N will be
  underestimated
• Aging errors will introduce further errors in the
  size of the cohorts (especially in oldest
  cohorts)
• No net immigration or emigration
• If immigrants are harvested cohort size will be
  inflated
• Handling mortality and bycatch will lead to
  underestimation

34
Virtual Population Analysisconclusions

• Uses commercial catch data to calculate stock
  sizes and mortality rate of age-based or
  length-based cohorts
• VPA does not by itself indicate how many
  individuals can be caught to meet a given
  objective,
• nor does it predict the future
• It explains the past, and if we know the
  historical age structure of a population we can
  see the consequences of changes in mortality
  rates using YPR methods

35
Virtual Population Analysis alternativesCatch-a
t-age

• Also known as stock synthesis or integrated
  analysis
• Another type of age-structured stock assessment
  method
• Develop a basic pop dyn model then relate
  predictions to observed data
• Statistical methodology used to find best set of
  model parameters that will fit observations

36
Virtual Population Analysis alternativesCatch-a
t-age

• Catch-at-age data are analyzed one cohort at a
  time, i.e.
• parameter estimates for one cohort are
  independent of estimates for others
• Age-specific and year-specific F (separable)
• Complex computationally (non-linear regression)
• Extremely flexible approach
• Overcomes problem with VPAs that require tuning
  to calculate precise abund estimates

37
Multispecies assessment(Chapter 8)

• Individual species do not live in a vacuum
• Biological interactions
• Predator-prey
• competition
• Technical interactions
• Fishing mortality on more than one stock by a
  single fishery
• However most management approaches are
  single-species based

38
Multispecies assessment

• Surplus production
• Generally consider only technical interactions
• Thus ignoring biological interactions

39
8.1
40
Multispecies assessment

• Surplus production
• Temporal multispecies production model
• Similar to single-species SP model
• Used most often in tropical fisheries many
  species

41

• Based on data from 13 deep-water spp
• Actual yield 96t
• Assumes fish pop at equil
• But total biomass of unfished pop may not be
  higher than fished due to pred-prey

MSY106 t, 901fd
8.2
42
Multispecies assessment

• Surplus production
• Spatial multispecies production model
• Use many sites rather than time series
• Treats replicate sites as replicate fisheries

43

• Based on data from 10 sites
• Snappers, groupers, grunts
• Assumes fish pop at equil
• Heterogeneity in gear used and species caught
• f has incr with time in Jamaica
• Really only comparing 2 sites

weakly exploited Belizian sites
Heavily exploited Jamaican sites
MSY1t/km2, 3600h/km2/y
8.3
44
Multispecies assessment

• MS YPR
• Similar to single-spp YPR,
• Except yields are summed among spp
• F is calculated for each spp in fishery
• Effects of varying F are then modeled to estimate
  catchability of each species if gear is changed
• To forecast equilibrium yields species-specific
  recruitment must be calculated
• No biological interactions

45

• 4 species provide 85 of yields on Georges Bank
• Cod, haddock, y-tail flounder, w flounder
• Spp rarely eat each other, low competition

overfished
underfished
46
Multispecies assessment

• MSVPA
• Extension of single-spp VPA
• M is split into 2 components
• M2 predation
• M1 other sources

47
8.5
48
Multispecies assessment

• MSVPA
• Extension of single-spp VPA
• M is split into 2 components
• Detailed infor on food habits
• e.g. functional responses

49
8.6
50
Multispecies assessment

• MSVPA
• Prey switching at low prey densities in type III
  FR may lead to overestimation of predation on
  rate spp
• Assumes total intake is constant from year to
  year
• Summed M2 and M1 across all predators used for
  backward calculation

51

• In North Sea MSVPA 10 main spp used
• Total biomass of each spp calculated

8.7
52

• F vs M2 for cod

8.8
53
Age lt1
Age gt1
8.9
54
Summary of MSVPA for Atlantic cod in N Sea,
1974-95
8.10
8.9
55
Summary of MSVPA for Atlantic cod in N Sea,
1974-95
Summary of MSVPA for Atlantic cod in N Sea,
1974-95
8.9
56
Summary of MSVPA for Atlantic cod in N Sea,
1974-95
Summary of MSVPA for Atlantic cod in N Sea,
1974-95
1/2 of human consumption
1/2 of predator consumption
8.9
57
How general are N Sea results?
8.11
58
Multispecies VPA

• MSVPA future?
• Use continues to grow
• Very data hungry
• Only considers impacts on prey (no pred growth)
• No multispp SR relationships
• Can improve estimates of M

59
Multispecies VPA
8.12
60
Predator-prey dynamics and exploitation
8.13
61
Competition and exploitation
8.14
62
Management implications
Mesh size
8.15
63
Ecosystem models

• Using ecosystem biology to understand links
  between exploitation and ecosystem components
• Ecopath
• Describes ecosystems by balancing flows between
  trophic groups

64
8.19
65
Ecosystem models

• Using ecosystem biology to understand links
  between exploitation and ecosystem components
• Ecopath
• Describes ecosystems by balancing flows between
  trophic groups
• Ecosim
• Dynamic simulation model which uses Ecopath
  results to predict ecosystem effects of fisheries

66
8.20
67
Ecosystem models

• Using ecosystem biology to understand links
  between exploitation and ecosystem components
• Ecopath
• Describes ecosystems by balancing flows between
  trophic groups
• Ecosim
• Dynamic simulation model which uses Ecopath
  results to predict ecosystem effects of fisheries
• Ecospace
• Incorporates spatial dynamics

68
What needs to be done to improve implementation
of ecosystem considerations into fisheries
management?

• Clearly define fishery goals in an ecosystem
  context
• Ecosystem metrics and indicators must be
  developed
• More appropriate theory, models and methods need
  to be developed and applied
• Monitoring should be maintained and expanded
• Formalize plans for fisheries in the context of
  ecosystems