Surplus Production models

1
Surplus Production models

• Surplus production vs Dynamic pool vs Cohort
  models
• Logistic growth
• MSY
• Catch-effort
• How to fit, examples
• Alternatives
• Chapter 7 in text

2
Fishery (single-species) models

• Examine impact of fishing and other non-natural
  sources of mortality on the growth, mortality,
  and reproductive potential of fish populations

3
Surplus production models

• View population as one unit of biomass subject to
  constant growth and mortality rates

4
Surplus production models

• View population as one unit of biomass subject to
  constant growth and mortality rates
• Basic theory of sustainable exploitation

5
Surplus production models

• View population as one unit of biomass subject to
  constant growth and mortality rates
• Basic theory of sustainable exploitation and
  capture the basic logic of density-dependence

6
Surplus production models

• View population as one unit of biomass subject to
  constant growth and mortality rates
• Basic theory of sustainable exploitation and
  capture the basic logic of density-dependence
• Production models, stock production models,
  surplus yield models, biomass dynamic models

7
Surplus production models

• View population as one unit of biomass subject to
  constant growth and mortality rates
• Basic theory of sustainable exploitation and
  capture the basic logic of density-dependence
• Peaked in popularity during the 1950s-1970s

8
Dynamic pool models

• recognize that growth, mortality, and
  reproductive potential may vary by age

9
Dynamic pool models

• recognize that growth, mortality, and
  reproductive potential may vary by age
• still used today to examine reproduction and
  recruitment potential.

10
Cohort models

• trace the decline in abundance of groups of fish
  of similar age (cohorts) as they age through the
  population,

11
Cohort models

• trace the decline in abundance of groups of fish
  of similar age (cohorts) as they age through the
  population, and use this decline to determine
  mortality rates

12
Cohort models

• trace the decline in abundance of groups of fish
  of similar age (cohorts) as they age through the
  population, and use this decline to determine
  mortality rates
• their popularity has grown since the early 1970s.

13
Surplus production models

• rely on the principle that fish populations, on
  the average, produce more offspring than
  necessary to replenish the populations abundance
  of spawning adults

14
Surplus production models

• rely on the principle that fish populations, on
  the average, produce more offspring than
  necessary to replenish the populations abundance
  of spawning adults
• On the average, fisheries may be able to crop
  this excessive (or surplus) production without
  endangering the population.

15
Surplus production models

• On the average, fisheries may be able to crop
  this excessive (or surplus) production without
  endangering the population
• ideally, the population could be fished at a
  level that maximizes the harvest biomass every
  year

16
Surplus production models

• On the average, fisheries may be able to crop
  this excessive (or surplus) production without
  endangering the population
• ideally, the population could be fished at a
  level that maximizes the harvest biomass every
  year
• Termed maximum sustainable yield (MSY)

17
Surplus production models

• Population biomass depends on growth,
  reproduction, natural and fishing mortality

Fig 7.1
18
Surplus production models

• Density dependence allows population to sustain
  fishery mortality

Fig 7.2
19
Surplus production models

• Logistic growth

Fig 7.3a
20

• Growth is max at intermediate levels

Fig 7.3b
21

• Growth is max at intermediate levels

22
early

• Growth is max at intermediate levels

middle
late
23

• Growth is max at intermediate levels

24

• MSY at Fmsy

Fig 7.3c
25

• MSY at Bmax/2

26

• If catch and effort are proportional to biomass,
  then MSY can be derived on a catch vs effort plot

27

• Fmsy is Fopt

28
SY vs Catch-effort curves

• logistic equation (rate of change of biomass)
• dB/dt r B 1-B/B8

29
SY vs Catch-effort curves

• logistic equation (rate of change of biomass)
• dB/dt r B 1-B/B8
• catch rate, catch or yield (Y) per year is
  deducted
• dB/dt r B 1-B/B8-Y

30
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• catch rate, catch or yield (Y) per year is
  deducted
• dB/dt r B 1-B/B8-Y
• At equilibrium, removals growth, (dB/dt0)
• Y r B 1-B/B8 (1)

31
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• catch rate, catch or yield (Y) per year is
  deducted
• dB/dt r B 1-B/B8-Y
• At equilibrium, removals growth, (dB/dt0)
• Y r B 1-B/B8 (1)
• Parabola describing yield vs biomass

32
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• At equilibrium, removals growth, (dB/dt0)
• Y r B 1-B/B8 (1)
• Yield catchabilityeffort biomass, (YqfB),
  and sinceY/fCPUE, CPUEqB
• BCPUE/q (2)

33
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• Yield catchabilityeffort biomass, (YqfB),
  and sinceY/fCPUE, CPUEqB
• BCPUE/q (2)
• Substituting 2 in 1
• Yf(CPUE)r(CPUE/q) 1-(CPUE/q)/(CPUE8/q)
• where CPUE8 is CPUE at max biomass (B8) of the
  stock

34
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• BCPUE/q (2)
• Yf(CPUE)r(CPUE/q) 1-(CPUE/q)/(CPUE8/q)
• Dividing by CPUE
• fr/q 1-CPUE/CPUE8

35
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• BCPUE/q (2)
• Yf(CPUE)r(CPUE/q) 1-CPUE/q)/CPUE8/q)
• Dividing by CPUE
• fr/q 1-CPUE/CPUE8
• CPUECPUE8-CPUE8q/r f

36
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• BCPUE/q (2)
• Yf(CPUE)r(CPUE/q) 1-CPUE/q)/CPUE8/q)
• fr/q 1-CPUE/CPUE8
• CPUECPUE8-CPUE8q/r f
• Which is a straight line, CPUE a bf

37
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• BCPUE/q (2)
• Yf(CPUE)r(CPUE/q) 1-CPUE/q)/CPUE8/q)
• fr/q 1-CPUE/CPUE8
• CPUECPUE8-CPUE8q/r f
• Which is a straight line, CPUE a bf
• slope, b -CPUE8q/r
• intercept, a CPUE8

38
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• BCPUE/q (2)
• Yf(CPUE)r(CPUE/q) 1-CPUE/q)/CPUE8/q)
• fr/q 1-CPUE/CPUE8
• CPUECPUE8-CPUE8q/r
• CPUE a bf
• Multiplying by effort and since Yf(CPUE)
• Yaf bf2

39
SY vs Catch-effort curves

• dB/dt r B 1-B/B8
• dB/dt r B 1-B/B8-Y
• Y r B 1-B/B8 (1)
• BCPUE/q (2)
• Yf(CPUE)r(CPUE/q) 1-CPUE/q)/CPUE8/q)
• fr/q 1-CPUE/CPUE8
• CPUECPUE8-CPUE8q/r f
• Yaf bf2 (3)
• Schaefers model where yield is related to
  fishing effort

40
Catch-effort curvesan example sea bass (Lates
calcalifer) data
hmnd 100 m of net used per day
41
Catch-effort curvesan example sea bass (Lates
calcalifer) data
slope, b -0.0002047
Y-int 25.6
Effort (hmnd)
42
Catch-effort curvesan example sea bass data
43
Catch-effort curvesan example sea bass data
44
Catch-effort curvesMSY and fmsy

• How to solve for MSY and fmsy?
• Take the derivative of Yield equation and equal
  to zero (i.e. when is slope 0?)
• a 2bfmsy 0
• fmsy -a / (2b) (4)
• Substitute (4) into the Schaefer equation (3)
• MSY -a(a/2b) b (a/2b)2 -a2/(4b)

45
Catch-effort curvesMSY and fmsy

• Applying these to the bass example
• fmsy -a /(2b) 62,530 hmnd
• MSY -a2/(4b) 800,390 kg
• A SY of approximately 800t may be taken by 62,500
  hmnd or by 42 fishers using 1500m of gill net,
  and fishing for an average of 100d/yr

46
Catch-effort curvesMSY and fmsy
MSY
fmsy
47
Schaefer curveseffects of reducing effort

• Fishing effort increased dramatically between
  1972-1979 (see table)-using these data

MSY994
79
fmsy69,129
48
Schaefer curveseffects of reducing effort

• In 1980 fishing effort was reduced yield after
  1980 remained low and approached the original
  yield curve from below a new equilibrium?

49
Schaefer curvesregulating a fishery

• 2 general methods
• Fixed quota setting a limit, Q, on the number of
  fish harvested per season regardless of the
  number in the population

Q1
Q2
Q1
50
Schaefer curvesregulating a fishery

• 2 general methods
• Fixed effort limiting effort (e.g. number of
  permits, length of season, spatial restrictions,
  etc)

High effort
Low effort
51
Schaefer curvesregulating a fishery

• 2 general methods
• Fixed effort 5 different efforts in 5 different
  years and resulting catches

Yield
Effort 3
Effort 1
52
Schaefer curvesregulating a fishery

• 2 general methods
• Fixed effort those same catches plotted against
  effort

Effort
53
Catch-effort curvesstability of Schaefer model
7.4a
54
Catch-effort curvesstability of Schaefer model

• Populations should never be exploited at MSY
  using constant catch rates, why?
• Any reduction in Bmsy will crash the population,
• i.e. the MSY equilibrium is not stable
• However, the MSY equilibrium is stable when
  constant proportions of biomass (i.e. fixed
  effort) are caught,
• But only if the effort curve crosses the yield
  curve

55
Catch-effort curvesstability of Schaefer model
7.4b
56
Catch-effort curvesalternatives to Schaefer

• Fox curve (7.3) is more appropriate for biomass
  measurements (logistic usually with numbers)

57
Catch-effort curvesalternatives to Schaefer

• Fox curve (7.3) is more appropriate for biomass
  measurements (logistic usually with numbers)
• MSY to the left of logistic level

58
Catch-effort curvesFox curve example
59
Catch-effort curvesalternatives to Schaefer

• Pella-Tomlinson model (7.4) allows for
  flexibility in shape of production curve

60
Catch-effort curvesalternatives to Schaefer

• Pella-Tomlinson model (7.4) allows for
  flexibility in shape of production curve
• MSY to the left or right logistic level (m)

61
Surplus production approachassumptions

• instantaneous reaction of stock
• symmetric parabola
• need large range of efforts (high and low)
• stock is self-contained
• any loss is mortality
• no interspecific interactions
• the environment is constant
• fishing is density-independent

62
Surplus production approachadvantages

• calculate MSY and Fopt without catchability
• uses only catch and effort data
• do not need ages
• cheap

63
Surplus production approachdisadvantages

• not incorporate ecosystem environmental factors
• exclusion of trophic linkages
• assumes stock has stabilized at current rate of
  fishing

64
Surplus production approachfitting models to
data

• index of abundance related to true abundance

65
Surplus production approachfitting models to
data

• Equilibrium methods
• Assumes stock has stabilized at current rate of
  fishing

66
Surplus production approachfitting models to
data

• Equilibrium methods
• Assumes stock has stabilized at current rate of
  fishing
• Non-equilibrium methods
• Process-error methods
• No equilibrium assumption

67
Surplus production approachfitting models to
data

• Equilibrium methods
• Assumes stock has stabilized at current rate of
  fishing
• Non-equilibrium methods
• Process-error methods
• No equilibrium assumption
• All error in population growth relationship

68
Surplus production approachfitting models to
data

• Equilibrium methods
• Assumes stock has stabilized at current rate of
  fishing
• Non-equilibrium methods
• Process-error methods
• No equilibrium assumption
• All error in population growth relationship
• Catch and effort data measured without error

69
Surplus production approachfitting models to
data

• Equilibrium methods
• Assumes stock has stabilized at current rate of
  fishing
• Non-equilibrium methods
• Process-error methods
• No equilibrium assumption
• All error in population growth relationship
• Catch and effort data measured without error
• Observation-error methods
• All error in catch and effort data

70
Surplus production approachequilibrium models
the Peruvian anchovy
Fig 7.6
GRT gross registered tonnage
71
Surplus production approachcomparing fitting
techniques
data
equilibrium
process error
observation error
7.7
72
Surplus production approachlessons

• Fisheries are rarely at equilibrium
• Stability is the exception
• CPUE is problematic
• Best way to find Fopt is to overfish
• Pooling ages isnt always advisable

73
Surplus production approachdelay-difference
models

• Deriso/Schnute
• Lag between spawning and recruitment
• Only 2 age groups
• Include natural mortality, body growth, and
  recruitment
• Derivation in box 7.1
• Can produce good fits but show sensitivity to
  parameter uncertainty and large errors

74
Surplus production approachdelay-difference
models
yellowtail flounder
7.8