dynamic programming part ii
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Dynamic programming part II. Life history evolution in cod From individual states to populations. Evolution emerges. Trade-offs emerge. A population is a collection of individuals and their actions. Patterns emerge. Bioenergetics. Physical forcing. Individual state. - PowerPoint PPT PresentationTRANSCRIPT
Dynamic programming part II
- Life history evolution in cod- From individual states to populations
Physical Physical forcingforcing
Individual Individual statestate
Trade-offs emerge
A population is A population is a collection of a collection of individuals and individuals and
their actionstheir actions
Patterns emergeEvolutionemerges
BioenergeticsBioenergetics
Northeast Arctic codNortheast Arctic cod
Marshall CT, Yaragina NA, Ådlandsvik B, Marshall CT, Yaragina NA, Ådlandsvik B, and Dolgov AV. 2000. Reconstructing and Dolgov AV. 2000. Reconstructing the stock-recruit relationship for the stock-recruit relationship for Northeast Arctic cod using a Northeast Arctic cod using a bioenergetic index of reproductive bioenergetic index of reproductive potential. potential. Can. J. Fish. Aquat. Sci.Can. J. Fish. Aquat. Sci., , 5757: : 2433-2442.2433-2442.
Why is state dependence Why is state dependence important?important?
An example: An example: Recruitment in fishRecruitment in fish..
SomethingSomething
RecruitmentRecruitment
??
What is ’something’ that we can What is ’something’ that we can measure?measure?
Biomass?Biomass?
RecruitmentRecruitment
Mature biomass?Mature biomass?Spawning stock biomass?Spawning stock biomass?
But, what about But, what about juvenile and juvenile and
immature stages?immature stages?But, what about But, what about mature fish that mature fish that do not spawn?do not spawn?
Recruitment in Icelandic codRecruitment in Icelandic cod
Marteinsdottir G and Thorarinsson K. 1998. Improving the stock-Marteinsdottir G and Thorarinsson K. 1998. Improving the stock-recruitment relationship in Icelandic cod (recruitment relationship in Icelandic cod (Gadus morhuaGadus morhua) by including age ) by including age diversity of spawners. diversity of spawners. Can. J. Fish. Aquat. Sci.Can. J. Fish. Aquat. Sci., , 5555: 1372-1377.: 1372-1377.
What is ’something’ that we can What is ’something’ that we can measure?measure?
RecruitmentRecruitment
Spawning stock biomass?Spawning stock biomass?SSB and age?SSB and age?
Condition and recruitmentCondition and recruitmentR
ecru
itm
ent
to a
ge
3
Marshall CT, Yaragina NA, Ådlandsvik B, and Dolgov AV. 2000. Marshall CT, Yaragina NA, Ådlandsvik B, and Dolgov AV. 2000. Reconstructing the stock-recruit relationship for Northeast Arctic cod using Reconstructing the stock-recruit relationship for Northeast Arctic cod using a bioenergetic index of reproductive potential. a bioenergetic index of reproductive potential. Can. J. Fish. Aquat. Sci.Can. J. Fish. Aquat. Sci., , 5757: : 2433-2442.2433-2442.
What is ’something’ that we can What is ’something’ that we can measure?measure?
RecruitmentRecruitment
SSB and condition?SSB and condition?SSB and age?SSB and age?
Population structurePopulation structure
• Describing a population by more Describing a population by more than abundance or biomass:than abundance or biomass:– Length.Length.– Age and length.Age and length.– Age and length and condition.Age and length and condition.
A state-dependent dynamic programming model.A state-dependent dynamic programming model.
Patterns in a structured population.Patterns in a structured population.
Food Food intakeintake
Stored energy
OffspringOffspringOffspringOffspring
GrowthGrowth
A model for energy allocationA model for energy allocation
Bioenergetic description of energy allocation.Bioenergetic description of energy allocation.
State-dependent life history optimized using reproductive value.State-dependent life history optimized using reproductive value.
External factors
Mortality Food intake Migration costs
States
Age Body length Stored energy
Model presented in: Jørgensen C and Fiksen Ø. In press. State-dependent energy allocation in cod (Gadus morhua). Can J Fish Aquat Sci.
Energy utilization in the Energy utilization in the modelmodel
Food Food ingestedingested monthly (variable) monthly (variable)
–– Routine Routine metabolismmetabolism
== Energy for Energy for allocationallocation
[Spawning season]:[Spawning season]:
Total Total storedstored energy energy
– – Energy required for Energy required for migrationmigration (both (both ways)ways)
== Energy available for Energy available for egg productionegg production
StoreStore
GrowthGrowth
State dynamicsState dynamics
Energy infood E
EG
ES
G ·
S ·
3 31 / Gtt ELL
Stt ESS 1
Growth:Growth:
Energy stores:Energy stores:
At spawning:At spawning: tt SFec
FecSa+1,LVPSa,LV tttSt 111 ,max),(
(1-)
StochasticityStochasticity
Stores
Growth
Len
gth
(cm
)
0
20
40
60
80
100
120
Wei
gh
t (k
g)
0
5
10
15
20
25
30
Age (years)
5 10 15 20
Fec
un
dit
y
0
10
20
2
Allo
cati
on
Model presented in: Jørgensen C and Fiksen Ø. In press. State-dependent energy allocation in cod (Gadus morhua). Can J Fish Aquat Sci.
Predicted growth in the Predicted growth in the modelmodel
0
20
40
60
80
100
120
140
0 5 10 15Age (years)
Length
(cm
)
Barents SeaLofotenModel
Life history Life history evolution:evolution:
EffectsEffects of fisheries of fisheries
Spawner fisherySpawner fisherySpawner fisherySpawner fisherySpawner fisherySpawner fishery
Northeast Arctic codNortheast Arctic cod
Feeder fisheryFeeder fisheryFeeder fisheryFeeder fisheryFeeder fisheryFeeder fishery
More than 1000 yearsMore than 1000 years
Since ~1920Since ~1920
Mortality in
Mortality in feederfeeder fishery
fishery(year(year -1-1)) Mortality in
Mortality in spawner
spawner fishery
fishery
(year(year-1-1 ))
Mea
n M
ean
age
age
at m
atur
atio
n (y
ear)
at m
atur
atio
n (y
ear)
Historic fishing
Present trawling
Skipped spawningSkipped spawning
Stores
Growth
Len
gth
(cm
)
0
20
40
60
80
100
120
Wei
gh
t (k
g)
0
5
10
15
20
25
30
Age (years)
5 10 15 20
Fec
un
dit
y
0
10
20
2
Allo
cati
on
Model presented in: Jørgensen C and Fiksen Ø. In press. State-dependent energy allocation in cod (Gadus morhua). Can J Fish Aquat Sci.
Effects of mortalityEffects of mortality
• In general:In general:– Increasing Increasing mortalitymortality decreases the value of decreases the value of
future reproductions.future reproductions.– Current reproduction becomes more important.Current reproduction becomes more important.– Skipped spawning becomes Skipped spawning becomes less frequentless frequent..
10
20
30
40
50
0.00.5
1.01.50.0
0.51.0
1.5
Sk
ipp
ed
sp
aw
nin
g(%
of
rep
ea
t s
pa
wn
ers
)
Spawner fisheries
mortality
(year-1 )
Feeder fisheries mortality (year -1)
Skipped spawning:Skipped spawning:
Ecological Ecological relationshipsrelationships
Mean condition of mature population in January
0.8 0.9 1.0 1.1 1.2 1.3
Pro
po
rtio
n s
kip
pin
g s
pa
wn
ing
0.0
0.2
0.4
0.6
0.8
1.0
The effect of conditionThe effect of condition
SpawningSpawning
Not spawningNot spawning
Interaction: condition and Interaction: condition and lengthlength
Length (cm)
60 80 100 120 140
En
erg
y s
tore
d (
% o
f m
ax
)
0
20
40
60
80
100
60 65 70 75 80 85 90 95Mean length of spawning females (cm)
0.8
1
1.2
1.4
Me
an r
ela
tiv
e c
on
dit
ion
of
sp
awn
ing
fem
ales
(K
n)
North-east Arctic cod
Richard Nash, Institute of Marine Research, unpublished data.
Relationship with food Relationship with food availabilityavailability
Food availability last two years relative to mean0.4 0.6 0.8 1.0 1.2 1.4 1.6
Po
pu
lati
on
fe
cu
nd
ity
rela
tive
to
me
an
0.0
1.0
2.0
3.0
4.0
5.0
20
40
60
0.60.8
1.01.2
1.4
0.1
0.2
0.3
0.4
Skipped %Repeat NatMort FoodIntake
Natural morta
lity
Natural morta
lity
(year(year-1-1 ))
Relative food intake
Relative food intake
Ski
pp
ed s
paw
nin
gS
kipp
ed
sp
aw
nin
g
(% o
f re
peat
spaw
ners
)(%
of
rep
eat
spaw
ners
)
Skipped spawning: Skipped spawning:
Relationships with Relationships with ageage
0
20
40
60
80
100
0 5 10 15 20
Age (years)
Pote
nti
al re
peat
spaw
ners
th
at
skip
spaw
nin
g (
%)
Skipped spawning and ageSkipped spawning and age
Present growthPresent growth
Continued fishingContinued fishing
Historic growthHistoric growth
Harvest:Skipped spawning more common
Evolution:Skipped spawning less common
Histology in Barents Sea Histology in Barents Sea codcod
Oganesyan, S. A. (1993). Periodicity of the Barents Sea cod reproduction. ICES CM 1993/G:64.
0
20
40
60
80
100
50 60 70 80 90Length (cm)
Skip
per
s (%
)
Barents SeaBear Island bank
0
20
40
60
80
100
0 5 10 15 20
Years since maturation (years)
Pote
nti
al re
peat
spaw
ners
th
at
skip
spaw
nin
g (
%)
Young mature cod skip Young mature cod skip moremore
Present growthPresent growth
Continued fishingContinued fishing
Historic growthHistoric growth
HAVFORSKINGSINSTITUTTETINSTITUTE OF MARINE RESEARCH
Evidence of skipping
Num
ber
of fi
sh
0
10000
20000
30000
40000
50000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Post-maturation years = observed spawning zones
2nd-time spawners strongly underrepresented
1st-time spawners
2nd-time spawners
‘5th-time spawners’
Spawning area
Slide and data courtesy of Georg Engelhard and Mikko Heino.
How to predict recrutiment?How to predict recrutiment?
SomethingSomething
RecruitmentRecruitment
Individual state and Individual state and fecundityfecundity
Fec
un
dit
y (m
illi
on
eg
gs)
Fec
un
dit
y (m
illi
on
eg
gs)
Fec
un
dit
y (m
illi
on
eg
gs)
Fec
un
dit
y (m
illi
on
eg
gs)
Population measures and Population measures and fecundityfecundity
Including Energy StoresIncluding Energy Stores
RemovingRemovingSkippedSkipped
SpawnersSpawners
Liver energy and fecundityLiver energy and fecundity
To
tal
egg
pro
du
ctio
n
Fec
un
dit
y (m
illi
on
eg
gs)
IndividualIndividual PopulationPopulation
Physical Physical forcingforcing
Individual Individual statestate
Trade-offs emerge
A population is A population is a collection of a collection of individuals and individuals and
their actionstheir actions
Patterns emergeEvolutionemerges
BioenergeticsBioenergetics
AcknowledgementsAcknowledgements
• Collaborators and co-authors: Collaborators and co-authors: Øyvind Fiksen (supervisor)Øyvind Fiksen (supervisor)Bruno ErnandeBruno ErnandeUlf DieckmannUlf DieckmannMikko HeinoMikko HeinoRichard NashRichard Nash
• Thanks to the Research Council of Thanks to the Research Council of Norway for financial support.Norway for financial support.