dynamic programming part ii

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.