Ecosim & the foraging arenaEcosim & the foraging arena

IncoFish Workshop, WP4

September, 2006

IncoFish Workshop, WP4

September, 2006

Villy Christensen

EwE includes two dynamic modulesEwE includes two dynamic modules

Both build on the Ecopath model:

• Ecosim: time dynamics;

• Ecospace: spatial dynamics.

Both build on the Ecopath model:

• Ecosim: time dynamics;

• Ecospace: spatial dynamics.

Information for management from single-species to ecosystem approachesInformation for management from single-species to ecosystem approaches

AbundanceGrowthMortalityRecruitmentCatchesCatchability (dens-dep.)

AbundanceGrowthMortalityRecruitmentCatchesCatchability (dens-dep.)

MigrationDispersalMigrationDispersal

Feeding ratesDietsInteraction termsCarrying capacityHabitats

Feeding ratesDietsInteraction termsCarrying capacityHabitats

OccurrenceDistributionOccurrenceDistribution

CostsPricesValuesExistence values

CostsPricesValuesExistence values

BiologyBiology EcologyEcology BiodiversityBiodiversity

EconomicsEconomics

Y/R VPASurplus production….

Y/R VPASurplus production….

EcopathEcosimEcospace….

EcopathEcosimEcospace….

Single-species approaches

Single-species approaches

Ecosystem approachesEcosystem approaches

Social & cultural considerations

Social & cultural considerations

EmploymentConflict reduction...

EmploymentConflict reduction...

Tactical Strategic

• Includes biomass and size structure dynamics: mixed differential and difference equations;

• Variable speed splitting: dynamics of both ‘fast’ (phytoplankton) and ‘slow’ groups;

• Effects of micro-scale behaviors on macro-scale rates;

• Use mass-balance assumptions (Ecopath) for parameter initialization.

• Includes biomass and size structure dynamics: mixed differential and difference equations;

• Variable speed splitting: dynamics of both ‘fast’ (phytoplankton) and ‘slow’ groups;

• Effects of micro-scale behaviors on macro-scale rates;

• Use mass-balance assumptions (Ecopath) for parameter initialization.

Main elements of EcosimMain elements of Ecosim

Mass balance: cutting the pieMass balance: cutting the pie

Other mortalityOther mortality

HarvestHarvest

ConsumptionConsumption

PredationPredation

PredationPredation

PredationPredation

Predation

Other mortality

Other mortality

Other mortality

PredationPredation Respi- rationRespi- ration

HarvestHarvest

Unassi-milated food

Unassi-milated food

Respi- rationRespi- ration

Unassi-milated food

Unassi-milated food

Unassi-milated food

Unassi-milated food

Respi- rationRespi- ration

• Multi-stanza size/age structure by monthly cohorts, density- and risk-dependent growth;

• Keeps track of numbers, biomass, mean size accounting via delay-difference equations;

• Recruitment relationship as ‘emergent’ property of competition/predation interactions of juveniles.

• Multi-stanza size/age structure by monthly cohorts, density- and risk-dependent growth;

• Keeps track of numbers, biomass, mean size accounting via delay-difference equations;

• Recruitment relationship as ‘emergent’ property of competition/predation interactions of juveniles.

Size-structured dynamicsSize-structured dynamics

Single-species assessment model

Bt+1 = gtBt + Rt exp(vt)

gt = S[1-exp(qEt)][mt+]

== ++Stochastic variation in

juvenile survival

Constant

survival

Survival from

fishing

Body mass growth

Biomassnext year

Growth/survivalof biomass thisyear

Biomass ofnew recruits

Multi-species production model (Ecosim)

Bt+1 = gtBt + Rt exp(vt)

gt = S[1-exp(qEt)][mt+]

==== ++++

Deterministic variation due to

predation, feeding & growth

Survival from

predation

Survival from

fishing

Body mass growth from prey

consumption

Biomassnext year

Growth/survivalof biomass thisyear

Biomass ofnew recruits

• Gross food conversion efficiency, GE = Production / Consumption

• dB/dt = GE · Consumption - Predation - Fishery + Immigration - Emigration - Other Mort.

• Consumption = micro-scale rates

• Predation = micro-scale rates

• Gross food conversion efficiency, GE = Production / Consumption

• dB/dt = GE · Consumption - Predation - Fishery + Immigration - Emigration - Other Mort.

• Consumption = micro-scale rates

• Predation = micro-scale rates

Biomass dynamics in EcosimBiomass dynamics in Ecosim

The guts of Ecosim: Foraging arena The guts of Ecosim: Foraging arena

What happened& whatif?

Foraging arena is a ‘theoretical entity’Foraging arena is a ‘theoretical entity’

• May be impossible to

observe directly or

describe precisely;

• Useful as a logical

device for constructing

predictions and

interpreting data.

• May be impossible to

observe directly or

describe precisely;

• Useful as a logical

device for constructing

predictions and

interpreting data.

Organisms are not chemicals!Organisms are not chemicals!Ecological interactions are highly organizedEcological interactions are highly organized

Big effects from small changes in space/time scale

Reaction vat model Foraging arena model

Preyeaten

Prey density

Preyeaten

Prey density

Prey behaviorlimits ratePredator handling

limits rate

Functional response

Prey density

Pre

y at

tack

ed

I

II

III

Holling’s

Holling 1959Holling 1959

Buzz

Unavailable prey B-V

Unavailable prey B-V

Available prey, VAvailable prey, V

v’Vv’V

Predator, PPredator, P

Prey vulnerability: top-down/bottom up controlPrey vulnerability: top-down/bottom up control

v = predator-prey specific behavioral exchange rate (‘vulnerability’)Also includes: Environmental forcing, nutrient limitation, mediation, handling time, seasonality, life stage (age group) handling,

v = predator-prey specific behavioral exchange rate (‘vulnerability’)Also includes: Environmental forcing, nutrient limitation, mediation, handling time, seasonality, life stage (age group) handling,

aVPaVP

v(B-V)v(B-V)

A critical parameter: vulnerabilityA critical parameter: vulnerability

It’s all about carrying capacityIt’s all about carrying capacity

v = v = Max

Max

Baseline

Baseline

Predator abundancePredator abundance

Predicted predation mortality ‘T

radi

tiona

l’

‘Tra

ditio

nal’

EcosimEcosim

Predation mortality: effect of vulnerabilityPredation mortality: effect of vulnerability

Bottom-upBottom-upTop-DownTop-Down

High vHigh v Low vLow v

Carrying capacity

Carrying capacity

00 Ecopath baselineEcopath baseline

?? ??

Limited prey vulnerability causes compensatory (surplus) production

response in predator biomass dynamics

Limited prey vulnerability causes compensatory (surplus) production

response in predator biomass dynamics

Predator Q/Bresponse-- given fixedtotal prey abundance

Predator Q/Bresponse-- given fixedtotal prey abundance

Predator abundancePredator abundance

If predator biomass is halved

If predator biomass is halved

0.0

-0.5

0.5

1.0

If predator biomass is doubled

If predator biomass is doubled

CarryingCapacityCarryingCapacity

00

Foraging arena theory argues that the same fine-scale variation that drives

us crazy when we try to survey abundances in the field is also critical

to long term, large scale dynamics and stability

Foraging arena theory argues that the same fine-scale variation that drives

us crazy when we try to survey abundances in the field is also critical

to long term, large scale dynamics and stability

Fine-scale arena dynamics: food concentration seen by predators should be

highly sensitive to predator abundance

“Invulnerable”prey (B-V)

“Vulnerable”prey (V)

Predationrate:

aVP(mass actionencounters,within arena)

This structure implies “ratio-dependent” predation rates:

V=vB/(v+v’+aP)

(rate per predator decreases with increasing predator abundance P)

v

v’

Arena food concentration (V) should be highly sensitive to

density (P) of animals foraging

dV/dt = (mixing in)-(mixing out)-(consumption) = vI -v’V -aVP

Fast equilibration of concentration implies

V = vI / ( v’ + aP )

Fast equilibration of food concentration implies:

V = vI / ( v’ + aP )

Effect of Local Competition on Food Density

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15

Competitor Density (N)

Are

na

Fo

od

De

ns

ity

(C

)

Strong effects at low densities:

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000

Yearling Density (fish/ha)

Fin

al B

od

y W

eig

ht

(g)

Ungrazed, Lo Fry

Ungrazed, Hi Fry

Grazed, Lo Fry

Grazed, Hi Fry

Power (Series5)

Behavior implies Beverton-Holt recruitment model(1) Foraging arena effect of density on food available:

Food density

Juvenile fish density(2) implies linear effect on required activity and predation risk:

(3) which in turn implies the Beverton-Holt form:

Net recruitssurviving

Initial juvenile fish density

Activity, mortality

Juvenile fish density

Strong empiricalsupport

Emerging empiricalsupport (Werner)

Massive empiricalsupport

Beverton-Holt shape and recruitment “limits” far below trophic potential

(over 600+ examples now):

Predicting consumption: (Pg 87 in your manual)Predicting consumption: (Pg 87 in your manual)

Qij =Q

ij =

aij

• vij

• B

i • P

j • T

i • T

j • S

ij • M

ij / D

ja

ij • v

ij • B

i • P

j • T

i • T

j • S

ij • M

ij / D

j

vij

+ vij

• T

i • M

ij + a

ij • M

ij • P

j • S

ij • T

j / D

jv

ij + v

ij • T

i • M

ij + a

ij • M

ij • P

j • S

ij • T

j / D

j

Q = consumption; a = effective search rate; v = vulnerability; B = biomass;P = predator biomass or number; S = seasonality or long-term forcing; M = mediation; T = search time; D = f(handling time)

Q = consumption; a = effective search rate; v = vulnerability; B = biomass;P = predator biomass or number; S = seasonality or long-term forcing; M = mediation; T = search time; D = f(handling time)

Qij =Q

ij =

aij

• vij

• B

i • P

ja

ij • v

ij • B

i • P

j

vij

+ vij

+ aij • P

jv

ij + v

ij + a

ij • P

j

Basic consumption equation

Adding additional realism to the consumption equation

Deriving parameters for the consumption equation

• Given Ecopath estimates of Bi Pi and Qij, solve

Qij =Q

ij =

aij

• vij

• B

i • P

ja

ij • v

ij • B

i • P

j

vij

+ vij

+ aij • P

jv

ij + v

ij + a

ij • P

j

for aij conditional on vij

aij =a

ij =

-2Qijvij-2Qijvij

Pj(Qij-vijBi)Pj(Qij-vijBi)yields

Thus the parameters of interest are Bi, Pj, Qij, and vij

Ecosim parameters

• Vulnerability;• Density-dependent

catchability; • Switching?• Max rel. feeding time (FT)

(mainly used for marine mammals);– FT adjustment rate;

– Sensitivity of ‘other mortality’ to FT;

– Predator effect on FT;

• Qmax/Q0 (handling time)– If a good reason for it

For multi-stanza groups:

• Wmat / Wω;

• VBGF curvature par.;• Recruitment power par.;

Forcing functions:• Mediation, time forcing,

seasonal egg production,

Ecosim seeks to predict changes in mortality rates, Z

Ecosim seeks to predict changes in mortality rates, Z

• Zi = Fi + sum of Mij (predation components of M)

– where Mij is Qij/Bi (instantaneous risk of being eaten)

– Mij varies with

– Changes in abundance of type j predators

– Changes in relative feeding time by type i prey

• Zi = Fi + sum of Mij (predation components of M)

– where Mij is Qij/Bi (instantaneous risk of being eaten)

– Mij varies with

– Changes in abundance of type j predators

– Changes in relative feeding time by type i prey

Running Ecosim: ± Foraging arena

With mass-action (Lotka-Volterra) interactions only:

With foraging arena interactions:

Ecosim predicts ecosystem effects of changes in fishing effort

Ecosim predicts ecosystem effects of changes in fishing effort

Fishing effort over time

Biomass/original biomass

How can we ‘test’ complex ecosystem models?

How can we ‘test’ complex ecosystem models?

• No model fully represents natural dynamics, and hence every model will fail if we ask the right questions;

• A ‘good’ model is one that correctly orders a set of policy choices, i.e. makes correct predictions about the relative values of variables that matter to policy choice;

• No model can predict the response of every variable to every possible policy choice, unless that model is the system being managed (experimental management approach).

• No model fully represents natural dynamics, and hence every model will fail if we ask the right questions;

• A ‘good’ model is one that correctly orders a set of policy choices, i.e. makes correct predictions about the relative values of variables that matter to policy choice;

• No model can predict the response of every variable to every possible policy choice, unless that model is the system being managed (experimental management approach).

So how can we decide if a given model is likely to correctly order a set of specific policy choices?

So how can we decide if a given model is likely to correctly order a set of specific policy choices?

• Can it reproduce the way the system has responded to similar choices/changes in the past (temporal challenges)?

• Can it reproduce spatial patterns over locations where there have been differences similar to those that policies will cause (spatial challenges)?

• Does it make credible extrapolations to entirely novel circumstances, (e.g., cultivation/depensation effects)?

• Can it reproduce the way the system has responded to similar choices/changes in the past (temporal challenges)?

• Can it reproduce spatial patterns over locations where there have been differences similar to those that policies will cause (spatial challenges)?

• Does it make credible extrapolations to entirely novel circumstances, (e.g., cultivation/depensation effects)?

Ecosim can use time series dataEcosim can use time series data

Fishing effort over time

Biomass/original biomass

1978 19831973 1988 1993

Time series dataTime series data

• Fishing mortality rates

• Fleet effort

• Biomass, catches, Z (forced)

• Time forcing data (e.g., prim. prod., SST, PDO)

• Fishing mortality rates

• Fleet effort

• Biomass, catches, Z (forced)

• Time forcing data (e.g., prim. prod., SST, PDO)

• Biomass (relative, absolute)

• Total mortality rates

• Catches

• Average weights

• Diets

• Biomass (relative, absolute)

• Total mortality rates

• Catches

• Average weights

• Diets

Drivers:Drivers: Validation:Validation:

Yes, lots of Monte CarloYes, lots of Monte Carlo

Time series fitting: Strait of Georgia

• Possible to replicate development over time (tune to biomass data);

• Requires more data – but mainly data we should have at hand in any case: ‘the ecosystem history’;

• Be careful when comparing model output (EM) to model output (SS)

• Supplements single species assessment, does not replace it;

• Possible to replicate development over time (tune to biomass data);

• Requires more data – but mainly data we should have at hand in any case: ‘the ecosystem history’;

• Be careful when comparing model output (EM) to model output (SS)

• Supplements single species assessment, does not replace it;

Experience with Ecosim so far:

• When we have a modelthat can replicate development over time we can (with some confidence) use it for ecosystem-based policy exploration.

• When we have a modelthat can replicate development over time we can (with some confidence) use it for ecosystem-based policy exploration.

Formal estimation

Ecosystem model (predation,

competition, mediation,

age structured)

Ecosystem model (predation,

competition, mediation,

age structured)

ClimateClimate NutrientloadingNutrientloading

FishingFishing

Predicted C, B, Z, W, dietsPredicted C,

B, Z, W, diets

ObservedC,B,Z,W, diets

ObservedC,B,Z,W, diets

Log Likelihood

Log Likelihood

(BCC/B0)(BCC/B0)

(Diet0)(Diet0)

(Z0)(Z0)

Habitat area

Habitat area

Errorpattern

recognition

Errorpattern

recognition

Choice of parametersto include in final

estimation (e.g., climate anomalies)

Choice of parametersto include in final

estimation (e.g., climate anomalies)

Judgmental evaluationJudgmental evaluation

Modeling process: fitting & drivers

Search Search

How many variables can one estimate?How many variables can one estimate?

• A few per time series (not a dozen)– the fewer the better

• Try estimating one vulnerability for each of the more important groups – use sensitivity analysis to choose groups

• Estimate system-level productivity – by year or spline as judged appropriate

• Or, better, use environmental driver

• A few per time series (not a dozen)– the fewer the better

• Try estimating one vulnerability for each of the more important groups – use sensitivity analysis to choose groups

• Estimate system-level productivity – by year or spline as judged appropriate

• Or, better, use environmental driver

EndModels are not like religion– you can have more than one– and you shouldn’t believe them

When you get a good fit to time series data:Discard and do it againDiscard and do it again…Find out what is robust

Interdependence of system components & harvesting of forage fishes

Norway pout in the North Sea, 1981

Feeding triangles: North SeaFeeding triangles: North Sea

Other fish

KrillKrill

Norwaypout

Norwaypout

CopepodsCopepods

4

1

505

17

100

11

2

Feeding triangles: North SeaFeeding triangles: North Sea

Other fish

Other fish

KrillKrill

Norwaypout

Norwaypout

CopepodsCopepods

44

11

505

17

100

11

22

Feeding triangles: North SeaFeeding triangles: North Sea

Other fish

Other fish

KrillKrill

Norwaypout

Norwaypout

CopepodsCopepods

44

11

505055

1717

100100

1111

22