ecosim & the foraging arena incofish workshop, wp4 september, 2006 incofish workshop, wp4...
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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
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