Ecosim

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Ecosim the foraging arena

• IncoFish Workshop, WP4
• September, 2006

Villy Christensen
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EwE includes two dynamic modules

• Both build on the Ecopath model
• Ecosim time dynamics
• Ecospace spatial dynamics.

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Information for management from single-species
to ecosystem approaches
Biology
Ecology
Biodiversity
Abundance Growth Mortality Recruitment Catches Cat
chability (dens-dep.)
Migration Dispersal
Feeding rates Diets Interaction terms Carrying
capacity Habitats
Occurrence Distribution
Economics
Costs Prices Values Existence values
Single-species approaches
Social cultural considerations
Ecosystem approaches
Employment Conflict reduction ...
Ecopath Ecosim Ecospace .
Y/R VPA Surplus production .
Tactical
Strategic
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Main elements of Ecosim

• 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.

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Mass balance cutting the pie
Other mortality
Harvest
Unassi- milated food
Predation
Harvest
Respi- ration
Respi- ration
Predation
Predation
Unassi- milated food
Other mortality
Consumption
Other mortality
Unassi- milated food
Predation
Predation
Respi- ration
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Size-structured dynamics

• 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.

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Single-species assessment model
Biomass next year
Stochastic variation in juvenile survival
Growth/survival of biomass this year
Biomass of new recruits


Bt1 gtBt Rt exp(vt)
Constant survival
Survival from fishing
Body mass growth
gt S1-exp(qEt)a/mtr
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Multi-species production model (Ecosim)
Deterministic variation due to predation, feeding
growth
Biomass next year
Growth/survival of biomass this year
Biomass of new recruits


Bt1 gtBt Rt exp(vt)
Survival from predation
Survival from fishing
Body mass growth from prey consumption
gt S1-exp(qEt)a/mtr
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Biomass dynamics in Ecosim

• 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

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The guts of Ecosim Foraging arena
What happened what if?
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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.

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Organisms are not chemicals!
Ecological interactions are highly organized
Reaction vat model
Foraging arena model
Prey behavior limits rate
Predator handling limits rate
Big effects from small changes in space/time scale
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Functional response
I
II
Prey attacked
III
Hollings
Buzz
Prey density
Holling 1959
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Prey vulnerability top-down/bottom up control
Predator, P
aVP
Available prey, V
v(B-V)
vV
Unavailable prey B-V
v predator-prey specific behavioral exchange
rate (vulnerability) Also includes
Environmental forcing, nutrient limitation,
mediation, handling time, seasonality, life stage
(age group) handling,
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A critical parameter vulnerability
Its all about carrying capacity
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Predation mortality effect of vulnerability
Predicted predation mortality
Traditional
Ecosim
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Carrying capacity
Predator abundance
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Limited prey vulnerability causes compensatory
(surplus) production response in predator biomass
dynamics
1.0
If predator biomass is halved
Predator Q/B response -- given fixed total prey
abundance
0.5
0.0
If predator biomass is doubled
-0.5
CarryingCapacity
0
Predator abundance
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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
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Fine-scale arena dynamics food concentration
seen by predators should be highly sensitive to
predator abundance
Predation rate
v
Invulnerable prey (B-V)
Vulnerable prey (V)
aVP
(mass actionencounters,within arena)
v
This structure implies ratio-dependent
predation rates VvB/(vvaP) (rate per
predator decreases with increasing predator
abundance P)
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Arena food concentration (V) should be highly
sensitive to density (P) of animals foraging
dV/dt (mixing in)-(mixing out)-(consumption)
vI -vV -aVP
Fast equilibration of concentration implies V
vI / ( v aP )
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Fast equilibration of food concentration
impliesV vI / ( v aP )
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Strong effects at low densities
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Moving predictions to larger scales
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Behavior implies Beverton-Holt recruitment model
(1) Foraging arena effect of density on food
available
Strong empirical support
(2) implies linear effect on required activity
and predation risk
Emerging empirical support (Werner)
(3) which in turn implies the Beverton-Holt form
Massive empirical support
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Beverton-Holt shape and recruitment limits far
below trophic potential (over 600 examples now)
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Predicting consumption (Pg 87 in your manual)
Basic consumption equation
aij vij Bi Pj
Qij
vij vij aij Pj
Adding additional realism to the consumption
equation
aij vij Bi Pj Ti Tj Sij Mij / Dj
Qij
vij vij Ti Mij aij Mij Pj Sij Tj
/ Dj
Q consumption a effective search rate v
vulnerability B biomassP predator biomass
or number S seasonality or long-term forcing
M mediation T search time D f(handling
time)
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Deriving parameters for the consumption equation

• Given Ecopath estimates of Bi Pi and Qij, solve

aij vij Bi Pj
Qij
for aij conditional on vij
vij vij aij Pj
-2Qijvij
aij
yields
Pj(Qij-vijBi)
Thus the parameters of interest are Bi, Pj, Qij,
and vij
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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 / W?
• VBGF curvature par.
• Recruitment power par.
• Forcing functions
• Mediation, time forcing, seasonal egg production,

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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

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Running Ecosim Foraging arena
With mass-action (Lotka-Volterra) interactions
only
With foraging arena interactions
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Ecosim predicts ecosystem effects of changes in
fishing effort
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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).

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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/depensatio
  n effects)?

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Ecosim can use time series data
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Time series data
Drivers
Validation

• 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

Yes, lots of Monte Carlo
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Time series fitting Strait of Georgia
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Experience with Ecosim so far

• 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

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

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Formal estimation
Modeling process fitting drivers
Fishing
Ecosystem model (predation, competition,
mediation, age structured)
(Diet0)
Log Likelihood
Predicted C, B, Z, W, diets
(Z0)
(BCC/B0)
Observed C,B,Z,W, diets
Nutrient loading
Habitat area
Climate
Search
Judgmental evaluation
Choice of parametersto include in final
estimation (e.g., climate anomalies)
Errorpattern recognition
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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

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End
Models are not like religion

• you can have more than one
• and you shouldnt believe them

When you get a good fit to time series
data Discard and do it again Discard and do it
again Find out what is robust
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Interdependence of system components
harvesting of forage fishes
Norway pout in the North Sea, 1981
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Feeding triangles North Sea
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Other fish
1
2
Norwaypout
50
5
17
Krill
11
100
Copepods
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Feeding triangles North Sea
4
Other fish
1
2
Norwaypout
50
5
17
Krill
11
100
Copepods
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Feeding triangles North Sea
4
Other fish
1
2
Norwaypout
50
5
17
Krill
11
100
Copepods