Transcript Tales from the foraging arena

Ecosim & the foraging arena
IncoFish Workshop, WP4
September, 2006
Villy Christensen
EwE includes two dynamic modules
Both build on the Ecopath model:
• Ecosim: time dynamics;
• Ecospace: spatial dynamics.
Information for management
from single-species to ecosystem approaches
Biology
Abundance
Migration
Growth
Dispersal
Mortality
Recruitment
Catches
Catchability
(dens-dep.)
Single-species
approaches
Ecology
Feeding rates
Diets
Interaction terms
Carrying capacity
Habitats
Ecosystem
approaches
Y/R
VPA
Surplus production
….
Ecopath
Ecosim
Ecospace
….
Tactical
Strategic
Biodiversity
Occurrence
Distribution
Economics
Costs
Prices
Values
Existence
values
Social & cultural
considerations
Employment
Conflict
reduction
...
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.
Mass balance: cutting the pie
Harvest
Predation
Harvest
Predation
Other
mortality
Other
mortality
Unassimilated
food
Respiration
Predation
Unassimilated
food
Predation
Predation
Other mortality
Unassimilated
food
Respiration
Respiration
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.
Single-species assessment model
Biomass
next year
=
Bt+1
=
Growth/survival +
of biomass this
year
g tB t
Constant
survival
+
Survival
from fishing
Biomass of
new recruits
Stochastic variation
in juvenile survival
Rt exp(vt)
Body mass
growth
gt = S[1-exp(qEt)][a/mt+r]
Multi-species production model (Ecosim)
Biomass
next year
=
Bt+1
=
Growth/survival +
of biomass this
year
g tB t
Survival from
predation
+
Survival
from fishing
Biomass of
new recruits
Deterministic variation
due to predation,
feeding & growth
Rt exp(vt)
Body mass growth from
prey consumption
gt = S[1-exp(qEt)][a/mt+r]
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
What
happened
&
what
if?
The guts of Ecosim: Foraging arena
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.
Organisms are not chemicals!
Ecological interactions are highly organized
Reaction vat model
Prey
eaten
Foraging arena model
Prey
eaten
Predator handling
limits rate
Prey density
Prey behavior
limits rate
Prey density
Big effects from small changes in space/time scale
Functional response
Prey attacked
I
II
III
Buzz Holling’s
Prey density
Holling 1959
Prey vulnerability: top-down/bottom up control
Predator, P
aVP
Available prey, V
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,
A critical parameter: vulnerability
It’s all about carrying capacity
Predation mortality: effect of vulnerability
Predicted
predation
mortality
v=
Max
Baseline
0
?
Ecopath
baseline
Top-Down
High v
?
Carrying
capacity
Predator abundance
Bottom-up
Low v
Limited prey vulnerability causes
compensatory (surplus) production
response in predator biomass dynamics
1.0
Predator
Q/B
response
-- given
fixed
total prey
abundance
If predator
biomass is
halved
0.5
0.0
If predator
biomass is
doubled
-0.5
Carrying
Capacity
0
Predator abundance
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)
v
v’
“Vulnerable”
prey (V)
Predation
rate:
aVP
(mass action
encounters,
within arena)
This structure implies “ratio-dependent” predation rates:
V=vB/(v+v’+aP)
(rate per predator decreases with increasing predator abundance P)
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 )
Arena Food Density (C)
Effect of Local Competition on
Food Density
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
Competitor Density (N)
15
Strong effects at low densities:
600
Final Body Weight (g)
Ungrazed, Lo Fry
500
Ungrazed, Hi Fry
Grazed, Lo Fry
Grazed, Hi Fry
400
Power (Series5)
300
200
100
0
0
500
1000
1500
2000
Yearling Density (fish/ha)
2500
3000
Behavior implies Beverton-Holt recruitment model
(1) Foraging arena effect of density on food available:
Food
Strong empirical
density
support
Juvenile fish density
(2) implies linear effect on required activity and predation risk:
Activity,
mortality
Emerging empirical
support (Werner)
Juvenile fish density
(3) which in turn implies the Beverton-Holt form:
Net recruits
surviving
Massive empirical
support
Initial juvenile fish density
Beverton-Holt shape and recruitment
“limits” far below trophic potential
(over 600+ examples now):
Predicting consumption: (Pg 87 in your manual)
Basic consumption equation
Qij =
aij • vij • Bi • Pj
vij + vij + aij • Pj
Adding additional realism to the consumption equation
Qij =
aij • vij • Bi • Pj • Ti • Tj • Sij • Mij / Dj
vij + vij • Ti • Mij + aij • Mij • Pj • Sij • Tj / Dj
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)
Deriving parameters for the consumption
equation
• Given Ecopath estimates of Bi Pi and Qij, solve
Qij =
aij • vij • Bi • Pj
vij + vij + aij • Pj
yields
for aij conditional on vij
-2Qijvij
aij =
Pj(Qij-vijBi)
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);
For multi-stanza groups:
• Wmat / Wω;
• VBGF curvature par.;
• Recruitment power par.;
Forcing functions:
– FT adjustment rate;
– Sensitivity of ‘other mortality’ • Mediation, time forcing,
to FT;
seasonal egg production,
– Predator effect on FT;
• Qmax/Q0 (handling time)
– If a good reason for it
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
Running Ecosim: ± Foraging arena
With mass-action (Lotka-Volterra) interactions only:
With foraging arena interactions:
Ecosim predicts ecosystem effects
of changes in fishing effort
Biomass/original biomass
Fishing effort over time
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).
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)?
Ecosim can use time series data
Biomass/original biomass
Fishing effort over time
1973
1978
1983
1988
1993
Time series data
Drivers:
• Fishing mortality rates
• Fleet effort
• Biomass, catches, Z
(forced)
• Time forcing data (e.g.,
prim. prod., SST, PDO)
Yes, lots of Monte Carlo
Validation:
• Biomass (relative,
absolute)
• Total mortality rates
• Catches
• Average weights
• Diets
Time series fitting: Strait of Georgia
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 model
that can replicate development over time
we can (with some confidence) use it for ecosy stem -based policy exploration.
Modeling process: fitting & drivers
Formal estimation
Fishing
(Diet0)
(Z0)
(BCC/B0)
Ecosystem model
(predation,
competition,
mediation,
age structured)
Climate Nutrient
loading
Predicted C,
B, Z, W, diets
Observed
C,B,Z,W, diets
Habitat
area
Search
Judgmental evaluation
Choice of parameters
to include in final
estimation (e.g., climate
anomalies)
Log
Likelihood
Error
pattern
recognition
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
Models are not like religion
– you
can have more than one
End
– and you shouldn’t 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
Interdependence of system components
& harvesting of forage fishes
Norway pout
in the
North Sea, 1981
Feeding triangles: North Sea
4
Other
fish
1
2
5
50
Norway
pout
17
Krill
11
100
Copepods
Feeding triangles: North Sea
4
Other
fish
1
2
5
50
Norway
pout
17
Krill
11
100
Copepods
Feeding triangles: North Sea
4
Other
fish
1
2
5
50
Norway
pout
17
Krill
11
100
Copepods