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Ecosim & the foraging arena IncoFish Workshop, WP4 September, 2006 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. 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 Abundance Growth Mortality Recruitment Catches Catchability (dens-dep.) Abundance Growth Mortality Recruitment Catches Catchability (dens-dep.) Migration Dispersal Migration Dispersal Feeding rates Diets Interaction terms Carrying capacity Habitats Feeding rates Diets Interaction terms Carrying capacity Habitats Occurrence Distribution Occurrence Distribution Costs Prices Values Existence values Costs Prices Values Existence values Biology Ecology Biodiversity Economics Y/R VPA Surplus production …. Y/R VPA Surplus production …. Ecopath Ecosim Ecospace …. Ecopath Ecosim Ecospace …. Single-species approaches Ecosystem approaches Social & cultural considerations Employment Conflict reduction... Employment Conflict reduction... TacticalStrategic

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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 Ecosim

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

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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 dynamics

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Single-species assessment model B t+1 = g t B t + R t exp(v t ) g t = S[1-exp(qE t )][ m t + ] =+ Stochastic variation in juvenile survival Constant survival Survival from fishing Body mass growth Biomass next year Growth/survival of biomass this year Biomass of new recruits

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Multi-species production model (Ecosim) B t+1 = g t B t + R t exp(v t ) g t = S[1-exp(qE t )][ m t + ] ==++ Deterministic variation due to predation, feeding & growth Survival from predation Survival from fishing Body mass growth from prey consumption Biomass next year Growth/survival of biomass this year Biomass of new recruits

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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 Ecosim

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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. 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 Big effects from small changes in space/time scale Reaction vat modelForaging arena model Prey eaten Prey density Prey eaten Prey density Prey behavior limits rate Predator handling limits rate

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Functional response Prey density Prey attacked I II III Holling’s Holling 1959 Buzz

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Unavailable prey B-V Available prey, V v’V Predator, P Prey 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, aVP v(B-V)

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A critical parameter: vulnerability It’s all about carrying capacity

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v = Max Baseline Predator abundance Predicted predation mortality ‘Traditional’ Ecosim Predation mortality: effect of vulnerability Bottom-up Top-Down High v Low v Carrying capacity 0 0 Ecopath baseline ? ? ? ?

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Limited prey vulnerability causes compensatory (surplus) production response in predator biomass dynamics Predator Q/B response -- given fixed total prey abundance Predator Q/B response -- given fixed total prey abundance Predator abundance If predator biomass is halved 0.0 -0.5 0.5 1.0 If predator biomass is doubled Carrying Capacity 0 0

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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 “Invulnerable” prey (B-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) v v’

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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 -v’V-aVP Fast equilibration of concentration implies V = vI / ( v’ + aP )

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Fast equilibration of food concentration implies: V = vI / ( v’ + aP )

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Strong effects at low densities:

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Moving predictions to larger scales Hour Season/ Year Day Decade MeterPatchReachLandscape Arena Dynamics Local Recruitment Population Dynamics Beverton-Holt equation Ideal Free distrib., simulations

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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 recruits surviving Initial juvenile fish density Activity, mortality Juvenile fish density Strong empirical support Emerging empirical support (Werner) 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) Q ij = a ij v ij B i P j T i T j S ij M ij / D j v 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 ij = a ij v ij B i P j v ij + v ij + a ij P j Basic consumption equation Adding additional realism to the consumption equation

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Deriving parameters for the consumption equation Given Ecopath estimates of B i P i and Q ij, solve Q ij = a ij v ij B i P j v ij + v ij + a ij P j for a ij conditional on v ij a ij = -2Q ij v ij P j (Q ij -v ij B i ) yields Thus the parameters of interest are B i, P j, Q ij, and v ij

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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; Q max /Q 0 (handling time) –If a good reason for it For multi-stanza groups: W mat / W ω ; 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 Z i = F i + sum of M ij (predation components of M) –where M ij is Q ij /B i (instantaneous risk of being eaten) –M ij varies with –Changes in abundance of type j predators –Changes in relative feeding time by type i prey Z i = F i + sum of M ij (predation components of M) –where M ij is Q ij /B i (instantaneous risk of being eaten) –M ij 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 Fishing effort over time Biomass/original biomass

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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). 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/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)?

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Ecosim can use time series data Fishing effort over time Biomass/original biomass 19781983197319881993

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Time 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: Validation: Yes, lots of Monte Carlo

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Time series fitting: Strait of Georgia

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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 model that can replicate development over time we can (with some confidence) use it for ecosystem-based policy exploration.

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Formal estimation Ecosystem model (predation, competition, mediation, age structured) Climate Nutrient loading Nutrient loading Fishing Predicted C, B, Z, W, diets Observed C,B,Z,W, diets Observed C,B,Z,W, diets Log Likelihood (B CC /B 0 ) (Diet 0 ) (Z 0 ) Habitat area Habitat area Error pattern recognition Choice of parameters to include in final estimation (e.g., climate anomalies) Judgmental evaluation Modeling process: fitting & drivers Search

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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 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 shouldn’t believe them When you get a good fit to time series data: 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 Other fish Krill Norway pout Copepods 4 1 505 17 100 11 2

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Feeding triangles: North Sea Other fish Other fish Krill Norway pout Copepods 4 4 1 1 505 17 100 11 2 2

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Feeding triangles: North Sea Other fish Other fish Krill Norway pout Copepods 4 4 1 1 50 5 5 17 100 11 2 2

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