Ecosim & the foraging arena

1. Ecosim & the foraging arena IncoFish Workshop, WP4 September, 2006 Villy Christensen

2. EwE includes two dynamic modules Both build on the Ecopath model: • Ecosim: time dynamics; • Ecospace: spatial dynamics.

3. Information for management from single-species to ecosystem approaches Biology Ecology Biodiversity Abundance Growth Mortality Recruitment Catches Catchability (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

4. 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.

5. 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

6. 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.

7. Single-species assessment model Biomass next year Stochastic variation in juvenile survival Growth/survival of biomass this year Biomass of new recruits = + Bt+1 = gtBt + Rt exp(vt) Constant survival Survival from fishing Body mass growth gt = S[1-exp(qEt)][a/mt+r]

8. 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 = + Bt+1 = gtBt + Rt exp(vt) Survival from predation Survival from fishing Body mass growth from prey consumption gt = S[1-exp(qEt)][a/mt+r]

9. 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

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

11. 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.

12. Prey eaten Prey eaten Prey density Prey density 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

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

14. Prey vulnerability: top-down/bottom up control Predator, P aVP Available prey, V v(B-V) v’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,

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

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

17. 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

18. 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

19. 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: V=vB/(v+v’+aP) (rate per predator decreases with increasing predator abundance P)

20. 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 )

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

22. Strong effects at low densities:

23. Food density Activity, mortality Juvenile fish density Juvenile fish density Net recruits surviving Initial juvenile fish density 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

24. Beverton-Holt shape and recruitment “limits” far below trophic potential (over 600+ examples now):

25. 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 = biomass;P = predator biomass or number; S = seasonality or long-term forcing; M = mediation; T = search time; D = f(handling time)

26. 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

27. 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 parameters

28. 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

29. Running Ecosim: ± Foraging arena With mass-action (Lotka-Volterra) interactions only: With foraging arena interactions:

30. Ecosim predicts ecosystem effects of changes in fishing effort Biomass/original biomass Fishing effort over time

31. 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).

32. 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)?

33. Ecosim can use time series data Biomass/original biomass Fishing effort over time 1973 1978 1983 1988 1993

34. 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 Time series data Drivers: Validation: Yes, lots of Monte Carlo

35. Time series fitting: Strait of Georgia

36. 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.

37. Modeling process: fitting & drivers Formal estimation 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

38. 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

39. Models are not like religion End • 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 Discard and do it again … Find out what is robust

40. Interdependence of system components & harvesting of forage fishes Norway pout in the North Sea, 1981

41. Feeding triangles: North Sea 4 Other fish 1 2 Norwaypout 5 50 17 Krill 11 100 Copepods

42. Feeding triangles: North Sea 4 Other fish 1 2 Norwaypout 5 50 17 Krill 11 100 Copepods

43. Feeding triangles: North Sea 4 Other fish 1 2 Norwaypout 5 50 17 Krill 11 100 Copepods