Lecture 6 review

1. Lecture 6 review • Direct estimation of total abundance is needed in many contexts • Preferred method is direct counting, followed by density x area expansions, followed by direct U estimation methods and mark-recapture • Big assessment models require dangerous assumptions about vulnerability and stationarity of recruitment relationships, often drastically overestimate abundance

2. Lecture 7: Foraging arena theory and Stock-Recruitment relationships • Theory (Foraging arena theory) • Practice (Problems with data)

3. Tales from the foraging arena Are we finally able to develop useful predictive models for ecosystem management?

4. Many patterns in population and community dynamics can be explained by the proposition that predation risk drives evolution of foraging in spatially restricted “arenas” • Food “limitation” in the presence of apparent plenty • Beverton-Holt recruitment relationships (recruitment independent of parental abundance) • Weak dependence of natural mortality rates on predator abundances, even when most mortality is due to predation • Ratio- or predator-dependence in functional responses, implying dynamic stability, positive correlations between prey and predator abundances along productivity gradients, and high biodiversity

5. Willie asked the right question... • Why don’t the fish eat them all, dad?

6. Fine-scale arena dynamics: food concentration seen by predators should be highly sensitive to predator abundance Predation rate: k1 “Invulnerable” prey (N-V) “Vulnerable” prey (V) aVP (mass actionencounters,within arena) k2 This structure implies “ratio-dependent” predation rates: V=k1N/(k1+k2+aP) (rate per predator decreases with increasing predator abundance P)

7. Food concentration in arenas should be highly sensitive to density of animals foraging there dC/dt = (mixing in)-(mixing out)-(consumption) = kI -mC -aCN Fast equilibration of concentration C implies C = kI / ( m + aN )

8. Fast equilibration of concentration C implies: C = kI / ( m + aN )

9. Strong effects at low densities:

10. Prey eaten Prey eaten Prey density Prey density Big effects from small changes in space/time scale (size matters) Reaction vat model Foraging arena model Prey behavior limits rate Predator handling limits rate

11. Spatial organization in foraging bouts by schooling fish • Properties of the water volumes actually searched: • Never cover the entire water column and prey population • Intense competition and localized prey depletion within volumes actually searched as schools disperse • Larger, faster fish gain disproportinate access to “new” prey as fish move upward in the water column • Do “detailed” IBMs account for these effects?

12. Decade Ideal Free Distn., simulations Population Dynamics Season/ Year Local Recruitment Day Arena Dynamics Beverton-Holt equation Hour Meter Patch Reach Landscape Moving Predictions to larger scales

13. Mesoscale overlap patterns may limit trophic interactions; we rely mainly upon diet composition data to “measure” such effects Decade Season/ Year Day Arena Dynamics Arenas Hour Meter Patch Reach Landscape

14. Beverton-Holt shape and recruitment “limits” far below trophic potential (over 300 examples now):

15. 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

16. Arena competition + predation risk while foraging -> Beverton-Holt • Cases: vary foraging time to maintain constant growth rate, or vary total time required to reach defined recruitment size • Same result both cases, but easiest to derive for animals trying to maintain constant growth rate G • Starts with growth rate G = e a C Pe=growth efficiency, aC=food intake/timeP=proportion of time spent in arena

17. Arena competition + predation risk while foraging -> Beverton-Holt • Maintaining growth rate G=eaCP constant means varying feeding time P so that P=G/(eaC) • But if C varies with N as C=kI/(m+aN), animals must vary feeding time as P=(m+aN)(G/eakI) • If predation rate is proportional to foraging time P, ie loss=RP, should see Beverton-Holt linear density dependence: dN/dt = -RPN = -a1 N - a2 N2 where a1=Rm/eakI and a2=Ra/eakI

18. Thus the Beverton-Holt parameters have a very special interpretation • (Recruits)=K1(Eggs)/[1+K2(Eggs)] is theintegral of dN/dt = -a1 N - a2 N2with N starting at Eggs • the maximum survival rate K1 turns out to be K1=exp(- a1T}=exp{-(Tm/eak)(R/I)}where R/I is “risk ratio” of predation rate per time feeding to overall food “supply” in the system (see that m/g?)

19. One very scary prediction • Suppose maximum juvenile survival is order 5% (eg, coho salmon) • Then Recruitment should vary with risk ratio as:

20. Have small changes in R/I been responsible for coho declines?

21. We confidently predicted that coho would double: Here is what we finally got:

22. Estimating recruitment relationships • What exactly are we trying to estimate? • What limits our ability to do estimation, especially of compensation ratios? • Lack of contrast • Errors in variables effects • Time series bias (mad scientist effects)

23. SURVIVING RECRUITS EGGS What is a “stock-recruit relationship” as used in developing harvest management policies? • It is NOT a deterministic prediction of the exact recruitment to be seen at each adult stock size or egg deposition. • Rather, it is a collection of probability distributions whose means vary in a relatively simple way with stock size: The “stock-recruit function” is a model for predicting the means of these distributions

24. The most obvious problem is lack of statistical contrast (information) High variance does NOT prevent us from getting accurate estimates of mean recruitment at high stock sizes RECRUITS ? EGGS But this is a huge issue no matter how many observations we have

25. Measured Actual RECRUITS EGGS The “errors in variables” problem: apparent contrast in stock size (X values ) due to errors in measuring it High recruits at apparently low Eggs make us think compensation is strong, when in fact we actually do not know!

26. The time series (“mad scientist”) problem: recruitment variation causes stock variation, nonrepresentative sampling of R,E pairs Too many high points at low stock size RECRUITS Too many low points at high stock size EGGS High recruits at apparently low Eggs make us think compensation is strong, when in fact we actually do not know!

27. Foraging arena theory predicts less variation in natural mortality rate than would be expected from changes in predator abundance Traditional (mass action) Predicted predation mortalityrate Mijof type iprey dueto type jpredators Ecosim Base estimatefrom Ecopath 1 Predator abundance

28. EwE can incorporate many functional groups (100+) and fisheries (20+)

29. Ecosim is being widely tested against historical trend data • Georgia Strait • Northwest Hawaiian Shelf • North Sea • Gulf of Thailand • Great Lakes • Bering Sea • Gulf of Mexico • Chesapeake Bay

30. Time predictions from an ecosystem model of the Georgia Strait, 1950-2000 With mass-action (Lotka-Volterra) interactions only: With foraging arena interactions:

31. Time predictions from an ecosystem model of the Georgia Strait, 1950-2000

32. Northwest Hawaiian Islands (French Frigate Shoals) Fishing effort: Initial ecosim runs: fishing+ Trophic interactions only did not explain monk seal decline, predicted lobster recovery Satellite chlorophyll data indicate persistent 40-50% decline in primary production around 1990; this “explains” both continued monk seal decline and persistent low lobster abundance Lo chl

33. North Sea time series from MSVPA compared to Ecosim

34. Gulf of Thailand survey data compared to Ecosim

35. Preliminary but promising results fromLake Superior, showing that partial model “failures” do not necessarily contaminate all predictions

36. Fish and fishing interactions in the Central North Pacific

37. Do measured changes in coastal nutrient loading predict fish abundance changes, Florida Bays?

38. Should we trust the policy predictions of these models, about trophic interaction effects? • Of course not, nor should we implement policies that will only work if any particular model is correct • But they have a far better chance of directing us to wise policy choices than some of the boneheaded arguments that are now being used to justify policies that ignore interaction effects: • The mammals will simply find other food sources when we appropriate the production of their favored prey • Fishing at less than the natural mortality rate (F<M) should not impair the ability of a species like menhaden to support its valued predators like striped bass

39. Views of ecosystem dynamics NATURE BENIGN Stable production dynamics, unpredictablechange driven by environmental factorsPREDICTED BY ECOSIM TO BE COMMON NATURE RESILIENT NATURE CHAOTIC Unstable production dynamics, unpredictablechange driven by biological interactions“FORBIDDEN” BY FORAGING ARENA THEORY? Stable production dynamics within stabilitydomains, multiple stable statesPREDICTED BY FAT TO BE UNCOMMON

40. One of those really smart quotes: “We believe the food web modelling approach is hopeless as an aid to formulating management advice; the number of parameters and assumptions required are enormous.” Hilborn and Walters (1992, p. 448)

41. Trophic interaction predictions are critical in many applied settings, eg the Grand Canyon Peregrine falcon Cowbird Water birds Sparrows etc. Exotic fishes Native fishes Aquatic insects Terrestrial insects Detritus Benthic algae Riparian vegetation Flow Turbidity Temperature Water management regime

42. Why we started wondering... • Density dependence where there shouldn’t be:

43. Watching a fishery die…

44. Prey eaten Prey eaten Prey density Prey density Big effects from small changes in space/time scale (size matters) Reaction vat model Foraging arena model Prey behavior limits rate Predator handling limits rate

45. Traditional Issues (Hairston, Smith and Slobodkin) Predators Who’s going to eat me? Population What’s for supper? Resources (Predation and resource availability treated as separate issues)

46. Modern synthesis Who’s going to eat me when I go out for supper? Predators Population And the score at the Coliseum after 11 innings is Lions 11, Christians 0 Arena Resources (Predation and resource availability inextricably linked)