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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

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

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

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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

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

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Fine-scale arena dynamics: food concentration seen by predators should be highly sensitive to predator abundance “Invulnerable” prey (N-V) “Vulnerable” prey (V) Predation rate: aVP (mass action encounters, within arena) This structure implies “ratio-dependent” predation rates: V=k 1 N/(k 1 +k 2 +aP) (rate per predator decreases with increasing predator abundance P) k1k1 k2k2

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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 )

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

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Strong effects at low densities:

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

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Spatial organization in foraging bouts by schooling fish Properties of the water volumes actually searched: 1.Never cover the entire water column and prey population 2.Intense competition and localized prey depletion within volumes actually searched as schools disperse 3.Larger, faster fish gain disproportinate access to “new” prey as fish move upward in the water column Do “detailed” IBMs account for these effects?

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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 Distn., simulations

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

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

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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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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 P e=growth efficiency, aC=food intake/time P=proportion of time spent in arena

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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 = - 1 N - 2 N 2 where 1 =Rm/eakI and 2 =Ra/eakI

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Thus the Beverton-Holt parameters have a very special interpretation (Recruits)=K 1 (Eggs)/[1+K 2 (Eggs)] is the integral of dN/dt = - 1 N - 2 N 2 with N starting at Eggs the maximum survival rate K 1 turns out to be K 1 =exp(- 1 T}=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 /g?)

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

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

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

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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)

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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: EGGS SURVIVING RECRUITS The “stock-recruit function” is a model for predicting the means of these distributions

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

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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! EGGS RECRUITS Actual Measured

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

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Foraging arena theory predicts less variation in natural mortality rate than would be expected from changes in predator abundance Predator abundance Predicted predation mortality rate M ij of type i prey due to type j predators 1 1 Ecosim Traditional (mass action) Base estimate from Ecopath

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

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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

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

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Time predictions from an ecosystem model of the Georgia Strait,

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Northwest Hawaiian Islands (French Frigate Shoals) 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 Fishing effort: Lo chl

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North Sea time series from MSVPA compared to Ecosim

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Gulf of Thailand survey data compared to Ecosim

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Preliminary but promising results from Lake Superior, showing that partial model “failures” do not necessarily contaminate all predictions

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Fish and fishing interactions in the Central North Pacific

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

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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

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Views of ecosystem dynamics NATURE BENIGN NATURE CHAOTIC NATURE RESILIENT Stable production dynamics, unpredictable change driven by environmental factors PREDICTED BY ECOSIM TO BE COMMON Unstable production dynamics, unpredictable change driven by biological interactions “FORBIDDEN” BY FORAGING ARENA THEORY? Stable production dynamics within stability domains, multiple stable states PREDICTED BY FAT TO BE UNCOMMON

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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)

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

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

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Watching a fishery die…

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

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

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

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