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Decision making and optimal foraging Logic Elements Prey choice model Patch choice model

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Optimality modeling Logic –Natural selection generates behavioral responses that maximize fitness by balancing benefits against costs - “evolutionary economics” Advantages –Makes assumptions explicit –Generates testable predictions –Suggests new hypotheses if model doesn’t fit Criticisms –Behavior may not always be optimal

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Optimality model elements Decision variable –Behavioral option, e.g. pursue prey or not Currency –Must correlate with fitness (LRS) –Often maximize rate of net energy intake (E/T) Constraints –Intrinsic limitations in ability (running speed) or tolerances (nutrition requirement) –Extrinsic - imposed by environment (prey density)

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Prey choice model Problem: should lion eat water buffalo or Thompson’s gazelles or both?

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Prey choice model - assumptions Decision –When a lion encounters a prey, should it attack or search for another prey? Currency - maximize profitability (E/T) Constraints –Prey are encountered sequentially –Time spent searching and handling are independent –Lions have perfect knowledge, i.e. profitabilities and densities of prey are known

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Prey choice model - definitions Define variables –E i = energy provided by prey i –h i = time required to catch and consume (handle) each prey type –S i = search time required to find prey i (depends on relative abundance of prey) –Profitability = P i = E i / h i Assume –E wb = 40 kcalE tg = 10 kcal –h wb = 2 hh tg = 1 h Then –P wb = 40 kcal/2 h = 20 kcal/h (most profitable) –P tg = 10 kcal/1 h = 10 kcal/h

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Prey choice model - solution Catch and eat current prey only if the energy gained exceeds that expected if it searches for alternative prey –E current /h current > E other /(S other + h other ) –If water buffalo is encountered: E wb /h wb > E tg /(S tg + h tg ) 40/2 > 10/(S tg + 1) This is always true, even when S tg = 0, so lions should always eat buffalo

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Prey choice model - solution If a gazelle is encountered: –E tg /h tg > E wb /(S wb + h wb ) Rearranging gives –S wb > (E wb / E tg )(h tg ) - h wb So pursue a gazelle whenever –S wb > (40 kcal / 10 kcal) (1h) - 2h –S wb > 2 h Therefore, if finding a water buffalo takes 1 h, then the lion should forego catching impala, but if it takes 3 h, then she should pursue impala

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Prey choice model - predictions Always eat the most profitable prey type –E 1 /h 1 > E 2 /h 2 Include less profitable prey only if –S 1 > (E 1 /E 2 )h 2 - h 1 (where E 1 > E 2 ) The inclusion of less profitable prey does not depend on its abundance (which dictates the search time), only on the abundance of more profitable prey Specialists on prey 1 should switch and become generalists both suddenly and completely when prey 1 becomes rare

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Shore crabs feeding on mussels Profitability Prey size distribution in diet Most profitable prey are taken most often

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Trout acquire optimal diet

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Great tits and mealworms

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Multiple prey choice Rank all prey by profitability –E 1 /h 1 > E 2 /h 2 > E 3 /h 3 To decide whether or not to include a prey item when encountered, its profitability must exceed the net profitability of all higher ranking prey: –E 3 /h 3 > (E 1 + E 2 )/(S 1 + h 1 + S 2 + h 2 )

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Inuit (Eskimo) prey choice Handling rate = prey profitability

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Reasons for partial preferences Discrimination error (mistake prey type) Lack of complete information –Experiments with pigeons show that increasing experience with a particular combination of prey profitabilities and encounter rates results in step function decisions Variation in prey size Simultaneous encounters with multiple prey Short term sampling rule for estimating encounter rate

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Patch choice model Decision –When is the optimal time to leave a patch? –Examples: hummingbird or bee visiting flowers Currency - maximize profitability (E/T) Constraints –Time spent searching in patches and traveling between patches are independent –Foragers encounter patches sequentially –Perfect knowledge, i.e. energy gain in a patch and patch locations are known –Energy gain in patches shows diminishing return

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Energy gain in a patch Diminishing returns due to patch depletion or prey evasion

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Patch choice solution: marginal value theorem

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Patch choice predictions Optimal search time in patch is greater when travel time between patches is longer

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Patch choice: great tits Mealworms hidden in sawdust in pots hanging from trees Two experimental conditions: long and short travel time achieved by making lids easy or hard to remove Actual patch residence times were close to predictions of MVT

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Central place foraging: starlings Starlings must collect beetle larvae from feeder and return to nest to feed chicks Load curve shows diminishing returns because it becomes harder to probe as bill fills Use MVT because parents want to maximize energy gain of chicks Observations fit MVT predictions

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What if optimality fails? Consider simpler decision rules Include additional constraints –Predation risk –Minimum nutrient requirements –Avoidance of toxins –Starvation risk avoidance (next lecture) Consider currency other than profitability –Efficiency (E gained /E spent )

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Simple decision rules Bluegill overestimate giving up times

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Constraints: prey choice vs predation

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Constraints: minimum nutrient uptake Moose have minimum energy and sodium requirements and limited stomach capacity Columbian ground squirrels have minimum time, energy and limited gut capacity

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Constraints: toxin avoidance Scarlet macaws eat clay after consuming fruit with tannins or alkaloids

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Alternative currencies Nectar load that bees can carry shows diminishing returns because larger loads take more energy Data fit efficiency maximization (E gained /E spent ), not profitability Selection on hive rather than worker favors efficiency

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