Decision making and optimal foraging

• Logic

• Elements

• Prey choice model

• Patch choice model

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

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)

Prey choice model

• Problem: should lion eat water buffalo or Thompson’s gazelles or both?

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

Prey choice model - definitions• Define variables

– Ei = energy provided by prey i– hi = time required to catch and consume (handle) each

prey type– Si = search time required to find prey i (depends on

relative abundance of prey)– Profitability = Pi = Ei / hi

• Assume– Ewb = 40 kcal Etg = 10 kcal– hwb = 2 h htg = 1 h

• Then– Pwb = 40 kcal/2 h = 20 kcal/h (most profitable)– Ptg = 10 kcal/1 h = 10 kcal/h

Prey choice model - solution

• Catch and eat current prey only if the energy gained exceeds that expected if it searches for alternative prey– Ecurrent/hcurrent > Eother /(Sother + hother)

– If water buffalo is encountered:• Ewb/hwb > Etg/(Stg + htg)

• 40/2 > 10/(Stg + 1)

• This is always true, even when Stg = 0, so lions should always eat buffalo

Prey choice model - solution• If a gazelle is encountered:

– Etg/htg > Ewb/(Swb + hwb)

• Rearranging gives– Swb > (Ewb/ Etg)(htg) - hwb

• So pursue a gazelle whenever– Swb > (40 kcal / 10 kcal) (1h) - 2h– Swb > 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

Prey choice model - predictions

• Always eat the most profitable prey type– E1/h1 > E2/h2

• Include less profitable prey only if– S1 > (E1/E2)h2 - h1 (where E1 > E2)

• 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

Shore crabs feeding on mussels

Profitability

Prey size distribution in diet

Most profitable prey are takenmost often

Trout acquire optimal diet

Great tits and mealworms

Multiple prey choice

• Rank all prey by profitability– E1/h1 > E2/h2 > E3/h3

• To decide whether or not to include a prey item when encountered, its profitability must exceed the net profitability of all higher ranking prey:– E3/h3 > (E1 + E2 )/(S1 + h1 + S2 + h2)

Inuit (Eskimo) prey choice

Handling rate = prey profitability

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

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

Energy gain in a patch

Diminishing returns due to patch depletion or prey evasion

Patch choice solution:marginal value theorem

Patch choice predictions

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

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

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

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 (Egained/Espent)

Simple decision rules

Bluegill overestimategiving up times

Constraints: prey choice vs predation

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

Constraints: toxin avoidance

Scarlet macaws eat clay after consuming fruit with tannins or alkaloids

Alternative currencies

• Nectar load that bees can carry shows diminishing returns because larger loads take more energy

• Data fit efficiency maximization (Egained/Espent), not profitability

• Selection on hive rather than worker favors efficiency