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Optimal theory

Optimal theory

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Optimal theory

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  1. Optimal theory • The theory used to generate hypotheses about the adaptive value of characteristics which analyzes the costs and benefits of alternative decisions in terms of their fitness payoffs • Decision variable – behavioral options • Currency – often related to fitness • Constraints – intrinsic vs. extrinsic

  2. Advantages • Make assumption explicit • Generate testable prediction • Suggest new hypothesis if model does not fit • Criticism • Behavior may not always optimal

  3. Optimal diet E1 E2 E2 E1 E1h2 ----- > ----- , if ----- > ------- => S1 > -------- - h1 h1 h2 h2 S1+h1E2 • Always eat the most profitable prey type • Include less profitable prey only if S1 > (E1h2/E2) - h1

  4. Inclusion of the less profitable prey does not depend on its abundance, only on the abundance of the more profitable prey • Specialist on prey 1 will switch and become generalist both suddenly and completely when prey 1 become rare

  5. Multiple prey choice • Rank all prey by profitability • To decide whether to include a prey item when encounter, its profitability must exceed the net profitability of all higher ranking prey E3 > (E1 + E2)/(h1 + s1 + h2 + s2)

  6. Reasons for partial preference • Discrimination error • Lack of complete information • Variation in predator or prey • Simultaneous encounter of multiple prey • Short term sampling rule for estimating encounter rate

  7. Patch choice model • When is the optimal time to leave a patch? • e.g. hummingbird or bee visiting flowers • Constraints • Time spent searching in patches and traveling between patches are independent • Perfect knowledge • Energy gain in patches show diminishing gain

  8. Marginal value theorem – patch residence time

  9. Great tit • Meal worm hidden in sawdust in pots hanging from trees • Long and short travel time achieved by making lids hard or easy to remove • Actual patch resident time ~ prediction

  10. Central place foraging • Starling travel between feeder and nest • Load curve shows diminishing return because it becomes harder to probe as bill fills • Observation fits MVT prediction

  11. What if optimality fails • Nutrients, predation, competition, risk of starvation, age, experience, etc. • Consider currency other than profitability • Efficiency, Egain/Espent

  12. Nectar load of bee shows diminishing return because larger loads take more energy • Fit maximize efficiency model but not maximize profitability • Selection on hives favor efficiency

  13. Foraging in a variable environment • Immediate response • Risk sensitive foraging • Long-term response • Topor or hibernation • Fat storage • Caching or hoarding • agriculture

  14. Risk sensitive foraging • Choose to forage in constant or variable (unpredictable) environment • Risk averse vs risk prone

  15. Foraging in Juncos • Two pans: one with a non-variable modest reward and the other with a variable but higher pay-off reward • The birds that were non-energy limited chose the lower payoff pan over the higher payoff, but risky pan. When food was limited, they opted for the higher payoff but risky pan.

  16. Why hoarding instead of fat storage • Fat increase body mass and predation risk • If food is super-abundant, not all can be stored as fat • Large store provide food supply for a group over winter • Can be more easily transferred to offspring

  17. Anti-predator strategies • making detection less likely • egg-shell removal • camouflage & cryptic behavior • industrial melanism in moth • Freezing • removing evidence of presence • broken-winged display

  18. Cost of cryptic behavior • Time lost for other activities • Belding’s ground squirrels respond to alarm call: hiding in underground burrows = time not spent feeding • Cost of time lost for feeding varies among individuals depending on their nutritional status. Well-fed individuals should have less to gain from additional feeding

  19. Trinidadian guppies • Males court most vigorously at moderate light intensity (low light, not visible to females; high light, too visible to predators) • Small males court more vigorously , especially at high light intensity

  20. making attack less likely • physical and chemical repellents and weapons • warning coloration & behavior • bright color wings under dull color wings, big eye-spots • hiss sound, inflation and increase body size, tail of rattlesnake, stripes and hand-stand of skunks • mimicry

  21. stotting--hypotheses • alarm signal hypothesis • social cohesion hypothesis • confusion effect hypothesis • pursuit-deterrent (un-profitability advertisement hypothesis) • anti-ambush hypothesis • handicap principle • startle effect

  22. making capture less likely • vigilance, e.g. moth-bat • misdirecting a predator's attack • fleeing • Cooperative defense • vigilance • selfish herd • dilution effect • group mobbing

  23. Key prediction of selfish herd hypothesis • Individuals should compete for access to safest spots in the herd • Individuals in least safe spots in the herd should be safer than are solitary individuals • e.g. blue-gill sunfish breeds in colony. Males compete for central territory which is preferred by females and lower in predation risk. Solitary males experiencing higher rate of infestation/predation than edge males

  24. Cooperative defense: mobbing • Hypothesis: If mobbing protects eggs and young, the degree of protection should be proportional to the intensity of the mobbing • Test: placing eggs along a transect from inside to outside the border of the colony • Results: mobbing rates increased toward center of colony and predation rate decreases as mobbing rates increased

  25. Hypothesis: comparative method • Related species nesting in habitats less vulnerable to terrestrial predation should not exhibit the behavior – kittiwake • Unrelated species nesting in similar habitats should demonstrate mobbing – swallow, ground squirrels

  26. Alarm call

  27. Ideal free distribution • Animal sequentially fill available habitat staring with best patches • Assumption • “ideal” by possessing perfect info about resource quality • “free” to disperse appropriately • Expectation – animals disperse to equalize energy intake or reproduction

  28. Deviation from IFD • 16/20 studies show too many in poor habitat or too few in rich habitat • Perception error • Differences in competitive ability • Dominants exclude subordinates

  29. Dominance – how? • Resource holding potential - ability of control access to a resource • Correlate w/ body size, experience, matrilineal relationship, fat reserves, prior success or failure, etc. • Require recognition or status badge

  30. Economics of territoriality • Resource must be defendable • Renewable, not ephemeral or super-abundant • Benefit > cost of defense • Energetic cost increase w/ # of intruders, territory size • Benefit accrue by increasing energy intake rate, reducing energy cost and starvation risk

  31. If nectar level increase from 2 to 3 ul per flower, the bird save 1.3 hr per day foraging time and save (1000x1.3) – (400x1.3) = 780 cal • But the bird spent 0.28 hr per day defending and the cost of defending = (3000x0.28) – (400x0.28) = 728 cal  Economically defendable