Optimal foraging theory

Transcription

1 Optimal foraging theory Christopher Furlong/Getty Images 2007 John Vucetich John Ascher Where is Moriarty going? Purpose of trip: buy ice cream for home Moriarty wants to get home as fast as possible Moriarty knows layout of local streets 2012 Google How to build an optimality model 1. Choose the decision you want to predict 2. Make assumptions about: Fitness currency Constraints on behavior Where is Moriarty going? Purpose of trip: buy ice cream for home Moriarty wants to get home as fast as possible Moriarty knows layout of local streets 2012 Google 1

2 How to build an optimality model 1. Choose the decision you want to predict 2. Make assumptions about: Fitness currency Constraints on behavior The habitat 3. Predict animal s behavior assuming it maximizes fitness currency within constraints 4. Test your prediction Some classical optimal foraging models: Optimal diet: What types of food to include in diet? Marginal value theorem: How long should one forage in a patch? Food types can vary in handling time and # of calories Optimal diet Decision: Which foods to include in diet Currency: Rate of energy intake Forager knows food quality and abundances Can only deal with one food item at a time No learning How to determine optimal diet # calories Rank foods based on handling time 1: 2: 3: Always eat best food Eat next-best too if best food scarce Eat third-best too if best 2 foods scarce Etc. 2

3 Testing the optimal diet model Results of conveyor belt studies: When high quality items scarce, animals generalize When high quality items abundant, animals usually reject low quality items, regardless of their abundance But: low quality items never completely dropped from diet e.g., Krebs et al Optimal diet Decision: Which foods to include in diet Food types can vary in handling time and # of calories Currency: Rate of energy intake Forager knows food quality and abundances Can only deal with one food item at a time No learning 2007 John Vucetich Moose diets Aquatic plants Terrestrial plants (Belovsky 1978) Energy per gram 3.8 kcal 3.0 kcal If both food types are abundant, what does our model predict moose should eat? Time needed to eat 1 gram 0.05 min 0.06 min 3

4 Optimal diet Decision: Which foods to include in diet Food types can vary in handling time and # of calories Currency: Rate of energy intake Forager knows food quality and abundances Can only deal with one food item at a time No learning 2007 John Vucetich Moose diets (Belovsky 1978) Rumen capacity is limited and aquatic plants are very bulky Aquatic plants Terrestrial plants Energy per gram 3.8 kcal 3.0 kcal Bulkiness (% rumen capacity/g) 0.07% 0.01% 2007 John Vucetich Moose diets (Belovsky 1978) Moose need sodium in their diet Terrestrial plants have almost no sodium but aquatic plants are a good source Aquatic plants consumed (g) A more realistic model Rumen capacity Minimum energy requirement A B Terrestrial plants consumed (g) C D Belovsky 1978 Minimum sodium requirement 4

5 Marginal value theorem Decision: How long to forage in a patch Currency: Rate of energy intake Food in discrete patches (All patches identical) Moving to new patch takes time Patches are depleted as animal forages (Charnov 1976) Marginal value theorem Decision: How long to forage in a patch Currency: Rate of energy intake Food in discrete patches (All patches identical) Moving to new patch takes time Patches are depleted as animal forages (Charnov 1976) Forager knows: Quality of current patch Average patch quality and travel time Energy in patch Rate of energy intake = Time in patch + Travel time 5

6 Energy in patch Rate of energy intake = Time in patch + Travel time Which gives the highest rate of energy intake? Slope = Travel time Travel time Marginal rate of energy intake = energy intake in next micro-moment Marginal Value Theorem: Animal should leave patch when its marginal rate of energy intake = the overall average rate of energy intake it can achieve in its habitat Travel time Travel time 6

7 What happens if you change travel time? Bumblebees visiting Delphinium nelsonii Hodges 1985 Travel Travel time Travel time time Paul Slichter John Ascher Flowers visited Observations: Bees leave when nectar/flower declines to a threshold (Hodges 1985) MVT correctly predicts #s of flowers visited/plant (Pleasants 1989) plant density -> # flowers visited/plant (Cibula and Zimmerman 1984) The Hummingbird Game A web exercise on optimal foraging in the form of a game: Optional Exercise! For class participation credit, play the hummingbird game: Design a set of rules used to leave patch Collect data on how the different rules perform Report results and interpretation in 1-2 typed pages Hints for full credit: Be systematic in how rules vary. Use multiple replicates per rule. 7

8 Patch use in bluegill sunfish # of prey eaten Crowley et al (min) OK Dept. of Wildlife Conservation Fish stay in patches much longer than predicted! Many other animals also stay longer than predicted (Nonacs 2001) Why??? Marginal value theorem Decision: How long to forage in a patch Currency: Rate of energy intake Food in discrete patches (All patches identical) Moving to new patch takes time Patches are depleted as animal forages (Charnov 1976) Forager knows: Quality of current patch Average patch quality and travel time 8