An introduction to Foraging

1. An introduction to Foraging

2. Most important concept: Learning is a product of evolution • Learning = strongest “inherited” behavior • Animals learn how the environmental predictors events • Must learn to predict and control our environment • We want to understand best way to optimize! • This is learning • Question for biologists: how does learning and behavior affect biological fitness • Question for psychologists: how does biological fitness affect learning and behavior?

3. Several models of optimization • Behavioral economics • Assume organism is free to choose consequences • Based on economics: we will work to get access to commodities. • Animals choose based on value of outcome • Utility versus perceived utility • Problem in theory: • not able to predict each individual behavior in set situation • Better at making general rules or heuristics

4. Several models of optimization • Matching law • Assume organism is free to choose consequences • Choose based on value of combined outcomes • Value of Choice A in comparison to Choice B • Idea is that you match behavior: some of choice a, some of choice b, in order to get the most • Problem in theory: animals show three consistent violations: • Undermatching • Overmatching • Bias • Only look at individual, not social group behavior

5. Optimal foraging or Ideal Free Distribution Models • Group model, not a model of individuals • Very different from most theories in psychology • Assume group is free to choose consequences • Assume group is aware of value of choices • Choose based on value of combined outcomes • Value of Choice A in comparison to Choice B • Idea is that group divides itself so that whole group gets the most • E.g.: Choice A = 8 pellets; Choice B = 2 pellets: • 4 animals in group of 5 go to Choice A • 1 animal in grouo of 5 goes to Choice B • Everybody gets 2 pellets • Think of a group of animals as a group of “careful shoppers”

6. So, What is foraging? • Models based on optimal foraging possess: • An objective function or goal • energy maximization • starvation minimization • Minimization of predation threat • Set of choice variables or options available to the organism • Constraints on the set of choices available to the organism • Genetics, physiology, neurology, morphology • Behavior • Experience or learning • Basic premise: choose the option that maximizes the objective, subject to the constraints

7. Problems with “optimal” foraging • Optimality becomes major focus but not explain how it happens. • Do animals optimize, or • Do animals“Get by”? • To what does optimality refer? • Not really optimal but perceived optimality • Not really maximizing, but making do • Making best choice: psychologists call this melioration • Note that optimal foraging does not imply that • Only the best is acceptable • Animals engage in higher level math or highly cognitive and complex thinking • Optimal foraging is MUCH more complex than first thought: • Many more controlling and modulating variables • Both within and outside the animal. • Not include issues such as predation danger that might change choice of which “patch” you visit!

8. Three major issues: • Predation danger vs. acquisition of food • Get the food • Or get eaten! • State dependence: • Tactical choices of forager might depend on state variables • E,g, Hunger, fat reserves • Learning base • Social factors: • Forage with a group? • Forage alone? • Benefits and losses for either choice • Games animals play!

9. Attack and Exploitation models • Stephens and Krebs developed “diet” and “patch” models • Guides kinds of decisions animals make • Diet models: analyze decision to attack or not attack • Forager must decide whether to spend • necessary handling time and eating an item • Passing over it to search for something else • Foragers should ignore low profitability prey types and access higher profitability prey types when high profitability prey types more common • When high profitability prey types are scarce, shift strategy • Important concept: LOST opportunity • Do you risk losing a sure thing for a lesser probability event? • Do you risk losing a sure but smaller reward for a larger one? • What if!?!?!!

10. Factors in Diet/Patch models • Resources with diminishing returns • Value is discounted over time • Value is discounted as consume patch • Maximize the overall rate of energy gain suggests you should change patches when more can be obtained by moving on • Win/shift or win/stay? • E.g., enter rich patch, but are eating it away • When should you shift? • When value of patch drops below the value of shifting to other patch • Look at long-term gain not just momentary • Marginal value theorem: • Must estimate the value of the patch under varying conditions • Vary behavior depending on environmental variables • Data generally support diet/patch models • But, are very simplistic • Sometimes difficult to determine WHAT factors the animal appears to be considering

11. Changed Constraints • Several variables must be considered • multiple choice situations: Rarely is life just one or two choices • Changing conditions: life doesn’t stay the same • Nutritional constraints: different needs at different times • Predators: where and when and who • Discriminated constraints: how good are you at detecting the above? • Simultaneous encounter models: • deal with situations involving multiple choice • Strong preference for immediacy • (Psychologists see this as lack of self control!) • Biologists see this as energy maximization!

12. Why is immediacy valuable? • Delayed food =worth less • might get interrupted and never get it! • Bird in the hand vs. two in the bush! • Human discounting about 4%/year • In animals: may be as much as 50%/sec! • Why this difference? • Ecological rationality hypothesis: • Animals perform poorly when we test them in simultaneous choice situations • misapply the rules that are more appropriate for sequential choice situations • Impulsiveness is not consequence of economic forces that discount delayed benefits • Impulsiveness = consequence of rule that achieves high long-term gains in naturally occurring choice situations

13. Importance of information • Value of information in foraging situation: • Many paths to same goal • Typically one goal is most optimal • When use a strategy, it shapes what information you gain, and how you gain it • thus, strategies may limit information about the world • Must understand what information an animal has, and how it got it, and what it does with that information

14. Criticism of Optimal foraging: Absolute Knowledge • Assumes absolute knowledge • Obviously, can’t be true! • We might call this learning to asymptote • In first few moments of foraging in patch, do gain much info • This info shapes behavior and choices • Information is quickly obtained • Can model this problem statistically: • Statistical distribution represents forager’s prior info • Forager’s actions/subsequent experience provide updated distribution of states (via Baye’stheorum or posterior distribution) • Use updated information to choose better behavioral alternatives

15. Two questions emerge • Do foragers, and how do foragers, change behavior to obtain updated distribution of states? • How forager should act in response to changes in updated information? • What do YOU do versus what should you do?

16. Consumer choice • Think of an animal as a consumer • Face several trade-offs • Increasing gain of 1 factor (e.g., fitness) compromises attainment of another factor (safety) • Must assign “utility” value to each factor • What is utility or cost for each factor • E.g., matching law, behavioral economics • Is food or water more important? • Is $10 now or $100 in 2 weeks better? • Problem for modeling these factors: • Different “currencies” • Can we put predation risk and diet needs in same “currency”? • Comparing the proverbial apples to oranges

17. Dynamic Optimization • Real world foraging is dynamic, not static • World is always changing • Animals still should change within a set of constraints • Develop rubrics or strategies to deal with real world, within set limitations • More recently, developed dynamic state variable models which can mathematically model these changes • Resolves different currencies issues • With computers, can now model more easily • Models becoming closer to real life

18. Dynamic state variable models • Start with algorithm to solve foraging problem • E.g., T • Terminal fitness function • Empirical relation between thevalues of the state variables and fitness • Use T to assign value to every possible outcome in last period • Next: use T to find analogous values for second to last period: T-1 • Can then determine every value of the state variables of decisions that leads to highest expected fitness in final period • Then compute T-2, and so on • Use backward strategy to derive entire strategy • The fitness maximizing behavioral choice for every value of the state variable at every time • Remember is MODELING • Why can’t we do this in the real world?

19. Why use dynamic models? • Invaluable addition to foraging theory • Two fundamentally important advances: • Established widely applicable notion of state dependence • Formalize interaction between state and action • Connect short-term behavioral decisions to long-term fitness consequences • Provide deep insight into trade off between food and safety • Differing effects of feeding and predation can be accommodated within unified framework • Can now put in same ‘currency’

20. Variance-Sensitive Foraging • In real world: variations occur in • Prey size • Handling time • Time between successive prey encounters, etc. • Thus is variance around expected returns for particular foraging strategies • Variance can greatly change outcomes! • Obviously, animals must be sensitive to these variations • Variance sensitivity is expected whenever the absolute value of fitness effects of returns above and below the mean gain are unequal • There should be range of acceptable and unacceptable variability • Psychology better at addressing these issues

21. Rules of Thumb • Animals tend to use “rules of thumb” or heuristics, rather than algorithms • This is focus of many animal cognitivists • What factors do animal use? • How do animals develop these rubrics? • What mechanisms are involved • This is the role of learning! • Innate behavior must be acknowledged • Learning/experience changes innate behavior • What is the intricate dance between innate and learned? • Are rules of thumb always accurate?

22. Foraging Games • Most animals are social • Live and work in groups • More than one increases complexity of decision making • What decision 1 animal makes affects others! • Think of it as a game: • Players • Strategies • Rules • Payoffs • 1 player’s actions rarely maximize payoff for other players • Players have conflict of interest • One’s gain comes at other’s expense • Could end up being 0-sum gain • We see this in real world of psychology: • Tragedy of the commons • Locus of control • Can we assume that all players use the same rules, strategies or have same payoff? • This changes nature of the game! • We can model the variations of the games using computational models • Prisoner’s dilemma, etc. • Now really made foraging situation complex!

23. So, what is a Psy 331 student to do? • Let’s combine the theories • What is we examined individual differences within the context of the group? • Let’s embrace competition and examine effects! • Examine how utility/best choice changes with • Species • Strain of rat • Competition factors • Environmental factors • Ideas?

24. Now: • Break up into your groups • Each group should provide me with: • List of names of individuals in your group • Days/times your group will be in the lab each day (allow 1 hour/day) • Each individual should be in lab 2.5 hours/week • Get this to me by end of period!