Loading in 5 sec....

Storage for Good Times and Bad: Of Squirrels and MenPowerPoint Presentation

Storage for Good Times and Bad: Of Squirrels and Men

- 249 Views
- Updated On :
- Presentation posted in: Pets / Animals

Storage for Good Times and Bad: Of Squirrels and Men. Ted Bergstrom, UCSB. A fable of food-hoarding,. As in Ae sop and Walt Disney… The fable concerns squirrels, but has more ambitious intentions. What can evolution tell us about the evolution of our preferences toward risk?

Storage for Good Times and Bad: Of Squirrels and Men

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Storage for Good Times and Bad:Of Squirrels and Men

Ted Bergstrom, UCSB

- As in Aesop and Walt Disney…
- The fable concerns squirrels, but has more ambitious intentions.
- What can evolution tell us about the evolution of our preferences toward risk?
- For the moral of the story, we look to the works of another great fabulist…
- Art Robson

- Robson (JET 1996) : Evolutionary theory predicts that:
- For idiosyncratic risks, humans should seek to maximize arithmetic mean reproductive success. (Expected utility hypothesis.)
- For aggregate risks, they should seek to maximize geometric mean survival probability.

- Squirrels must gather nuts to survive through winter.
- Gathering nuts is costly—predation risk.
- Squirrels don’t know how long the winter will be.
- How do they decide how much to store?

- There are two kinds of winters, long and short.
- Climate is cyclical; cycles of length k=kS+kL, with kSshort and k Llong winters.
- Two strategies, S and L. Store enough for a long winter or a short winter.
- Probability of surviving predators: vS for Strategy S and vL=(1-h)vS for Strategy L.

- A squirrel will survive and produce ρ offspring iff it is not eaten by predators and it stores enough for the winter.
- If winter is short, Strategy S squirrel survives with probability vS and Strategy L with probability vL<vS.
- If winter is long, Strategy S squirrel dies, Strategy L squirrel survives with prob vL

- Reproduction is asexual (see Disney and Robson). Strategies are inherited from parent.
- Suppose pure strategies are the only possibility.
- Eventually all squirrels use Strategy L.
- But what if long winters are very rare?

- How about a gene that randomizes its instructions.
- Gene “diversifies its portfolio” and is carried by some Strategy S and some Strategy L squirrels.
- In general, such a gene will outperform the pure strategy genes.

- A randomizing gene tells its squirrel to use Strategy L with probability ΠL and Strategy S with probability ΠS.
- The reproduction rate of this gene will be
- SS(Π)= vS ΠS+vL ΠL, if the winter is short.
- SL(Π)=vL ΠLif the winter is long.

- Expected number of offspring of a random strategist over the course of a single cycle is
ρkSS(Π) kSSL(Π) kL

- Optimal strategy chooses probability vector Π=(ΠL ,ΠS )to maximize above.
- A gene that does this will reproduce more rapidly over each cycle and hence will eventually dominate the population.

- There is a mixed strategy solution if
aL=kL/k<h.

- Mixed solution has ΠL =aL/h and
SL/SS= aL(1-h)/(1- aL)h.

- If aL>h, then the only solution is the pure strategy L.

- If long winters are rare enough, the most successful strategy is a mixed strategy.
- Probability matching. Probability of Strategy L is Is aL /h , proportional to probability of long winter.
- For populations with different distributions of winter length, but same feeding costs the die-off in a harsh winter is inversely proportional to their frequency.

- Model extends naturally to the case of many possible lengths of winter.
- Replace deterministic cycle by assumption of iid stochastic process where probability of winter of length t is at
- Choose probabilities Πt of storing enough for t days. Let St(Π) be expected survival rate of type if winter is of length t.

- Then the optimal mixed strategy will be the one that maximizes the product S1(Π) a1S2(Π) a2… SN(Π) aN.
- Standard result of “branching theory.” Application of law of large numbers. See Robson, JET.

- Biologists discuss examples of phenotypic diversity despite common genetic heritage.
- Period of dormancy in seed plants—Levins
- Spadefoot toad tadpoles, carnivores vs vegans.
- Big variance in size of hoards collected by pikas, golden hamsters, red squirrels, and lab rats—Vander Wall

- Well, yes, this model says so.
- Alternative method of producing variation—sexual diploid population, with recessive gene for Strategy S.
- Whats wrong with this? Strategy proportions would vary with length of winter.
- But gambling genes would beat these genes by maintaining correct proportions always.

- Humans are able to run redistributional lotteries. What does this do?
- This possibility separates diversification of outcomes from diversification of production strategies.
- If some activities have independent risks, individuals can choose those that maximize expected risks, but then gamble.

- Suppose squirrels can gamble nuts that they have collected in fair lotteries.
- Let v(y) be probability that a squirrel who collects y days supply of nuts is not eaten by predators.
- Expected nuts collected is yv(y).
- Optimal strategy for gene is to have its squirrels to harvest y* where y* maximizes yv(y) and then gamble.

- Humans are able to run redistributional lotteries. What does this do?
- This possibility separates diversification of outcomes from diversification of production strategies.
- If some activities have independent risks, individuals can choose those that maximize expected risks, but then gamble.