1-1. It's getting dark. A juvenile rabbit feeding in a meadow must find refuge for the night. If it heads north, out of the meadow along trails in the tall grass, most of the time (75%) it will reach reach the meadow's edge (and safety) in about five minutes.... if, however it gets lost in the labyrinth of trails in the grass (this happens 25% of the time), it will take the rabbit an additional 25 minutes to reach the edge of the meadow. In contrast, if the rabbit takes the longer route to the south, it almost always takes about 10 minutes to reach the meadow's edge, although 5% of the time the rabbit gets bogged down in muddy areas. The mud adds 5 minutes to the route. Assuming risk of predation is equal in all parts of the meadow and linearly related to time spent moving to the edge, which strategy minimizes the risk of being eaten (i.e. to minimize its time in the meadow, should the rabbit head south or north)?

1-2. You are trying to decide whether or not to pursue a higher degree in Molecular Biology. If you do, you figure you have a 20% chance of eventually landing a tenure-track position at a university making $40,000/year, a 40% chance of working for a local genetic engineering firm at $30,000/year, and the remaining chances of ending up as a bottle washer somewhere making $15,000/yr. Alternatively, you can enter a graduate program in Behavioral Ecology, with a 30% chance of landing a $40,000/yr. university position and 70% chance of landing a job as wildlife biologist in Costa Rica that pays $25,000/yr. Considering monetary remuneration only, which graduate program should you choose?

2-1. Suppose Senator Swamp has damning evidence in his files, detailing how he personally benefited from the award of a large defense contract to a specific company. Across the hall, Senator Nefarious was also in on the deal. He too made a similar profit and has similar documentation of his activities. Each Senator knows about the other's files. If both keep their mouths shut, the chances of either being found out and indicted by the Senate Anti-corruption Committee is only 10%. On the other hand, if one of them shreds his own files and mentions to the New York Times that it might be fun to look in the other's files, he looks so honest and righteous that his chances of being indicted drop to 5%. Were he to do so, the chances of the other senator being indicted increases to 30%. If both senators shred their own files and rat on the other, they both look like such crooks that the chances of indictment rise to 15% for each. Assuming they want to avoid indictment, what is the ESS (and is there a moral here)? Click here to see the answer to question # 2-1

 

2-2. Two foraging squirrels may sometimes simultaneously come upon a nut. Under such circumstances, they have two behavioral options: They can either attack the other squirrel or they can make an appeasement display. If both squirrels show appeasement displays, there is an equal chance that they will get the nut to themselves or they will get nothing at all. Squirrels that are attacked while showing an appeasement display are immediately driven away from the nut at no cost, which is then acquired, at no cost, by the attacking squirrel. If two squirrels both attack there is, again, an equal chance that they will win or lose. Presuming: a) that squirrels seek to maximize their caloric intake; b) that a healthy nut represents a potential net gain of 60 calories of nutrition (80 calories in the nut, minus the 20 calories expended while opening it); and c) that fighting consumes 30 calories, calculate how a squirrel should behave during the winter, when only 50% of nuts are healthy. The rest are rotten inside (no nutritional value, but this cannot be determined until the nut has been opened).

How would your answer change if, in the spring time, the percentage of healthy nuts increased to 75%?

Click here to see the answer to question # 2-2