Diatoms are common marine algae that account for most of the pho- tosynthesis that occurs in the ocean.

mathematics

Description

(1) Diatoms are common marine algae that account for most of the pho- tosynthesis that occurs in the ocean. As Vogel (2004) discusses, although diatoms live in the top layers of the ocean, they are denser than the water around them, so they sink slowly in still water. Only the constan tmixing of water in the ocean prevents them from sinking into the deeper layers of the ocean. Diatoms are also apparently adapted to sink as slowly as possible, by evolving shapes that have very high fluid dynamic re- sistance. One such shape is a long filament. Why do they have this shape? In this problem you will compare sinking of filamentous diatoms and spherical diatoms

(a) We want to consider the effect of changing the volume of the diatom upon its sinking velocity. Supposing that the diatom is a sphere, its volume is given by

(2) How cooperative behaviors can evolve is an open problem in biology. A cooperative behavior is one in which each organism performs a costly task, but the reward from performing this task is shared somewhat indiscriminately among organisms. For example, emperor penguins huddle together to keep warm during the cold Antarctic winter. The penguins at the edge of the flock endure the worst wind, but their bodies shield the penguins inside the flock. If penguins take it in turns to be on the outside, the cost (shield other penguins with your body) and the reward (being warmed and shielded from the wind) are shared quite evenly between penguins. Although cooperation benefits the population as a whole, it is also vulnerable to an effect called defection. If a single organism decides not to cooperate then it will still share in the rewards from cooperation, but will not need to pay the cost. For example, a penguin could choose to not spend any time at the edge of the flock, so it is shielded from the wind by the other penguins but does not take its turn shielding the others.