Swim in company

1 · Compare the strategies

Two cells in line, 5 cell radii apart. Gains measured against two cells swimming alone.

Beginner

How do two selfish cells fare compared with two cells that keep their solo strokes and only fall into step?

Better: 29% against 17% The same: both gain 17% Worse: 14% against 17%

2 · Weigh the relatedness

Relatedness ρ: 1 for clones, 0 for strangers, negative for rivals. Gain of the pair over two selfish cells: (2ρ − ρ²) times the full cooperative gain.

Intermediate

With ρ = 0.5, what share of the cooperative gain does the pair recover?

75% 50% 25%

3 · Turn the cells into rivals

Expert

Two rivals with ρ = −1: how does each fare, compared with a selfish pair?

Each gains the full cooperative gain Each loses three times the cooperative gain Nothing changes, they ignore each other

4 · Leave the flat world

The study is two-dimensional, where a swimmer's flow fades as 1/ℓ. In three dimensions, it fades as 1/ℓ².

Expert

What happens to the dilemma in three dimensions?

It is confined to close neighbours It reaches farther than in two dimensions It disappears entirely

Dilemma understood

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