Abstract
We present a systematic and quantitative model of huddling
penguins. In this mathematical model, each individual penguin in the huddle
seeks only to reduce its own heat loss. Consequently, penguins on the boundary
of the huddle that are most exposed to the wind move downwind to more sheltered
locations along the boundary. In contrast, penguins in the interior of the
huddle neither have the space to move nor experience a significant heat loss,
and they therefore remain stationary. Through these individual movements, the
entire huddle experiences a robust cumulative effect that we identify,
describe, and quantify. This mathematical model requires a calculation of the
wind flowing around the huddle and of the resulting temperature distribution.
Both of these must be recomputed each time an individual penguin moves since
the huddle shape changes. Using our simulation results, we find that the key
parameters affecting the huddle dynamics are the number of penguins in the
huddle, the wind strength, and the amount of uncertainty in the movement of the
penguins. Moreover, we find that the lone assumption of individual penguins
minimizing their own heat loss results in all penguins having approximately
equal access to the warmth of the huddle.