Modeling the huddling behavior of Emperor penguins: everybody gets equal warmth

August 18, 2020 • 9:15 am

Every winter (spring in the Northern Hemisphere), after having produced a chick, female Emperor penguins  (Aptenodytes forsteri) head off to sea for two months to fatten up, while the males stay behind, foodless for over 100 days, to tend the chicks. (The males get their turn to eat later, but often walk about 100 km to get to the water.)  With air temperatures as low as -40° C (same in Fahrenheit), and the winds blowing as hard as 140 kph (90 mph), it gets deadly cold.  And that’s when the penguins huddle together for warmth.

Here’s a short PBS video of penguin huddles.  Note the constant shifting of the birds.

And the huddle really keeps them warm. A 2012 paper in PLOS ONE (screenshot below, pdf here, reference at bottom) reported that the temperature inside the huddle can reach 20°C-37.5°C (68°F-100°F). Individuals outside the huddle, exposed to the air and wind, however, don’t get as warm. As the video shows above, the penguins move constantly, with exterior penguins going into the middle and then being expelled to the margins again. These huddles appear to last only a few hours—during bad storms.

If you click on the screenshot below, you’ll go to a paper in which the three authors, using several simple assumptions, try to predict what shape the huddle will assume, and how it will change over time.  There’s also a shorter but easier-to-understand summary that’s just been published in Quanta Magazine

The authors’ assumptions are these:

  1. The penguins form a huddle, and they’re packed in the most efficient way: hexagonally. (This corresponds to how they appear to be packed in nature.)
  2. The huddle is assumed to be on a plane, and the penguins have a uniform size and shape. They encounter wind.
  3. The penguins have an assumed rate of heat loss, with the ones on the outside losing more heat.

Then the authors then do their simulation, which involves one chilly penguin moving at a time to get warmer. Here are the steps they simulate:

  1. Generate a huddle and determine the huddle boundary.
  2. Compute the wind flow around the huddle.
  3. Compute the temperature profile around the huddle.
  4. Compute the local rate of heat loss for each penguin.
  5. Add random variations to the rate of heat loss (optional).
  6. Identify the penguin with the highest rate of heat loss (the “mover”) and move it to a location on the boundary where heat loss is minimal.
  7. Determine the new huddle boundary.
  8. Repeat over the desired number of iterations by going back to Step 2.

Quanta shows a diagram of how the simulation works:

Samuel Velasco/Susan D’Agostino/Quanta Magazine; based on: Modeling Huddling Penguins

You’ll notice immediately that some of these assumptions are oversimplified—especially that the coldest penguin is the one that moves, and he (it’s a male) moves to the warmest spot on the periphery, not to just a warmer spot. The video of the huddle above doesn’t seem to show only one penguin moving at a time, nor does it seem realistic that the mover can find the warmest possible spot. Note, though, that as the coldest penguin (on the windward side, of course) moves, an interior penguin becomes an exterior penguin, and that generates a new mover, and so on and so on. Eventually, the shape of the huddle changes.

As the diagram from the paper shows below, the model shows the huddle changing from irregular to roughly rectangular, with one small side of the rectangle facing the wind. (The short faces of the rectangle are actually rounded, not straight.) After about 50 iterations of the model, the steady-state shape begins to emerge. Here’s a diagram from the paper showing the shape change over time (iterations) with the wind coming from the left.



One interesting outcome of the model is that, in the end, all penguins have experienced about the same loss of heat and have had roughly equal access to the warmth inside the huddle. This is an example of a selfish behavior acting to produce heat equity for all. The authors also note that the model does not produce the least heat loss for the colony as a whole, which I think would come from a sphere. (I’m just guessing here.)

Now the value of this simulation is only as good as its predictive power. Do penguin huddles really assume these shapes over time? The answer appears to be, well, not really: they are not elongated rectangles but are more irregular in shape. (One prediction that was confirmed previously, though, is that in the huddle the penguins are packed hexagonally.)

The authors tweaked the model by allowing random variations in the heat loss of individual penguins, which generate more irregular shapes that, say the authors, produce a shape of the huddle “qualitatively similar to that of real huddles.” They point to a figure that supposedly shows the qualitative similarity (Fig. 5a), but it doesn’t show that: it shows that huddles become more irregular in shape as the degree of random perturbation increases.  It would have been better had they shown some real shapes of huddles evolving over time.

The Quanta article links to studies of heat loss and penguin movement in progress that may eventually yield this data, but it doesn’t exist now. But the data do show that, as predicted, individuals tend to move from the windward to the leeward side of the huddle, and that this movement is more pronounced when wind speed is stronger.

A lot remains to be done, including observations of colonies to see how individuals move. But that’s very hard given the terrible weather conditions and the problems of putting researchers on the site near these fragile colonies (One of the cited papers describes a remote-controlled observatory.) And of course, if the assumptions of the model prove to be wrong, as a couple seem to be, then the model needs to be severely refined. But at least the authors have singled out a cool problem that may eventually have a fairly simple solution. But I think that solution will have to involve more than one penguin moving at a time!

h/t: Paul


Article: A. Waters, F. Blanchette F, and A. D. Kim. (2012) Modeling huddling penguins. PLOS ONE 7(11): e50277.

25 thoughts on “Modeling the huddling behavior of Emperor penguins: everybody gets equal warmth

  1. Cool – I mean – warm!

    I wonder if/when an innovative penguin will realize: heat rises! Get on TOP!

    1. Warm air rises, yes, but then you’d be exposed to the frigid wind. Far better off staying right in the middle of the huddle.

  2. Very cool science article.

    Though hopefully it will warm up when it gets another article on the other side of it. 🙂

  3. You make a couple of fascinating points about the behavior of individuals in complex adaptive (social) systems, namely, selfish behavior by all produces equality but does not necessarily maximize the social benefit, in this case warmth. It seems for that principle to apply, however, it would need to be tweaked with the qualifier “equally competent,” viz. equally competent selfish behavior by all produces equality but does not necessarily maximize social benefit. Less competent individuals in the group, say those that are older and weaker, will eventually, at the margin, be unable to move around from the windward side to the leeward side, and perish. Among individuals of other species, some may be less competitive than others due to weakness or, simply, disposition, which could lead to potentially massive inequalities. But it would still remain true that selfish behavior by all does not necessarily produce maximum social benefit (contrary to classical economic theory).

    1. But to follow your thoughts to conclusion… what natural mechanism will produce maximum social benefit?

      Unless you propose some variant of group selection all evolution has to ‘play’ with is individuals and their genes. A sub-optimal social benefit may be a consequence of the most evolutionarily fit individuals leaving more copies of their genes and less fit individuals leaving fewer copies. Evolution doesn’t care. Not about optimum social benefits or the fate of individuals.

    2. Less competent individuals in the group, say those that are older and weaker, will eventually, at the margin, be unable to move around from the windward side to the leeward side, and perish.

      Maybe, but they’ll get some protection by simply moving out of the face of the wind (i.e. they don’t have to go all the way around to get benefit), and not every penguin necessarily stays an equal time on the windward side. The weaker penguins probably spend less time on windward before they get uncomfortable enough to move.

      Additionally, I imagine 20-38 C is quite toasty for a healthy, fat Emperor penguin. If the older weaker penguins have less fat/insulation, then there is probably some natural sorting where the oldsters are happier in the middle while the middle age and younger penguins are actually happier not being in the middle.

    3. PCC conjectures that the socially optimum herd would be circular (a “sphere” of penguins would be a sight to behold). I believe that would be correct with zero wind because the circle minimizes the length of the boundary and thus the heat loss. But with a wind, my intuition suggests you would want a shape elongated in the direction of the wind for a social optimum. This reduces the boundary on the windward side and reduces heat loss to the colony from wind chill. Thus the selfish herd and the socially optimal herd would both be elongated, I think. Whether the selfish herd would be more elongated than optimal is an interesting question.

      1. Thinking more about this, I think the selfish herd or huddle cannot minimize the heat loss of the group because of the shuffling, more than the shape. Shuffling means that a cold penguin is replaced by a warmer one, which has to increase the heat loss as compared to the no shuffle case. The social optimum in terms of heat loss would require a huddle where every penguin keeps its place, or at least exchanges places only with others of equal warmth. Of course, the outer penguins are miserable. I will forgo any comparison to human society.

  4. First assume a hexagonal penguin … that’s how you know this paper was written by mathematicians, not biologists 🙂

  5. Swallows huddle too when the need arises. At dusk April 3 some 10-12 swallows were tightly huddled together on the ledge of my bathroom window sheltering from a bitter north wind. Temperatures in Greece at the time were some 6-8 degrees lower than normal. Also, as Spring was quite late this year, when they arrived there were virtually no insects for them to replenish energy. So they were weak and cold; grim prospects; one was dead in my bathroom in the morning. It was a bad day for me. Sadly,very few, if any, are now in the Balkans.

  6. So very ‘heartwarming’. I note that due to this virtually impossible climate and weather, there is no predation on the chicks. Appears a good strategy.

  7. The research is very interesting. However, the extremely organized penguin huddle, in order maximize heat distribution between themselves, is astonishing.

  8. No huddling here – we have a local heat wave. But else this is a nice collective model.

    But I think that solution will have to involve more than one penguin moving at a time!

    Maybe, but we don’t know it is necessary (I suspect not). The better idea may be to improve movement from wind side after a delta chill to random positions on the lee side. (In which case it is easier to implement simultaneous moves – no search for maximum heat involved.) Almost certainly penguins orient after the wind under these conditions of poor sight and no time to waste on looking for optimal temperatures – I would.

    1. No huddling – local heat wave, and of course the pandemic.

      Also, I inserted an unnecessary, unreasonable appeal to anecdote. Guess it’s time for a coffee break!

  9. “…the model does not produce the least heat loss for the colony as a whole, which I think would come from a sphere” – You probally meant a circle which would indeed be optimal but for the wind.

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