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Now in 3-D: The shape of krill and fish schools


Watching videos of fish feeding frenzies is a very emotional experience for me. You know the videos I'm talking about (personal favorites here, 0:55 in, and here). They feature a swirling, glittering mass of fish that seems to dance and flit as a single entity while being torn apart by three or four types of predators such as seabirds, sharks, whales and dolphins. On the one hand, I want to give the school of fish a good shake and yell, "YOU IDIOTS! If you stick together in a tight ball like that, you're cornered! You're all gonna die!" But, on the other hand, I'm amazed by their resilience and ability to not get thrown to opposite corners of the ocean during the turmoil. How do they do it?

This latter emotion appeals to my human sentimentality, imagining the fishes holding out with their fishy family to the very end. Of course, this is entirely delusional: these fish are not in it together due to any sense of solidarity, but rather because sticking together works for each of them most of the time. But what is it about schooling that helps them better survive in the open and vast three-dimensional marine universe?

Akule (big-eyed scad) in Keauhou Bay, Hawaii forming a dense school because of diver or predator disturbance. Image © Bo Pardeau 2010 - Link

Why do fish form schools?

If I were a lone fish swimming in the vast ocean, I would probably have a heart attack. I would assume that every watery vibration was a shark and be constantly looking for somewhere to hide. But of course, this is open water we're talking about! There are no hiding spots!

In 1971, W. D. Hamilton asserted that this is the purpose of flocks, herds and shoals: to provide hiding spots for organisms traveling openly. His theory of "marginal predation" states that a predator will attack the prey to which it is closest, and thus individuals on the edges of a group are at the most risk. These aggregations of fish form because the fish are trying to hide behind one another and, in the process, push their brethren into danger. Not the idealized image we have of group living, no? In Hamilton's words, "behaviour of this kind certainly cannot be regarded as showing an unselfish concern for the welfare of the whole group."

Image from W. D. Hamilton's paper (1971) illustrating that, even if organisms (here, frogs) aren't traveling as a group, if a predator comes near, they will try to get behind another to avoid being the closest to the predator. Hence, forming an aggregation, which he calls "selfish geometry."

There are other advantages to aggregating into shoals, defined as any group of fish, or eventually schools, when fish travel and turn together as if one organism. First off, if there are more fish for a predator to choose from, each individual is less likely to get eaten. If the fish look enough alike in both size and coloring, the predators can become confused, unable to pick one fish out of the bunch and thus are less efficient hunters. Larger groups also are better at watching for predators because there are more eyes on the lookout (Megurran 1990).

When the fish are all riled up in the presence of a predator, they do form these dense bait balls as each fish scrambles to get to the center to hide. This centripetal motion literally forms a sphere: the shape that has the most interior volume and keeps the fewest number of fish on the surface and thus more vulnerable to predators. Of course, this is not the shape that a shoal traveling casually forms. Instead, we have "circles, discs, ellipses, triangles, wedges, crescents, and lines" (McFarland and Moss 1967). Thus predation alone cannot be the only factor shaping shoals; is there another central factor and what is it?

In October, Andrew Brierley and Martin Cox from the University of Saint Andrews in Scotland published a paper in which they investigated this very question.

The geometry of schools: what defines their shape?

Brierley and Cox were using multibeam sonar to study the 3-D shape of krill shoals in the Antarctic when they found an intriguing pattern. Their own sampling of 1006 krill shoals produced an average roughness of 3.3/m. Roughness, the ratio of surface area-to-volume, is a simple and descriptive measurement of shape. They describe this shape as a “multifaceted lozenge;” to me, a large shoal with a roughness of 3.3/m looks like a brazil nut, while a medium-sized shoal looks like an almond.

Ideal shoal shapes, defined by a roughness (surface area: volume ratio) of 3.3/m. They look like nuts, in my opinion. Figure modified from Brierley and Cox 2010.

When they looked through the literature of roughness in fish schools, the 4 other species studied previously had this identical average roughness of 3.3/m. They had identified a common variable to describe fish shoals that crossed species boundaries! But why is a roughness of 3.3/m so ideal? What factor is trading off with predation to form this shape?

Most research to this point has focused on the trade-off between foraging and avoiding predation (such as Morrell and Romey 2008). If you're all squished in the middle of a ball of your fish brethren, it's hard to reach food resources. Thus fish should find a medium position between the outside of the shoal to take advantage of food and the center to avoid a sudden predator attack.

Brierley and Cox suspected that foraging was not a key factor, but instead access to oxygen. Their reasoning is that the basics of survival in the open ocean are (1) breathing and (2) not being eaten. They admit that eating and reproducing are also important, but, as they astutely put it, "individuals that fail in the former two objectives cannot achieve these."

In the 1960s, William McFarland and Sanford Moss observed that, while fish shoals will generally hold to a consistent shape, the fish are constantly changing their positions within the interior, resulting in the ever-shifting, almost kaleidoscopic shoals we observe (Science 1967). They measured pH, carbon dioxide and oxygen throughout shoals of striped mullet, and found drastic drops of 25% dissolved oxygen in the center of the shoal. When there was a sudden drop in oxygen, they could watch the shoal reorganize itself. A pretty awesome finding: that there can be enough fish packed into the center of a shoal to actually deplete the seawater of oxygen!

Brierley and Cox used this idea to create a model that compared the benefit to each individual fish at different shoal roughnesses, incorporating oxygen diffusion rates in seawater at different temperatures, packing density and size by fish species, and shoal shapes. And what did their results show? The shapes that provide the greatest benefit to the most individuals, trading off between oxygen and predation risk, have a roughness of 3.3/m. They also ran their model to find the roughness with the greatest benefit, this time balancing foraging ability and predation, and got a roughness ratio of 2.1/m, which does not fit with the observed results.

The direct correlation between their model and field observations provides great support that the shape of a shoal is determined by this balance between the needs to breathe and to not get eaten. As multibeam sonar is used more frequently to capture the 3-D shapes of shoals, we will have more field observations which will help to show just how widespread this phenomenon is.

Interpretation of Brierley and Cox's results. I apologize to the authors. Fish photo by Johnny Baru - Link.

Oxygen and predation as shoal definers in today's world

Knowing that the amount of oxygen dissolved in water defines shoal geometry can help us to predict the ecology of fish shoals under the influence of our current human-caused climate change, global warming. One of the basic laws of physics, Henry's Law, shows that oxygen is better able to dissolve in cold water than warm. Many studies have shown that ocean temperature is increasing (Garcia et al. 2005; Stramma et al. 2010). What effect will this have on shoals and beyond?

If oxygen is less able to dissolve in seawater, fish shoals should shrink in size while maintaining their roughness ratio of 3.3/m. If fish are already struggling to breathe at the interior of shoals because they themselves are using up the oxygen, a lower baseline of oxygen will no longer be able to support shoals as large as exist now.

Typically a larger shoal provides more protection from predation, as predators do get full at some point. It's more likely that some of the individual fish will escape uneaten, instead of the entire shoal being devoured. Here come the unknowns: How much does seawater temperature have to rise to create a drop in dissolved oxygen that will significantly affect shoal size? How small does a shoal have to get so that it is consistently devoured in its entirety? Will they shrink enough that fish-eating predators will have trouble finding food? I hope we never find out the answers to these questions.

A reduction in shoal size could also have effects that ripple out even to human predators, fishermen. Fishermen have long used the ecology of shoaling fish to better their fishing methods (Parrish 1999). The estimate that shoaling fish make up 50% of our net fisheries catch is a conservative one, at 35-40 million metric tons each year. Part of the reason we catch shoaling fish is because it is easy to get a lot of them at once (Parrish 1999). A significant decrease in shoal size could reduce our ease at catching the amount of fish we do now; once again, at what point shoals become small enough to have an effect is the unknown.

I've presented you with a number of unanswered questions here at the end, which is frustrating to me as well (I assure you). But this is the age we live in: an age when the climate is changing, but it is unknown what the particular effects will be in the long run. This is why it's important to continue to study marine ecology and the factors that influence a major food source both for marine life and for ourselves. The more we know about present conditions, the better we can predict and prepare for the changes to come.


Brierley, Andrew S. and Martin J. Cox. 2010. Shapes of krill swarms and fish schools emerge as aggregation members avoid predators and access oxygen. Current Biology 20: 1-5.

Garcia, Hernan E., Tim P. Boyer, Sydney Levitus, Ricardo A. Locarnini, and John Antonov. 2005. On the variability of dissolved oxygen and apparent oxygen utilization content for the upper world ocean: 1955 to 1998. Geophysical Research Letters 32: L09604.

Hamilton, W. D. 1971. Geometry for the selfish herd. Journal of Theoretical Biology. 31: 295-311.

McFarland, William N. and Sanford A. Moss Internal behavior in fish schools. 1967. Science 156: 260-262.

Megurran, Anne E. 1990. The adaptive significance of schooling as an anti-predator defense in fish. Annales Zooligici Fennici 27: 51-66.

Morrell, Lesley J. and William L. Romey. 2008. Optimal individual positions within animal groups. Behavioural Ecology 19: 909-919.

Parrish, Julia K. 1999. Using behavior and ecology to exploit schooling fishes. Environmental Biology of Fishes 55: 157-181.

Stankowich, Theodore. 2003. Marginal predation methodologies and the importance of predator preferences. Animal Behaviour 66: 589-599.

Stramma, Lothar, Sunke Schmidtko, Lisa A. Levin, and Gregory C. Johnson. 2010. Ocean oxygen minima expansions and their biological impacts. Deep Sea Research Part I: Oceanographic Research Papers 57: 587-595.

About the Author: Hannah Waters is a graduate of Carleton College, where she studied Biology and Latin, and currently works as a research specialist in Philadelphia using yeast to study the epigenetics of aging. When she gets home from work, she writes about ecology and evolution at her blogs, Culturing Science and the marine-focused Sleeping with the Fishes. Her non-science interests include making soup, acquiring colorful sweaters, reading apocalyptic fiction, and listening to all the good songs ever recorded. You can find her on twitter @culturingsci.


The views expressed are those of the author and are not necessarily those of Scientific American.

The views expressed are those of the author and are not necessarily those of Scientific American.

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