I recently saw W D Hamilton’s 1970 paper “Geometry for the Selfish Herd” described as “a classic in its own right.” As a long-time bibliophile this made it irresistible, but I was also intrigued by the incongruity of “selfish herd” and of linking geometry to animals. I have to report that the paper certainly is a classic, for all the wrong reasons, but it contains a valuable message.

The introduction to the paper began with:
This paper presents an antithesis to the view that gregarious behaviour is evolved through benefits to the population or species. Following Galton (1871) and Williams (1964) gregarious behaviour is considered as a form of cover-seeking in which each animal tries to reduce its chance of being caught by a predator.
You can see that from the outset there will be no attempt at providing complementary analysis, to build on previous work, no attempt to expand the horizon of human knowledge. From the outset this paper attempts to reject a particular view and replace it with another. This is not going to be about optional extras or “the big picture.” In fact it’s so “small picture” that although the paper has only progressed for two sentences a glaring weakness has already emerged that will destroy any conclusions reached. Despite predation being the focus of the entire paper, the author has already lost sight of gregariousness in predators.

Hamilton began his argument with what he called a model of predation in one dimension.
Imagine a circular lily pond. Imagine that the pond shelters a colony of frogs and a water-snake. The snake preys on the frogs but only does so at a certain time of day - up to this time it sleeps on the bottom of the pond.
Shortly before the snake is due to wake up …
The scenario that follows contains the following rock-hard propositions; “imagine” (4 times) “it is supposed” (once) “suppose” (twice) “usually” (once) “assuming” (once) and included a geometrical analysis of how the individual frogs would position themselves around the edge of this fictional pond to best survive at the expense of their fellows. Hamilton was honest enough to conclude “It may seem a far cry from such a phantasy (sic) to the realities of natural selection.” But he ruined it by; “Nevertheless I think there can be little doubt that behaviour which is similar in biological intention to that of the hypothetical frogs is an important factor in the gregarious tendencies of a very wide variety of animals.” From hypothetical frogs to a wide variety of animals? I don’t think so.

Hamilton then moved to a two-dimensional model. He referred to the problem herd animals have with various biting insects, and implied that the herding tendency was also a response to these types of attacks. What he failed to mention was that animals do not only congregate when attacked by insects, they then display group behaviours of mutual aid. They stand in relation to each other in such a way that tail movement by one protects another. This is certainly not herding to reduce risk of personal attack in the sense stated by Hamilton, as his risk reduction was a purely statistical, selfish, “safety in numbers” approach.

He then discussed outright predation as a factor causing the evolution of herding, in particular the marginal predation by lions whereby animals on the fringe of a herd are most at risk. “In 1871 Francis Galton published in Macmillan’s Magazine an article entitled “Gregariousness in Cattle and in Men”. In it he outlined a theory of the evolution of gregarious behaviour based on his own observations of the behaviour of the half wild herds of cattle owned by the Damaras in South Africa. In spite of the characteristically forceful and persuasive style of his writing, Galton’s argument is not entirely clear and consistent. Some specific criticisms will be mentioned shortly. Nevertheless it does contain in embryo the idea of marginal predation as a force of natural selection leading to the evolution of gregarious behaviour.”
The following quote from Galton was presented as the foundation of Hamilton’s hypothesis of selfish herds; “Yet although the ox has so little affection for, or individual interest in, his fellows, he cannot endure even a momentary severance from his herd. If he be separated from it by stratagem or force, he exhibits every sign of mental agony; he strives with all his might to get back again and when he succeeds, he plunges into its middle, to bathe his whole body with the comfort of closest companionship.”
That’s it. Hamilton drew from that one passage the concept of selfish herds. Unusual or unjustifiable though his logic might be, we cannot dismiss it as just a harmless idiosyncrasy on Hamilton’s part, as he ignored all of Galton’s observations that did not support his hypothesis.

Hamilton now had at his disposal a valuable historical account of herd behaviour, but chose instead to launch immediately into an unnecessary and misleading thought experiment that he later admitted is not realistic; “Although as Galton implies, lions, like most other predators, usually attack from outside the herd, it is possible to imagine that in some circumstances a lion may remain hidden until the cattle are feeding on all sides of it. Consider therefore a herd grazing on a plain and suppose that its deep grass may conceal – anywhere - a lion. The cattle are unaware of danger until suddenly the lion is heard to roar. By reason of some peculiar imaginary quality the sound gives no hint of the whereabouts of the lion but it informs the cattle of danger. At any moment, at any point in the terrain the cattle are traversing, the lion may suddenly appear and attack the nearest cow.”
There are several problems with this. Contrary to what Hamilton would like us to think, it’s not “possible to imagine”, it’s almost impossible to imagine the scenario he presented. Lions attack from downwind to avoid detection. Encirclement by cattle is therefore almost out of the question, not only for this reason, but also because a lion would feel insecure among a mass of trampling hooves and lunging horns. And lions do not roar when hunting, again to avoid detection. Any conclusions that are drawn from this exercise will be of no use at all.

Hamilton then gave an extensive geometry-based explanation of the behaviour that would ensue if one cow detected the lion, and concluded; “Thus even for the most unpromising initial conditions it remains evident that predation should lead to the evolution of gregarious behaviour. No story even as poorly realistic as the foregoing can be given for the case of predation in three dimensions.” So that’s two imaginary scenarios, both completely fanciful, from which conclusions about animal behaviour have been drawn.

Amazingly, Hamilton then began attacking Galton for not complying with Hamilton’s simplistic, reductionist view of herd dynamics.  “Whether or not marginal predation is, as I believe it to be, a common primary cause of the evolution of gregariousness, it is surprising that the idea of such a cause has received so little attention from biologists…Galton himself is certainly largely to blame for this. With one exception he did not relate his idea to species other than cattle and sheep, and the one exception was man…Another probable reason for the neglect of Galton’s idea is that he himself presented it mixed up with another really quite separate idea which he treated as if it were simply another aspect of the same thing. This was that every cow, whether marginal or interior, benefited by being part of a herd, and that therefore herding was beneficial to the species. His supporting points are undoubtedly forcible; (sic) he mentions mutual warning and the idea that by forming at bay in outward-facing bands the cattle can present a really formidable defense against the lions. However, whether or not the cattle actually do, in the last resort, overcome their centripetal inclination and turn to face the predator (as smaller bands of “musk ox” certainly do), these points raise a different issue, as do the mass attacks on predators by gregarious nesting birds. My models certainly give no indication that such mutualistic defense is a necessary part of gregarious behaviour.”
Please read that last sentence again. Here we have a biologist pontificating on animal behaviour, using field observations to make his point when it suits, ignoring field observations of the most crucial nature when it does not suit, and relying on the relevance and significance of mathematical modeling to arrive at a conclusion. This is outrageous. And his excuse for ignoring data? He claimed that mutual defense “probably” only occurs when animals are related and can recognize each other, or “probably” when they undertake a risk assessment and decide that the risk is small! Right. You’ll notice that in that extract Hamilton chastised Galton for restricting his conclusions to the species that Galton had actually observed. In other words, sober, considered, reasonable analysis is regarded with contempt.
His dismissal of Galton ended by quoting the following wonderful description by Galton of the benefits that accrue from group activity; “To live gregariously is to become a fibre in a vast sentient web overspreading many acres; it is to become the possessor of faculties always awake, of eyes that see in all directions, of ears and nostrils that explore a broad belt of air; it is to become the occupier of every bit of vantage ground whence the approach of a lurking enemy might be overlooked.”
Hamilton refuted this view with; “But there is of course nothing in the least altruistic in keeping alert for signs of nervousness in companions as well as for signs of the predator itself, and there is, correspondingly, no difficulty in explaining how gregariousness on this basis could be evolved.” Possibly so. So why did Hamilton not explain gregariousness on this basis? Why resort to untestable geometry, “phantasies” and ignoring of data? Herd activities such as mutual defense against predators, mutual defense against pests and so on, can be explained on the basis of individual survival. Why is this approach rejected out of hand? It’s rejected because there is a consequence to this line of thought about which the “evolution-as-selfishness” crowd wants you to remain in the dark. You will notice that Hamilton carefully directed the discussion away from the group, which Galton was discussing, to a discussion of the individual. But the group cannot be ignored, particularly in this case where even Hamilton acknowledged the significance of group behaviour. Once it is conceded that group behaviours can assist the survival of the individual, as Hamilton reluctantly concedes, it follows that group behaviour is a factor in evolution. Then the genie really is out of the bottle.

This fact, the significance of group behaviour in evolution, is so important, so undermining of selfish gene theory, that its advocates will go to any length to refute it. For example, it has been argued elsewhere that the “stotting” of the Thompson gazelle, in which an individual bounds away from a predator in a flashy display of exaggerated leaps, is based only on selfishness, as it allegedly tells the predator that this particular individual is so healthy and virile that any attempt at pursuit would be a waste of time. The people making these types of claims must not realise how foolish they look. This behaviour is not restricted to the Thompson gazelle. The Australian wallaby also behaves this way, and it’s clear to an observer, from the loud thumping sound that ensues, that the principal aim of the exaggerated leaps is not to attract the attention of the predator, it’s to make sufficient noise as its feet hit the ground, that other wallabies who might have their heads down as they graze are alerted to the danger. But why does the escaping animal not give alarm calls as it flees? This would be simpler and more energy-efficient surely. The answer is that most if not all species of wallaby, have very little vocal capacity. And it’s a safe bet that the gazelle has to deal with the same inability.

The paper ended poorly. Hamilton was unable to produce a firm conclusion despite a confident no-nonsense attitude throughout, and was forced to finally concede that his predation hypothesis was merely an alternative to other explanations for group behaviours. But it did not have to end that way. If Hamilton had merely attempted an explanation for the initiation of the herding tendency, rather than a simplistic total picture of all the countless currents that make up social interactions then he could have produced something of genuine and lasting significance. For it’s undeniable that herding to reduce the odds of predation is a reality. But to claim as Hamilton did, that this is the only noteworthy feature of herding, is just plain foolish, because if it’s not foolish it’s deceitful. Hamilton somehow decided, for reasons we can only guess at, to ignore the volumes of observations collected through the centuries, of animals congregating for reasons other than cover-seeking. 
There’s a lesson to be learnt from Geometry for the Selfish Herd.
Biologists should refrain from lecturing on animal behaviour until they have spent a considerable period of time in the field. In Hamilton’s paper there is not one reference to a behaviour studied by the author himself. We do not see Darwin, Wallace, Mayr or Diamond making strenuous claims for selfishness in evolution, for a very good reason. These were men who grew up, who became men, in the wild, remote, hazardous regions of the world. They lived hard. Isolated from the protections that modern technological society provides, they exposed themselves to the forces of natural selection. They saw mutual aid as a factor in their own survival, and saw mutual aid mitigating the harshness of competition in every forest and foothill, every steppe and swamp, every nook and cranny of the natural world.
In short, as they say in the classics, when it comes to natural selection, don’t talk the talk until you’ve walked the walk.