Original ArticleFight the power: Lanchester's laws of combat in human evolution
Introduction
“Words are inadequate to describe the emotion aroused by the prolonged movement in unison that drilling involved. A sense of pervasive well-being is what I recall; more specifically, a strange sense of personal enlargement; a sort of swelling out, becoming bigger than life, thanks to participation in a collective ritual.”
William McNeill (1995, p. 2)
“We've got them!”
George Armstrong Custer, at the Battle of the Little Bighorn.
Stephen Ambrose (1975, p. 438)
On 2 August 1867, Crazy Horse led a force of one thousand Sioux warriors in an attack on a US Army outpost near Fort Phil Kearny in northern Wyoming. Captain J. N. Powell gathered 26 soldiers and a handful of armed civilians in a corral of wagons, and they prepared to defend themselves. The Sioux initially circled Powell's position on horseback, firing arrows, intending to exhaust the cavalrymen's ammunition, but to no avail. Powell had stockpiled several thousand rounds, and the soldiers kept up a constant hail of fire. Eventually, Crazy Horse pulled his warriors back into a ravine, where they were partially protected from the gunfire. From here, the Indians attempted to attack on foot. The ravine was narrow which, as Stephen Ambrose describes, meant that “the men in front masked the mass of warriors in the rear, making it impossible for them to fire … Powell only had to deal with a handful of Indians, Crazy Horse and his fellow shirt-wearers [Sioux leaders] at the apex of the charge” (Ambrose, 1975, pp. 294–295). At this point, the outcome of the battle remained far from certain to those present. As one soldier recounted, “It chilled my blood … Hundreds and hundreds of Indians swarming up a ravine about ninety yards [away]… Our fire was accurate, coolly delivered and given with most telling effect, but nevertheless it looked for a minute as though our last moment on earth had come” (Ambrose, 1975, p. 295). Against their volleys of arrows and some astonishingly brave charges, the withering fire from the cavalry's new breech-loading rifles wore the Indians down and, after several hours' fighting, they withdrew to the mountains.
Against the backdrop of the earlier Fetterman massacre of 1866, when Crazy Horse and two thousand Sioux had surrounded Captain William Fetterman's force of 81 cavalrymen and annihilated them to a man, Powell's victory against the odds seemed nothing less than a miracle. But the reason Powell lived to see another day may well have been down to some fundamental mathematical principles of battle. Crazy Horse's congested attack up the ravine meant he was not able to bring his superior numbers and their deadly arrows to bear—even on a tiny enemy force. Meanwhile, Powell's concentrated fire on the lead ranks of Indians meant that, despite Powell's force being outnumbered 25 to 1, any Indian that squeezed onto the frontline fell into the sights of several American soldiers at once. Despite Crazy Horse's numerical supremacy and the advantage of surprise, the deck was stacked against him.
The “Wagon Box Fight” of 1867 reflects the mathematical patterns of Lanchester's Laws of Combat (Lanchester, 1916). These “laws” are mathematical equations that model the dynamics of conflict and its outcomes, and were originally developed with modern human warfare in mind. Although they have long been used in military operational research (for reviews, see MacKay, 2006, Wrigge et al., 1995), they have only recently been applied to explain variation in the patterns of conflict in animals such as ants, birds, lions, and chimpanzees (Franks and Partridge, 1993, Mosser and Packer, 2009, Plowes and Adams, 2005, Shelley et al., 2004, Whitehouse and Jaffe, 1996), including manipulation experiments showing variation in fighting behavior as parameters were changed (McGlynn, 2000, Wilson et al., 2002).
Much of the literature on Lanchester's Laws looks at models and data with regard to combat outcomes. In this paper we make a rather different kind of argument. First, we argue that Lanchester's Square Law, under which imbalances in numbers are disproportionately advantageous to the larger side, is especially applicable to pre-military human conflict, and is likely to have influenced its dynamics for several million years. This provides substantive support to theories about the importance of human groups and coalitions in early warfare (Alexander, 1987, Bingham, 2000, Pitman, 2011, Wrangham, 1999a).1
Second, the question then naturally arises: Have we evolved corresponding assessment strategies that influence when (and how) we choose to fight? Violent conflict is argued to have played a major role in our ancestral past (Buss and Shackelford, 1997, Ferguson, 2012, Gat, 2006, Guilaine and Zammit, 2004, Keeley, 1996, LeBlanc and Register, 2003, Potts and Hayden, 2008, Wrangham and Peterson, 1996, though for an earlier, contrasting view see Knauft 1991). Empirical studies suggest that warfare accounted for around 15% of male deaths among archeological and ethnographic data (and much more in some societies Bowles, 2006, Keeley, 1996, Otterbein, 1989), implying strong selection pressure on adaptations for fighting—and winning. We therefore hypothesize that natural selection should have favored assessment mechanisms that take the Square Law into account, leading to an evolved “Square Law heuristic” in the context of coalitionary conflict. Thus the Square Law becomes more than a post hoc model of conflict outcomes: rather it may be an evolved heuristic that influences decisions about whether or not to fight in the first place, continuing to affect decisions about conflict today. If so, this carries major implications for understanding human conflict in our past, present, and future.
Section snippets
Lanchester's Laws of Combat
Although there are variations in how the models are set up, and in real life there are many complicating factors (Adams and Mesterton-Gibbons, 2003, Johnson and MacKay, 2011, MacKay, 2011), the underlying logic of Lanchester's Laws capture the essence of conflict processes irrespective of species or setting—“elementary principles”, as Lanchester called them, “which underlie the whole science and practice of warfare in all its branches” (Lanchester, 1916, p. 39). The key insight is the
Which law applied in human evolution?
The dramatic difference between the Linear and Square Laws suggests that humans may have evolved rather different adaptations to conflict, depending on what type of conflict was dominant in human evolutionary history. We discriminate two distinct possibilities in particular: Hypothesis 1 (H1) If lethal conflict in human evolutionary history was primarily either duel-like (only one individual tended to fight one other at a time, so there was no opportunity for multiple attacks) or in the form of formal pitched
Implications for modern war
While a Square Law heuristic may have been adaptive in the small-scale inter-group conflicts of our evolutionary past (for which we argue it was designed), it may be maladaptive in conflict today, and especially in modern warfare. An evolved Square Law heuristic may prompt aggression in modern settings where there is numerical asymmetry but where the underlying dynamics, owing to weapons or circumstances, are no longer Square Law. Of course an unarmed crowd is unlikely to attack a small number
Possible empirical tests
The possibility that humans have an evolved Square Law heuristic leads to a variety of predictions that future empirical and experimental studies could test (summarized in Table 3). The core prediction is that human assessments of fighting strength increase in proportion to group size squared (relative to opponent group size). An auxiliary prediction is that we should observe a Square Law heuristic among men but not (necessarily) among women, since they were less likely to have participated in
Conclusions
The predominant form of deadly conflict in human evolutionary history, as well as among chimpanzees and some social carnivores, appears to have been asymmetric raiding, in which an attacking group has an overwhelming numerical advantage and uses it to ambush and kill members of rival groups at little cost to themselves (Manson and Wrangham, 1991, Wrangham, 1999a). Attack is concentrated while defense is divided, leading to Lanchester's Square Law, under which the fighting strength of a group is
Acknowledgments
We are grateful for comments and criticisms from Dan Blumstein, Oliver Curry, Jaimie Krems, Robert Kurzban, Steven LeBlanc, Anthony Lopez, Sarah Mathew, Raphael Sagarin, John Orbell, Michael Wilson, Richard Wrangham, and the participants at the Institute of Cognitive and Decision Sciences' 2008 meeting “Evolutionary Perspectives on War: An Interdisciplinary Conference”, in Eugene, Oregon.
References (137)
- et al.
Aggression and the self: High self-esteem, low self-control, and ego threat
- et al.
Human aggression in evolutionary psychological perspective
Clinical Psychological Review
(1997) - et al.
Lanchester battles and the evolution of combat in ants
Animal Behaviour
(1993) - et al.
The evolution of error: Error management, cognitive constraints, and adaptive decision-making biases
Trends in Ecology & Evolution
(2013) - et al.
Is military incompetence adaptive? An empirical test with risk-raking behaviour in modern warfare
Evolution & Human Behaviour
(2002) - et al.
Group territoriality and the benefits of sociality in the African lion, Panthera leo
Animal Behaviour
(2009) - et al.
Competition, coalitions and canine size in primates
Journal of Human Evolution
(1995) Settlement fortification in village and ‘tribal’ society: Evidence from contact-era New Guinea
Journal of Anthropological Archeology
(2008)- et al.
Lanchester's attrition models and fights among social animals
Behavioral Ecology
(2003) The biology of moral systems
(1987)
Crazy Horse and Custer: The Epic clash of two great warriors at the little bighorn
How the weak win wars: A theory of asymmetric conflict
The naval battle: Studies of tactical factors
Human evolution and human history: A complete theory
Evolutionary Anthropology
Death from a distance and the birth of a humane universe
The causes of war
Hierarchy in the forest: The evolution of egalitarian behavior
The evolution of irregular war: Insurgents and guerrillas from Akkadia to Afghanistan
Foreign Affairs
Warring ants: Lessons from Lanchester's theory of combat?
Journal of Biosciences
Group competition, reproductive leveling, and the evolution of human altruism
Science
Did warfare among ancestral hunter-gatherers affect the evolution of human social behaviors?
Science
Coordinated punishment of defectors sustains cooperation and can proliferate when rare
Science
Yanomamo
Party size in chimpanzees and bonobos: A reevaluation of theory based on two similarly forested sites
The evolution of the human capacity for “killing at a distance”: The human fossil evidence for the evolution of projectile weaponry
Violence: A micro-sociological theory
Throwing fire: Projectile technology through history
Density-dependent intraspecific aggression regulates survival in northern Yellowstone wolves (Canis lupus)
Journal of Animal Ecology
The Greek and Persian wars 499–386 BC
Peacemaking among primates
Chimpanzee politics: Power and sex among apes
Bonobo: The forgotten ape
A Lanchester model of guerrilla warfare
Operations Research
A verification of Lanchester's law
Journal of the Operational Research Society
The calculus of conventional war: Dynamic analysis without Lanchester theory
Why model?
Journal of Artificial Societies and Social Simulation
Tribal warfare
New or old wars? Debating a Clausewitzian future
Journal of Strategic Studies
Attrition models of the Ardennes campaign
Naval Research Logistics
The foundations of the science of war
Social organization, group conflict and the demise of neanderthals
Mankind Quarterly
War in human civilization
The role of rewards in motivating participation in simple warfare
Human Nature
What is negative about positive illusions? When benefits for the individual harm the collective
Journal of Social and Clinical Psychology
The chimpanzees of Gombe
The origins of war: Violence in prehistory
Yellowstone wolves in the wild
A journey from Prince of Wales's fort in Hudson's Bay to the Northern Ocean, 1769, 1770, 1771, 1772
Cited by (49)
Sex (similarities and) differences in friendship jealousy
2022, Evolution and Human BehaviorThe solution of Lanchester's equations with inter-battle reinforcement strategies
2022, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :Lanchester’s equations [1] form a very simple mathematical model for warfare, and have been applied to the study of historic battles [2] including the 1994–45 Battle of the Bulge[3], the 1940 Battle of Britain [4], and the 1916 Battle of Jutland [5]. They have also been applied in other contexts including combat in the animal kingdom [6] and human evolution [7]. While Lanchester’s work was arrived independently and almost simultaneously by Osipov [8], we will continue with the tradition of describing the mathematical model using Lanchester’s name.
Advertising patterns in a dynamic oligopolistic growing market with decay
2021, Journal of Economic Dynamics and ControlThe evolutionary anthropology of war
2020, Journal of Economic Behavior and OrganizationThe logic of animal intergroup conflict: A review
2020, Journal of Economic Behavior and OrganizationMaking ‘my’ problem ‘our’ problem: Warfare as collective action, and the role of leader manipulation
2020, Leadership QuarterlyCitation Excerpt :The resultant adaptations would represent a set of psychologically-instantiated conditional strategies (or ‘decision rules’) that guide personal intuition in wartime and are adaptively sensitive to context. For example, there is now growing evidence that mechanisms designed by natural selection to regulate individual participation in coalitional aggression should be highly attuned to individual risk and the distribution of risk within the group (Tooby & Cosmides, 1988), the balance between risk and reward (Glowacki & Wrangham, 2013), individual formidability (Archer, 1988; Parker, 1974; Sell et al., 2009), relative numbers (Johnson & MacKay, 2015; Wrangham, 1999), and a perceived probability of success which would be a joint function of such variables (Archer, 1988; Gat, 2009; Parker, 1974; Sell et al., 2009).7 Adaptive mechanisms regulating the individual decision of whether to participate is the necessary starting point since it is these variables that mechanisms designed for manipulation should be designed to track and recalibrate in others.