Not all ants are the thrifty creatures of our imaginations: army ants and slave-making ants wage war and capture prisoners. Two of Lanchester's most famous models of combat that apply to these ants are the Square Law and the Linear Law.
The former assumes that each individual is vulnerable to attack from every individual on the opposing side. During battle, the side that has the smallest army finds itself being attacked more fiercely since each soldier is attacked by more than one member of the opposition. The disparity between the two sides should increase through time, and the larger the army, relative to its enemy, the fewer casualties it will sustain.
This strategy is exactly the kind used by army ants. They regularly engage in deadly battles against other social insects, which they then eat. Army ants raid with enormous numbers of relatively small workers, none of which is a particularly good soldier. In some species, up to 200,000 ants can participate in a single raid. In comparison, the prey species numbers only a few thousand.
Army ants concentrate thousands of workers at the attack front, and, by sheer force of numbers, can overwhelm each colony they come to. One type of ant, Eciton burchelli, has several different sizes of ant in its army, but the smallest make up almost all of the foot soldiers in the front line.
The Square Law offers the best explanation for this, since if numbers are more important than individual fighting value, it is better to produce vast numbers of small soldiers. But Lanchester's Linear Law shows how an outnumbered force can turn the tables on its enemy. Instead of entering a free-for- all, the smaller army engages its opponents in a series of duels. If the soldiers in the smaller army are slightly stronger, each one can fight and win a whole series of duels.
Slave-making ants, as their name suggests, fight and capture ants from other species, and have become almost totally dependent on their prisoners for their livelihood. The problem is that the masters are doomed to be outnumbered by potential slaves, so the warring ants release 'propaganda' substances that act like the alarm signals used by the slaves themselves. In the ensuing melee, the confused slaves are unable to marshal their defences and can thus be picked off by the masters in a series of one-to-one duels.
But what if the soldiers on each side are similar? The American honey pot ant, for example, enslaves its own species. Different colonies of honey pot ants, acting with sinister similarity to humans, are like rival nations that size each other up before going to war.
Dr Franks says that opposing colonies go to a specialised tournament ground. 'They stand on extended legs, as if they are on stilts, and strut past each other. It seems very much as if they are weighing up numbers on the other side.'
Since the larger colonies have slightly larger workers, 'if you parade past 10 workers and they are all smaller than you, you know they are a smaller colony'. These rituals seem to be sufficient for the colonies to decide whether to go to war and, naturally, it is the side with the largest ants that launches the attack.
Lanchester's work has been used to study war. His theories have been applied, for example, to the battle of Iwo Jima, an island taken from the Japanese by the Americans in Febuary 1945. However, they have mainly been applied retrospectively. As Dr Franks explains: 'It is difficult to try to apply them to human warfare because military propaganda naturally lies.'