In a population entirely composed of solitary prey, the fitness payoff to individuals is P. But then mutant individuals arise that use others as living shields. When a solitary individual is found and used by a social type for protection, the solitary animal loses some fitness (B) to the social type. The costs (C) to social individuals include time spent searching for another individual to hide behind. We will assume that when two social individuals meet, each has an equal (1/2) chance of being the one to hind behind the other when a predator attacks.

Explanation:

Initial fitness is P. Now after the solitary individual being used is social mutant, then the solitary animal drops fitness by B

In such case, the net fitness of Solitary would be ;

P-B

Now the costs (C) for finding a new animal and training it;

P+B-C

Now when the two social types interact, they have a 1/2 chance of being behind the other when a predator attacks

Safest when solitary

P+B/2-B/2-C = P-C

Since P-C would be less than P so the initial condition was better than this one

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