An evolutionarily stable strategy approach to indiscriminate spite

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Abstract
AN individual behaves spitefully when it harms itself in order to harm another individual more(1). Hamilton(1,2) predicted that spite may evolve if it is expressed only in those encounters that occur between individuals of less than average relatedness. More recently Verner(3) suggested that territory size may become super-optimal because of a selective advantage arising from the spiteful exclusion of others from limited resources. His model is essentially different from Hamilton's in that spite is directed at individuals indiscriminately with respect to relatedness. Recently Rothstein(4) has shown analytically that the initial spread of spiteful traits will be very slow in all but the smallest populations. He also argued verbally that indiscriminate spite can never be evolutionarily stable even if it should spread (see also Davies(5)). The question of evolutionary stability is clearly important, but its resolution requires an analytical approach. We report here an approach based on Maynard Smith's(6) concept of the evolutionarily stable strategy (ESS), a strategy which, when common, does better than any alternative strategy played by a rare mutant. We show that spite can be an ESS, but that the magnitude of spite will be small in large populations.