The number of immune defense and counter-defense systems sustained in the arms race between procaryotes and viruses

Prokaryotes have evolved various mechanisms to counter viruses, which in their turn developed numerous strategies to avoid defenses of the hosts. Dozens of such defense and counter-defense mechanisms have recently been discovered, yet the number of such systems held by a given virus or its host is limited. Here, we present numerical and theoretical arguments for the existence of the maximal number of ecologically and evolutionary sustainable defense and counter-defense systems maintained by both sides at any time of the never-ending evolutionary arms race. We find that the number of such systems is of the order of 10 for a broad range of assumptions about the costs and benefits of defense and counter-defense mechanisms and their specificity. This optimum in the number of defense and counter-defense systems appears as a result of a compromise between the metabolic and autoimmune costs of adding a new layer of defense and the benefits it conveys. 1 Significance statementAlmost all living creatures are either predators or prey (and many are both). At all scales of life, from single cells to largest mammals, prey evolve defenses against predators and predators in their turn evolve counter-defense mechanisms. As a result of this ever-lasting arms race, each organism usually possesses multilayer defense and counter-defense arsenals. Is there a limit to the size of these arsenals? In this work we present a proof-of-principle argument that such a limit indeed exists. Using for definity an example of prokaryotes as the prey and their viruses as predators, we show that the number of distinct defense and counter-defense system that the prey and predators possess is limited by a number of the order of 10 and is only weakly dependent on the ecology of predator-prey interactions. Similar principles and limits likely emerge universally in various antagonistic conflicts such as crime and law enforcement or real arms race.