Abstract
As a heritable sequence-specific adaptive immune system, CRISPR-Cas is a powerful molecular mechanism shaping strain diversity in host-virus systems. Nevertheless, the structure and dynamics of host-virus interactions associated with diversification remain largely unexplored. We quantified the network structures of infection ('who infects whom') and immunity ('who is protected from whom') in a stochastic Lotka-Volterra model of host and viral populations including evolution. The coevolutionary dynamics exhibit an alternation between periods of virus-host diversification and host control. In periods of diversification, infection networks are partitioned into modules of hosts and viruses, reflecting the emergence of niches within which viruses can grow as the result of negative frequency-dependent selection. Acquisition of immunity closes available niches and builds a weighted-nested immunity network, representing redundant protection and causing a shift to a host-controlled regime. The nested structure enforces an orderly virus extinction which in turn increases the potential for an escape mutation in viruses and another transition to a virus-diversification regime. These dynamics and structures are not obtained under neutral scenarios lacking specific immunity. FInally, the immunity networks in three empirical systems also exhibit weighted nestedness, a pattern our theory shows is indicative of host control. Our findings emphasize the role that network structure plays in CRISPR-induced host-virus coevolution, providing one explanation for existing host/viral diversity in natural and empirical systems.