Host-virus-predator coexistence in a grey-box model with dynamic optimization of host fitness

Lytic viruses are believed to affect both flow patterns and host diversity in microbial food webs. Models resolving host and virus communities into subgroups can represent both aspects. However, when flow pattern is the prime interest, such models may seem unnecessary complex. This has led to proposals of black-box models using only total community sizes as state variables. This simplification creates a coexistence problem, however, since predator and virus communities then compete for the same, shared, prey = host community. Mathematically, this problem can be solved by introducing feedbacks allowing community-level properties to adapt. The different mathematical alternatives for such feedback represent different ecological assumptions and thus different hypotheses for how the balance between predators and viruses is controlled in nature. We here explore a model where the feedback works through an increase in host community resistance in response to high virus abundances, thereby reducing virus production. We use a dynamic "strategy" index S to describe the balance between defensive and competitive abilities in the host community, and assume the rate of change in S to be proportional to the local slope of the per capita fitness gradient for the host. We explore how such a "grey-box" model can allow stable coexistence of viruses and predators, and how equilibrium food web structure, virus-to-host ratio, and partitioning of host production varies; both as functions of host community traits, and as functions of external bottom-up and top-down drivers.