Currently, theories of viability are unequipped to deal with most biological phenomena as they work at the level of individual agents. In the natural world, organisms are rarely isolated and meaningfully influence each other’s survival. To close this gap, we take one analysis framework, viability space decomposition , and expand it to analyze an idealized model of two interacting, heterogeneous protocells. This ultimately involves thinking about life and death as taking place in a hybrid dynamical system and leads to new global manifolds in viability space that are unique to multi-agent systems. We conclude by discussing how this method scales with the number of agents and the organizing principles it suggests for the global structure of viability in multi-agent systems.

The notion of a viability constraint that determines the range of conditions under which a biological individual can survive plays a central role in work in artificial life and theoretical biology. However, while there has been considerable attention paid to the case where this constraint is defined externally, very little work has been done on the more natural case where this constraint arises intrinsically from the operational closure of the individual itself. Using a glider in the Game of Life as a toy model, we show how to systematically derive the intrinsic viability constraint of an emergent individual from its closed network of constitutive process interdependencies.

Under what conditions will an organism remain viable as numerous forces threaten its self-construction, and what does this abstract space of possibilities look like? A growing body of work has begun to confront this question by imposing viability limits on dynamical system models to separate sets of viable and nonviable states. Since the viability limits are not implicit in the equations that govern the dynamics, there is no guaranteed equivalence between the phase portrait and the basins of initial conditions that will remain viable. This means that the topology of a dynamical system model with imposed viability limits demands richer analyses, which we refer to as characterizing viability space . In this paper, we set the groundwork for such techniques using a protocell model governed by nonlinear ordinary differential equations, including the development of novel criteria for bifurcations so that entire classes of systems can be studied.