Analysis of a mechanistic model of corals in association with multiple symbionts: within-host competition and recovery from bleaching.

Coral reefs are increasingly experiencing stressful conditions, such as high temperatures, that cause corals to undergo bleaching, a process where they lose their photosynthetic algal symbionts. Bleaching threatens both corals' survival and the health of the reef ecosystems they create. One possible mechanism for corals to resist bleaching is through association with stress-tolerant symbionts, which are resistant to bleaching but may be worse partners in mild conditions. Some corals have been found to associate with multiple symbiont species simultaneously, which potentially gives them access to the benefits of both stress-sensitive and -tolerant symbionts. However, within-host competition between symbionts may lead to competitive exclusion of one partner, and the consequences of associating with multiple partners simultaneously are not well understood. We modify a mechanistic model of coral-algal symbiosis to investigate the effect of environmental conditions on within-host competitive dynamics between stress-sensitive and -tolerant symbionts and the effect of access to a tolerant symbiont on the dynamics of recovery from bleaching. We found that the addition of a tolerant symbiont can increase host survival and recovery from bleaching in high-light conditions. Competitive exclusion of the tolerant symbiont occurred slowly at intermediate light levels. Interestingly, there were some cases of post-bleaching competitive exclusion after the tolerant symbiont had helped the host recover.

Timescale separation and models of symbiosis: state space reduction, multiple attractors and initialization.

Dynamic Energy Budget models relate whole organism processes such as growth, reproduction and mortality to suborganismal metabolic processes. Much of their potential derives from extensions of the formalism to describe the exchange of metabolic products between organisms or organs within a single organism, for example the mutualism between corals and their symbionts. Without model simplification, such models are at risk of becoming parameter-rich and hence impractical. One natural simplification is to assume that some metabolic processes act on 'fast' timescales relative to others. A common strategy for formulating such models is to assume that 'fast' processes equilibrate immediately, while 'slow' processes are described by ordinary differential equations. This strategy can bring a subtlety with it. What if there are multiple, interdependent fast processes that have multiple equilibria, so that additional information is needed to unambiguously specify the model dynamics? This situation can easily arise in contexts where an organism or community can persist in a 'healthy' or an 'unhealthy' state with abrupt transitions between states possible. To approach this issue, we offer the following: (a) a method to unambiguously complete implicitly defined models by adding hypothetical 'fast' state variables; (b) an approach for minimizing the number of additional state variables in such models, which can simplify the numerical analysis and give insights into the model dynamics; and (c) some implications of the new approach that are of practical importance for model dynamics, e.g. on the bistability of flux dynamics and the effect of different initialization choices on model outcomes. To demonstrate those principles, we use a simplified model for root-shoot dynamics of plants and a related model for the interactions between corals and endosymbiotic algae that describes coral bleaching and recovery.