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Abstract The coral-dinoflagellate endosymbiosis is based on nutrient exchanges that impact holobiont energetics. Of particular concern is the breakdown or dysbiosis of this partnership that is seen in response to elevated temperatures, where loss of symbionts through coral bleaching can lead to starvation and mortality. Here we extend a dynamic bioenergetic model of coral symbioses to explore the mechanisms by which temperature impacts various processes in the symbiosis and to enable simulational analysis of thermal bleaching. Our model tests the effects of two distinct mechanisms for how increased temperature impacts the symbiosis: 1) accelerated metabolic rates due to thermodynamics and 2) damage to the photosynthetic machinery of the symbiont caused by heat stress. Model simulations show that the model can capture key biological responses to different levels of increased temperatures. Moderately increased temperatures increase metabolic rates and slightly decrease photosynthesis. The slightly decreased photosynthesis rates cause the host to receive less carbon and share more nitrogen with the symbiont. This results in temporarily increased symbiont growth and a higher symbiont/host ratio. In contrast, higher temperatures cause a breakdown of the symbiosis due to escalating feedback that involves further reduction in photosynthesis and insufficient energy supply for$$\hbox {CO}_2$$ ${\text{CO}}_2$concentration by the host. This leads to the accumulation of excess light energy and the generation of reactive oxygen species, eventually triggering symbiont expulsion and coral bleaching. Importantly, bleaching does not result from accelerated metabolic rates alone; it only occurs as a result of the photodamage mechanism due to its effect on nutrient cycling. Both higher light intensities and higher levels of DIN render corals more susceptible to heat stress. Conversely, heterotrophic feeding can increase the maximal temperature that can be tolerated by the coral. Collectively these results show that a bioenergetics model can capture many observed patterns of heat stress in corals, such as higher metabolic rates and higher symbiont/host ratios at moderately increased temperatures and symbiont expulsion at strongly increased temperatures. 

Abstract 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.