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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 In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of exponential growth we show power-law relationships that relate variability in the time required to reach a threshold population size to growth rate and inoculum size. Population-growth experiments inE. coliandS. aureuswith inoculum sizes ranging between 1 and 100 are consistent with these relationships. We quantify how noise accumulates over time, finding that it encodes—and can be used to deduce—information about the early growth rate of a population. 

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. 

Abstract Multispecies mutualisms are embedded in a network of interactions that include predation, yet the effects of predation on mutualism function have not been well integrated into mutualism theory. Where predators have been considered, the common prediction is that predators reduce mutualist abundance and, as a consequence, decrease service provision. Here, we use a mathematical model of a predatory fish that consumes two competing coral mutualists to show that predators can also have indirect positive effects on hosts when they preferentially consume competitively dominant mutualists that are also lower in quality. In these cases, predation reverses the outcome of competition, allowing the higher quality mutualist to dominate and enhancing host performance. The direction and strength of predator effects depend on asymmetries in mutualist competition, service provision, and predation vulnerability. Our findings suggest that when the strength of predation shifts (e.g., due to exploitative harvest of top predators, introduction of new species, or range shifts in response to climate change), mutualist communities will exhibit dynamic responses with nonmonotonic effects on host service provision.