Temporal and spatial coral-algae dynamics with larval dispersal
Creators: Hua, Xiaotian
Publisher: name: University of Alberta Library
Year: 2023

<p>Coral reefs are essential to the marine ecosystem, and provide some of the most diverse habitats in the world. Coral reef fisheries contribute 6.8 billion to the economy a year globally. However, coral reefs are under significant threat because of human activities such as overfishing, ocean pollution, and habitat destruction. Overfishing leads to shrinkage of the herbivorous fish population, and ocean pollution results in the rapid growth of nutrients in the water. These activities give rise to macroalgae, since herbivorous fish eat many algae and excessive nutrients provide macroalgae with abundant necessities to grow. Macroalgae constantly compete with coral for living space. Adult coral and algae can grow by overgrowing other functional groups or available space. Coral larvae and algae propagules can recruit into adult coral and algae by dispersal and settlement onto available space. Existing literature mainly treats the whole coral reefs as one big patch and focused on one functional group overgrowing other functional groups. However, that is rarely the case in nature. Coral reefs are composed of hundreds of coral skeleton patches and between each patch are sand and rocks. Living coral, macroalgae, and turf algae grow on the coral skeletons. The mechanism of how coral, macroalgae, and turf algae occupy available space while competing; and how macroalgae invade coral and turf algae spatially through larval or propagules dispersal and settlement is still poorly understood. We develop several differential equation models from the first principles and a solid biological background to answer<br>
those two questions in chapters 2 and 3. We also give conditions under which coral will retreat or expand. The interactions between macroalgae and coral were widely studied, but how turf algae interact with other benthic groups is still poorly understood. We also generate some insights into the role of turf algae from the analysis from chapters 2 and 3.</p>

<p>In chapter 2, we develop a one-patch ordinary differential equation model by introducing available space explicitly and incorporating larval dispersal. We undertake bifurcation analysis to understand the effect of grazing on the coral-algae dynamics. We show coral persist under high grazing pressure. We show reasonable fishing helps maintain the herbivorous fish population, and a healthier herbivorous fish population can support a higher level of coral cover. We find coral are more resistant to the decline of larval recruitment when the rate of turf algae occupying available space is high.</p>

<p>In the chapter 3, we consider multiple patches and derive a weakly-coupled network of ordinary differential equations and a reaction-diffusion equation model for the continuous space case from the first principles for modelling brooding coral dynamics. We use the spatially explicit reaction-diffusion equation model to understand the spatial dynamics of the coral-algae ecosystem, and we simulate travelling waves to explain how the macroalgae invade coral spatially through larval dispersal at different grazing levels.</p>