Connectivity modelling of the coral reef ecosystem

In science there has been a growing focus on networks as a way of understanding complex systems. Nowhere is this more apparent than in marine ecology where strong currents driven by wind, tide and oceanic flows can move larval particles vast distances. The networks created between source and recruitment sites are often complex and large. This capacity has not been adequately addressed in the modelling and conservation literature. This thesis addresses the role of graph theory in advancing applied and pure marine ecology from structural descriptions to conservation planning. Chapter 2 identified the network structure of the Great Barrier Reef as generated by hydrodynamic modelling and Lagrangian particle transfer. We discovered that passive particle dispersal in the Great Barrier Reef forms a topology called “small world”. Small world topology is defined by the capacity of sparsely connected networks to remain comparatively small in their diameter (defined as the minimum number of links between the furthest vertices). We also compared the Great Barrier Reef network to a range of other topologies from simple lattices to intricate scale free graphs. In chapter 3, we described the impact that various dispersal topologies have on the metapopulation persistence of marine species. The stochastic metapopulation model developed by Drechsler (Drechsler M (2009) Predicting metapopulation lifetime from macroscopic network properties. Mathematical Biosciences, 218, 59-71) was adapted to explicitly incorporate graph theory metrics. This work highlighted the importance of topology on the metapopulation dynamics which will be overlooked by researchers using simple diffusion models to represent dispersal. In particular we discovered that networks with clusters (groups of highly connected populations also known as hubs) were more persistent across a range of extinction and colonisation rates. Enhancing metapopulation persistence is a desired outcome of conservation planning so understanding what effect the topology has on optimal reserve placement is critical. In chapter 4 we optimised the metapopulation mean life time, described in chapter 3, by reconfiguring the reserve design. These simulations were based on a variety of network topologies. We found that the optimal persistence of a metapopulation is best achieved by choosing sites in well connected clusters. We also discovered that additional reserves should then be allocated to sites that are relatively isolated from the main clusters. From a conservation perspective, metapopulations, that are predominantly clustered (e.g. having a small world topology), have an increased persistence when sites are protected using knowledge of dispersal topology. While using hydrodynamic models to inform the network structure can be instructive, the reality is that larval transfer between populations is only part of the recruitment process. Issues such as settlement mortality and interspecies competition are highly variable and difficult to assess directly. Chapter 5 utilises population genetics to discover the parental identity of successful recruits. Using the differences in microsatellites loci, population compositions can be compared and measures of similarity generated. We use this methodology and discovered that the genetic network structure of Seriatopora hystrix coral has a small world topology. However the collection and processing of samples for population genetic purposes is limited by resources and therefore lacks the coverage of hydrodynamic models. Describing the biodiversity of the marine world requires information on the spatial assemblage of clusters. These clusters can be defined in terms of genetic similarity or functionally described by oceanography. In chapter 6 we described a conceptual model that compared clusters between disparate networks since the genetic data was sparse while the hydrodynamic models were comprehensive. Using an evidence-based probabilistic framework, this model was able to estimate the likelihood of a particular genetic composition, for a population, from the conditional probabilities derived from a hydrodynamic model. This means the genetic information collected so far can be extended to coral reefs that have not been sampled and, importantly, the model highlighted the coral reefs that are a high priority for future sampling. This thesis utilises graph theory to explore the interconnected world of coral reefs. In particular the Great Barrier Reef was found to have a “small world” topology based on hydrodynamic modelling. We showed that the topology of the dispersal networks has implications for the persistence of the coral and fish metapopulations. We established that optimising the allocation of marine reserves to suit the topological configurations results in the maximum persistence of a metapopulation. We recognised the limitations of hydrodynamic modelling to describe the recruitment process and incorporated population genetics as a measure of coral reef interconnectivity. We discovered that, despite the limited coverage, the genetic network of the coral Seriatopora hystrix also had a small world topology. To help complete the description of the S. hystrix metapopulation structure we combined the genetic and hydrodynamic network information to create a conceptual model that described the cluster configuration. Overall this thesis highlights that the topological character of dispersal networks is highly influential on marine metapopulation dynamics and associated conservation planning. It develops some tools and ideas that help to describe, understand and potentially manage that complexity