Determining the community structure of the coral Seriatopora hystrix from hydrodynamic and genetic networks

Abstract

The exchange of genetic information between coral reefs through the transport of larvae can be described in terms of networks that capture the linkages between distant populations. A key question arising from these networks is the determination of the highly connected modules (communities). Communities can be defined using genetic similarity or distance statistics between multiple samples but due to limited specimen sampling capacity the boundaries of the communities for the known coral reefs in the seascape remain unresolved. In this study we use the microsatellite composition of individual corals to compare sample populations using a genetic dissimilarity measure (F_ST) which is then used to create a complex network. This network involved sampling 1025 colonies from 22 collection sites and examining 10 microsatellites loci. The links between each sampling site were given a strength that was created from the pair wise F_ST values. The result is an undirected weighted network describing the genetic dissimilarity between each sampled population. From this network we then determined the community structure using a leading eigenvector algorithm within graph theory. However, given the relatively limited sampling conducted, the representation of the regional genetic structure was incomplete. To assist with defining the boundaries of the genetically based communities we also integrated the communities derived from a hydrodynamic and distance based networks. The hydrodynamic network, though more comprehensive, was of smaller spatial extent than our genetic sampling. A Bayesian Belief network was developed to integrate the overlapping communities. The results indicate the genetic population structure of the Great Barrier Reef and provide guidance on where future genetic sampling should take place to complete the genetic diversity mapping.

Introduction

The exchange of genetic information, through coral larvae exchange, is fundamentally important for the function of the Great Barrier Reef (Hughes et al., 1999, Ayre and Hughes, 2004). Recruitment rates and resilience to disturbances are influenced by the migration of coral larvae that either settle locally or are transported across large distances (van Oppen and Gates, 2006). However the marine environment is not always favourable for coral growth and coral reefs are subject to cyclic natural disturbances which shape the community composition (Wakeford et al., 2008). Understanding the broad scale boundaries of the communities defined by genetic grouping can assist the development of appropriate management strategies (Lubchenco et al., 2003, Kerrigan et al., 2010). Reserve design informed with the knowledge of the genetic diversity and the larval exchange processes can optimise the persistence of marine species.

Due to the difficulties in measuring larval exchange (Palumbi, 2003), connectivity research is heavily reliant on hydrodynamic simulations (James et al., 2002, Werner et al., 2007). While the models have become more sophisticated in recent years (Legrand et al., 2006, Luick et al., 2007) the simulations of larval movements are limited in scale, sensitivity testing and behavioural responses (Baums et al., 2006). Critically, understanding population connectivity is not limited to just the transport of larvae but also includes settlement success and juvenile mortality (Mumby, 1999). Tracing the natal colonies of individuals that have successfully established is paramount to understanding the structure of marine metapopulation dynamics. A metapopulation is characterised by the extent that the dynamics of local populations are influenced by a nontrivial external replenishment of larvae across a range of spatial scales and are therefore strongly dependent upon local demographic processes (Kritzer and Sale, 2004).

An alternative method of measuring the metapopulation structure is to examine the genetic composition of individual corals in a small locality and then statistically compare sample populations across the region (Hellberg, 2007, Underwood et al., 2007, van Oppen et al., 2008). DNA markers, like microsatellites, have sufficient variability to analyse how individuals relate to the sampled populations (Pritchard et al., 2000) yet the allele proportions are not expected to be distorted by local selection pressures. The microsatellite composition of each individual can be used as the basis for determining the linkages between populations (Arens et al., 2007). Any individual can theoretically be associated with all of the populations in the sample, albeit with a very small probability. One approach is to find the individuals that do not seem to originate from the local population using exclusion tests. However these exclusion tests are limited by the genetic diversity present in, and divergence among, the metapopulation. If several populations are genetically similar then migrants will not be correctly identified if they cross from one population to another (Piry et al., 2004). The F_ST metric, commonly used to describe genetic differentiation, implies that when two populations are not significantly different (i.e. F_ST = 0) that high levels of genetic exchange have occurred previously. Each sampled population pair can then be assigned a F_ST weighting as a measure of their connectedness.

These connections create complex networks with properties that highlight the nature of coral reef ecology. Brooding corals will have reduced dispersal capabilities compared with broadcasting coral species (Ayre and Hughes, 2000) and this enables finer spatial resolution of the dispersal patterns. Each species is likely to have particular dispersal properties across a range of scales (Kinlan et al., 2005) and more research is required to understand the comprehensive metapopulation dynamics (Cowen et al., 2002).

This paper describes the network created from the genetic analysis of the brooding pocilloporid coral Seriatopora hystrix Dana 1846 by van Oppen et al. (2008). S. hystrix is a common coral in many parts of the world (Veron, 2000) despite being a predominantly self recruiting species. The life history of S. hystrix, in which eggs are fertilised internally and then released at an advanced developmental stage, ensures that larvae can settle within hours to days and this tends to limit long distance dispersal (Ayre and Dufty, 1994, Underwood et al., 2007). The majority of larvae settle within 100 m of the natal colony but a small percentage (2–6%) are successful in moving large distances (Underwood et al., 2007). The larvae are equipped with maternal zooxanthellae and could exist for many weeks in the water column (Underwood et al., 2007). Given the velocity of the currents within the GBR (James et al., 2002, Luick et al., 2007), settlement at distant reefs is conceivable.

The use of hydrodynamics to inform the dispersal processes in marine systems is an established and expanding research field (Knights et al., 2006, Luick et al., 2007). While modelling across the regional scales and complexity of the Great Barrier Reef requires the acknowledgement of limiting assumptions (such as the resolution of the digital elevation model) the capacity to understand the underlying processes is compelling.

The results of the population differentiation analysis can be used to construct a network of nodes and edges (Fortuna et al., 2009). A connecting edge can be formed from the centroid of the possible natal population to the centroid of the population where the migrant was found. The edges can then be combined to construct a network (or ‘graph’ in mathematical disciplines). The analysis of this network can utilise graph theory concepts and methods (Steuer and Lopez, 2008, Dorogovtsev, 2010).

While there is significant interest in the role played by individual reefs in the regional dispersal process, the key focus for conservation planners is the ‘community’ (Garcia-Charton and Perez-Ruzafa, 1999, Kerrigan et al., 2010). Genetically this can be defined as a set of local populations that are more similar in their microsatellite composition than compared to the wider metapopulation (Fortuna et al., 2009). This loose definition can also be adapted to networks describing the interconnected nature of the populations. Using graph theory, a community based on dispersal processes can be described as a set of populations that are more connected through dispersal to each other than to the remaining populations. The differentiation of communities within a network has been vigorously pursued over recent years and a range of methods exists to automatically find the network's subunits (Fortunato, 2010).

One method that produces consistently good results was developed by Newman, 2006a, Newman, 2006b and is based on optimising a benefit function called modularity (Newman and Girvan, 2003). Modularity can be defined as:

Q = (number of edges within communities) − (expected number of such edges) (Newman, 2006a) and can be optimised for a range of community detection algorithms. For the present study we chose the leading eigenvector algorithm (Newman, 2006a), as implemented in igraph (Csardi and Nepusz, 2006). The result is a set of communities that are optimised for the network structure being examined. Recent advances have extended the analytical capacity from undirected networks to weighted directional networks (Leicht and Newman, 2008).

A leading question, in the context of metapopulation dynamics, is how to resolve the boundaries of the genetically based communities when sampling is sparse? One possible approach is to use the hydrodynamic communities as a surrogate for the population structure. One limitation to this approach is that the Lagrangian particle model developed by James et al. (2002) considers the coral reef as a single uniform entity from which coral is released as a function of the external boundary. This ignores the substantial lagoon structure that dominates many coral reefs (Hopley, 1982). The genetic samples were taken in both the lagoons and the reef crests and the role of geomorphology and the hydrodynamics was apparent (van Oppen et al., 2008). Modelling limitations aside, the capacity for hydrodynamic based dispersal models to inform the inter-population connections, and hence the overall metapopulation structure, is worth investigation.

Comparing communities developed from the hydrodynamic networks to those created from the genetic F_ST statistics is not a trivial exercise. The size and membership of each set of communities are influenced by the selection of threshold values that exclude the ‘weaker’ edges. When the nodes are fully connected to each other the community sorting algorithms will identify only one large community. If the threshold is such that few edges remain then the communities will be solitary nodes and be uninformative. Comparing the disparate communities is possible using a conditional probability framework such that the membership of one community can change our expectation (i.e. belief) of the structure of another community given the evidence collected so far. Bayesian Belief Networks (BBN) adopt a graphical approach to help characterise the inferential structure (i.e. conditional probabilities) that exist between variables under consideration (Jensen, 2001). This approach which combines graph and probability theory seeks to manage uncertainty and complexity within the modelling environment. The use of BBN in ecology is established as a mechanism of informing dependencies despite a paucity of data (Borsuk et al., 2002, Wooldridge and Done, 2003). There are two key principles in operation within a BBN. The first is Bayes rule whereby the probability that a variable is in a certain state is dependent on the state of another variable or in symbols;

P(a|b) = P(b|a) × P(a)/P(b) where a and b are the states of variables A and B respectively. The second principal is the chain rule which is able to depict the joint probabilities; P(A,B) = P(B|A)P(A). This is useful for BBN since the structure of the graph (i.e. edges connecting nodes) describes the conditional probabilities (P(B|A)). Once the BBN is constructed then the conditional probability table for each variable can be updated based on the available evidence. Given the state of a variable in the BBN the state of any other variable can be calculated. This ‘calibrated’ BBN then enables probabilistic predictions of the ‘most likely’ state of an unmeasured variable given the state of the other variables within the network.