Network theory and metapopulation persistence: incorporating node self‐connections

Offshore oil and gas infrastructure plays a minor role in marine metapopulation dynamics

Decommissioning consequences of offshore oil and gas infrastructure removal on marine population dynamics, including connectivity, are not well understood. We modelled the connectivity and metapopulation dynamics of three fish and two benthic invertebrate species inhabiting the natural rocky reefs and offshore oil and gas infrastructure located in the Bass Strait, south-east Australia. Using a network approach, we found that platforms are not major sources, destinations, or stepping-stones for most species, yet act as modest sources for connectivity of Corynactis australis (jewel anemone). In contrast, sections of subsea pipelines appear to act as stepping-stones, source and destination habitats of varying strengths for all study species, except for Centrostephanus rodgersii (long-spined sea urchin). Natural reefs were the main stepping-stones, local source, and destination habitats for all study species. These reefs were largely responsible for the overall metapopulation growth of all study species (average of 96 % contribution across all species), with infrastructure acting as a minor contributor (<2 % average contribution). Full or partial decommissioning of platforms should have a very low or negligible impact on the overall metapopulation dynamics of the species explored, except C. australis, while full removal of pipelines could have a low impact on the metapopulation dynamics of benthic invertebrate species and a moderate impact on fish species (up to 34.1 % reduction in the metapopulation growth). We recommend that the decision to remove offshore infrastructure, either in full or in-part, be made on a platform-by-platform basis and consider contributions of pipelines to connectivity and metapopulation dynamics.

Network topology and patch connectivity affect dynamics in experimental and model metapopulations

Biological populations are rarely isolated in space and instead interact with others via dispersal in metapopulations. Theory predicts that network connectivity patterns can have critical effects on network robustness, as certain topologies, such as scale-free networks, are more tolerant to disturbances than other patterns. However, at present, experimental evidence of how these topologies affect population dynamics in a metapopulation framework is lacking. We used experimental metapopulations of the aquatic protist Paramecium tetraurelia to determine how network topology influences occupation patterns. We created metapopulations engineered to be comparable in linkage density, but differing in their degree distribution. We compared random networks to scale-free networks by evaluating local population occupancy and abundance throughout 18-30 protist generations. In parallel, we used simulations to explore differences in patch occupation patterns among topologies. Our experimental results highlighted the importance of the balance between dispersal and extinction in the interaction with spatial network topology. Under low dispersal conditions, random metapopulations of P. tetraurelia reached higher abundance and higher occupancy (proportion of occupied patches) compared to scale-free systems in both experimental and simulated systems. Under high dispersal conditions, we did not detect differences between types of metapopulations. Increasing patch degree (i.e. number of connections per patch) reduced the probability of extinction of local populations in both types of networks. We suggest the interaction between colonization/extinction rates and network topology alters the likelihood of rescue effects which results in differential patterns of occupancy and abundance in metapopulations.

Local connections and the larval competency strongly influence marine metapopulation persistence

The relationship between metapopulation stability and connectivity has long been investigated in ecology, however, most of these studies are focused on theoretical species and habitat networks, having limited ability to capture the complexity of real-world metapopulations. Network analysis became more important in modeling connectivity, but it is still uncertain which network metrics are reliable predictors of persistence. Here we quantify the impact of connectivity and larval life history on marine metapopulation persistence across the complex seascape of southeast Australia. Our work coupled network-based approaches and eigenanalysis to efficiently estimate metapopulation-wide persistence and the subpopulation contributions. Larval dispersal models were used to quantify species-specific metapopulation connectivity for five important fisheries species, each summarized as a migration matrix. Eigenanalysis helped to reveal metapopulation persistence and determine the importance of node-level network properties. Across metapopulations, the number of local outgoing connections was found to have the largest impact on metapopulation persistence, implying these hub subpopulations may be the most influential in real-world metapopulations. Results also suggest the length of the pre-competency period may be the most influential parameter on metapopulation persistence. Finally, we identified two major hot spots of local connectivity in southeast Australia, each contributing strongly to multispecies persistence. Managers and ecologists would benefit by employing similar approaches in making more efficient and more ecologically informed decisions and focusing more on local connectivity patterns and larval competency characteristics to better understand and protect real-world metapopulation persistence. Practically this could mean developing more marine protected areas at shorter distances and supporting collaborative research into the early life histories of the species of interest.

Ecological networks: Pursuing the shortest path, however narrow and crooked

Representing data as networks cuts across all sub-disciplines in ecology and evolutionary biology. Besides providing a compact representation of the interconnections between agents, network analysis allows the identification of especially important nodes, according to various metrics that often rely on the calculation of the shortest paths connecting any two nodes. While the interpretation of a shortest paths is straightforward in binary, unweighted networks, whenever weights are reported, the calculation could yield unexpected results. We analyzed 129 studies of ecological networks published in the last decade that use shortest paths, and discovered a methodological inaccuracy related to the edge weights used to calculate shortest paths (and related centrality measures), particularly in interaction networks. Specifically, 49% of the studies do not report sufficient information on the calculation to allow their replication, and 61% of the studies on weighted networks may contain errors in how shortest paths are calculated. Using toy models and empirical ecological data, we show how to transform the data prior to calculation and illustrate the pitfalls that need to be avoided. We conclude by proposing a five-point check-list to foster best-practices in the calculation and reporting of centrality measures in ecology and evolution studies.

Node self-connections and metapopulation persistence: reply to Saura (2018)

Saura () claims that studies using the Probability of Connectivity metric (PC) had already demonstrated the importance of including node self-connections in network metrics. As originally defined and used, PC cannot test the importance of self-connections. However, with key terms redefined, PC could be a useful tool in future work.

Designing connected marine reserves in the face of global warming

Marine reserves are widely used to protect species important for conservation and fisheries and to help maintain ecological processes that sustain their populations, including recruitment and dispersal. Achieving these goals requires well-connected networks of marine reserves that maximize larval connectivity, thus allowing exchanges between populations and recolonization after local disturbances. However, global warming can disrupt connectivity by shortening potential dispersal pathways through changes in larval physiology. These changes can compromise the performance of marine reserve networks, thus requiring adjusting their design to account for ocean warming. To date, empirical approaches to marine prioritization have not considered larval connectivity as affected by global warming. Here, we develop a framework for designing marine reserve networks that integrates graph theory and changes in larval connectivity due to potential reductions in planktonic larval duration (PLD) associated with ocean warming, given current socioeconomic constraints. Using the Gulf of California as case study, we assess the benefits and costs of adjusting networks to account for connectivity, with and without ocean warming. We compare reserve networks designed to achieve representation of species and ecosystems with networks designed to also maximize connectivity under current and future ocean-warming scenarios. Our results indicate that current larval connectivity could be reduced significantly under ocean warming because of shortened PLDs. Given the potential changes in connectivity, we show that our graph-theoretical approach based on centrality (eigenvector and distance-weighted fragmentation) of habitat patches can help design better-connected marine reserve networks for the future with equivalent costs. We found that maintaining dispersal connectivity incidentally through representation-only reserve design is unlikely, particularly in regions with strong asymmetric patterns of dispersal connectivity. Our results support previous studies suggesting that, given potential reductions in PLD due to ocean warming, future marine reserve networks would require more and/or larger reserves in closer proximity to maintain larval connectivity.

Node self-connections in network metrics

Zamborain-Mason et al. (Ecol. Lett., 20, 2017, 815-831) state that they have newly proposed network metrics that account for node self-connections. Network metrics incorporating node self-connections, also referred to as intranode (intrapatch) connectivity, were however already proposed before and have been widely used in a variety of conservation planning applications.