Data from: Next-generation matrices for marine metapopulations: the case of sea lice and salmon farms

AbstractClassifying habitat patches as sources or sinks and determining metapopulation persistence requires coupling connectivity between habitat patches with local demographic rates. While methods to calculate sources, sinks, and metapopulation persistence exist for discrete-time models, there is no method that is consistent across modelling frameworks. In this paper, we show how next-generation matrices, originally popularized in epidemiology to calculate new infections after one generation, can be used in an ecological context to calculate sources and sinks as well as metapopulation persistence in marine metapopulations. To demonstrate the utility of the method, we construct a next-generation matrix for a network of sea lice populations on salmon farms in the Broughton Archipelago, BC, an intensive salmon farming region on the west coast of Canada where certain salmon farms are currently being removed under an agreement between local First Nations and the provincial government. The column sums of the next-generation matrix can determine if a habitat patch is a source or a sink and the spectral radius of the next-generation matrix can determine the persistence of the metapopulation. With respect to salmon farms in the Broughton Archipelago, we identify the salmon farms which are acting as the largest sources of sea lice and show that in this region, the most productive sea lice populations are also the most connected. The farms which are the largest sources of sea lice have not yet been removed from the Broughton Archipelago, and warming temperatures could lead to increased sea louse growth. Calculating sources, sinks and persistence in marine metapopulations using the next-generation matrix is biologically intuitive, mathematically equivalent to previous methods, and consistent across different modelling frameworks.

摘要：将生境斑块划分为源、汇斑块，并确定集合种群的存续性，需要将生境斑块间的连通性与局域种群动态速率相结合。尽管针对离散时间模型，已有可计算源、汇斑块与集合种群存续性的方法，但目前尚无在各类建模框架下均保持一致的通用方法。本文阐述了下一代矩阵（next-generation matrix）——最初在流行病学领域被提出，用于计算单代传播后的新增感染数——如何应用于生态学场景，以计算海洋集合种群中的源、汇斑块与集合种群存续性。为验证该方法的实用性，我们针对加拿大西海岸集约化三文鱼养殖区域不列颠哥伦比亚省布劳顿群岛的三文鱼养殖场海虱种群网络构建了下一代矩阵。根据当地原住民部落与省政府达成的协议，该区域内部分三文鱼养殖场目前已被拆除。下一代矩阵的列和可用于判定某一生境斑块属于源还是汇，而该矩阵的谱半径则可用于判定集合种群的存续性。针对布劳顿群岛的三文鱼养殖场，我们识别出了海虱最大源种群所在的养殖场，并发现该区域内海虱种群生产力最高的养殖场同时也是连通性最强的养殖场。目前，作为海虱最大源种群的养殖场尚未从布劳顿群岛拆除，而气温升高可能会促进海虱种群的增殖。利用下一代矩阵计算海洋集合种群的源、汇斑块与存续性，具备生物学直观性，在数学上与既往方法等价，且可在不同建模框架下保持一致。