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      Detecting hierarchical levels of connectivity in a population of Acacia tortilis at the northern edge of the species’ global distribution: Combining classical population genetics and network analyses

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          Abstract

          Genetic diversity and structure of populations at the edge of the species’ spatial distribution are important for potential adaptation to environmental changes and consequently, for the long-term survival of the species. Here, we combined classical population genetic methods with newly developed network analyses to gain complementary insights into the genetic structure and diversity of Acacia tortilis, a keystone desert tree, at the northern edge of its global distribution, where the population is under threat from climatic, ecological, and anthropogenic changes. We sampled A. tortilis from 14 sites along the Dead Sea region and the Arava Valley in Israel and in Jordan. In addition, we obtained samples from Egypt and Sudan, the hypothesized origin of the species. Samples from all sites were genotyped using six polymorphic microsatellite loci.Our results indicate a significant genetic structure in A. tortilis along the Arava Valley. This was detected at different hierarchical levels—from the basic unit of the subpopulation, corresponding to groups of trees within ephemeral rivers (wadis), to groups of subpopulations ( communities) that are genetically more connected relative to others. The latter structure mostly corresponds to the partition of the major drainage basins in the area. Network analyses, combined with classical methods, allowed for the identification of key A. tortilis subpopulations in this region, characterized by their relatively high level of genetic diversity and centrality in maintaining gene flow in the population. Characterizing such key subpopulations may enable conservation managers to focus their efforts on certain subpopulations that might be particularly important for the population’s long-term persistence, thus contributing to species conservation within its peripheral range.

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          Modularity and community structure in networks

          M. Newman (2006)
          Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets.
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            A measure of betweenness centrality based on random walks

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              Finding community structure in very large networks

              The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: InvestigationRole: SoftwareRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: Data curationRole: Formal analysisRole: MethodologyRole: SoftwareRole: Writing – review & editing
                Role: MethodologyRole: ResourcesRole: SoftwareRole: Writing – review & editing
                Role: ConceptualizationRole: Formal analysisRole: Funding acquisitionRole: Project administrationRole: ResourcesRole: SoftwareRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: MethodologyRole: Project administrationRole: ResourcesRole: SupervisionRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                12 April 2018
                2018
                : 13
                : 4
                : e0194901
                Affiliations
                [1 ] Mitrani Department of Desert Ecology, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, Israel
                [2 ] The Dead Sea-Arava Science Center, Tamar Regional Council, Neve Zohar, Israel
                [3 ] Department of Biology, Stanford University, Stanford, California, United States of America
                [4 ] The Remote Sensing Laboratory, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, Israel
                Universita degli Studi della Tuscia, ITALY
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0001-9997-2034
                Article
                PONE-D-18-00647
                10.1371/journal.pone.0194901
                5896914
                29649222
                a00d9e84-8153-4ac2-aa02-c7b80a7b6a04
                © 2018 Rodger et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 8 January 2018
                : 12 March 2018
                Page count
                Figures: 3, Tables: 1, Pages: 16
                Funding
                Funded by: Albert Katz International School for Desert Research, Ben-Gurion University of the Negev, Israel
                Award Recipient :
                Funded by: The Israeli Ministry of Science and Technology (MOST)
                Award Recipient :
                Albert Katz International School for Desert Research, Ben-Gurion University of the Negev, Israel supported YSR, outside of the submitted work. The Israeli Ministry of Science and Technology (MOST) supported GW, outside of the submitted work. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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                Evolutionary Biology
                Population Genetics
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