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Here, we analyse phenotypic and genetic variation involved in the successful establishment of a marine fish (sand goby, <jats:italic>Pomatoschistus minutus<\/jats:italic>) over a steep salinity drop from 35 PSU in the North Sea (NE Atlantic) to two PSU in the inner parts of the post\u2010glacial Baltic Sea. We first show that populations are adapted to local salinity in a key reproductive trait, the proportion of motile sperm. Thereafter, we show that genome variation at 22,190 single nucleotide polymorphisms (SNPs) shows strong differentiation among populations along the gradient. Sequences containing outlier SNPs and transcriptome sequences, mapped to a draft genome, reveal associations with genes with relevant functions for adaptation in this environment but without overall evidence of functional enrichment. The many contigs involved suggest polygenic differentiation. We trace the origin of this differentiation using demographic modelling and find the most likely scenario is that at least part of the genetic differentiation is older than the Baltic Sea and is a result of isolation of two lineages prior to the current contact over the North Sea\u2013Baltic Sea transition zone.<\/jats:p>","DOI":"10.1111\/jeb.13668","type":"journal-article","created":{"date-parts":[[2020,6,23]],"date-time":"2020-06-23T15:29:44Z","timestamp":1592926184000},"page":"138-156","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Post\u2010glacial establishment of locally adapted fish populations over a steep salinity gradient"],"prefix":"10.1093","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7160-2290","authenticated-orcid":false,"given":"Erica H.","family":"Leder","sequence":"first","affiliation":[{"name":"Centre for Marine Evolutionary Biology University of Gothenburg Gothenburg Sweden"},{"name":"Department of Biology University of Turku Turku Finland"},{"name":"Natural History Museum University of Oslo Oslo Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4404-7292","authenticated-orcid":false,"given":"Carl","family":"Andr\u00e9","sequence":"additional","affiliation":[{"name":"Centre for Marine Evolutionary Biology University of Gothenburg Gothenburg Sweden"},{"name":"Tj\u00e4rn\u00f6 Marine Laboratory Department of Marine Sciences University of Gothenburg Str\u00f6mstad Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan","family":"Le Moan","sequence":"additional","affiliation":[{"name":"Centre for Marine Evolutionary Biology University of Gothenburg Gothenburg Sweden"},{"name":"Tj\u00e4rn\u00f6 Marine Laboratory Department of Marine Sciences University of Gothenburg Str\u00f6mstad Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7989-696X","authenticated-orcid":false,"given":"Mats","family":"T\u00f6pel","sequence":"additional","affiliation":[{"name":"Centre for Marine Evolutionary Biology University of Gothenburg Gothenburg Sweden"},{"name":"Department of Marine Sciences University of Gothenburg Gothenburg Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1260-3920","authenticated-orcid":false,"given":"Anders","family":"Blomberg","sequence":"additional","affiliation":[{"name":"Centre for Marine Evolutionary Biology University of Gothenburg Gothenburg Sweden"},{"name":"Department of Chemistry and Molecular Biology University of Gothenburg Gothenburg Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6721-7763","authenticated-orcid":false,"given":"Jonathan N.","family":"Havenhand","sequence":"additional","affiliation":[{"name":"Centre for Marine Evolutionary Biology University of Gothenburg Gothenburg Sweden"},{"name":"Tj\u00e4rn\u00f6 Marine Laboratory Department of Marine Sciences University of Gothenburg Str\u00f6mstad Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8356-5538","authenticated-orcid":false,"given":"Kai","family":"Lindstr\u00f6m","sequence":"additional","affiliation":[{"name":"Environmental and Marine Biology \u00c5bo Akademi University Turku Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4342-4295","authenticated-orcid":false,"given":"Filip A. 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