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. 2019 May 21;9:7671. doi: 10.1038/s41598-019-43792-5

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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The causes of variation in the timing of breeding modelled in a linear mixed-effects model in the white-throated dipper in Lyngdalsvassdraget 1978–2011. Effects are shown for the following fixed effects, using model predictions and a restricted data set: (a) altitude (m above sea level), (b) the interaction between distance from the coast (m) and population density, where population density is ordered from low to high with decreasingly light grey tones, (c) the interaction between overall mean territory occupancy rate and population density, where population density is ordered as in (b), and (d) the interaction between overall mean territory brood size and population density, where population density is ordered as in (b) and (c),with the crossed random effects year, female identity and territory identity, on the hatching day-of-year. N = 992.