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. 2019 Mar 12;9:4254. doi: 10.1038/s41598-019-40597-4

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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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Components of the novel wCTU model of development and sex determination for the TSD Painted Turtle, Chrysemys picta. (a) Developmental rate by temperature function obtained by applying the nlCTE model¹⁴ to incubation data of Painted Turtles (see text for details). OTR = Optimal Temperature Range for C. picta¹⁴. VTR = Viable Temperature Range (temperatures that induce a developmental rate > 0). Blue dots denote actual (rather than predicted) developmental rate from constant incubation experiments to illustrate de good fit of the model. (b) Cumulative Temperature Units (CTUs) sensu²⁴ above (blue areas) and below (orange areas) the pivotal temperature (dotted line) which is 28.5 °C in C. picta used in this study. Each hourly temperature is multiplied by the developmental rate it induces (calculated from panel a to obtain the weighted CTUs (wCTUs). (c) Sex ratios of C. picta as a function of wCTUs, and fitted logistic regression (black line). Sex ratio data derive from constant and simplistic fluctuations from^14,25, plus data from the novel experiments from this study. (d) Density distribution and quantile plot of temperatures from the thermal profile NatFem-ON ±6 °C that resulted in 100% mortality. The 25% to 75% quantile box depicts the average temperature (diamond) and the median temperature line. The bottom bars illustrate temperature ranges within the OTR that induce males (blue) or females (red), the ranges outside the OTR but within the VTR (gray), and the temperatures lower or higher than the most extreme values in all other profiles (black). Note that most temperatures of the NatFem-ON ±6 °C profile fell below the pivotal temperature (purple vertical line) and a substantial portion fell in the gray areas where development is retarded or in the black range of temperatures that may be lethal, perhaps explaining the high mortality of this treatment.