Table 1 Model estimates (treatment contrasts with the intercept) for 6 male morphological traits involved in sexual selection from wild type and comet mutants (type) across 5 breeding temperatures.

From: Sexual selection contributes to partial restoration of phenotypic robustness in a butterfly

Posterior pupil surface (mm², square root transformed)	Estimate	Std.Error	95% credible interval	p
Intercept	0.7756	0.0304	[0.7124; 0.8374]	<0.0001***
forewing surface (mm², centred on the mean)	0.0063	0.0012	[0.0040; 0.0087]	<0.0001***
type (stock)	−0.2017	0.0671	[−0.3379; −0.0676]	0.0058**
temperature (°C, centred on 27 °C)	−0.0154	0.0037	[−0.0228; −0.0080]	<0.0001***
type * temperature	0.0446	0.0105	[0.0239; 0.0656]	<0.0001***
Posterior pupil length/width (log transformed)	Estimate	Std.Error	95% credible interval	p
Intercept	−0.0084	0.0318	[−0.0726; 0.0558]	0.7806
type (stock)	0.0811	0.0777	[−0.0750; 0.2391]	0.3030
temperature (°C, centred on 27 °C)	−0.0780	0.0046	[−0.0871; −0.0689]	<0.0001***
type * temperature	0.0603	0.0138	[0.0327; 0.0876]	<0.0001***
First androconial patch surface (mm²)	Estimate	Std.Error	95% credible interval	p
Intercept	0.5576	0.0206	[0.5161; 0.5994]	<0.0001***
hindwing surface (mm², centred on the mean)	0.0032	0.0007	[0.0018; 0.0045]	<0.0001***
type (stock)	0.1037	0.0422	[0.0234; 0.1867]	0.0160*
temperature (°C, centred on 27 °C)	0.0160	0.0022	[0.0117; 0.0204]	<0.0001***
type * temperature	−0.0308	0.0057	[−0.0421; −0.0198]	<0.0001***
Second androconial patch surface (mm²)	Estimate	Std.Error	95% credible interval	p
Intercept	1.0250	0.0341	[0.9579; 1.0915]	<0.0001***
forewing surface (mm², centred on the mean)	0.0094	0.0011	[0.0073; 0.0115]	<0.0001***
type (stock)	0.0350	0.0692	[−0.1020; 0.1677]	0.5984
temperature (°C, centred on 27 °C)	0.0580	0.0033	[0.0514; 0.0647]	<0.0001***
type * temperature	−0.0111	0.0088	[−0.0289; 0.0057]	0.2050
Presence of well-developed first hairpencil	Estimate	Std. Error	z value	p
Intercept	4.6489	0.6301	7.3778	<0.0001***
type (stock)	−1.8899	1.2852	−1.4706	0.1414
temperature (°C, centred on 27 °C)	0.7554	0.0968	7.8064	<0.0001***
type * temperature	−4.8537	432.6316	−0.0112	0.9910⁺
Presence of well-developed second hairpencil	Estimate	Std. Error	z value	P
Intercept	−0.9744	0.3671	−2.6545	0.0079**
type (stock)	4.5342	1.4172	3.1994	0.0014**
temperature (°C, centred on 27 °C)	0.6429	0.1514	4.2467	<0.0001***
type * temperature	−0.54	0.2825	−1.9113	0.0560(*)

The four first models are linear mixed models with family as random effect (not shown) and normal error distribution. The inference on model parameters is based on 10000 MCMC simulations. The two last models (presence/absence of well-developed hairpencils) are generalized linear mixed models with family as random effect (not shown), binomial error distribution and logit link function. The inference on parameters is based on approximate z tests. The temperature values are centred on 27 °C so that type effect estimates the difference between comet and wild type at 27 °C. (⁺) The type x temperature interaction was not significant for the first androconial hairpencil (p > 0.99), but this model had some estimation problems due to the high proportion of “presence” in wild type individuals; yet the graphs (Fig. 2 panels E, F) show that the models provide a good fit of the data and that there is no doubt that the differences observed between comet and wild type for the androconial hairpencils depend on temperature (i.e. significant interaction) too.

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Table 1 Model estimates (treatment contrasts with the intercept) for 6 male morphological traits involved in sexual selection from wild type and comet mutants (type) across 5 breeding temperatures.

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