Table 1 Model outputs of linear mixed models for the key explanatory variables of the ‘baseline innate immune models’ (response variables: hemagglutination, hemolysis, bacteria-killing capacity and baseline haptoglobin) and ‘innate immune response model’ (response variable: haptoglobin response, quantified as the difference between baseline haptoglobin concentration and haptoglobin concentration post-injection of lipopolysaccharides).

Measurement	Study period	N		Model output ‘pair morph’ explanatory variable						Model output ‘body mass index’ explanatory variable
Measurement	Study period	Like	Mixed	Estimate	SE	χ2	ndf	ddf	P	Estimate	SE	χ2	ndf	ddf	P
Baseline innate immune models
Hemagglutination	2015–2019	98	81	0.247	0.172	2.07	1	172	0.156	0.003	0.002	3.94	1	172	0.047
Hemolysis	2015–2019	98	81	0.030	0.147	0.04	1	172	0.837	0.002	0.001	1.34	1	172	0.225
Baseline haptoglobin	2015–2019	99	78	0.012	0.021	0.32	1	169	0.574	-0.001	0.001	0.24	1	169	0.624
Bacteria killing	2015–2019	91	77	0.008	0.030	0.08	1	161	0.783	0.001	0.001	0.90	1	161	0.344
Innate immune response model
Haptoglobin response	2018–2019	30	19	-0.158	0.307	0.27	1	41	0.607	-0.001	0.003	0.16	1	41	0.694

Key explanatory variables are parental ‘pair morph’ (factor in two levels: ‘like-morph’: dark-dark D♂D♀ and light-light L♂L♀; or ‘mixed-morph’: dark–light D♂L♀ and light–dark L♂D♀, the reference category is ‘mixed-morph') or the ‘body mass index’. All ‘baseline innate immune models’ were fitted with individual ‘sex’ (male or female), ‘age’ (numeric, in days: 20–35), ‘brood size’ (numeric, 1–3), ‘seasonality’ (numeric, week number: 22–46), and ‘time of the day’ when sample was obtained (numeric, hour: 7–17) as additional co-variates and territory ID as a random factor. Bacteria-killing and baseline haptoglobin concentration were log-transformed, the baseline haptoglobin model included an additional co-variate: a reading at 450 nm to control for plasma redness. The ‘innate immune response model’ was fitted with two baseline readings (650 nm and 450 nm) to control for initial haptoglobin concentration and plasma redness, ‘sex’, ‘age’ (numeric, week number: 22–35), ‘brood size’, ‘seasonality’ (numeric, week number: 23–43), as co-variates and territory ID as a random factor. All response variables were scaled and centred to the mean of the year, whereas all continuous variables were scaled. Study period (in years), sample size (N, for mixed- and like-morph), numerator and denominatior degrees of freedom (ndf and ddf) given in respective columns. See tables S1-S9 for full model outputs.

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