1 Table S1 Multivariable phylogenetic generalized least squares (PGLS) model 2 for egg size (n = 65 each) using male fork depth instead of female fork depth

Predictor Coefficient ± SE 95% CI

Response: log(egg length) log(wing length) 0.42 ± 0.12 0.18 to 0.65 Bill length 0.40 ± 0.14 0.13 to 0.67 Tail fork depth (male) -0.06 ± 0.07 -0.21 to 0.08 Migrant or not 0.16 ± 0.14 -0.12 to 0.44 Open nest (yes = 1) -0.81 ± 0.27 -1.34 to-0.27

Response: log(egg breadth) log(wing length) 0.48 ± 0.11 0.26 to 0.69 Bill length 0.36 ± 0.12 0.12 to 0.60

Tail fork depth (male) -0.13 ± 0.07 -0.26 to 0.003 Migrant or not 0.23 ± 0.13 -0.03 to 0.49 Open nest (yes = 1) -0.28 ± 0.25 -0.77 to 0.20

Response: log(egg volume) log(wing length) 0.46 ± 0.11 0.25 to 0.68 Bill length 0.38 ± 0.12 0.14 to 0.62

Tail fork depth (male) -0.11 ± 0.07 -0.24 to 0.02 Migrant or not 0.21 ± 0.13 -0.05 to 0.46 Open nest (yes = 1) -0.47 ± 0.25 -0.96 to 0.02

3 Model-averaged coefficient, SE, and 95% confidence intervals (CIs) are shown 4 (model-averaged lambdas for egg length, egg breadth, and egg volume were 5 0.56, 0.49, and 0.54, respectively). All variables were standardized to zero 6 mean and unit variance. Significant test results (i.e., 95% CI does not contain 7 zero) are indicated in bold 8 Table S2 Multivariable phylogenetic generalized least squares (PGLS) model 9 for clutch size (n = 65 each) using male fork depth instead of female fork depth

Predictor Coefficient ± SE 95% CI

log(wing length) 0.10 ± 0.18 -0.26 to 0.46 Bill length 0.01 ± 0.21 -0.40 to 0.42 Tail fork depth (male) 0.00 ± 0.11 -0.21 to 0.22 Migrant or not 0.43 ± 0.22 0.003 to 0.85 Open nest (yes = 1) -0.14 ± 0.42 -0.95 to 0.67 Model-averaged coefficient, SE, and 95% confidence intervals (CIs) are shown (model- averaged lambda was 0.65). All variables were standardized to zero mean and unit variance. Significant test results (i.e., 95% CI does not contain zero) are indicated in bold 10 Table S3 Data set of the current study of the family Hirundinidae from Turner and Rose (1994) Clutch Female traits (mm) Egg size (mm) size Male traits (mm) O p e Scientific name n Migrant n Length Breadth or not? e s Wing Central Bill t Fork Central length tail length length ? depth tail length Alopochelidon fucata 100 44 7 1 0 17 12 4 0 44 Stelgidopteryx ruficollis 100 48 9 1 0 19 13 5 0 52 Stelgidopteryx serripennis 104 47 10 1 0 18 13 6 0 50 Tachycineta bicolor 115 46 9 1 0 19 13 5 8 46 Tachycineta albilinea 94 37 11 0 0 17 12 4 5 37 Tachycineta albiventer 104 38 11 1 0 19 13 4 8 38 Tachycineta thalassina 114 41 9 1 0 18 13 5 8 41 Tachycineta leucorrhoa 115 45 11 1 0 19 13 6 6 45 Tachycineta meyeni 110 45 10 1 0 20 13 5 7 45 Notiochelidon murina 111 41 9 0 0 18 13 2 17 41 Notiochelidon pileata 95 37 7 0 0 16 12 4 16 37 Pygochelidon cyanoleuca 94 39 7 1 0 17 12 4 10 39 Atticora fasciata 101 35 8 0 0 18 12 4 31 35 Atticora melanoleuca 93 39 7 0 0 18 12 3 38 39 Progne tapera 124 50 15 1 0 23 16 4 13 50 Progne subis 141 52 14 1 0 24 17 5 17 57 Progne chalybea 130 50 14 1 0 23 16 5 15 48 Progne dominicensis 140 52 14 1 0 23 16 5 18 54 Progne modesta 121 47 13 1 0 22 15 2 12 50 Riparia paludicola 104 53 8 0 0 17 12 3 0 53 Riparia riparia 107 42 9 1 0 17 12 5 9 42 Riparia cincta 130 61 12 1 0 22 15 3 0 61 Psalidoprocne fuliginosa 104 44 7 0 0 18 12 2 19 44 Psalidoprocne albiceps 102 47 7 1 0 19 13 3 24 51 Psalidoprocne pristoptera 106 41 7 1 0 18 12 2 28 45 Psalidoprocne obscura 96 46 7 0 0 18 12 2 61 33 Psalidoprocne nitens 93 49 7 0 0 20 13 2 0 49 Cheramoeca leucosterna 102 35 8 0 0 17 12 5 37 35 Pseudhirundo griseopyga 97 38 8 0 0 16 11 3 38 38 Phedina borbonica 116 46 11 0 0 21 15 2 8 46 Phedina brazzae 100 46 8 0 0 18 12 3 0 46 Hirundo rupestris 130 54 11 1 1 20 14 3 0 54 Hirundo fuligula 129 55 10 0 1 20 14 2 0 55 Hirundo concolor 106 45 8 0 1 17 13 3 0 45 Hirundo rustica 121 42 12 1 1 19 13 4 61 42 Hirundo lucida 111 40 10 0 1 18 13 3 21 40 Hirundo angolensis 119 43 11 0 1 18 13 3 16 46 Hirundo tahitica 105 50 11 0 1 17 12 2 9 50 Hirundo neoxena 112 46 9 0 1 18 13 4 31 46 Hirundo albigularis 128 42 12 1 1 20 14 3 32 44 Hirundo aethiopica 106 36 10 0 1 18 13 4 27 36 Hirundo smithii 110 36 9 1 1 17 13 3 50 42 Hirundo nigrita 106 37 11 0 1 18 13 3 5 37 Hirundo leucosoma 99 35 9 0 1 19 13 4 13 35 Hirundo dimidiata 102 41 9 1 1 17 12 2 24 39 Hirundo atrocaerulea 107 41 10 1 1 18 13 3 92 43 Hirundo nigrorufa 108 44 9 1 1 18 13 3 16 44 Hirundo cucullata 125 51 10 1 0 21 14 3 51 51 Hirundo abyssinica 106 44 9 1 0 19 13 3 50 50 Hirundo semirufa 132 55 11 1 0 23 15 3 83 53 Hirundo senegalensis 144 49 13 0 0 21 14 3 56 51 Hirundo daurica 121 43 11 1 0 21 14 3 59 42 Hirundo striolata 124 47 11 0 0 20 14 4 51 47 Hirundo preussi 95 42 8 0 0 18 12 2 11 42 Hirundo rufigula 97 41 8 1 0 19 13 2 9 41 Hirundo spilodera 111 51 8 1 0 20 14 2 0 51 Hirundo fuliginosa 88 39 8 0 0 18 12 2 5 39 Petrochelidon pyrrhonota 109 48 9 1 0 20 14 3 0 48 Petrochelidon fulva 102 44 8 1 0 19 13 4 0 44 Hirundo fluvicola 91 44 8 1 0 18 13 3 0 44 Hirundo ariel 91 41 7 1 0 17 12 4 6 41 Hirundo nigricans 107 45 9 1 0 17 13 4 7 45 Delichon urbicum 110 42 9 1 0 19 13 4 20 40 Delichon dasypus 108 42 8 1 0 20 14 3 5 42 Delichon nipalense 95 38 7 0 0 18 12 3 0 38 11 12 13 14

15 Phedina borbonica Phedina brazzae Riparia cincta Riparia riparia Riparia paludicola Tachycineta thalassina 16 Tachycineta bicolor Tachycineta albilinea Tachycineta albiventer Tachycineta meyeni 17 Tachycineta leucorrhoa Notiochelidon pileata Atticora fasciata Alopochelidon fucata Notiochelidon murina 18 Atticora melanoleuca Pygochelidon cyanoleuca Stelgidopteryx serripennis Stelgidopteryx ruficollis Progne tapera 19 Progne subis Progne dominicensis Progne modesta Progne chalybea Cheramoeca leucosterna 20 Pseudhirundo griseopyga Psalidoprocne nitens Psalidoprocne albiceps Psalidoprocne obscura Psalidoprocne fuliginosa 21 Psalidoprocne pristoptera Delichon urbicum Delichon dasypus Delichon nipalense Hirundo senegalensis 22 Hirundo fuliginosa Hirundo leucosoma Hirundo cucullata Hirundo atrocaerulea Hirundo nigrorufa 23 Hirundo preussi Hirundo rufigula Hirundo rupestris Hirundo concolor Hirundo fuligula 24 Hirundo dimidiata Petrochelidon fulva Petrochelidon pyrrhonota Hirundo semirufa Hirundo abyssinica 25 Hirundo striolata Hirundo daurica Hirundo spilodera Hirundo ariel Hirundo fluvicola 26 Hirundo nigricans Hirundo tahitica Hirundo neoxena Hirundo albigularis Hirundo smithii 27 Hirundo nigrita Hirundo rustica Hirundo angolensis Hirundo aethiopica 28 Hirundo lucida 29 30 Fig. S1 The majority-rule consensus phylogenetic tree of the current data set 31 from the family Hirundinidae derived from the function “consensus” in the R 32 package “ape” using 1000 trees obtained from birdtree.org (see “Materials and 33 Methods” for detailed information). 34