Adult sex ratio

We systematically searched for shorebirds’ ASR data in reference works (for example, birds of Western Palaearctic and birds of North America), and by extensively searching the primary literature through the Web of Knowledge (using keywords ‘shorebird*’, ‘wader*’, and English and scientific names of specific taxa such as ‘sandpiper*’ and ‘Calidris’, in combination with ‘sex ratio*’ and ‘ASR’). We calculated ASR as the ratio of adult males to all adults (males plus females) in the populations. When several estimates were available for a species, we used their mean value. In intensively studied breeding populations, ASR was often based on censuses of individually marked breeding adults. From the non-breeding period, we only included data if the ASR estimates were consistent among studies31,32,33. For 14 species, ASR data were taken from the original source, whereas for an additional 4 species, ASR was calculated using the data from the original sources. By restricting the analyses to the former 14 species, our results do not change qualitatively (Supplementary Table S4). In two species (Jacana spinosa and Metopidius indicus), separate estimates were available for (i) breeding birds and (ii) breeders plus non-breeders; we repeated the analyses using both sets of data and the results remained highly consistent (Supplementary Table S4).

We aimed at obtaining ASR for as many shorebird species as possible, including both sex-role reversed and non-reversed species. In the main analyses (Fig. 1a–d), we used all ASR data (that is, mean values of all estimates regardless of the methods), whereas in the method-specific analyses (Supplementary Table S3), we separated estimates into two groups (breeding censuses versus others) to maximize the number of species in the latter analysis. All data and references are provided in Supplementary Tables S5 and S6.

Social and genetic mating system

We used two variables to describe social mating systems. First, we recorded the percentages of socially polygamous individuals separately for males and females30, using reference works and primarily literature (Supplementary Tables S5 and S6). Both simultaneous and sequential polygamy were included for both sexes, and if both types of social polygamy occurred within a sex, we used their sum. If several estimates of polygamy were reported for a species, we used their mean. We considered males (or females) monogamous if social polygamy was not reported for the given sex. Lekking birds (two species P. pugnax and Scolopax minor) do not exhibit social pair bonds, thus to express the common assumption that male–male competition is intense in lekking species34, we allocated 100% male polygamy for these species. We calculated mating system bias to represent the species’ social mating systems as % male polygamy−% female polygamy. We did not find data on polygamy frequency for two species (Charadrius nivosus and Rostratula benghalensis), so the maximal sample size for mating system bias tests is 16 species.

Second, we also used mating system scores as a proxy variable of social mating systems for two reasons: (i) these scores are robust to observer errors in frequency estimates and (ii) to include the two species in the analyses (see above) that did not have frequency data available. We scored the overall incidence of polygamy for each sex on a 0–4-point scale35, with ‘0’ corresponding to no (or very rare) polygamy (<0.1% of individuals), ‘1’ to rare polygamy (0.1–1%), ‘2’ to uncommon polygamy (1–5%), ‘3’ to moderate polygamy (5–20%) and ‘4’ to common polygamy (> 20%). For C. nivosus and R. benghalensis, we estimated mating system scores using verbal description of their mating behaviour and pair bonds. Mating score bias was then calculated as the difference between the male and female scores.

Extra-pair paternity data were collected from published sources (see Supplementary Tables S5 and S6) and presented as % of broods that include extra-pair offspring.

Parental care

We used two variables to estimate the role of the sexes in care provisioning. First, we scored the participation of males on a five-point scale (0–4) for five types of parental behaviour: nest building, incubation, nest guarding (guarding and defending the nest during incubation), chick brooding and chick guarding (guarding and defending of the brood after hatching)30,35. We did not include chick feeding because most shorebirds are precocial, so that the parents do not feed their young. We also did not include post-fledging care because many shorebirds do not care for the fledged offspring, and also because data are limited on post-fledging care. For all types of care, score ‘0’ indicated no male participation (that is, all care carried out by females), score ‘1’ indicated 1–33% male care, score ‘2’ indicated 34–66% male care, score ‘3’ indicated 67–99% male care and score ‘4’ indicated 100% male care (that is, no female care). These scores were based on quantitative data if such data were available (for example, % incubation provided by males) or on qualitative descriptions of care in the data source. For example, when a source stated that ‘most brooding is provided by females’, then brooding was scored as 1 to express the small involvement of male. We calculated parental care bias as the mean score of the five parental activities. For three species (Actitis macularius, Coenocorypha aucklandica and Jacana jacana) and an additional one (R. benghalensis), we did not find reliable data on some aspect of care, so for these species the mean score was calculated using four (or two) types of care, respectively. Our scoring expresses male care relative to female care, which is directly relevant for quantifying parental sex roles. For example, a score of 4 refers to complete parental sex-role reversal.

Second, we estimated the duration of parental care for each sex according to how long the adult cared for the offspring. Following a previous comparative study24, the length of incubation and brood care were divided into three periods (scores 1–3 and 4–6). If a parent did not incubate, it was given a score of 0, and if it stayed until the chicks fledged, it scored 7. Sex bias in care duration was calculated as male score minus female score.

In New Zealand snipe C. aucklandica both parents care, although after the hatching of the eggs the males and the females divide the brood and care for half of the brood alone. Because this is not entirely the same as biparental care of the brood exhibited by other shorebirds, we investigated the sensitivity of the results to this data point. Nevertheless, the results qualitatively remain highly consistent when this species is excluded from the analyses (Supplementary Table S4).

Breeding density

We followed Owens21 to obtain comparable breeding density data. We searched for maximum breeding density and took the number of nests or pairs per hectare. Then, we followed Owens’ protocol and used a 1–6-point scale21 to convert breeding density into density scores. We used breeding density in the analyses in two ways: (i) density scores were included in multivariate models as a predictor in addition to ASR and (ii) log-transformed density was included in multivariate models together with log-transformed female body mass and ASR; body mass was included in the models because it strongly correlates with density21. We repeated the latter analysis with male mass and reached qualitatively consistent results with those using female mass (results not shown).

Phylogenetic comparative analyses

We used Phylogenetic Generalized Least Squares (PGLS) with maximum likelihood to find the best fitting λ17,18. For most analyses, we used a supertree of shorebirds36, from which we pruned species with missing data, and following a recent molecular phylogenetic study, we separated C. nivosus from C. alexandrinus37 (Supplementary Fig. S2). This phylogenetic hypothesis is based on recent advances in molecular phylogenetics and morphology, and has been often used in comparative studies of shorebirds.

We checked the robustness of the results in two ways. First we re-run the key PGLS models using a sample of 100 trees from the most recent comprehensive avian phylogeny20 to which we added C. nivosus as described above (Supplementary Fig. S1). Second, we repeated the analyses using three alternative phylogenetic hypotheses38,39,40 (Supplementary Table S1). Because branch lengths were not available for the latter trees (either because no branch length were provided or because we added some of the species to the phylogenetic tree and hence were unable to use the original branch lengths), we used branch lengths estimated by Nee’s method as implemented in Mesquite 2.74 (refs 41,42). To assess the sensitivity of the analyses to the branch-length assumption, we repeated the analyses with unit branch length (Supplementary Table S1). All analyses were carried out using the ‘caper’ package in R43. Correlation effect sizes were calculated from the output of the PGLS models44. All statistical tests were two-tailed.