ELECTRONIC SUPPLEMENTARY MATERIALS Accompanying Greenberg and Danner (Climate, Ecological Release, and Bill Dimorphism in an Island Songbird) METHODS Bill size dimorphism index Dimorphism was quantified as the percentage difference of male to female bill surface area: ((mean ♂ bill surface area/mean ♀ bill surface area)-1)*100. Subtracting one from the ratio of male bill size to female bill size centers the index on zero. Therefore, no dimorphism = 0, larger bills in males would be positive, and larger bills in females would be negative. This method has been used by many studies, including Selander [1] and Santiago-Alarcon and Parker [2]. Linear modeling Linear models were built in R [3] using maximum likelihood with function lm. Model fits were compared with AICc (Akaike Information Criteria (corrected) [4, 5], following methods of Burnham and Anderson [6]) using package AICcmodavg [7] in R. In addition to slopes and the intercept, function lm counts standard deviation as a parameter. For the island data, we report sex-specific parameter estimates (slopes) and confidence intervals of bill size in relation to temperature. Standard errors for the slope of females (the non-reference level sex) were calculated using the delta method with R package msm [8]. Diagnostics based on residual plots were conducted on the top models to ensure that 1 they conformed to the assumptions of normally distributed errors, linearity, and homoscedasticity. Model formulation We tested if dimorphism differed between the islands and mainland, and with temperature within both of those locations. Null models to patterns of dimorphism were the top models from Greenberg and Danner [9, see Tables S5 and S6]. The null models were additive and contained (among other variables): sex, island/mainland origin, and temperature. Alternate models, which would indicate patterns of dimorphism, included interactions between sex and island/mainland origin or sex and temperature. The variables are described in detail in Greenberg and Danner [9]. Temperature was the mean high temperature for the hottest month of the year. Temperature data for the Coronado Islands came from the Secretaria de Marina (SEMAR) of the Mexico (http://meteorologia.semar.gob.mx/meteorologia/coronado.htm) and the Scripp’s Institution of Oceanography (http://www.cordc.ucsd.edu/projects/sboo/coronadoislands/metstation.php) and were collectively recorded from 2001–2011. Temperature data from the rest of the California islands consisted of 30-year averages with a resolution of 4km (1981–2011, [10]). Body size was quantified using a Principle Component based on tarsus and wing chord. The PCA body size factor was entered as a covariate in models assessing bill size variation [11]. The sine and cosine of date of collection (converted to radians) were used to model the annual cycle in a circular fashion [9, 12]. Because sine(date) accounted for substantial amounts of variation in nearly all models, but cos(date) explained almost no variation and 2 was not significant in any model, we dropped the cos(date) term from the analyses to economize on parameters used to describe date. For analyses that included mainland data, we included distance from the coast and squared terms of temperature and distance from the coast. To reduce collinearity, squared terms were centered by subtracting the mean. Greenberg and Danner [9] found that the other variables used here had low collinearity (variance inflation factors were below 4), so they were not centered. For island analyses, we included island size. Multiple comparisons To correct for three multiple comparisons posed by correlations between bill size dimorphism and i) male bill size, ii) female bill size, and iii) island size, we used the sequential Bonferonni technique [13]. Under this technique, the p-value thresholds indicating significance for the three tests (from smallest p to largest p) are: 0.017, 0.025, and 0.05. RESULTS Acronyms of variables used in models (see Methods for details) DISTANCE = distance from the coast (for mainland specimens only) IorM = island or mainland origin of specimen IS = island size in km2 LATITUDE = latitude MAXTEMP = maximum monthly average temperature SEX = male or female 3 SINDT = the sine of ordinal date transformed to radians SIZE = body size Difference in dimorphism between island and mainland Table S1. Models that relate island/mainland origin and sex to bill size in California song sparrows using data from the islands and all of California. Explanatory variables, the log of the maximum likelihood (logL), number of parameters (k), AICC, ΔAICC, and model weights are shown. Measurements were taken from 1423 museum specimens collected on islands or within 220 km interior to the coast from 32–38N. The variable IorM indicates if the specimen is from an island or the mainland. Both models include the variables SINDT (the sine of date), SIZE (body size), LATITUDE, DISTANCE, DISTANCE2, MAXTEMP, and MAXTEMP2, which are denoted by BASE (See Methods above and Table S5 in [9]). Model logL k AICc ΔAICc Model weight BASE + SEX * IorM -4411.12 12 8846.46 0 0.95 BASE + SEX + IorM -4415.07 11 8852.32 5.86 0.05 4 Table S2. Models that relate island/mainland origin and sex to bill size in California song sparrows restricted to samples from the islands and coastal Southern California. Explanatory variables, the log of the maximum likelihood (logL), number of parameters (k), AICC, ΔAICC, and model weights are shown. Measurements were taken from 584 museum specimens collected on islands or on the mainland within 5 km of the coast from 32–35N. The variable IorM indicates if the specimen is from an island or the mainland. Both models include the variables SINDT (the sine of date), SIZE (body size), LATITUDE, DISTANCE, DISTANCE2, MAXTEMP, and MAXTEMP2, which are denoted by BASE (See Methods above and Table S5 in [9]). Model logL k AICc ΔAICc Model weight BASE + SEX + IorM + SEX * IorM -1729.63 12 3483.82 0 0.70 BASE + SEX + IorM -1731.53 11 3485.52 1.71 0.30 5 Dimorphism in relation to temperature and island size Table S3. Models that relate sex and high temperature to bill size in song sparrows of the California islands. Explanatory variables, the log of the maximum likelihood (logL), number of parameters (k), AICC, ΔAICC, and model weights are shown. Measurements were taken from 462 museum specimens. Both models include the variables SINDT (the sine of date), SIZE (body size), and IS (island size), which are denoted be BASE (See Methods above and Table S6 in [9]). Model logL k AICc ΔAICc Model weight BASE + SEX + MAXTEMP + SEX * MAXTEMP -1328.12 8 2672.56 0 0.94 BASE + SEX + MAXTEMP -1331.98 7 2678.21 5.65 0.06 6 Table S4. Models that relate sex and high temperature to bill size in song sparrows of mainland California. Explanatory variables, the log of the maximum likelihood (logL), number of parameters (k), AICC, ΔAICC, and model weights are shown. Measurements were taken from 961 museum specimens. Both models include the variables SINDT (the sine of date), SIZE (body size), LATITUDE, DISTANCE, and DISTANCE2, which are denoted by BASE (See Methods above and Table S5 in [9]). Model logL k AICc ΔAICc Model weight BASE + SEX + MAXTEMP + MAXTEMP2 -3017.17 10 6054.58 0 0.75 -3016.24 12 6056.82 2.23 0.25 BASE + SEX + MAXTEMP + SEX * MAXTEMP + SEX * MAXTEMP2 7 REFERENCES 1. 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