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
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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 32–38N. 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 32–35N. 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
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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
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