2.3 Morphometric data and analysis
The following seven linear morphological characters were measured in 151
preserved adult frogs (100 males, 51 females): snout-vent length (SVL),
tibia length (TL), femur length (FL), head length (HL), head width (HW),
radio-ulnar length (RU), and hand length (HDL) according to Castellano
and Giacoma (1998). Measurements were taken solely by the first author
and repeated three times. We discarded the first set of measurements and
tested the second and third measurements for repeatability (Pearson
correlation coefficient (r > 0.9)). Once accepted,
we used the third measurement for morphometric analyses.
We performed a PCA on the seven linear measurements in which PC1 was
used as a proxy for body size. We also calculated relative leg length
and generated a geometric morphometric variable for head shape using the
program package SHAPE v.1.3 (Iwata & Ukai, 2002) based on photographs
of 142 preserved frogs (97 males, 45 females) that were in sufficient
condition. SHAPE traces the contour shape from an image, delineates the
contour shape with elliptic Fourier descriptors (EFDs), and finally
performs a principal component analysis of the EFDs to summarize the
shape information (Iwata & Ukai, 2002). We retained the first principal
component summarizing head shape for further analysis.
We used a random forest (RF) model within the randomForest R
package (Liaw & Wiener, 2002) to determine the relative importance of
each of the 12 uncorrelated environmental variables to body size,
relative leg length, and head shape. RF is an ensemble learning method
for nonlinear multiple regressions. When compared to similar approaches,
RF consistently outperformed other methods (Cutler et al., 2007) and was
among those least sensitive to spatial autocorrelation (Marmion et al.,
2009). For each analysis, the data was first divided into training
(70%) and testing (30%) sets to determine the optimal number of
variables to split at each node in the tree before running a RF
regression analysis based on 10,000 trees. Predictor variables were
ranked in order of importance based on the number of times a given
metric decreased the mean squared error (MSE) of the model. We then used
the rfPermute R package to estimate the significance of
importance metrics in all subsequent RF analyses. The response variable
was permuted 1000 times on each of the 10,000 regression trees to create
a null distribution against which the observed value was compared. Only
significant (p < 0.05) environmental variables were retained
in the final model that was used to extrapolate patterns of
environmentally-associated morphological variation across the study
area. To further explore the direction of associations between
environmental predictor variables and body size, we performed a multiple
linear regression model with significant predictor variables detected in
RF modeling. Site origin was included as a factor in all analyses.