2.3 Data analysis
For this study, we performed all
analyses in R 4.2.0 (R Development Core Team, 2022). We improved
the residual normality and reduced the heteroscedasticity of our data by
log-transforming (natural logarithm) female snout-vent length. To answer
our central questions regarding the determinants of intraspecific
variation in female body size across geographical gradients, we
constructed linear mixed models using the lmer function
implemented in the lme4 package (Bates et al., 2015). For each
model, we used the lizard population origin as a random intercept;
because this allows us to account for the non-independence of lizards
within populations (Bolker et al., 2009).
First, we asked whether the
geographical patterns of body size at the intraspecific level of lizards
vary with altitude; to achieve this, we constructed a simple linear
model of ln-transformed body sizes of lizards as the response variable
with altitude (binned into three categories) as the predictor variable.
We then determined the significance using the Anova function from
the car package (Fox and Weisberg, 2019). Further, we constructed
a post hoc test for our model using the emmeans function from theemmeans package (Lenth, 2019) to specifically test for
differences in body size between our three levels of altitude.
we then fit univariate linear models of each environmental factor
(annual mean temperature, annual mean precipitation, temperature
seasonality, and precipitation seasonality) as the response variable
with the altitude as the predictor variable in each case to understand
the relationship between climatic conditions and altitude in our study.
Next, we asked whether female body size varied with resource
availability and/or in response to the changing climatic and seasonal
conditions across altitudes. However, we could not achieve a single
model for all our predictor variables due to the significant
collinearity between net primary productivity and annual mean
temperature (r = 0.70; p <0.0001) and net
primary productivity and annual mean precipitation (r = 0.96;p <0.0001), which resulted in all linear mixed models
failing to converge. Thus, we fit two alternative models to explore
climate-body size relationships: (1) with net primary productivity,
temperature seasonality, and precipitation seasonality; and (2) with
annual mean temperature, annual mean precipitation, temperature
seasonality, precipitation seasonality and altitude as our predictor
variables. In all our fitted models, we included altitudes as a
covariate because climatic and seasonal changes that influence the
life-history traits of species significantly vary across geographic
gradients such as altitudes (Hille and Cooper, 2015; Laiolo and Obeso,
2015).
We binned elevation in our models
because of the discontinuous elevational distribution of the lizards
(Fig. 1). Due to the discontinuous nature of the elevational data,
modeling it as continuous led to model failure. Therefore, we follow the
approach of Bhat et al. (2020) to categorize the lizard populations in
our data into three altitudinal levels (low altitudes:
<1,000m; mid altitudes: 1,000–2,000 m; high altitudes:
>2,000 m asl).