3.3 Variation in Local Environments and Association with
Circadian Period
Univariate linear regression revealed elevation as a strong predictor
for both the mean circadian period among populations (F = 7.01; p =
0.01) as well as the range of circadian period values found within a
population (F = 14.45; p < 0.001) (Fig. 4a and b). More
specifically, shorter circadian periods with a more constrained range of
values were observed at higher elevations; at lower elevations, a
greater range of circadian period values were found. For both the
spatial error and spatial lag multivariate regression models, the
spatial independent variables were not significant for either of the two
response variables, mean circadian period for the population or range of
family values within each population. Akaike Information Criterion, used
to select the best-fit model, further indicated that linear models
excluding a spatial component had greater explanatory power than those
with spatial variables. The latter two results indicate that spatial
autocorrelation did not account for the association between elevation
and either circadian period or circadian range.
Populations were separated by an 800m difference in elevation; the
lowest elevation population (North Brush Creek (NBC), 2460m) and the
highest (Libby Flats (LIB), 3300m) were both located in the Medicine Bow
Mountains. The most widely separated populations (Sandstone (SDS) vs
Middle Crow Creek (MCC)) were found 150km apart. Over this spatial
range, environmental variables estimated by the Worldclim models for the
30 populations were highly varied. Mean annual temperature varied by 4.5
degrees and annual precipitation varied by over 200mm (Table 3). Climate
variables had a strong association with elevation, showing decreasing
temperature and increasing moisture for sites at higher elevation. The
tested soil samples were variable among the populations (Fig. 5). Higher
elevation populations were more strongly associated with reduced pH,
higher content of sand and silt within the soil, and increased soil
moisture.
Given that spatial structure did not account for population differences
in circadian traits, we were interested to test for associations between
circadian parameters and not only elevation but also environmental
variables. Many of the measured environmental variables correlated with
elevation, and multicollinearity analysis demonstrated strong
associations among the environment variables. Principal component
analysis was used to reduce the dimensionality of the data (Table 4).
Along the first axis in the PCA, populations from high elevation
(>3000m) separated from those from low elevation
(<2800m; Fig. 6). Populations between high and low elevation
fell between them on the PCA but appeared to be more strongly associated
with low elevation.
We used principal component and partial least squares regression models
to reduce the dimensionality of the environmental variable. As the
predictor variables were shown to have high multicollinearity, the PCR
and PLS regression allow a stronger estimation of the variables at the
population sites that may affect or impose selection on circadian
period. By comparing the PC and PLS regressions to each other and to
linear regression models, these analyses indicate the models that best
explain the variation in period mean and within-population range. For
population mean circadian period, the PCR model best explains the
variation (98.2% of the variation in predictors accounted for, 30.8%
of the variation of the population mean) while reducing the data to
three dimensions. For within-population range, the PLS model explains
the data best (91.8% of the variation in predictor variables, 35.2% of
the population range) by only using the first component. The most
informative coefficients are the same for both models (PLS and PCR) for
each of the response variables (population mean and within-population
range). For population mean circadian period, annual precipitation,
elevation, and annual range of temperature at the site were the
strongest predictors (Table 5). Elevation was the single most important
predictor in the model for within-population range, but total annual
precipitation and annual temperature range were also strong contributors
(Table 6).