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).