Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Variability in light absorption and scattering of phytoplankton in Patagonian waters: Role of community size structure and pigment composition

Intense phytoplankton blooms were observed along the Patagonian shelf-break with satellite ocean color data, but few in situ optical observations were made in that region. We examine the variability of phytoplankton absorption and particulate scattering coefficients during such blooms on the basis of field data. The chlorophyll-a concentration, [Chla], ranged from 0.1 to 22.3 mg m−3 in surface waters. The size fractionation of [Chla] showed that 80% of samples were dominated by nanophytoplankton (N-group) and 20% by microphytoplankton (M-group). Chlorophyll-specific phytoplankton absorption coefficients at 440 and 676 nm, a*ph(440) and a*ph(676), and particulate scattering coefficient at 660 nm, b*p(660), ranged from 0.018 to 0.173, 0.009 to 0.046, and 0.031 to 2.37 m2 (mg Chla)−1, respectively. Both a*ph(440) and a*ph(676) were statistically higher for the N-group than M-group and also considerably higher than expected from global trends as a function of [Chla]. This result suggests that size of phytoplankton cells in Patagonian waters tends to be smaller than in other regions at similar [Chla]. The phytoplankton cell size parameter, Sf, derived from phytoplankton absorption spectra, proved to be useful for interpreting the variability in the data around the general inverse dependence of a*ph(440), a*ph(676), and b*p(660) on [Chla]. Sf also showed a pattern along the increasing trend of a*ph(440) and a*ph(676) as a function of the ratios of some accessory pigments to [Chla]. Our results suggest that the variability in phytoplankton absorption and scattering coefficients in Patagonian waters is caused primarily by changes in the dominant phytoplankton cell size accompanied by covariation in the concentrations of accessory pigments.