Partial Least Squares Regression for analyzing walnut phenology in California

Abstract Many biological processes produce only one quantitative outcome per year, resulting from temperatures and precipitation during hundreds of days leading up to the event. Traditional regression approaches incur problems in such a setting, because independent variables are highly autocorrelated and their number often greatly exceeds the number of observations. Partial Least Squares Regression (PLS), a statistical analysis tool developed to handle these situations and widely used in hyperspectral remote sensing, was tested for its usefulness for explaining the climate responses of biological processes, using walnut phenology in California as an example. Observations of first female bloom, first male bloom and leaf emergence of three walnut cultivars at Davis, CA were coupled with daily temperature data since 1951. The dataset was analyzed by PLS, using three temperature inputs: (1) daily mean temperatures, (2) 11-day running means of daily mean temperatures and (3) monthly mean temperatures. For all data constellations, the Variable-Importance-in-the-Projection (VIP) statistic indicated a number of periods, during which temperatures were important determinants of phenological events, and the model-coefficients-of-the-centered-and-scaled-data (MC) statistic showed the direction, in which high temperatures during these phases influenced walnut flowering and leaf emergence. In all analyses, a delaying effect of warm winters, and an advancing effect of warm springs were clearly visible. It was also possible to identify the transition between the chilling and forcing phases, and the VIP and MC plots indicated quantitative differences in the effectiveness of winter chill during different phases of the dormancy season. Such effects have not been captured in any phenology models currently applied to fruit trees, indicating that PLS has potential to help refine such models. PLS can also be used for guiding experimental research by pinpointing the parts of the season that are most important for the timing of budburst. Results suggested that more than 20 years of observed data were necessary for producing clearly recognizable temperature response patterns, limiting the applicability of PLS to long time series.