Exploring relationships between phenological and weather data using smoothing

Abstract

Stepwise regression is often used to draw associations between phenological records and weather data. For example, the dates that a species first flowers each year might be regressed on monthly mean temperatures for a period preceding flowering. The months that 'best' explain the variation in first flowering dates would be selected by stepwise regression. However, daily records of weather are usually available. Stepwise regression on daily temperatures would not be appropriate because of high correlations between neighbouring days. Smoothing methods provide a way of avoiding such difficulties. Regression coefficients can be smoothed by penalising differences in slopes between neighbouring regressors. The resultant curve of regression gradients is intuitively attractive. Various possible approaches to smoothing regression coefficients are discussed. We illustrate the use of one method, P-spline signal regression, which is particularly appropriate when there are many more regressors than observations. Smoothing can be applied to more than one set of regressors. This results in a multi-dimensional surface of regression coefficients. We use this approach to investigate how the time of year that a plant species tends to flower affects its relationship with temperature records. Using this method, we found that later species tend to be affected by later temperatures.

Identifying the best climatic predictors in ecology and evolution

“…Alternatives, limitations and future avenues Roberts (2008) and Teller et al (2016) have suggested alternative explorative methods to identify the critical time window, but their ability to distinguish true from false signals and accuracy and precision of most of the key metrics are unknown. These studies used multiple regression methods in which each daily, weekly or monthly mean temperature is used as a separate predictor variable, and subsequently identified which predictor variables over which time window best explain the variation in the response variable.…”

“…Nonetheless, the output from weightwin that describes the best supported weather signal can be directly compared to the output from models fitted by the slidingwin function to investigate whether a weighted mean model is better supported by the data than, for example, a model with the aggregate statistic unweighted mean (see Appendix S2). For alternative nonparametric methods using smoothing, see Roberts (2008) and Teller et al (2016).…”

Wavelet Signatures of Climate and Flowering: Identification of Species Groupings

“…Correspondingly an upper threshold temperature of 16.1ºC was demonstrated for mean temperature for this species by Hudson et al (2011b) via GAMLSS modelling. There is evidence of this cycling in correlation between flowering and climate in previous research -specifically this 6 month cycling phenomenon can be observed in the reported tables and/or figures of the following studies; [1] in an examination of flowering commencement between 1954 -1989 (by multiple linear regression) and the effect of mean monthly temperature by Fitter et al (1995, Figure 4); [2] in an examination of flowering commencement, from 1978 to 2001, with respect to mean daily maximum temperature using P-splines by Roberts (2008, Figure 3) -there being an approximately 6 month period in which the sign of the smoothed regression coefficients of Roberts changed from negative to positive (see also Roberts 2010Roberts , 2011[3] in Sparks and Carey (1995, see Table 2 of that study) there is evidence of this cycling in correlation between the flowering in wood anemone and turnip and monthly temperature in central England, for the months preceding mean observed date, over a 212 year period (1736 -1947). Until now this phenomenon of 6 monthly cycling has not been commented on, apart from the recent studies of Hudson et al (2010a,b) , nor formalised quantitatively as is achieved in this present chapter (via wavelets).…”

Comparison of regression methods for phenology

“…Examples include thermal time models, such as the spring warming and sequential models (Chuine et al 1998;Linkosalo et al 2008). Linear regression is also used, including the commonly used stepwise regression (Draper and Smith 1981;Fitter et al 1995;Sparks and Carey 1995;Roy and Sparks 2000;Sparks and Tryjanowski 2010) and the recently introduced penalised signal regression (Roberts 2008;Roberts 2010). Whilst less clearly driven by biological knowledge, regression has the benefits of ease of use, flexibility and robustness, the latter being particularly important for relatively small datasets.…”