Special Issue Paper Environmetrics Received: 4 April 2014, Revised: 13 August 2014, Accepted: 18 August 2014, Published online in Wiley Online Library: 15 September 2014 (wileyonlinelibrary.com) DOI: 10.1002/env.2304 Statistical modeling and forecasting of fruit crop phenology under climate change S. Cai a * , James V. Zidek b , Nathaniel K. Newlands b,c and Denise Neilsen d Phenology, the study of the association between biological development stages and variations in climate, has greatly increased in importance because of concerns arising from climate change. This paper presents a general stochastic approach to the modeling of the relationship between phenological events and climate variables, and gives a prediction method based on this approach to provide full predictive distributions for future events. The proposed methods are then applied to the modeling and prediction of the bloom dates of six high-valued fruit crops. In particular, we use our approach to explore how the bloom dates are related to the accumulation of growing degree days, to provide a sensible estimate of an important parameter T base in phenological study, and to assess the prediction of bloom dates with a leave-one-out pro- cedure. Most importantly, the impact of future climate change on bloom dates is studied with temperature outputs from well-established coupled global climate models under a high greenhouse gases scenario. Copyright © 2014 John Wiley & Sons, Ltd. Keywords: bloom date; global climate model; growing degree day; phenological events; prediction; predictive distribution; time- to-event analysis; time-dependent covariates 1. INTRODUCTION Phenology is the study of the relationships between variations, especially seasonal and inter-annual variations, in climate and periodic biological phenomena, such as bird migration (Bauer et al., 2008) and plant development stages including first leaf date (Schwartz et al., 2006) and first budding date as well as senescence (Thompson and Clark, 2006). Such studies help us understand the impact of climate change on biological development cycles and provide indicators for planning and management that may increase the yields of crops of high commercial values and help conserve endangered species. This paper presents a novel statistical approach to analyzing the relationship between bloom dates of economically important fruit crops and daily temperature, and to predicting future bloom dates. This approach is based on a discrete stochastic model especially tailored for crop phenology, but it can be used more broadly for analyzing similar time-to-events data with time-dependent covariates. Only single events are considered here, but the model derived from our approach is readily extended to multiple progressive events (details are given in the online supplementary document). Right-censored phenological events can also be incorporated in this approach (Cai et al., 2010). Our work is based on the first instance on empirical studies of crop phenology that began more than three centuries ago (de Réaumur, 1735) but most is of relatively recent vintage (see for example Beaubien and Freeland, 2000). These studies led to the discovery that plant development stages correlate well with thermal energy represented as accumulated daily average temperature above a threshold, T base , to be determined. To be more precise, let T min and T max be the daily minimum and maximum temperature, respectively. Then traditionally, an unweighted sum of the so-called “growing degree day” (GDD), GDD D  1 2 .T min C T max /  T base if 1 2 .T min C T max />T base 0 otherwise ; (1) over time is used as a leading predictor for phenological events of plants (see for example Chuine, 2000; Beurs and Henebry, 2010). * Correspondence to: S. Cai, School of Mathematics and Statistics, Carleton University, 4302 Herzberg Laboratories, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5BS, Canada. E-mail: scai@math.carleton.ca a Carleton University, Ottawa, K1S 5BS, Canada b Department of Statistics, University of British Columbia, Vancouver, V6T 1Z4, Canada c Agriculture and Agri-Food Canada, Lethbridge Research Centre, Lethbridge, T1J 4B1, Canada d Agriculture and Agri-Food Canada, Summerland Research Centre, Summerland, V0H 1Z0, Canada Environmetrics 2014; 25: 621–629 Copyright © 2014 John Wiley & Sons, Ltd. 621