No abstract

Understanding the drivers of phenological events is vital for forecasting species' responses to climate change. We developed flexible Bayesian survival regression models to assess a 29-year, individual-level time series of flowering phenology from four taxa of Japanese cherry trees (Prunus spachiana, Prunus × yedoensis, Prunus jamasakura, and Prunus lannesiana), from the Tama Forest Cherry Preservation Garden in Hachioji, Japan. Our modeling framework used time-varying (chill and heat units) and time-invariant (slope, aspect, and elevation) factors. We found limited differences among taxa in sensitivity to chill, but earlier flowering taxa, such as P. spachiana, were more sensitive to heat than later flowering taxa, such as P. lannesiana. Using an ensemble of three downscaled regional climate models under the A1B emissions scenario, we projected shifts in flowering timing by 2100. Projections suggest that each taxa will flower about 30 days earlier on average by 2100 with 2-6 days greater uncertainty around the species mean flowering date. Dramatic shifts in the flowering times of cherry trees may have implications for economically important cultural festivals in Japan and East Asia. The survival models used here provide a mechanistic modeling approach and are broadly applicable to any time-to-event phenological data, such as plant leafing, bird arrival time, and insect emergence. The ability to explicitly quantify uncertainty, examine phenological responses on a fine time scale, and incorporate conditions leading up to an event may provide future insight into phenologically driven changes in carbon balance and ecological mismatches of plants and pollinators in natural populations and horticultural crops.

First flowering events in cherry trees are believed to be closely related to temperature patterns during the winter and spring months. Earlier works have incorporated the idea of temperature thresholds, defining chill and heat functions based on these thresholds. However, selection of the thresholds is often arbitrary and shared across species and locations. We propose a survival model with spatially and temporally varying covariates having functional forms representing chill and heat accumulation leading up to first flowering events. Thresholds are chosen utlizing the ranked probability scores, selecting the threshold pair that minimizes the difference between the predicted and observed cumulative probability curves. We first apply the model using temporally varying covariates to analyze 29 years of flowering data for four cherry species (Cerasus spp.) grown in Hachioji, Japan. This allows us to investigate whether relationship with temperature may vary between earlier and later flowering species. Next, the model is applied to 52 years of flowering data for 45 Cerasus spachiana × C. speciosa trees grown across Japan's Honshu Island using spatially and temporally varying covariates and spatial random effects. By exploring flowering dates across locations, we can explore how the relationship between temperature and first flowering events varies through space. Copyright © 2013 John Wiley & Sons, Ltd.

This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution theory for directional derivatives associated with a response variable assumed to follow a Gaussian process model. In the current work, these ideas are extended to additionally accommodate a continuous covariate whose directional derivatives are also of interest and to relate the behavior of the directional derivatives of the response surface to those of the covariate surface. It is of interest to assess whether, in some sense, the gradients of the response follow those of the explanatory variable. The joint Gaussian structure of all variables, including the directional derivatives, allows for explicit distribution theory and, hence, kriging across the spatial region using multivariate normal theory. Working within a Bayesian hierarchical modeling framework, posterior samples enable all gradient analysis to occur post model fitting. As a proof of concept, we show how our methodology can be applied to a standard geostatistical modeling setting using a simulation example. For a real data illustration, we work with point pattern data, deferring our gradient analysis to the intensity surface, adopting a log-Gaussian Cox process model. In particular, we relate elevation data to point patterns associated with several tree species in Duke Forest.