## Introduction

Temperature can significantly affect developmental rate in poikilothermic animals and plants (Sharpe and DeMichele 1977; Schoolfield et al. 1981; Craufurd et al. 1996; Ikemoto 2005; Trudgill et al. 2005). In the mid-temperature range, the relationship between developmental rate and temperature approximates linearity (Campbell et al. 1974; Shi et al. 2011). The linear model is widely used to describe the temperature-dependent developmental rates:

Here, *r* represents development rate (=1/*D*, where *D* represents developmental time required for completing a specific developmental stage) at constant temperature *T*;* a* and *b* are constants. There are two important thermal parameters related to the aforementioned linear model: the lower developmental threshold (LDT = *−a/b*) (also referred to as the base temperature, *T*_{base}, in the degree day model) and the sum of effective temperatures (SET =* *1*/b*). The LDT represents the temperature at which developmental rate equals zero, that is, the intersection between the straight line of developmental rate and *x*-axis; the SET represents the accumulated degree days (ADD) required for completing a specific developmental stage. For different developmental stages of the same species, the SETs might be different, but the LDTs were demonstrated to be identical for most insects and mites (Jarošík et al. 2002, 2004; Kuang et al. 2012). Eq. (1) can be rewritten as follows:

Here, *T* is constant temperature. When we attempt to use variable air temperature (as a function of time) to calculate ADD, the following equation is recommended (Aono 1993; Marletto et al. 1992; Lopez and Runkle 2004):

Here, *T*_{air, i} represents variable air temperature on the *i*-th day, which is a function of time *t* within 1 day; SD represents the starting date for a specific biological event; ED represents the ending date for this specific biological event; *T*_{base} is, as mentioned above, an equivalent concept of LDT. The integral symbol can be dropped if the fixed daily average temperature is used. For some insects and mites with small body size and short life cycle, the LDT and SET can be directly estimated by observing developmental times at different constant temperatures in the lab based on Eq. (1). However, many plants are larger and have a longer life cycle. Thus, these two thermal parameters, in general, cannot be obtained from an experiment of temperature-dependent development. Therefore, Eq. (3) is widely used to estimate these two thermal parameters without a requirement for setting different constant-temperature environments. In practice, a starting date and a base temperature of development are needed to be known to calculate the ADD required for reaching a specific biological event of plants.

The influence of air temperature from weather data on the first flowering date (FFD) in plants, especially the woody *Prunus* trees, has received much attention (Lindsey and Newman 1956; Lindsey 1963; Aono 1993; Fitter et al. 1995; Wielgolaski 1999; Ho et al. 2006; Chen et al. 2008; Miller-Rushing et al. 2008). Japanese cherry blossom (*Prunus yedoensis* Matsum) is an important ornamental plant in East Asia. Some studies have been carried out to explore the effect of air temperature in winter and early spring on the FFD of this plant (Aono 1993; Ho et al. 2006; Chen et al. 2008; Ohashi et al. 2012). Aono (1993) reported that the base temperature of *P. yedoensis* in Japan ranged from −2 to 6°C using the method of lowest root mean square errors (RMSEs) in days between the observed and predicted FFDs based on the mean of ADDs for some standard years; Ho et al. (2006) drew a conclusion that the base temperature of *P. yedoensis* in Seoul, Korea was 5.8°C by minimizing the standard deviation of ADDs; Ohashi et al. (2012) directly provided an empirical estimate of 5°C as the base temperature of *P*. *yedoensis*.

We provide a new method for estimating the starting date and base temperature of *P. yedoensis* based on the extensive meticulous FFD observations by Prof. Yihua Xiao and his daughter, Prof. Mei Xiao, in Wuhan University (30°32′21″N, 114°21′42″E) from 1951 to 2012. On the basis of the estimates of starting date and base temperature, we explored the influence of air temperature on the FFDs of *P. yedoensis*.