An augmented Arabidopsis phenology model reveals seasonal temperature control of flowering time


Author for correspondence:
Karen J. Halliday
Tel: +44 (0) 131 651 9083


  • In this study, we used a combination of theoretical (models) and experimental (field data) approaches to investigate the interaction between light and temperature signalling in the control of Arabidopsis flowering.
  • We utilised our recently published phenology model that describes the flowering time of Arabidopsis grown under a range of field conditions. We first examined the ability of the model to predict the flowering time of field plantings at different sites and seasons in light of the specific meteorological conditions that pertained.
  • Our analysis suggested that the synchrony of temperature and light cycles is important in promoting floral initiation. New features were incorporated into the model that improved its predictive accuracy across seasons. Using both laboratory and field data, our study has revealed an important seasonal effect of night temperatures on flowering time. Further model adjustments to describe phytochrome (phy) mutants supported our findings and implicated phyB in the temporal gating of temperature-induced flowering.
  • Our study suggests that different molecular pathways interact and predominate in natural environments that change seasonally. Temperature effects are mediated largely during the photoperiod during spring/summer (long days) but, as days shorten in the autumn, night temperatures become increasingly important.


Modelling the seasonal timing of biological events (phenology) is an important tool for understanding and managing the responses of crops, forests and natural plant communities to environmental change. The basic concept for phenology models was conceived in the 18th century by Réaumur, who suggested that transitional events such as flowering occurred when a critical value of accrued daily temperature was exceeded (as reviewed in Robertson, 1968). The notion of accumulated temperature, referred to as ‘degree-days’ or thermal time, suggested that developmental rate was a linear function of temperature (Monteith, 1981). It was later discovered that the accumulated temperature threshold required to trigger flowering changed with day length. This observation led to the development of a number of improved models that incorporated both temperature and photoperiod data (Robertson, 1968; Williams, 1974; Weir et al., 1984). Early photothermal models offered good predictive power even though they were based solely on field observations, recorded dates and meteorological data.

The early phenology models, however, did not consider genetic variability or the underlying biological pathways. A number of contemporary models exploit our growing knowledge of the molecular pathways that interpret environmental cues. In these models the incorporation of genetic and molecular information improved their predictive power as well as offering improved capability to decipher network behaviour (White & Hoogenboom, 1996; Messina et al., 2006; Salazar et al., 2009; Wenden et al., 2009). This class of model is more applicable to crop forecasting and molecular-assisted breeding programmes. Recently, we developed a photothermal model that describes the flowering time of the model species Arabidopsis thaliana (Wilczek et al., 2009). The design of this model originated in classical crop models which integrate photoperiod and thermal time. This model also incorporated the impact of vernalisation, a feature that is considered in many phenology models for temperate species (Wang & Engel, 1998; Chuine, 2000; Harrington et al., 2010). In addition, the model could account for genetic variation because individual factors in the model were linked to the activities of specific genes, particularly in the photoperiod and vernalisation pathways, which are important determinants of flowering.

In Arabidopsis GIGANTEA (GI), CONSTANS (CO) and FLOWERING LOCUS T (FT) genes lie at the core of the photoperiod pathway (Kobayashi & Weigel, 2007; Turck et al., 2008). The circadian clock component GI regulates the daily cycle of CO transcription, which in turn activates the transcription of floral promoter FT (Fowler et al., 1999; Park et al., 1999; David et al., 2006; Imaizumi & Kay, 2006; Yu et al., 2008; Tiwari et al., 2010). In day-night cycles, the timing of the peak CO mRNA relative to the day length ensures that CO promotes flowering only in long-day (LD) photoperiods that exceed a critical day length (Suarez-Lopez et al., 2001; Yanovsky & Kay, 2002). Under LDs CO mRNA peaks before the end of the day as a result of the activity of clock-controlled and light-activated FLAVIN-BINDING, KELCH-REPEAT, F-BOX (FKF1) which, together with GI, degrades CYCLING DOF FACTOR 1 (CDF1) and related repressors of CO (Yanovsky & Kay, 2002; Imaizumi et al., 2005; Fornara et al., 2009). As this peak occurs during daylight, CO protein is stabilised by the action of phytochrome A (phyA) and cryptochrome 2 (cry2) and flowering is thus promoted through CO regulation of FT (Valverde et al., 2004). In short days (SDs), as CO mRNA peaks during the night, CO transcript abundances are relatively low during the day. Under these conditions, the CO protein does not accumulate and FT mRNA levels remain low (Yanovsky & Kay, 2002; Valverde et al., 2004; Corbesier et al., 2007). Arabidopsis does eventually flower in SDs, as the gibberellin (GA) pathway takes over to promote floral induction (Wilson et al., 1992; Moon et al., 2003; Mutasa-Gottgens & Hedden, 2009; Dorca-Fornell et al., 2011; Mai et al., 2011; Yang et al., 2011).

Flowering can be accelerated by exposure to periods of prolonged cold in a process known as vernalisation. This is a strategy adopted by many species that overwinter to ensure that flowering occurs in more favourable spring conditions (Amasino, 2010). A central regulator of the vernalisation pathway is FLOWERING LOCUS C (FLC), which represses flowering (Michaels & Amasino, 1999) through FT and SUPPRESSOR OF OVEREXPRESSION OF CO 1 (SOC1) inhibition (Hepworth et al., 2002). FLC is gradually inactivated through epigenetic silencing when plants are exposed to a sustained period of cold. This time-dependent process relieves FLC suppression of flowering (Gendall et al., 2001; Bastow et al., 2004; Sung & Amasino, 2004; Greb et al., 2007; Swiezewski et al., 2009; Heo & Sung, 2011). In contrast to vernalisation, however, short periods of cold can delay flowering (Kim et al., 2004), while warm temperature accelerates flowering (Blazquez et al., 2003; Balasubramanian et al., 2006). A number of genes such as TFL1, SVP, FVE and FCA from the classical autonomous pathway, and some micro-RNAs have been reported to mediate these effects of ambient growth temperature on flowering (Blazquez et al., 2003; Kim et al., 2004; Lee et al., 2007; Strasser et al., 2009; Lee et al., 2010; Hanano & Goto, 2011; Kim et al., 2011).

Environmental light signals are known to impose strong regulation on flowering time. High vegetative shade or high light intensity can lead to a dramatic acceleration in flowering time (King et al., 2008; Franklin & Quail, 2010). These effects are largely mediated through the phytochrome photoreceptors that are accurate sensors of light quality and fluence rates. Two members of this photoreceptor family, phyA and phyB, have been shown to operate, at least in part, by regulating the stability of CO protein (Valverde et al., 2004). PhyA promotes flowering by boosting CO accumulation towards the end of a long day, while phyB suppresses flowering by preventing CO accumulation in the morning. phyA and phyB mutants have been shown to have altered flowering responses to different day lengths compared with wild type (Giakountis et al., 2010). It has also been shown that the effects of photoreceptors on flowering are temperature-sensitive (Blazquez et al., 2003; Halliday et al., 2003), illustrating that the photoreceptor pathways may provide a link between the temperature and photoperiod pathways in the regulation of flowering.

In this study, we utilised the Arabidopsis photothermal model of Wilczek et al. (2009) as an exemplar model to re-examine the contributions of temperature and photoperiod to promoting floral initiation. Field data on seven genotypes grown in multiple plantings at five sites across Europe (Wilczek et al., 2009) were also employed along with concurrent environmental measurements. Our analysis suggests that a strong floral stimulus is generated in the summer and spring when there is robust synchrony between the daily temperature and light-dark cycles. Under synchronised light–temperature cycles, daytime temperature was an important determinant of flowering time alongside photoperiod. In late autumn or winter, when the daily temperature cycle was more erratic, effects of night temperature became more significant. This was also the period when vernalisation occurred. Our study highlights the interaction between flowering pathways, with distinct pathways predominating in different seasons.


A variety of predictive crop models have been developed, the simplest of which uses daily average temperatures (Dingkuhn et al., 1995). Some crop models also use daily maximum and minimum, while some estimate hourly temperatures based on these extremes (Dingkuhn et al., 2008). The Wilczek et al. Arabidopsis photothermal model considers temperature on an hourly basis. It was developed based on a firm understanding of molecular pathway structure and physiological response. As such, the model is sufficiently complex that it can match genetic variability, yet its in-built simplicity provides flexibility and serves as an informative tool.

There are three main components in the Wilczek et al. (2009) Arabidopsis photothermal model: photoperiod, thermal time and vernalisation (Fig. 1). It computes on an hourly basis a modified photothermal unit (MPTU), which is a product of these main components.

Figure 1.

The three components of the Wilczek et al. (2009) photothermal model. (a) Photoperiod component, which is divided into three sections by two critical day lengths; (b) thermal time component, which considers only daytime hourly temperatures above 3°C; (c) vernalisation component, which has two subcomponents. The modifier represents the extent of vernalisation and depends on the accumulated vernalisation effectiveness at different temperatures; (d) the modified photothermal unit (MPTU) is a product of the three components. MPTU is accumulated every hour until a threshold value is reached to indicate the reproductive switch.

The photoperiod component uses a broken-stick function where two critical day lengths divide rate to bolting into three sections. Rate to bolting is at its minimum when the day length (dl) is at or below the critical short day length (CSDL). The rate increases linearly at day length above CSDL until it reaches the critical long day length (CLDL), where there is no further increase. The photoperiod effect on rate to bolting at each time-point τ is given by

image(Eqn 1)

where DSD and DLD are the minimum and maximum rates, respectively. This broken-stick response is reproducible both theoretically using the clock gene circuit model (Salazar et al., 2009) and experimentally (Pouteau et al., 2006, 2008; Pouteau & Albertini, 2009; Wilczek et al., 2009).

The thermal time component is given by

image(Eqn 2)
image(Eqn 3)

where P serves as a filter to consider only daytime temperatures. A base temperature, Tb, of 3°C is used in this model (Granier et al., 2002).

The vernalisation component consists of the following functions. The first is a beta function representing vernalisation effectiveness (ve) at different temperatures within the vernalising-temperature range, as follows:

image(Eqn 4)

where κ, ω and ξ are parameters in the beta function. The minimum (TVmin) and maximum (TVmax) vernalising temperatures used in the model are –3.5 and 6°C. These values were determined based on experimental data (Napp-Zinn, 1957) and model-fitting of field data (Wilczek et al., 2009).

Vernalisation also depends on the period of time exposed to these temperatures. The cumulative effective vernalisation hours (Vh) up to and including the hour that ends at τ is computed using a summation function as follows:

image(Eqn 5)

A time step, Δs, of 1 h is used in the model. The extent of vernalisation, Vern(τ), is then determined using the function below:

image(Eqn 6)

where Fb is a parameter representing baseline FLC repression. As the period of cold exposure increases, FLC becomes more repressed. A saturation point, Vsat, is reached when FLC is permanently inactivated. A Vsat of 960 h (or 40 d) has been set based on the literature (Napp-Zinn, 1957; Lee & Amasino, 1995). For vernalisation-insensitive genotypes such as the vin3-1 (in Col-FRI-Sf2) used in the study, Vern(τ) remains at the Fb value regardless of the number of vernalising hours.

A MPTU for every hour is calculated using Eqn 7 and then summed up beginning from sowing until a flowering threshold Th is reached:

image(Eqn 7)
image(Eqn 8)

The flowering threshold in the model is similar to that in classical crop models and it is consistent with molecular switch-like traits such as those shown by FT, LEAFY (LFY) and APETALA1 (AP1) (Jack, 2004; Corbesier et al., 2007; Sablowski, 2007).

The model was parameterised using field data from Arabidopsis thaliana (L.) Heynh plants of two Landsberg erecta (Ler) and five Columbia (Col) genotypes harbouring mutations or introgressions at known flowering time genes, planted at five sites across Europe in different seasons, that is, Valencia, Oulu, Cologne, Halle and Norwich, in the spring, summer and/or autumn (Fig. 2a) (Wilczek et al., 2009). The sites span a geographical range of different local climates, from the Mediterranean Valencia to oceanic Norwich to subarctic Oulu. Cologne and Halle are located at approximately the same latitude as Norwich but experience more continental climate, so cohorts planted at similar times at these sites would experience comparable photoperiods but different local weather. In total, there were nine plantings, including a repeat of Norwich Summer in 2007. Planting of each cohort was timed to coincide with the observed natural germination flush in the wild population, except for Oulu, where natural germination occurs in September. We used the global optimisation tool (active-set algorithm) in MATLAB (Mathworks, Cambridge, UK) to identify the parameter set that minimised the cost function, which was set as the coefficient of variation for the set of line × planting MPTU totals. This optimisation strategy was similar to that adopted in Wilczek et al. (2009). Parameters for Ler and Col were estimated separately to ensure switch-gene isogenicity.

Figure 2.

Analysis of model behaviour and meteorological data. (a) The timing of sowing (circles) and Col bolting (stars) in eight experimental plantings, which were timed to coincide with the germination of local natural populations (except for Oulu, where natural germination occurs in September). A ninth planting, Norwich Summer 2007, took place within 1 wk from the Julian dates of the 2006 Summer cohort. The latitude for each site is shown in brackets. This diagram was reproduced from Wilczek et al. (2009). (b) Predicted vs observed bolting times, with the diagonal line representing perfect fit. Error bars represent one standard error. The goodness of fit (GoF) showed distinctive regions as highlighted. Letters in parentheses link each region to the illustrations of associated meteorological data of a few representative days shown in (c) to (h). Model GoF (root-mean-squared error (RMSE) shown in d and coefficient of variation of the RMSE, CV(RMSE), shown as a percentage) correlated with the synchrony between thermophase and photophase.


Models perform better in highly synchronised light–temperature cycles

To examine the attributes of the Wilczek et al. model, we first conducted a detailed analysis of model behaviour alongside the meteorological data. Our analysis showed that the model could more accurately predict the flowering time for some Arabidopsis cohorts than for others. Fig. 2(b) plots the observed vs predicted values, showing that the model produced a good fit for plantings in the summer and spring. For Autumn cohorts, there are three distinctive regions of fit: the Valencia Autumn cohort scattered along the diagonal line, indicating a good match between observed and expected values (Fig. 2e); flowering times of Halle and Cologne Autumn cohorts were mostly overestimated (Fig. 2(f–g)); flowering times of late-flowering genotypes (gi-2, Col-FRI-Sf2, vin3-1 and fve-3) from Norwich Autumn were considerably underestimated (Fig. 2h). To determine the basis for goodness of fit (GoF) variation, the model was analysed using data subsets from cohorts in these different groups, then matched with the respective meteorological data (Fig. 2c–h). The GoF indicator used for subset cohorts was root-mean-squared error (RMSE) expressed in d, which estimates the differences between values predicted by a model and the field data. The RMSE was also normalised by the mean of the observations, which is a measure commonly referred to as the coefficient of variation of the RMSE, or CV(RMSE), and is expressed as a percentage. Larger values of the CV(RMSE) indicate more substantial relative deviations between model predictions and field data.

Our analysis showed that RMSE values were relatively low for Spring, Summer and Valencia Autumn plantings, indicating that the Wilczek et al. model could accurately predict flowering time of these cohorts (Fig. 2c–e). An incremental rise in RMSE was, however, observed for the Autumn cohorts at Halle, followed by Cologne and Norwich, where the discrepancies between model predictions and field data were the greatest (Fig. 2f–h). Analysis of the meteorological data revealed marked differences in the daily temperature trends through the seasons. The Valencia Autumn cohorts, as well as the Spring and Summer cohorts, typically experienced cooler night-time and warmer daytime temperatures (Fig. 2c–e). At the other Autumn sites, the temperature rhythm became less predictable, with occasional peaks at night (Fig. 2f–h). Figs 2(c–h) typify seasonal variation in daily temperature time series. Extended through time, this variation leads to distinctly different patterns of day vs night thermal time accumulation (Supporting Information, Fig. S2). It therefore appears that the model could match the flowering time data with greater accuracy when plants had experienced strong phase synchrony between light and temperature cycles, but was less precise when this was not the case.

Interestingly, the Wilczek et al. model produced comparable GoF for genotypes within each cohort, with the exception of Norwich Autumn where plants fell into two discreet groups: rapid cyclers and winter annuals (Fig. 2f–h). The model prediction for Col wild type (wt), Ler wt and co mutant from this cohort was good. These genotypes were planted in early autumn, compared with later plantings at the Cologne and Halle sites, to coincide with the natural germination flush, which starts earlier in Norwich (Fig. 2a) (Wilczek et al., 2009). During early development, these plants experienced long hours of daylight (11–13 h) and relatively warm daytime temperatures. They therefore adopted a rapid life cycle and bolted in the autumn without vernalisation. However, the model underestimated late-flowering genotypes, gi-2, Col-FRI-Sf2, vin3-1 and fve-3, from Norwich Autumn, which did not flower until the following spring.

The synchrony of thermal and photo-cycles was not explicitly included in the Wilczek et al. photothermal model, but during model optimisation the lowest cost function was achieved when the ‘thermal time’ component (see Fig. 1) considered only daytime temperatures (Wilczek et al., 2009). The model was therefore developed to include a filter P (Eqn 3) that captured the effect of temperature during the photoperiod, and night temperatures were disregarded in the accumulation of degree-days (Fig. 3a). This simple function generated higher MPTUs for genotypes exposed to highly synchronised light–temperature cycles, where temperature was low at night and rose during the day. Meteorological data illustrate that the Cologne and Halle Autumn cohorts did not experience robust daily oscillations; instead the temperature profile was more variable with prolonged periods of relative stability and occasional rises in night temperature relative to day (Fig. 2). As night temperatures can affect floral initiation (Thingnaes et al., 2003), we reasoned that the model may be less accurate at predicting flowering time of winter cohorts, as warm temperatures above the threshold for degree-day accumulation occurred more frequently during the night.

Figure 3.

Filter functions P that account for the differential effects of day and night temperatures. The black and white bars represent light–dark cycles. (a) In the Wilczek et al. (2009) model, only day temperatures are considered in the thermal time component by multiplying by a factor of 1 at daytime (Pday) and 0 at night-time (Pnight), thus forming a square waveform. (b) In Model 1 (gradual gating), a ‘triangle’ waveform is used with maximum factor (1) at mid-day and minimum factor (0) at mid-night. A constant factor Pdd is locked to dawn and dusk. (c) In Model 2 (step gating), a square waveform with a non-zero night factor (Pnight) is used.

To overcome these deficiencies, two new models which included night temperatures in the accrued degree-days were developed. These models incorporated variations of the filter function P in the Wilczek et al. model that considered night temperatures (Fig. 3). In the Wilczek et al. model, day temperatures were effectively taken into account by multiplying by a factor of 1 (Pday), while night temperatures were disregarded using a factor of 0 (Pnight), thus forming a square waveform (Eqn 3; Fig. 3a). In the first model variant (Model 1), a ‘triangle’ waveform function was used, where 1 and 0 were fixed to the middle of day and night, respectively (Fig. 3b). Such a function allows daytime as well as night-time temperatures to be considered in the accumulation of thermal time units that promote flowering, with the highest effect at midday and the lowest effect in the middle of the night. This function could serve as a proxy for circadian gating of the temperature response that is known to occur in Arabidopsis and other species (Rikin et al., 1993; Fowler et al., 2005; Espinoza et al., 2010). Thus, Model 1 accounts for a gradual gating of temperature effects. Factors at sunrise and sunset were set to a constant value (Pdd) so that the effects at lights-on and lights-off were always the same to allow tracking of dawn and dusk (Edwards et al., 2010). We also created Model 2, where a step gating function was introduced by setting (a priori) Pday as 1 as in the Wilczek et al. model; however, a non-zero night temperature factor (Pnight) applied universally across all plantings was estimated through model-fitting of field data (Fig. 3c). Both model variants contained an additional parameter each, that is, Pdd for Model 1 and Pnight for Model 2.

When compared with the Wilczek et al. model, the new models achieved comparable GoF of Spring, Summer and Valencia Autumn cohort data (with changes in RMSE < 0.5 d). In addition, both new models improved the fit for Autumn data. For the Cologne Autumn cohort, the RMSE was reduced from 23.4 d (20.1%) in the Wilczek et al. model to 16.1 d (13.8%) in Model 1 and 16.4 d (14.0%) in Model 2 (Figs 2, S1). There was also improvement for the Halle Autumn cohort, where RMSE decreased from 14.3 d (10.7%) in the Wilczek et al. model to 8.8 d (6.6%) in Model 1 and 10.2 d (7.7%) in Model 2. Concurring with the observed daily temperature cycles (Fig. 2), thermal time accumulated at a faster rate during the daytime than during the night, at the Spring, Summer and Valencia Autumn sites (Fig. S2). By contrast, thermal time accrued at a more comparable rate during the daytime and night-time at the Halle and Cologne sites. This seasonal difference in thermal time accumulation rate was a result of both reduced day–night amplitudes as well as longer nocturnal durations in the autumn. Collectively, our data indicate that the inclusion of night temperature effects in the thermal time component could be important for determining flowering time of Autumn cohorts.

Interestingly, the new model variants still could not describe the gi-2, Col-FRI-Sf2, vin3-1 and fve-3 late-flowering genotypes in Norwich Autumn. This put forward the possibility that the relatively poor performance of the Wilczek et al. model for Autumn cohorts was only a bias as the optimiser tried to split the difference between divergent genotypes, that is, the four ‘outlier’ genotypes vs the others. If that were true, removing the outliers should improve the fits of both the Wilczek et al. model and the new model variants. We therefore re-parameterised the Wilczek et al. model and our new models without the gi-2, Col-FRI-Sf2, vin3-1 and fve-3 data from Norwich Autumn. As can be seen in Table S1, there was not much improvement in the Wilczek et al. model even without the ‘outlier’ data, but both our new models which incorporated night temperature improved considerably. These results support the inclusion of night temperature in the models to accurately describe Autumn cohort data. As the proportion of temperature data considered by the Wilczek et al. model reduced with the falling photoperiod, our model improvements may simply arise from extending the period during which temperature was considered in the autumn and winter. However, we explored this possibility previously (Wilczek et al., 2009), and the overall fit deteriorated with the incremental inclusion of post-dusk temperature hours. Alternatively, the improved fitting in our new models may reflect seasonal differences in the effectiveness of day and night time temperatures in controlling flowering time.

Both our new model variants displayed improved fit, which was statistically expected with an increase in the number of parameters. We therefore used the second-order Akaike Information Criterion (AICc), which compares model accuracy but penalises for model complexity, to consider whether the additional parameter in each of our new models could justify the improved fit (Table S1a). Lower AICc values indicate the more strongly supported models. In general, both our model variants displayed lower AICc values compared with the original model in all cases except one, indicating that they have strong statistical backing. Model 1 displayed the best improved fit and lowest AICc values compared with Model 2. Nevertheless, owing to the additional flexibility offered by the P function in Model 2 (see phyB mutant section below), this step-gating model variant was selected for subsequent study. The parameter values for Model 2 are listed in Tables S2, S3.

Simulating night temperature effects

The inclusion of night temperature markedly improved the ability of the models to describe the field data, particularly for the Autumn cohorts (Fig. 4). We therefore tested whether our model adjustment was broadly applicable, and if the new step-gating model could simulate the published effect of night temperature on flowering time of Arabidopsis grown under laboratory conditions that combined day-night temperatures of 12, 17, 22 and 27°C (Thingnaes et al., 2003). The Wilczek et al. model predicted the same flowering time for plants grown under the same day temperature, regardless of night temperatures (Fig. 5). By contrast, for each set of day temperatures, step-gating Model 2 predicted a decreasing trend in flowering time as night temperature increased. This improved the overall GoF considerably, reducing the RMSE from 12.6 d (30.2%) in the Wilczek et al. model to 7.7 d (18.5%) in our new model. Improvement was especially significant when plants were grown under low day temperature (12°C) in combination with various night temperatures, conditions that had naturally occurred in Cologne and Halle during the autumn (Figs 2f–g, S2c). These results indicate that in comparison with the earlier Wilczek et al. model, our new model can more accurately simulate flowering time of plants subject to cool days vs warm nights, while retaining the ability to describe plants grown under warm days vs cool nights.

Figure 4.

Predicted vs observed bolting times of field data using our step-gating Model 2, with the diagonal line representing perfect fit. Arabidopsis thaliana late-flowering genotypes gi-2, Col-FRI-Sf2, vin3-1 and fve-3 from Norwich Autumn were excluded during parameter estimation. Therefore, these data points are not included in the figure. Error bars represent one standard error. RMSE, root-mean-squared error. CV(RMSE), coefficient of variation of the RMSE.

Figure 5.

The goodness of fit (GoF) of the Wilczek et al. model (open symbols) and our step-gating Model 2 (closed symbols) in describing the effect of day-night temperatures on flowering time. The observed experimental data were taken from Thingnaes et al. (2003). In the experiments, Arabidopsis thaliana plants were grown in controlled chambers under 16 different combinations of day and night temperatures (12, 17, 22 and 27°C). Square symbols indicate the data of plants grown under a day temperature (DT) of 12°C in combination with various night temperatures. CV(RMSE), coefficient of variation of the root-mean-squared error.

Predicting the bolting times of phyA and phyB mutants

One advantage of a genetically informed model is its ability to describe different genotypes by making simple changes to relevant model components. The photothermal model was parameterised using field data of seven genotypes impaired in the photoperiod, vernalisation or autonomous pathways. Here we explore the ability of the model to describe genotypes not previously used in model optimisation, that is, photoreceptor mutants. We first compared the published leaf number data (Giakountis et al., 2010) of phyA-201 and phyB-1 mutants with that of the Ler wt (Fig. S3a). These mutant alleles were also included in the field study (Wilczek et al., 2009). We used leaf number data for phenotypic comparison, as this indicator has been shown to be tightly coupled to bolting time within a wide photoperiod window (Koornneef et al., 1991; Pouteau et al., 2006). Leaf number data are also more widely available in the literature. We modified the parameters in the photoperiod component (CSDL, CLDL, DSD and DLD in Eqn 1) in Model 2 based on the proportional differences between the mutants and the wild type (Fig. S3a). While a proportional rate informed by leaf number data may not be quantitatively accurate, the data displayed a qualitative photoperiod response that supports the role of these mutants in the photoperiod pathway (see Fig. S3a and below). This qualitative response also concurs with early flowering time phenotype that has been reported for phyB mutants under both long- and short-day conditions (Mockler et al., 1999; Cerdan & Chory, 2003).

According to Fig. S3(a), the rate to bolting for phyA-201 during long days (with photoperiod above 10 h) was lower, correlating with a loss of phyA activity in stabilising CO protein (Valverde et al., 2004). However, the maximum rate was not altered, as there are other layers of CO regulation by FKF1 and GI (Salazar et al., 2009). For phyB-1, the rate was higher in general, following the role of activated phyB in promoting the degradation of CO protein in the morning (Valverde et al., 2004). In our model adjustment, we assumed that the phyB-1 rate to bolting would achieve its maximum at photoperiods of 16 h or above. Adjusted parameters are listed in Table S2. Fig. S3(b) shows that the modified model could predict the bolting times of phyA-201 mutant grown in the same field plantings in Wilczek et al. (2009) (Table S4), with a RMSE of 7.4 d (14.2%). The RMSE for phyB-1 was 7.6 d (19.1%) but deviations were uneven, with all Spring/Summer cohorts underestimated while Autumn cohorts were overestimated.

Published data have shown that phyB has a temperature-dependent role in flowering (Halliday et al., 2003; Halliday & Whitelam, 2003). As our earlier results suggested that the phase relationship between photoperiod and temperature cycles was significant, we sought to establish if our thermal-gating model might reveal any information regarding the dual role of phyB in light and temperature signalling. Using the new photoperiod parameters for phyB-1 as described earlier (Fig. S3a), we re-estimated both the day and night factors (Pday and Pnight) in step-gating Model 2 (Fig. 3c) to fit the phyB-1 field data while holding all other parameters to the values estimated earlier for the wild type. Intriguingly, we achieved optimal fitting when Pday and Pnight were at values of 0.5959 and 0.6856, respectively. This unexpected result suggested that temperature gating was almost abolished in phyB-deficient plants. To test this, we re-parameterised the model for phyB-1 by constraining Pday and Pnight to be equal and constant (Fig. S3c), in other words abolishing the gating effect. The modified model, with a constant ‘gating’ factor of 0.6279, showed a marked improvement with a RMSE of 4.9 d (12.5%) (Fig. 6) compared with 7.6 d (19.1%) in Fig. S3(b). Nevertheless, this improvement could be a mathematical artefact to compensate for the changes made in the photoperiod component. However, using Model 2 alone without any modification, that is, the model for Ler wt, resulted in a RMSE of 19.8 d (50.0%), suggesting that modification(s) was indeed required to describe phyB-1 field data. To further investigate this, we repeated the estimation of Pday and Pnight but without altering the photoperiod parameters. In this case, phyB-1 mutants experienced fully accelerated rate on days of intermediate (14 h) and not just very long (16 h) photoperiods. The optimised values for Pday and Pnight were 0.8291 and 0.6992, respectively, which again displayed a reduced gating effect. Comparison of AICc values for different modification schemes (Table S1b) supported the notion of constant gating for phyB-1. In addition, the model with double modifications that embodied a constant gating showed the lowest set of RMSE and AICc values. These results suggested that in order to describe the phyB-1 mutant field data, both the photoperiod and thermal-gating modifications were required.

Figure 6.

Predicted vs observed bolting times of Arabidopsis thaliana phyA-201 (open circles) and phyB-1 (closed circles) mutants using Model 2 (step gating). The photoperiod component was modified according to Supporting Information Fig. S2(a) for both mutants. For phyB-1, a constant gating of 0.6279 was adopted. The observed values are field data from the same plantings in Wilczek et al. (2009). The diagonal line represents the perfect fit. Error bars represent one standard error. CV(RMSE), coefficient of variation of the root-mean-squared error.


Thermal-gating models

In this paper, we have used a modelling approach to explore the relationship between thermoperiod and photoperiod effects on flowering time. The original Wilczek et al. photothermal model, which considered vernalising temperatures during both day and night but only daytime temperatures in the accumulated thermal time, was able to accurately predict the flowering time of Spring/Summer cohorts, but performed less well for the majority of Autumn cohorts (Fig. 2b). The meteorological data indicated that Spring/Summer cohorts typically experienced warmer days than nights and photoperiods of 10–20 h (Fig. S2; Wilczek et al., 2009). This suggests that, at least under these photoperiods, the dramatic rise (of up to 20°C) in near-ground daytime temperature is a strong determinant of flowering time, while reduced night temperatures have little impact so they can be ignored in the model. Incorporating night temperature in our models through either a gradual gating (Model 1) or a step gating (Model 2) improved the fit for the Autumn data from the field without causing changes for the Spring/Summer data. These results comply with the dramatic switch in diurnal temperature pattern in the autumn where the occurrence of non-vernalising promotory temperatures during the night was comparable with that during the day (Fig. S2). Model validation using flowering data of plants subjected to a range of day-night temperatures in the laboratory (Thingnaes et al., 2003) confirmed the importance of including night temperature effects (Fig. 5). Our findings concur with reports that night temperatures can strongly influence flowering time in plants exposed to alternating day-night temperatures (Moe, 1990; Yin et al., 1996; Thingnaes et al., 2003).

Increased overall accuracy in our thermal-gating models was the result of the improved fit to Autumn data, where plants had been subject to cooler but still inductive temperatures, with less predictable daily fluctuations. The GA pathway is known to regulate flowering time across photoperiods, but it has a predominant role in short days (Mutasa-Gottgens & Hedden, 2009). As day length shortens in the autumn, there is a switch from the CO photoperiod to the GA floral regulatory pathway (Wilson et al., 1992; Moon et al., 2003). The increased responsiveness to night temperature under short days may reflect the changeover to the GA signalling that is known to have differential sensitivity to day and night temperatures (Stavang et al., 2007, 2009; Arana et al., 2011). Our modelling approach highlights the importance of this change in responsiveness to non-vernalising promotory temperatures from daytime in long days to day-night in short days.

Neither the original nor the improved models could fit the Norwich Autumn gi-2, Col-FRI-Sf2, vin3-1 and fve-3 data as these genotypes were unusually late-flowering at this location. As the planting in Norwich occurred earlier than in Cologne and Halle, plants in Norwich were not exposed to vernalisation for a considerable time post-germination (Fig. S4). Instead plants were exposed to frequent drops in daily temperature, conditions that have been shown to induce C-REPEAT BINDING FACTORS (CBFs) and boost FLC expression levels (Seo et al., 2009). This period of intermittent cold could have caused an increase in FLC levels and thus increased the vernalisation requirement for these late-flowering genotypes. Additionally, there appears to be a feedback loop where FLC also enhances CBF expression through inhibition of SOC1, a negative regulator of CBFs (Seo et al., 2009). This causes a further delay of flowering. Including the crosstalk between CBFs and FLC in future models may therefore improve their accuracy.

Light–temperature–clock interaction in flowering

Previous work has implicated the photoreceptors phyA and phyB in flowering time regulation, operating through both CO-dependent and independent pathways (Suarez-Lopez et al., 2001; Cerdan & Chory, 2003; Valverde et al., 2004; Ishikawa et al., 2006). By modifying the photoperiod parameters, our model could predict phyA-201 bolting time of the field cohorts with reasonable accuracy. This result suggests that under field conditions phyA may operate largely through the photoperiod pathway. By contrast, modification of photoperiod parameters alone was insufficient to match the phyB-1 bolting data. Remarkably, an accurate fit to data was in fact only achieved when the temperature gating was removed in addition to the photoperiod adjustments. The implication here is that wild type phyB is not only required for photoperiod perception, it also moderates the impact of day and night temperatures on flowering time. A potential role for phyB in temperature gating concurs with the reported temperature-dependency of phyB-control of flowering time (Mazzella et al., 2000; Blazquez et al., 2003; Halliday et al., 2003). Furthermore, this proposition offers a mechanistic explanation for the paradoxical observation that phyB-overexpressors and phyB loss-of-function mutants are both early-flowering (Reed et al., 1993; Bagnall et al., 1995). If phyB null mutants lose the ability to sense day temperature effectively compared with the wild type (Fig. S3c), phyB-overexpressors would be predicted to ‘overreact’ to day temperature and this could lead to a more rapid accumulation of MPTUs during the daytime and thus early flowering. Looking forward, it will be important to clarify the relationship between phyB and temperature in the regulation of flowering, as current understanding is based upon limited data. In general, comprehensive ecological observatories will allow the collection of meteorological, physiological and genomic data on species with a range of adaptive strategies in their natural habitats. However, laboratory studies will be essential to validate the environmental factors inferred from the analysis of field data, but also to implement discriminating and often unnatural conditions that reveal underlying molecular mechanisms.

Concluding remarks

Genetically informed models provide opportunities to bridge between laboratory and field studies (Wilczek et al., 2010). At the largest field scales, climate change studies have shown that night temperature is increasing faster than day temperature, and this imparts a more significant effect on crop yield compared with day temperature increase (Easterling et al., 1997; Peng et al., 2004; Mohammed & Tarpley, 2009; Xia et al., 2009). This is particularly pertinent at the present time as crop yields are predicted to fall with global warming (Tao et al., 2006; Estrella et al., 2007; Luterbacher et al., 2007). Therefore plant models that consider the differential impact of night temperatures (e.g. the current model and, in rice, the model in Yin et al. (1997)) will be beneficial in the future.

Most crop models that embody differential effects of day and night temperatures used different functions for day and night temperatures (Robertson, 1968; Yin et al., 1997). Our improved model utilises a single function for day and night temperatures while also includes a simple gating feature P (Fig. 3c) that accounts for the distinct temperature sensitivities during photophase and skotophase. A real advantage of this feature is its flexibility, as P can be shifted relative to the timing of the day-night cycle to incorporate, for example, asynchrony of thermoperiod and photoperiod. In our study, asynchrony had a dramatic impact on Arabidopsis floral initiation, conditions that were also reported to alter flowering time in sorghum (Morgan et al., 1987). Our approach therefore provides a formal modelling structure to determine the influence of dynamic changes in daily light and temperature regimes (Fig. S2) on crop productivity. As our improved model considers both genetic factors and seasonal weather patterns, it could serve as a framework for studies in climate change and plant breeding.


We thank J. L. Roe, M. D. Cooper, C. Lopez-Gallego, J. Anderson, L. J. Martin, C. D. Muir, S. Sim and A. Walker for supervising the field experiments; M. Blazquez, G. Coupland, C. Dean, M. Hoffmann, M. Koornneef, H. Kuittenen and O. Savolainen for hosting them at the field sites; M. C. Knapp for weather station setup; and M. Knapp, A. Heim and A. Cobb for assistance in processing the weather data. The field experiments were supported by NSF Frontiers in Integrative Biological Research program grant EF-0425759 and an Alexander von Humboldt Research Award to J. Schmitt. Y. H. Chew is the recipient of a Darwin Trust PhD studentship, while K. J. Halliday is supported by the Biotechnology and Biological Sciences Research Council (ROBuST grant BBF005237/1) and the Scottish Universities Life Sciences Alliance.