www.sciencemag.org/cgi/content/full/1165826/DC1

Supporting Online Material for

Effects of Genetic Perturbation on Seasonal Life History Plasticity Amity M. Wilczek, Judith L. Roe, Mary C. Knapp, Martha D. Cooper, Cristina Lopez-Gallego,

Laura J. Martin, Christopher D. Muir, Sheina Sim, Alexis Walker, Jillian Anderson, J. Franklin Egan, Brook T. Moyers, Renee Petipas, Antonis Giakountis, Erika Charbit,

George Coupland, Stephen M. Welch, Johanna Schmitt*

*To whom correspondence should be addressed. E-mail: johanna_schmitt@brown.edu

Published 15 January 2009 on Science Express DOI: 10.1126/science.1165826

This PDF file includes: Materials and Methods

Figs. S1 to S11

Tables S1 to S6

References

Materials and Methods Sites, plant protocols and statistical analyses Field Experiments

Among the five field sites included in this experiment (Table S5), the common gardens in Finland and Spain represent the northern and southern European climatic limits of Arabidopsis thaliana, whereas the sites in Norwich, Cologne and Halle form a longitudinal transect from oceanic to continental climates at a similar latitude and photoperiodic amplitude. Seeds were stratified in the dark at 4 °C in 0.1% agar for four days prior to sowing. Seeds were sown onto the surface of a 4 cm diameter, peat-based plugit containing a small amount of slow release fertilizer surrounded by a permeable, biodegradable fabric (Bulrush Horticulture Ltd.; Co.Londonderry, N. Ireland; Recipe 5919). Seedlings of flowering time mutants and wild-type controls were germinated on these plugits under natural photoperiod conditions in the greenhouse, with the temperature set as close to current outdoor conditions as possible. Within ten days of germination, plugits were transplanted to the field to coincide with natural germination flushes in each site (Table S2).

Although there was no supplemental greenhouse light directly above the experimental seedlings in any planting, in Cologne and Valencia there were supplemental lights over nearby benches or in adjacent greenhouses. To block this indirect light in Cologne, light-excluding shade curtains on a twelve hour cycle were drawn over the experimental benches between civil and actual sunset, remaining in place until a point between civil and actual sunrise. In Valencia no such controls existed, but analyses treating days in the greenhouse as long days did not significantly alter the results of our model, even if they were considered as longer than the saturating 14 hour day length. We planted autumn cohorts in 2006 in Norwich, Cologne, Halle and Valencia, spring cohorts in March 2007 in Norwich and Cologne, and summer cohorts in Norwich (June 2006 and 2007) and Oulu (July 2006), with exact dates shown in Table S1. The timing of the plantings was set to coincide with observed natural germination flushes in wild populations at each site. These data were not available for Oulu at the time of sowing, but we later observed natural germination at this site in mid-September of 2006 and 2007. Three to five seeds of each ecotype were sown onto each plugit, and the single individual closest to the center was retained; the other remaining seedlings were thinned out prior to transplanting into the field, usually at the cotyledon to two leaf stage. In each planting, 15 to 24 replicate plugits of each genotype were transplanted in 10 cm x 10 cm grids within randomized blocks. Plants were watered as necessary for one week following transplant to alleviate mortality due to transplant shock, but after this time no water was added to the experimental plots. Fences to exclude vertebrate herbivores were in place at all sites, and molluscicide was added to plot perimeters in the Cologne and Norwich sites when slug attacks became frequent. Nonetheless, occasional herbivory due to molluscs, insects and rogue vertebrates was observed. Often, individuals that bolted uncharacteristically late (outliers) had experienced herbivory. Experimental plants were individually scored for the number of days to bolting (DTB; the initiation of inflorescence development), which was recorded once the reproductive shoot was visible to the naked eye. For each of the experimental plantings, an estimated mean squares ANOVA including genotype and block was conducted in JMP (SAS Institute, Cary, NC) on the bolting dates of surviving individuals. Rare outliers for which the absolute value of the Studentized residual was greater than 3.0 were removed from the analysis, and line means were calculated with the remaining

individuals (Table S2). Differences between mutant lines and their appropriate wild-type controls were tested using planned contrasts (Table S1).

In September 2007, we began a series of repeated plantings of two genotypes (Col and Col-FRI-Sf2, described below) into the field at our Cologne site. Plantings were spaced between one week and two months apart depending on the season. At each planting, seeds were stratified in the dark at 4 °C in 0.1% agar for four days prior to sowing. Seeds were sown onto the surface of a 4 cm diameter, peat-based plugit (described above) under natural photoperiod conditions in the greenhouse, with the temperature set as close to current outdoor conditions as possible. For plantings during the winter and early spring, plants were on a short-day (8 hour) curtain-controlled light schedule in the greenhouse but were transferred into cold frames with natural light within a week of sowing. All seedlings were transplanted to the field 14 days after sowing. Replicates of each line and planting date were placed in fully randomized positions within 12 blocks in the field; thus, there were 12 replicates per line per planting date, and individuals of the different lines and planting dates were spatially interspersed.

Chamber Experiments

To determine the relationship between photoperiod length and the rate of progression toward bolting, flowering time (1 cm bud) was scored in six different day lengths: 6, 8, 10, 12, 14 and 16 hours. Following stratification in the dark for 3 days at 4 °C, plants were grown in controlled environment growth chambers (Percival Scientific, Perry, IA) set to the assigned day length at 22 °C with a light intensity of 80 μE. A population of 18 individuals represented each line. The experimental design was a Randomized Complete Block (RCB).

Separate chamber experiments that varied temperature and photoperiod combinations were used to verify model predictions. In one experiment, seeds were sown on soil (Fafard Growing Mix #2 - 70% sphagnum peat, plus perlite and vermiculite; Conrad Fafard Inc, Agawam, MA), covered and stratified at 4 °C for 3 days, and then grown at constant temperature in a growth chamber with a mix of fluorescent and incandescent lighting (covering removed within a week of germination). Day lengths were 16 hr light/day for long days (LD) at 16 °C, 20 °C or 24 °C or 8 hr for Short Days (SD) at 20 °C or 24 °C. Seedlings were thinned to 2 per pot and pots were randomized within a treatment, with 20 seedlings per genotype included in each treatment. Pots were rotated within the chamber daily or every other day, and watered as needed. For some plantings, after approximately 30 leaves, a weak nutrient solution was applied weekly. Bolting was scored as the day on which the reproductive meristem could be distinguished with the naked eye. The other, previously published independent dataset (S1) comprises the treatments 16 °C in 16 hour days with and without 35 days of vernalization, and 23 °C in 16 and 8 hour days. Plant materials

For the field experiments, Col-0 (CS1092), gi-2 (CS3124), ld-1 (CS3127) (Col background), Ler-1 (CS6928) and co-2 (CS175) (Ler background) lines were obtained from the Arabidopsis Biological Resource Center (ABRC, Ohio State University). Seeds of fve-3 (Col background) were generously provided by Jose Martinez-Zapater. Seeds of fve-4 (Col background), Col-FRI-Sf2 (FRI region from the ecotype Sf-2 introgressed into Col background over 8 generations), flc-3 (Col-FRI-Sf2 background) and vin3-1 (Col-FRI-Sf2 background) were kindly donated by Richard Amasino and have been described previously (S2-S5). Strong loss of function alleles were chosen whenever possible, subject to the constraint that only non-

transgenic lines could be used in the field. All lines were bulked under common greenhouse conditions for a single generation.

In the photoperiod experiment, plant lines were Coupland lab stocks of co-2 and Ler (originally from the Thomas Altmann collection).

In the chamber experiment varying day length and temperature that was used for model verification, lines used were Ler-0 (CS20), Col-0 (CS22625) and co-3 (CS176) obtained from ABRC. Environmental measurement Photothermal models of plant development require temperature data to be recorded at a high temporal resolution over the interval of interest. The known influence of touch on Arabidopsis development (S6) plus the low transpiration rate of this species (leading to limited evaporative cooling) suggested that air temperatures at rosette level would give a preferable estimate of tissue temperature compared with the more standard contact thermocouple measurements. From sowing until transplantation, greenhouse temperatures were monitored by HOBO (HOBO H8 Pro Series, Onset Computer Corporation, Bourne, MA) units on the benches with the plant trays. Because greenhouse temperatures generally changed more slowly than those in exposed field plots, temperatures were recorded at 15 minute intervals. Field environments were monitored with sensing equipment from Campbell Scientific Inc. (Logan, Utah, USA). Five thermistor temperature sensors (model 107-I) were distributed within the field plot area. Each sensor was shielded from direct solar radiation by a cover that permitted free air flow at rosette height (ca. 1.5 cm). Air temperature was also recorded at 1.5 m over grass according to World Meteorological Organization methods (S7) with a sensor inside a radiation shield (respective part numbers CS500 and CS4020). All data were recorded with a model CR23 datalogger. Datalogger time bases across all sites were corrected to ca. 1 sec of synchrony as referenced to the international cellular telephone network. After uploading, all temperature data were filtered with quality control criteria adapted from the National Climatic Data Center (NCDC; Asheville, North Carolina, USA). A nearby reference station with at least 40 years of data was selected for each field site from the NCDC’s Global Surface Hourly Observation network (Table S5). The six minute data from each individual sensor were averaged for one hour intervals. Except for the winter months in Oulu, near-surface temperature averages were flagged if they (1) differed by more than 10 °C from the hourly average air temperature, (2) deviated from the hourly group near-surface average by more than 5 °C, or (3) fell more than 10 °C outside the reference station air temperature period-of-record extremes for that hour and day of year. At Oulu, the insulating effect of snow led to winter surface-to-air differences as great as 29 °C, so only criterion (2) was applied during this period. The percentage of observations flagged ranged from 0.12% in Norwich to 0.57% in Cologne. The most common cause of flagging, as recorded in field notes, was displacement of the radiation shield for short periods (a few hours) due to plant census or animal activities. Unflagged values were used to produce an hourly average near-surface temperature estimate. If all sensors were flagged a missing data code was assigned for the hour. Air temperature quality control measures were similar, in that data were coded as missing when the hourly average air temperature (1) fell outside the reference station extremes for that hour and day of year or (2) varied from the concurrent reference station temperature by more than 5 °C. To eliminate missing data, values were interpolated from immediately preceding and following readings. For air temperatures, interpolated values were compared to the reference station data. Hourly plant-

level and air temperature records are available from the authors on request. Day lengths (from/to solar elevations of zero degrees) for all sites and days were calculated from formulas in (S8).

Serially complete temperature datasets that spanned sowing to bolting intervals were created by concatenating the field and HOBO data. For most plantings the dataset included 251 days of data, but the Valencia fall 2006 and Norwich summer 2007 planting datasets were 203 and 239 days long, respectively. Although different replicate blocks were transplanted to the field on different days of each planting, over a 4 to 5 day range, preliminary analysis revealed that negligible error was introduced by starting the data set with the average sowing date and switching to field data on the average transplant date, both rounded to the nearest whole day.

For summary purposes, the number of hours in each 2 °C temperature category was tabulated after pooling the data across sites (Fig. S8). The data are grouped into day and night categories cross-classified by short days (SD) and long days (LD). Fig. S4 shows the hourly maximum, average, and minimum rosette-level temperatures for each site during the experiments. In general, the difference between daily maximum and minimum temperatures is greatest in the summer, but daily variation in excess of 10°C was common throughout the year. The extremes of temperatures that can occur in near-surface air temperatures over very short periods of time are especially noteworthy given the constancy typical in experimental laboratory environments. This variation depends on factors ranging from soil moisture, which modulates specific heat, to sky conditions that facilitate or limit rapid radiation heating and cooling. The variation itself is highly variable as is especially evident in Oulu (Fig. S4D), due to the wide range of day lengths (Fig. S2), the insulating effects of deep snow, and thermal buffering by mixtures of ice and water.

Field temperature data for Cologne were collected from May 15, 2007 through August 5, 2008 and quality-controlled using the methods described above to create a serially complete data set spanning the germination to bolting interval of planted and simulated genotypes in the June 15, 2007 to June 15, 2008 yearly cycle. Model background

Quantitative modeling of floral development in response to the environment dates to at least 1735, when it was noted that cumulative sums of daily average temperatures correlated with plant flowering dates across multiple years (S9). Later, photoperiod responses were merged with temperature to form the first of many photothermal models (S10), whose theory, application, and performance information have been extensively explored (S11-S14).

Many systems exist that quantify plant development by assigning specific numerical values to observable events (e.g. leaf emergence, bolting) (S15-S17). The timing of the events that define distinct developmental metrics may not change with strict proportionality across environments or genotypes (S18- S20), potentially leading to inconsistency among different scales. In the context of our model, development refers to advancement toward the vegetative/reproductive transition, for which bolting date is used as the observed, quantitative proxy. Photothermal models estimate progress within a developmental measurement scale by accumulating sums of environmentally-determined increments, each corresponding to a short period of time, typically one hour or one day. The assumption is that, in non-constant environments, the development occurring during a particular brief interval depends on the conditions within that interval. Since each increment describes an amount of development completed in a unit time, its numerical magnitude is a measure of developmental rate.

Alternative mathematical approaches differ only in the specifics of how environmental factors combine to determine the size of each increment.

Photothermal models specify that floral initiation will occur when the accumulating sum of environmentally-determined developmental units reaches a threshold value determined from data. At the biochemical level such a threshold might correspond to a gene product reaching a concentration sufficient to activate a molecular switch (S21-S23). The network positions of LEAFY (LFY) and APETALA1 (AP1), which connect environmental signal integrators to floral organ identity genes (Fig. S1), their mutual positive feedback, and escalating levels during induction are all switch-like traits (S24-S28). Corbesier et al (S29) show that pulses of FLOWERING LOCUS T (FT) expression increase in amplitude during induction under long days. Additionally, when not repressed by FLOWERING LOCUS C (FLC), FT expression amplitudes under short days are higher at 27 than at 23 °C (S30). FT upregulates AP1 and SUPRESSOR OF OVEREXPRESSION OF CONSTANS 1 (SOC1), the latter of which promotes LFY (S31). These features of FT are all consistent with the role of a proximal switch trigger.

The grounding notion of this modeling study is that the threshold level is biochemically determined by the genotypes of the switch and proximal trigger loci. Thus, the threshold will be numerically the same for lines isogenic at these locations. Floral phenological differences observed in such isogenic lines are assumed to result from environmental effects or upstream genetic modifications that alter the time at which this constant threshold is reached. The isogenic condition was met by the use of the common laboratory strains Col and Ler. The modeling tasks were: (1) devise a suitable surrogate for the biochemical threshold that can be calculated from environmental measurements, (2) estimate a numerical threshold value, (3) evaluate the resulting model against independent data, and (4) investigate the model’s behavior and sensitivity.

Developmental effects of non-vernalizing temperatures

Temperature affects the rates of many disparate physiochemical processes that occur within plants (S14) and other organisms, including the reactions of thermosensory molecules where such exist (S32). We evaluated two common thermal formulations. The first model is a simple thermal time (degree-hour) approach that assumes plant development rate is zero below a base temperature and linearly proportional to temperature above that critical value. The second model (S33-S35) assumes that the development rate is proportional to the beta function

( ) (min maxT T T T )η δ− − when the temperature, T , is between and , and zero otherwise. The constants minT maxT η and δ are parameter values determined from data. Depending on the values of η and δ , this curve can reproduce constant, linear, concave-down quadratic, U-shaped, and both symmetric and skewed unimodal forms. Preliminary parameter estimation runs revealed that, in this case, the beta developmental rate reaction norm was also highly linear across the range of field temperatures encountered (Fig. S9). Therefore we adopted the degree-hour model because it has only one free parameter -- the base temperature, . Previous work quantified the developmental rate of Col-0 across a broad temperature range and identified an optimal base temperature of (S36). We adopted this value for our model and explored the sensitivity of changes to this parameter, as described below (Table S4).

bT3 CbT = °

Developmental effects of photoperiod

The empirically observed broken stick model is commonly used in crop modeling to estimate development rate as a function of photoperiod (S37, S38). It divides day lengths into three ranges. The development rate is the same for all photoperiods below a critical short day length (CSDL). Between the CSDL and a critical long day length (CLDL) the development rate transitions in a linear fashion, increasing in the case of long day plants. Above the CLDL, the development rate again plateaus. A differential equation model was constructed (S39, S40) of a clock-regulated gene, C, resembling CONSTANS (CO) in that its net product production rate differs under light vs. dark conditions (S41). The next downstream gene, F, was assumed to increase its expression level in a manner proportional to the general level of C. The results of this model showed that plants perceiving day length by such a mechanism would not be able to discern differences between photoperiods less (greater) than a CSDL (CLDL), thus establishing a theoretical link between the broken stick model and gene network dynamics abstracted from CO and FT. We experimentally examined the effect of a wide range of controlled photoperiods on floral development in Ler wild-type and in a co-2 mutant (Table S6). Under constant conditions the developmental rate should be proportional to the reciprocal of developmental time (scored as total leaf number, TLN, at 1 cm bud; Fig. S5A). In this experiment, all conditions except photoperiod were consistent across treatments, allowing us to isolate the effects of day length on developmental rate for both wild-type and photoperiod-response-impaired lines. A graph of 1/TLN (Fig. S5B) shows a classic broken stick response and suggests a CSDL and CLDL of 10 and 14 hours, respectively. Merging photoperiod and non-vernalizing temperature effects

There are three general classes of methods by which models merge photoperiod and temperature inputs in order to estimate developmental rates: additive (S42), multiplicative (S43), or combined (S44). None of these methods have shown a sustained excess of predictive skill over any of the others. However, flowering time is mediated by a biochemical system and the mass action principle aligns more closely with multiplicative formulations. Multiplicative methods are commonly used in gene network modeling (S45, S46), including successful studies of floral phenology (S47, S48) .

As mentioned above, the broken stick model can be connected to simplified CO and FT dynamics. Additionally, studies have associated FT with thermo-responsive behavior (S30, S49- S51) . For these reasons, our basic photothermal model multiplies the outputs of broken stick and degree-hour submodels to obtain a preliminary index of development rate according to the formulas shown below. Photothermal units (PTU) is a generic, but accepted, appellation for the dimensions of such an index. Developmental effects of vernalizing temperatures

Arabidopsis development is accelerated after exposure to prolonged cold, and we therefore set out to scale the developmental index in order to reflect the effects of vernalization. We shall use the term “modified photothermal units” (MPTU) when referring to quantities whose calculation incorporates this adjustment. Extant models sometimes describe the effects of vernalization in terms of a reduction in some endpoint quantity like TLN or total vegetative thermal time (S52- S54), whereas phasic methods divide development into sequential time intervals and determine the environmental effects on each (S55). Alternatively, effectiveness functions that define relative rates of vernalization progress according to ambient temperature

conditions can be derived and combined with ongoing model processes such as the hour-by-hour accumulation of photothermal units (S56). For example, in such a scheme only 0.5 effective hours pass for each hour spent at a temperature in which plants take twice as long to fully vernalize as they would at optimal temperatures. The units of vernalization effectiveness are hrs/hr. We adopted this method because it most closely aligns with a conceptual model wherein upstream loci influence the behavior of proximal triggers whose products progressively approach a threshold fixed by downstream genotypes.

The vernalization effectiveness function was determined from data collected for 22 temperature × duration vernalization treatment combinations (S57). Bolting dates were converted to an equivalent number of (unmodified) PTU’s expressed as a fraction of the control and plotted against the chilling duration (Fig. S7A). The steepest declines (i.e. greatest vernalization effectiveness) were associated with the 2 and 4 °C treatments. These two treatments show a declining number of PTU’s from 0 to 38 days of chilling with smaller or no declines after that, a length of time similar to the 40 days necessary to fulfill vernalization requirements in Col-FRI-Sf2 (S3). The Napp-Zinn data (S57) showed no significant differences between the two temperatures within this range of chilling durations. Therefore, the 2 and 4 °C data were pooled to give the best possible estimate for peak vernalization effectiveness, which was later used in model sensitivity analysis. The fractional reduction in PTU’s at bolting was regressed against the numbers of days of chilling for each temperature. The resulting relationships were highly linear for the pooled 2 and 4 °C data (R2=99.1%) and the -0.5 °C data (R2=89.9%) but markedly less so at -3.5 °C (R2=14.9%).

The effectiveness value of each hour spent at a given temperature was calculated as the ratio of the corresponding regression slope to that of the pooled 2 and 4 °C data. Confidence limits (95%) for the -0.5 and -3.5 °C ratios were obtained by treating the regression coefficients as normal variates and applying the methodology in (S58). The lower vernalization threshold was set to -3.5 °C because the confidence limits for this ratio, [-0.108, 0.201], enclosed zero. We sought to adapt work in wheat and carrot (S56) that used a beta function to interpolate vernalization effectiveness at other temperatures. However, doing so requires an upper threshold, concerning which concrete data were lacking. Therefore, the entire model was repeatedly fit to the field data with upper thresholds at 2 °C intervals from 6 °C to 16 °C. At each temperature the vernalization effectiveness beta function was recalculated to maintain consistency with the Napp-Zinn data. Except for a low-effectiveness tail extending to higher temperatures, the resulting beta curves were largely similar. There were no statistically significant differences in model goodness-of-fit across the range of temperatures tested, so 6 °C was adopted (Fig. S7B) because the fit for that temperature was marginally the best.

The underlying genetic basis of Arabidopsis response to vernalization is mediated by the MADS box transcription factor FLC. FLC product levels, which decline in prolonged cold as a result of progressive epigenetic silencing (S4, S59, S60), provide a measure of vernalization response in the flowering time signaling pathways. A simple model for this process is to consider epigenetic silencing as a linear function of time spent under vernalizing conditions up to a point of saturation (Fig. S10; (S61). FLC interacts directly with the DNA of its targets to exert an elevated repressive influence on flowering, suggesting through the principle of mass action that a multiplicative formulation is an appropriate way to combine a measure of vernalization progress with the process of PTU accumulation. In our model, the number of PTU’s per hour is first calculated by the methods described above. Then, as shown in Fig. S10, the up-to-the-

moment accumulation of effective hours of vernalization, , is converted to a fraction, Vern. The fraction is multiplied by the PTU’s just calculated and the result, modified PTU’s (MPTU’s), is added to the running total that is accumulating toward the flowering threshold. Vern represents the extent of epigenetic silencing of FLC. When vernalization is complete, Vern=1, and MPTU’s advance as rapidly as environmental conditions permit. Prior to vernalization saturation, Vern<1 and progress towards bolting is necessarily slower. The line-specific baseline FLC repression values, , are determined from data. values are smaller for genotypes with functional FRI alleles or autonomous path mutants, indicating lesser initial repression of FLC (hence higher activity and initial floral repression) in these lines. The effect of FRI introgression on flowering time in Col in the field was entirely explained by its regulation of FLC; the flc-3 mutation in the Col-FRI-Sf2 background suppressed the delay caused by FRI and flowered at the same time as Col wild-type in all of the plantings (Table S1).

hv

bF bF

Napp Zinn (S57) found little or no additional acceleration of flowering in vernalization treatments exceeding 38 days in length. Similarly, after 40 days of vernalization Col and Col-FRI-Sf2 behaved very similarly (S3), suggesting that FLC had been fully suppressed by a saturating vernalization treatment. We therefore set the number of vernalization effective hours at which Vern=1, satV , to be equivalent to 40 days at 4 °C. Summary of model calculations and parameters

Formally, the bolting date of a plant of genotype G planted at site S at time t, ( )G SB t× , is defined by the integral equation

( )( )DG SB t

h tT dτ τ= ∫

× (1)

where ( )D τ is a measure of developmental rate at τ , an instant in time, and is a constant that specifies the corresponding switching threshold. As implemented, this integral is replaced by the discrete finite summation

hT

( ) ( )mptutype

hN

Tτ

typeτ τΣ

Σ∈

= Δ∑ (2)

where ( ) ( )D mptuτ τ= is modified photothermal units. The ordered set of times,

{ }1 2type typeN n n nΣ = < < <… Σ , extends in steps of one or more whole hours from sowing at to

bolting at 1n

( )1type G Sn B nΣ = × . We experimented with alternative definitions of (" " denotes “summation type”) depending on the fraction of diurnal values included, with results described below. The factor

typeNΣ typeΣ

( )type τΣΔ corresponds to the differential dτ , which has units of hours.

Modified photothermal units are computed as a product of three factors ( ) ( ) ( ) ( )mptu Vern Phot Thrmτ τ τ= τ (3)

The thermal component is

( ) ( ) ( ), Thrm

0 otherwisebT T Tτ τ

τ bT− ≥⎧= ⎨⎩

(4)

where ( )T τ is the average near-surface temperature (°C) for the hour that ends at τ and the parameter is the base temperature. bT

The photoperiod component is the broken stick model

( )( )( )

( ) ( ) ( )

D , dl ,Phot D , dl ,

D dl , D D , otherwise

SD

LD

SD LD SD

S CSDLS CLDL

S CSDL CLDL CSDL

ττ τ

τ

⎧ ≤⎪= ≥⎨⎪ + − − −⎡ ⎤⎣ ⎦⎩

(5)

The parameters are critical short day length (CSDL; hr), critical long day length (CLDL; hr), and short day development rate (DSD). Without loss of generality, the development rates were normalized so that , yielding a unitless measure. The function DLD =1 ( )dl ,S τ computes the day length (S8) in hours at site S for the calendar date that contains the hour ending at τ . Day length is the interval during which any part of the sun is above the geometric horizon, which may depart from the actual local horizon due to topographic or other features. Local standard time at all sites was used for τ . Calculating ( )Vern τ is a two-step process. The first is to calculate the cumulative effective vernalization hours up to and including the hour that ends at τ . Formally

( ) ( )1

h eV vn

s dsτ

τ = ∫We are using a beta function for the vernalization effectiveness, , and finite summation so ev

(6) ( ) ( ) ( ) ( ) ( )1

h min maxV exp 1 hrτ ω ξ

τ κ=

= − −⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦∑ V Vs n

T s T T T s ×

For a vin3 mutant, ( )hV τ is set to zero. The second step is to calculate the fraction of the total vernalization requirement that has

been satisfied.

( ) ( ) ( ) ( )h hV 1 , VVern

1, otherwiseb b satF F Vτ τ

τ+ − ≤⎧

= ⎨⎩

satV (7)

where the two parameters and bF satV are, respectively, the baseline FLC repression level and the number of effective hours of chilling needed to saturate vernalization. Because it is a fraction, ( )Vern τ is also unitless. The units of the threshold at which plants transition to bolting, , are degree-hours, which differs only by a conversion constant (24 hrs/day) from the common phenological modeling unit of degree-days.

hT

Parameter estimation

Table S3 lists all model parameters, their symbols and values. The majority of the values were obtained either directly from the literature sources indicated or by re-analysis of published data as described above. Only the short day development rate for the broken stick model and the initial FLC repression levels for the various lines (Ler, Col, Col-FRI-Sf2 and fve backgrounds) required estimation from the field data.

The model assumes that lines isogenic at switch and proximal trigger loci will have the same floral initiation threshold, which equates to the same accumulation of modified photothermal units as of the bolting date proxy. Therefore, the Solver module in Excel

(Microsoft) was used to find parameter estimates that minimized the coefficient of variation (CV) for the set of line × planting MPTU totals. To ensure isogenicity, we fit separate models for the Ler and Col backgrounds. Solver is sufficiently skillful that it has been previously used in floral phenology gene network optimization (S48). After optimization, the Jarque-Bera test (S62) was used to evaluate the normality of the set of MPTU totals; no significant departure was found (p=0.42 for the Col model, p=0.53 for the Ler model). The threshold was then estimated as the mean of the set of total accumulations. To facilitate evaluating the quality of the fit, 95% confidence limits for the CV were calculated with the Vangel method (S63).

Many extant photothermal models assume that photophase and scotophase temperatures ( DT and , respectively) act according to the same mechanisms. Yet there are clear but complex and interacting differences between the two phases at the genetic and physiological levels. Many studies have sought to detect how such differences might affect floral phenology. However, designing appropriate experiments to elucidate this issue is challenging, and a consistent pattern of plant response has yet to emerge. For example, influential early work (S64, S65) found night temperatures to be more important in determining the rate of development, but these studies exposed plants to

NT

DT for fewer hours (8 d-1) than to (16 dNT -1). When these data were subsequently reanalyzed in a manner that attempted to control for duration (S66), the difference appeared to evaporate. A seemingly simple protocol for avoiding this issue experimentally is to adopt a 12:12 hr treatment cycle (S67, S68), and yet these two studies found opposite results in rice and Arabidopsis. An unavoidable side effect of a 12 hour day (at least in these two species) is that plants are only subjected to photoperiods in excess of the CSDL. It is difficult to imagine a protocol bearing on this issue that would not involve some treatments with

(S49, S68). Yet such days are quite rare in nature (3.8% during vegetative intervals in our experiment). In addition to temperature magnitude differences, the phase relationship between thermal and illumination cycling can affect development (S69). In general, temperature cycles with daylight in natural settings, with the warmest conditions occurring in the afternoons (during the light phase) and the coolest conditions just prior to dawn. One interpretation is that phase sensitivity is a confounding effect obscuring the actual importance relationship between

NT T> D

DT and . Eliminating photothermal phase differences can be easily achieved experimentally under controlled conditions using a 12:12 hr protocol. An alternative view is that any effects of phototherma1 asynchrony are consequences of the genetic and physiological controls on flowering time and that either including or excluding the phenomenon can be equally informative. Finally, not only light duration, but also light quantity and quality must be given consideration, as major illumination differences between the two studies (S67, S68) may also have contributed to their conflicting results.

NT

We decided to see what patterns, if any, our data might reveal in relation to this issue. Covering the climatic range of the species, our experiment included the full range of temperatures and photoperiods normally encountered, with exposure to natural light quality, quantity and duration. Furthermore, our efforts to synchronize plantings with the phenology of local populations exposed plants to natural temperature and photoperiod combinations, whose diurnal phases had realistic degrees of asynchrony. Moreover, when tabulated across all plantings in the study, vegetative stages were exposed to nearly equal total hours of light (46.60%, Fig. S8) and darkness (53.40%), again in a range of combinations. We therefore assessed the relative accuracy with which our model could reproduce the observed field data using different methods for employing temperature to drive non-vernalizing development. Each

method entailed a separate parameter estimation run. The results were unambiguous, if somewhat surprising, considering the common modeling practice of treating given temperatures equivalently in both day and night. The model was significantly better at reproducing the field data when only day temperatures were used, as compared to night temperatures alone (p<<0.001) or all day and night temperatures combined (p=0.012) (Fig. S11). Yet, aside from its element-by-element linkage to known genetic processes, the model is not markedly different in form from many in the literature. This suggests that other photothermal models might benefit from further exploring the effects of day vs. night temperatures on development rates.

The apparent greater involvement of photophase temperatures in developmental rate suggested that the diurnal dynamics of CO and FT might be involved. Therefore we tried subsetting long day temperatures in various ways to see if any clear relationships emerged, but this revealed only a general trend toward degraded skill whenever larger amounts of scotophase data were used (Fig. S11). For this reason, only daytime temperatures were used to calculate the ambient temperature acceleration of development. However, it is certainly not our belief that temperature becomes irrelevant after sunset, and temperature data from all hours were used in computing the vernalization response. Future genetically aware models that explicitly incorporate nocturnal physiological processes may have even higher predictive power than the simple model presented here. Model sensitivity analysis

Each parameter was individually set to 105% and 95% of its estimated value (Table S3) and the change in number of accumulated MPTU’s at bolting computed for each line × planting combination. The absolute sensitivity was calculated for each combination by dividing the difference in MPTU’s by the (10%) difference in parameter values. This center-differencing scheme affords second order accuracy (S70). To facilitate comparisons, the absolute sensitivities were converted to relative sensitivities by dividing them by the ratio of the estimated MPTU’s to the estimated parameter value. The resulting values are interpretable as the fractional change in the timing of bolting (as determined by number of MPTU’s) per fractional change in the parameter. As noted above, some lines will not have the capacity to react to particular parameter changes. For instance, photoperiod mutants are not affected by changes to the critical day length parameter. An overall relative sensitivity (Table S3) was computed by averaging all planting × line-specific values for those lines genetically able to respond.

Values for , κ ω , and ξ in equation (6) describing the vernalization effectiveness function were obtained from the Napp-Zinn data (S57) as described previously. However, these parameters are not readily interpreted in biological terms. Therefore, to facilitate a meaningful sensitivity analysis, the beta function was reformulated in terms of biologically relevant parameters that yield the same functional shape. Two new parameters were the maximum vernalization effectiveness, ν , and the modal temperature, m, at which that maximum occurs. A third parameter measures the breadth of the temperature range that has high effectiveness. The beta function has a left flex point at which the vernalization effectiveness increases most rapidly with temperature. We termed the length of the interval between this point and the modal temperature the peak semi-width, σ . Equations were derived from information in (S71) that interrelated the new ( ) , ,ν σm and previous parameters ( ) , ,κ ω ξ . The bolting time sensitivity of these derived parameters was then determined (Table S3, Fig. S7).

Simulation of Reaction Norms to Variation in Germination Timing

Using weather data collected from our Norwich field site, we simulated bolting time for

Col, Col-FRI-SF2, gi-2 and vin3-1 plants germinating on successive days from June 15, 2006 to June 15, 2007. We employed our model to calculate daily photothermal unit accumulations as well as germination-day-specific calculations of effective vernalization hours. Taking into account the line-specific FLC repression values, we calculated the day at which the bolting threshold was reached for each genotype germinating on each day. The predicted reaction norms manifested a rapid transition in time to bolting in the early autumn across all genetic backgrounds (Fig. 4A). Our Norwich fall planting fell within this critical temporal window, which may explain both why we saw larger effects of mutational perturbation and also greater variability in bolting within lines across blocks in this planting. In the simulated reaction norms, we also noted a strong asymmetry in the predicted rise of bolting time in the autumn compared to the fall in bolting time in the spring, despite the fact that the yearly cycle in PTU’s accumulated per day is relatively symmetric (cf. Fig. S6A).

We applied these same techniques to simulate bolting time at our Cologne site for Col and Col-FRI-SF2 plants germinating on successive days from June 15, 2007 to June 15, 2008, employing on-site weather data from the field during this period to calculate developmental progression to bolting (Fig. 4B). The simulated reaction norms showed a predicted sharp transition in life history in the early autumn, very similar to the predictions for Norwich in the previous year. We then compared these simulated bolting dates to the actual bolting dates of individuals planted throughout the autumn, winter and spring at this site. The data from field-planted individuals confirmed the predicted pattern, and in fact the model accounted for 94% of the variation in real bolting time of this wholly independent data set. Col behaved as a rapid-cycler only in the earliest of the autumn plantings, and in later plantings Col bolted in the spring at a similar time to the Col-FRI-SF2 individuals. Both genotypes show the predicted transition to more rapid bolting in spring-germinating cohorts, demonstrating that the effect of FRI functionality on flowering is most pronounced for autumn cohorts.

Intrigued by the predicted sharp transition from rapid bolting to over-wintering life history during a narrow seasonal window of sensitivity, we set out to investigate the generality of this pattern over the range of climates found within the European geographic range of Arabidopsis thaliana. We took a broad-scale approach, calculating the days until bolting of our test genotypes germinating on successive days with the equations from (S72) for geographic variation in daily air temperature and day length between 10 and 55 °N (Fig. S6B). As these equations predict daily rather than hourly data, in this rough simulation we used the daily temperature value for all hours of the day. Despite the fact that only air temperature data were available for these simulations, we established that there was a very high correspondence between the predicted bolting time using air versus ground temperatures for our four test lines in all nine plantings (R2 = 0.97; Ground DTB = Air DTB* 1.10 – 4.11). The simulations demonstrated that this autumn window of sensitivity is indeed general across a wide climatic range, although at lower latitudes both the rapid transition in life history and the seasonal asymmetry in bolting time changes were attenuated. The width, amplitude and timing of the window varied with latitude and genetic background. In general, plants impaired in day length sensitivity exhibited a more gradual increase in time to bolting with later germination, and plants with elevated levels of FLC showed the largest and most abrupt shift in phenology. On the basis of the climate data used in simulating these reaction norms, vernalization was not expected to contribute to flowering time at the latitudes of 40° N and lower. Nonetheless, the sensitivity

window persisted even here, particularly in the high FLC lines. Thus these simulations showed that both germination timing and genetic background can lead to dramatic shifts in the flowering time of autumn cohorts at more northern latitudes. Closer to the equator, germination timing resulted in smaller changes to flowering phenology, and elevated expression of FLC resulted in a much more consistent flowering time delay over the course of the year. Simulations along a latitudinal transect using 30-year climate data showed a similar pattern in the overall range of the effect (data not shown), and we are currently pursuing more in-depth analyses of the responsiveness of this window to geographic variation in climate (current and future) and genetic sensitivity. Model verification

With the fitted model, the number of days for a genotype to reach the predicted threshold in each planting explained 85% to 99% of the variance in observed days to bolting in the Col background, 86-89% in the Ler background, and when all lines were combined the overall R2 value was 0.92 (Fig. 3A). However, a more rigorous test is to evaluate the model’s predictive skill against data not used in its construction, as was performed in the case of the Cologne repeated planting above. Therefore, we also applied the parameter values derived from the fitted field data to two independent chamber data sets that included treatments with different levels of vernalization, photoperiod and growth temperature. Temperature and day length information from these experiments was used to calculate the rate of accumulation of MPTU’s, and the expected date of bolting was compared to the observed phenotypes of the plants in these experiments. The model accurately predicted the behavior of Col, Ler and the co-2 mutant under controlled conditions in another study (S1) (R2 = 0.81) and in the chamber study described above with Ler, Col and co-3 (R2=0.87, Table S4, Fig. 3B). The overall fit for the two studies combined was 85% (Fig. 3B).

The field phenotypes observed in non-vernalizing summer conditions for our high FLC lines, e.g. Col-FRI-Sf2 and the autonomous pathway mutants, were unexpected given the phenotypes of these lines grown in chambers under long, warm days. It would therefore be inappropriate to apply our model to the phenotypes of these lines in chambers until the environmental factors that cause this difference in response have been identified and can be properly accounted for.

Figure S1

Fig. S1. A synthesis of known interactions among genes and signaling pathways involved in the transition to flowering in Arabidopsis thaliana (see main text). This diagram focuses on interactions among those genes for which mutant lines were grown in the field. The hierarchy of action is shown by the direction of arrows connecting interacting loci with arrowheads indicating promotion and bars indicating repression.

Figure S2

0

4

8

12

16

20

24D

ay L

engt

h (h

)

Norwich

Cologne

Halle

Oulu

Valencia

15-M

ay-06

15-Ju

l-06

15-S

ep-06

15-N

ov-06

15-Ja

n-07

15-M

ar-07

15-M

ay-07

Norwich

Cologne

Halle

Oulu

Valencia

Fig. S2: Photoperiod conditions and seasonal timing of cohorts across the European range of A. thaliana. (A) Yearly variation in day length at the five sites included in the experiment. Finland and Spain represent the northern and southern climatic limits of A. thaliana in Europe and show great disparity in day length over the course of the year. The sites in Norwich, Cologne, and Halle occur at a similar latitude and have smilar photoperiods throughout the year, and these sites form longitudinal transect across the species’ range. (B) The timing of sowing and Col bolting in eight experimental plantings, which were timed to coincide with natural germination flushes at each site (except Oulu, where natural germination occurs in September). The number of days prior to Col bolting differed drastically between seasons and geographic locations, ranging from 19-130 days. The ninth planting, Norwich summer 2007, took place within a week of the Julian dates of the 2006 summer cohort.

Figure S3

B

C

Fig. S3 . Environmental conditions experienced in each of the experimental plantings. (A) Day length from the day of sowing. (B) Cumulative degree-hours from the day of sowing, compared to the accumulation of degree-hours of a chamber kept at 16 °C. Degree-hours were calculated from measured plant-level temperatures, using a base temperature of 3 °C for degree-hour calculation. Hourly plant-level and air temperatures are available from the authors on request. (C) Effective vernalization hours from the day of sowing, contrasted with the accumulation of effective vernalization hours of a chamber kept at 4 °C. Effective vernalization hours were calculated with the beta function described in the Supplemental Methods.

Figure S4

-10

0

10

20

30

40

100 300 500 700

Tem

pera

ture

(Deg

. C)

A Norwich

-10

0

10

20

30

40

100 300 500 700

B Valencia

-10

0

10

20

30

40

100 300 500 700

Tem

pera

ture

(Deg

. C)

C Cologne

-10

0

10

20

30

40

100 300 500 700

D Oulu

-10

0

10

20

30

40

100 300 500 700Days after Jan 1, 2006

Tem

pera

ture

(Deg

. C)

E Halle

Fig. S4. Daily temperature variation across the five field sites in the experiment. The daily maximum (dark red), minimum (blue) and average (grey) temperatures for quality-controlled data spanning 203 to 251 day intervals are shown for (A) Norwich; (B)

Valencia; (C) Cologne; (D) Oulu; (E) Halle. Experimental sowing dates are indicated by arrows.

Figure S5

0

15

30

45

60

4 10 16 2

Photoperiod (hrs)

Tota

l Lea

f Num

ber

2

Lerco-2

0.00

0.02

0.04

0.06

0.08

0.10

0.12

4 10 16 22

Photoperiod (hrs)

1/TL

N

LerFieldco-2

B

A

Fig. S5. Progression towards flowering for Ler and co-2 across a range of photoperiods. (A) Developmental time as measured by total leaf number, TLN, at bolting. (B) Developmental rates as estimated by reciprocal TLN. Shown are means and standard deviations from 15-20 individuals per line per treatment. The horizontal extent of the dashed line indicates the range of photoperiods encountered in the field experiments.

Figure S6.

0

50

100

150

200

250

300

350

1/1 2/1 3/1 4/1 5/1 6/1 7/1 8/1 9/1 10/1 11/1 12/1 1/1Day of Year

Phot

othe

rmal

Uni

ts

30 N35 N40 N45 N50 N55 N

A

0

50

100

150

200

250

300

6/15 7/15 8/15 9/1510/1

511/1

512/1

51/15 2/15 3/15 4/15 5/15 6/15

Day of Germination

Day

s to

Bol

ting

0

20

40

60

5/15 6/15 7/15

B

Figure S6. Yearly variation in the accumulation of photothermal units and the predicted interval between germination and bolting. (A) Photothermal unit accumulations on each day of the year for plants that are day length sensitive. (B) Variation in predicted time to bolting with changes in genetic background and timing of germination. The inset depicts the bolting time of summer germinants at 30 °N and 55 °N. Although A. thaliana populations below 30 °N exist, most of these are found at high elevation or on islands. In order to better illustrate symmetry or lack thereof, the x-axis differs between the two panels. Latitude denoted by colors as in (A). Col = ; gi = X ; Col-FRI-Sf2 = ; vin3= ; with neighboring points separated by four days along x-axis (five days around new year).

Figure S7

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 4Days of Vernalization

Nor

mal

ized

PTU

's

0

Control-3.5 C-0.5 C2.0 C4.0 CSeries6Series7Series8

A

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0

Temperature (deg. C)

Vern

aliz

atio

n Ef

fect

iven

ess.

Bν = 1.089

σ = 2.946

= 3.063m0.0

0.2

0.4

0.6

0.8

1.0

1.2

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0

Temperature (deg. C)

Vern

aliz

atio

n Ef

fect

iven

ess.

Bν = 1.089

σ = 2.946

= 3.063m

Fig. S7. Defining a vernalization effectivness function. (A) Data from Napp-Zinn (S58) after conversion to unmodified PTU’s according to model formulas and normalization by the control treatment. (B) The fitted vernalization effectiveness function. The 6 °C data point was found by repeated model runs; others were computed as ratios of the line slopes in (A). The beta function (orange) is used to interpolate vernalization effectiveness values for other temperatures. Also shown are the three derived beta parameter values used in sensitivity analysis: maximum vernalization effectiveness, ν = 1.089 ; peak semi-width, σ = 2.946 ; and modal temperature, . = 3.063m

Figure S8

0

500

1000

1500

2000

2500

3000

(<,3]

(3,5]

(5,7]

(7,9]

(9,11

]

(11,13

]

(13,15

]

(15,17

]

(17,19

]

(19,21

]

(21,23

]

(23,25

]

(25,27

]

(27,29

]

(29,31

]

(31,33

]

(33,35

]

(35,37

]

(37,39

]

(39,41

]

Centigrade Ranges

Num

bers

of H

ours LD Nights

SD NightsLD DaysSD Days

Fig. S8. Distribution of temperature observations between day and night in short days versus long days in the field. The frequency of each temperature range was calculated across all sites during the time periods when one or more genotypes were in the vegetative stage. All hours with temperatures less than 3 °C were combined because they do not contribute degree-hours. Short days (SD) are defined as having sunrise-to-sunset photoperiods not exceeding ten hours; all greater photoperiods are classified as long days (LD).

Figure S9

0 5 10 15 20 25 30 35 40

Degrees Centigrade

Nom

inal

Dev

elop

men

t Rat

e

Deg-HrBeta

Fig. S9. Comparison of thermal developmental rate models. The functions have been differentially scaled to facilitate visual comparison of their respective linearity; magnitude differences between the traces are not meaningful. Near-surface temperatures experienced by vegetative-stage plants reached 37.8 °C but were exceedingly rare close to the beta function maximum (see Fig. S7).

Figure S10

Col fri, 0.402

Col FRI, 0.263

0

1

0 480 960 1440 1920

Cumulative Effective Vernalization (hrs)

Vern

aliz

atio

n M

odifi

er 960, 1

Fig. S10. Repression of FLC and acceleration of developmental rate as a result of vernalization. As the duration of chilling increases, the cumulative effective vernalization hours ( , horizontal axis) accumulate until saturation is reached at

. For the vin3-1 vernalization insensitive mutant, remains zero. The vertical axis is the acceleration scaling factor, , that modifies PTU values (equation [3]). The initial values of FLC repression,

hV= 960satV hV

Vern( ) =Vern 0 bF , are shown for FRI functional

and nonfunctional lines in the Col background. The autonomous path mutant fve-3 has a baseline value ( ), very similar to Col FRI. = 0.269bF

Figure S11

0%

10%

20%

30%

40%

50%

60%

NightOnly

Day Only All SD DayLD 0-18

SD All LD 0-18

SD DayLD 4-18

SD All LD 4-18

SD DayLD 0-12

SD All LD 0-12

SD DayLD 12-20

SD All LD 12-20

Coe

ffic

ient

of v

aria

tion

Fig. S11. Model accuracy varies with the diurnal temperature intervals used. Best-fit models that have a lower coefficient of variation (CV) of accumulated MPTU’s are more successful in reproducing the field data. Of the models tested, the best results are obtained when only temperatures during the day are included in MPTU calculations. Poor accuracy results when only night temperatures are included (left). Various combinations of “All” or “Day” time hours on short days (SD), cross classified with various long day intervals (LD; indicated in hours after dawn) yield intermediate results. The same result occurs when all day and night temperatures are employed. Shown are the CV’s of the fitted models with 95% confidence limits.

Table S1

Contrast Planting p-

value Diff in Days % Diff Norwich Summer ‘07 *** 13.1 60 Norwich Spring 2007 *** 8.1 16 Norwich Fall 2006 ** 21.7 52 Cologne Fall 2006 * 15.5 25 Halle Fall 2006 ns 0.8 1 Valencia Fall 2006 ** 13.5 18 Cologne Spring 2007 *** 9.7 20 Oulu Summer 2006 *** 11.1 61

Ler vs. co-2

Norwich Summer ‘06 *** 11.3 55

Norwich Summer ‘07 *** 14.5 71 Norwich Spring 2007 *** 13.3 26 Norwich Fall 2006 *** 63.7 137 Cologne Fall 2006 ** 16.8 16 Halle Fall 2006 ns 0.3 0 Valencia Fall 2006 *** 21.0 27 Cologne Spring 2007 *** 10.6 22 Oulu Summer 2006 *** 11.6 61

Col vs. gi-2

Norwich Summer ‘06 *** 8.3 38

Norwich Summer ‘07 *** 10.6 52 Norwich Spring 2007 *** 9.3 18 Norwich Fall 2006 *** 123.7 267 Cologne Fall 2006 *** 42.0 41 Halle Fall 2006 * 9.6 7 Valencia Fall 2006 *** 22.6 29 Cologne Spring 2007 *** 7.8 16 Oulu Summer 2006 *** 9.5 50

Col vs. Col-FRI-Sf2

Norwich Summer ‘06 *** 12.1 37

Norwich Summer ‘07 ns 2.0 6 Norwich Spring 2007 *** 16.0 26 Norwich Fall 2006 * 32.3 19 Cologne Fall 2006 ** 22.9 16 Halle Fall 2006 *** 51.4 37 Valencia Fall 2006 *** 35.6 36 Cologne Spring 2007 ** 7.0 13 Oulu Summer 2006 ns 1.1 4

Col-FRI-Sf2 vs. Col-FRI-Sf2 vin3-1

Norwich Summer ‘06 NA NA NA

Table S1 cont.

Norwich Summer ‘07 ns 0.8 -3 Norwich Spring 2007 ns 0.7 -1 Norwich Fall 2006 ns 15.1 -9 Cologne Fall 2006 ns 0.0 0 Halle Fall 2006 ns 2.2 2 Valencia Fall 2006 ns 5.8 6 Cologne Spring 2007 ns 0.5 1 Oulu Summer 2006 ns 0.3 1

Col-FRI-Sf2 vs. all autonomous

Norwich Summer ‘06 NA NA NA

Norwich Summer ‘07 ns 0.7 3 Norwich Spring 2007 ns 0.2 0 Norwich Fall 2006 ns 0.1 0 Cologne Fall 2006 ns 4.0 4 Halle Fall 2006 ns 5.8 -4 Valencia Fall 2006 ns 0.7 -1 Cologne Spring 2007 ns 0.3 1 Oulu Summer 2006 ns 0.8 -4

Col vs. Col-FRI-Sf2 flc-3

Norwich Summer ‘06 ns 1.3 -6

Norwich Summer ‘07 *** 9.9 -32 Norwich Spring 2007 *** 9.5 -16 Norwich Fall 2006 *** 123.8 -73 Cologne Fall 2006 *** 38.0 -26 Halle Fall 2006 *** 15.4 -11 Valencia Fall 2006 *** 23.3 -23 Cologne Spring 2007 *** 7.6 -14 Oulu Summer 2006 *** 10.3 -36

Col-FRI-Sf2 vs. Col-FRI-Sf2 flc-3

Norwich Summer ‘06 *** 13.4 -41 Table S1. Post hoc contrasts of flowering time between lines impaired in different flowering time pathways and their wild-type controls. Shown are significance values as well as the difference between the means in days and as a percent change compared to wild-type. *** for p<0.0001, ** for 0.01> p>0.0001, * for 0.05>p>0.01, ns for p>0.05.

Table S2

Planting Sowing

Date Transplant

Date

# Replicates

Sown Norwich Summer ‘06 5/25/06 6/6/06 20

Oulu Summer 7/7/06 7/19/06 24 Norwich Fall 9/6/06 9/20/06 15 Cologne Fall 9/27/06 10/11/06 15

Halle Fall 10/4/06 10/18/06 20 Valencia Fall 11/8/06 11/22/06 20

Norwich Spring 2/27/07 3/14/07 15 Cologne Spring 3/6/07 3/21/07 15

Norwich Summer ‘07 5/22/07 6/6/07 15 Ler co-2

Planting Mean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

BoltedMean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

Bolted Norwich Summer '06 21 0.40 2353 6/14/06 5 31 1.22 2457 6/25/06 4

Oulu Summer 18 0.44 2533 7/25/06 24 29 0.51 2605 8/5/06 19 Norwich Fall 42 2.83 2468 10/17/06 11 64 3.48 2550 11/9/06 12 Cologne Fall 63 5.47 1984 11/29/06 10 79 6.21 2065 12/14/06 10

Halle Fall 101 2.46 2160 1/13/07 17 102 3.98 2116 1/13/07 15 Valencia Fall 75 5.05 2309 1/21/07 14 88 1.84 2714 2/4/07 14

Norwich Spring 50 0.32 2439 4/18/07 14 59 0.96 2438 4/26/07 10 Cologne Spring 48 0.18 2500 4/23/07 9 58 0.33 2584 5/2/07 3

Norwich Summer '07 22 0.74 2271 6/12/07 14 35 0.94 2513 6/25/07 9

Table S2 cont.

Col gi-2 fve-3

Planting Mean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

Bolted Mean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

BoltedMean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

Bolted Norwich Summer '06 22 0.72 2695 6/15/06 9 30 0.50 2373 6/23/06 4 NA NA NA NA NA

Oulu Summer 19 0.49 2778 7/25/06 24 31 0.48 2679 8/6/06 23 28 0.71 2621 8/3/06 20 Norwich Fall 46 1.63 2748 10/22/06 14 110 12.23 3076 12/24/06 10 142 8.78 2885 1/25/07 9 Cologne Fall 102 3.54 2370 1/7/07 15 119 5.70 2537 1/23/07 13 144 7.63 2428 2/17/07 11

Halle Fall 130 2.73 2464 2/10/07 16 130 1.95 2407 2/10/07 17 142 2.91 2224 2/22/07 16 Valencia Fall 78 5.36 2366 1/24/07 16 99 1.68 3160 2/14/07 15 105 1.65 2797 2/20/07 16

Norwich Spring 51 0.51 2627 4/19/07 12 65 1.35 2773 5/2/07 13 60 0.50 2712 4/28/07 13 Cologne Spring 48 0.76 2528 4/23/07 9 59 0.83 2611 5/3/07 9 58 1.64 2925 5/3/07 11

Norwich Summer '07 20 0.42 2371 6/11/07 14 35 0.84 2511 6/25/07 11 29 0.92 2305 6/20/07 11 Col-FRI-Sf2 vin3-1 (in Col-FRI-Sf2) flc-3 (in Col-FRI-Sf2)

Planting Mean DTB

StErr of

DTB MPTU Avg. Date

of Bolt #

BoltedMean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

BoltedMean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

Bolted Norwich Summer '06 33 0.89 2565 6/27/06 5 NA NA NA NA NA 21 1.06 NA 6/14/06 8

Oulu Summer 28 0.79 2707 8/4/06 20 29 0.56 2723 8/5/06 22 18 0.60 NA 7/25/06 21 Norwich Fall 171 7.59 2643 2/24/07 7 204 15.00 3125 3/29/07 2 47 5.02 NA 10/23/06 11 Cologne Fall 143 8.07 3374 2/17/07 10 166 6.06 1960 3/12/07 5 106 5.93 NA 1/11/07 13

Halle Fall 140 2.10 2393 2/20/07 16 190 1.88 2357 4/12/07 8 124 2.56 NA 2/4/07 16 Valencia Fall 101 1.47 2105 2/16/07 13 136 3.66 2867 3/23/07 16 77 5.40 NA 1/23/07 16

Norwich Spring 61 0.80 2673 4/28/07 15 77 1.71 2707 5/14/07 10 51 0.45 NA 4/19/07 14 Cologne Spring 56 2.48 2559 4/30/07 6 63 1.01 2406 5/7/07 10 48 1.35 NA 4/23/07 10

Norwich Summer '07 31 0.47 2336 6/22/07 14 33 1.07 2491 6/24/07 13 21 0.50 NA 6/12/07 13

Table S2 cont. fve-4 ld-1

Planting Mean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

BoltedMean DTB

StErr of

DTB MPTU

Avg. Date of

Bolt #

Bolted Norwich Summer '06 NA NA NA NA NA NA NA NA NA NA

Oulu Summer 28 1.09 2706 8/4/06 17 31 1.01 2870 8/6/06 20 Norwich Fall 150 9.39 3024 2/3/07 8 172 4.74 3471 2/24/07 6 Cologne Fall 154 9.04 2774 2/27/07 6 135 3.32 2166 2/8/07 12

Halle Fall 143 3.64 2281 2/24/07 15 140 1.36 2175 2/21/07 16 Valencia Fall 98 2.36 2491 2/14/07 14 111 1.90 3220 2/27/07 15

Norwich Spring 59 0.61 2631 4/27/07 11 65 0.88 3059 5/2/07 10 Cologne Spring 52 1.76 2241 4/27/07 8 58 1.71 2813 5/2/07 8

Norwich Summer '07 30 0.34 2392 6/21/07 13 32 0.75 2470 6/22/07 12 Table S2. Summary of timing and bolting information for the field experiments. For each of the nine plantings, the timing of sowing and transplanting is shown along with the number of replicates planted. For each of the lines, the line mean and standard error of days to bolting are given along with the calendar date of bolting and the number of individuals for which bolting data were collected and included. Several lines were not available in the Norwich Summer 2006 planting. Where applicable, the modified photothermal units (MPTU’s) to bolting are given as well. The MPTU’s shown for fve-4 and ld-1 are from the model fitted with the fve-3 data to estimate the degree of FLC repression in autonomous pathway mutants. Fitting the model using either fve-4 or ld-1 did not give a significantly different fit, and the estimates of initial FLC repression were similar for all autonomous mutants, as well as for Col-FRI-Sf2.

Table S3

Ler Model

Symbol Parameter Description Value Lines Affected

Relative Sensitivity Source

Non-vernalizing development

bT Deg-Hr Base Temperature 3.00 all 0.319 Granier et al. 2002

CSDL Critical Short Day Length 10.00 Ler 0.281 fig. S7 CLDL Critical Long Day Length 14.00 Ler 0.235 fig. S7

DLD Long Day Development Rate 1.000 Ler NA Set a priori

DSD Short Day Development Rate 0.687 all -0.906 Estimated

Vernalization submodel parameters

minVT Minimum Vernalizing Temperature

-3.5 °C all NA Napp Zinn 1957

maxVT Maximum Vernalizing Temperature 6 °C all NA Set a priori

satV Effective Hours until Vernalization Saturation 960 all 0.077 Napp Zinn 1957, Lee

and Amasino 1995

bF Baseline FLC repression for:

Ler fri 0.366 all -1.133 Estimated

κ Overall scaling factor -5.17 all NA Napp Zinn 1957

ω Exponent on difference from minVT 2.23 all NA Napp Zinn 1957

ξ Exponent on difference from maxVT 1.00 all NA Napp Zinn 1957

Beta function reparameterization for sensitivity analysis

ν Vernalization Maximum Effectiveness 1.09 all -0.078

Calculated from , κω and ξ

σ Peak Semi-Width 2.95 all -0.062 Calculated from , κ

ω and ξ

m Modal Temperature 3.06 all -0.066 Calculated from , κ

ω and ξ Symbol Description Estimate 95% CI

hT Threshold MPTU 2392 2293-2491

CV Coefficient of variation 8.47% 6.35-12.75%

Table S3 cont. Col Model

Symbol Parameter Description Value Lines Affected

Relative Sensitivity Source

Non-vernalizing development

bT Deg-Hr Base Temperature 3.00 all 0.302 Granier et al. 2002

CSDL Critical Short Day Length 10.00 all but gi 0.217 fig. S7 CLDL Critical Long Day Length 14.00 all but gi 0.229 fig. S7

DLD Long Day Development Rate 1.000 all but gi NA Set a priori

DSD Short Day Development Rate 0.626 all -0.516 Estimated

Vernalization submodel parameters

minVT Minimum Vernalizing Temperature

-3.5 °C

all but vin3 NA Napp Zinn 1957

maxVT Maximum Vernalizing Temperature 6 °C all but

vin3 NA Set a priori

satV Effective Hours until Vernalization Saturation 960 all but

vin3 0.148 Napp Zinn 1957, Lee and Amasino 1995

bF Baseline FLC repression for:

Col fri 0.402 Col, gi -1.069 Estimated

Col-FRI-Sf2 0.263 Col-FRI-Sf2, vin3 -0.623 Estimated

fve 0.269 fve -0.585 Estimated

κ Overall scaling factor -5.17 all but vin3 NA Napp Zinn 1957

ω Exponent on difference from T minV

2.23 all but vin3 NA Napp Zinn 1957

ξ Exponent on difference from T maxV

1.00 all but vin3 NA Napp Zinn 1957

Beta function reparameterization for sensitivity analysis

ν Vernalization Maximum Effectiveness 1.09 all but

vin3 -0.004Calculated from , κ

ω and ξ

σ Peak Semi-Width 2.95 all but vin3 -0.101

Calculated from , κω and ξ

mκ

Modal Temperature 3.06 all but vin3 -0.105

Calculated from , ω and ξ

Symbol Description Estimate 95% CI

hT Threshold MPTU 2604 2516-2692

CV Coefficient of variation 10.75% 8.77-13.91% Table S3. Model summary, including parameter values, sources and sensitivities.

Table S4 16°C, LD 20°, LD 24°, LD 20°, SD 24°C, SD Genotype Mean St Dev Mean St Dev Mean St Dev Mean St Dev Mean St Dev

Col 38.80 2.67 NA NA 20.75 1.48 93.75 8.10 87.78 7.23 co-3 50.75 2.71 NA NA 32.79 3.41 63.30 2.99 57.16 3.93 Ler 35.85 1.73 24.59 2.00 23.63 2.24 65.30 3.08 56.75 2.29

Table S4. Days to bolting of Col, Ler and co-3 under a combination of temperature and day length conditions. Shown are means and standard deviations from 20 individuals per line per treatment.

Table S5

Site Latitude Longitude No. 6-min obs.

Comparison Site NCDC/AWS ID

Lat. Of Wx

Long. Of Wx

Elev. (m)

Norwich 52.624 1.218 724940 NORWICH WEA CNTRE 34920 52.633 1.317 18Cologne 50.958 6.857 590890 KOLN/BONN (CIV/MIL) 105130 50.867 7.167 91Halle 51.495 11.993 922100 LEIPZIG 104710 51.317 12.417 151Oulu 65.058 25.462 536625 OULU 28750 64.933 25.367 15Valencia 39.611 -0.407 358520 VALENCIA/AEROPUERTO 82840 39.5 -0.467 62

Table S5. Reference station names and coordinates for each field site. The geographic coordinates are given in decimal degrees, where East and North are positive values

Table S6 6H 8H 10H 12H 14H 16H DTB StDev DTB StDev DTB StDev DTB StDev DTB StDev DTB StDev

Ler 69.6 5.4 50.2 2.5 42.9 2.9 33.8 2.2 24.6 1.4 20.0 3.1 co-2 NA NA 49.4 2.5 49.8 1.1 43.7 2.5 45.2 3.6 39.3 2.7

6H 8H 10H 12H 14H 16H TLN StDev TLN StDev TLN StDev TLN StDev TLN StDev TLN StDev

Ler 40.0 3.2 35.0 2.3 35.0 4.7 16.0 1.4 10.0 1.1 10.0 1.1 co-2 NA NA 38.0 2.6 35.0 3.3 33.0 6.0 32.0 3.3 33.0 3.2

Table S6. Changes in developmental rate as a result of differing photoperiod. Both days to bolt (DTB) and total leaf number at bolting (TLN) for Ler and co-2 over a range of photoperiods are presented, from a sample of 15-20 plants per line per treatment.

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