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Journal of Experimental Botany, Vol. 52, No. 357, pp. 655-662, April 15, 2001
© 2001 Oxford University Press


Review Article

Improving quantitative flowering models through a better understanding of the phases of photoperiod sensitivity

Steven R. Adams1,3, Simon Pearson2 and Paul Hadley2

1 Horticulture Research International, Wellesbourne, Warwick CV35 9EF, UK
2 Department of Horticulture, School of Plant Sciences, The University of Reading, Reading, Berkshire RG6 6AS, UK

Received 10 April 2000; Accepted 20 October 2000


    Abstract
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
A quantitative understanding of the phases of sensitivity to photo-thermal environment is important if the accuracy of flowering models is to be improved and if the timing of long and short day treatments in protected cropping is to be optimized. A simple method of quantifying the duration of the phases of sensitivity to photoperiod is through the use of reciprocal transfer experiments where plants are transferred between long and short days at regular intervals throughout development. The advantages and disadvantages of different analytical approaches used to analyse such data sets are examined. Inconsistencies between the approaches are highlighted, as are differences in the way authors have interpreted data. The problem of confounding the effects of photoperiod and light integral is considered, as is the need to separate the number of inductive cycles needed for flower commitment from the length of the juvenile phase. The effects of photo-thermal environment on the duration of these phases of photoperiod sensitivity are discussed, together with topics requiring further development.

Key words: Reciprocal transfer, photoperiod, flowering, juvenility, modelling.


    Introduction
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
Studies of flowering have traditionally been aimed at either understanding the underlying physiological process of flowering (Bernier et al., 1981Go) or producing a quantitative analysis of the effects of the photo-thermal environment on the timing of flowering (Ellis et al., 1990Go). These latter studies have often concentrated on the effects of mean temperature and photoperiod on the time from sowing to first flowering. However, flowering in many plants is known to have distinct phases of sensitivity to the photo-thermal environment (Roberts et al., 1986Go). An understanding of when plants are sensitive to photoperiod is necessary if the accuracy of flowering models is to be improved and they are to have a more robust physiological basis.

In terms of commercial floriculture, it is often desirable to lengthen natural daylengths by applying photoperiodic lighting treatments to long day plants (LDP) to minimize the duration to flowering. However, if such treatments are confined to phases of sensitivity to photoperiod this can enable flowering to be hastened, while reducing the cost of lighting and the loss of plant quality through lengthening of internodes (this occurs because tungsten lamps are often used for daylength extension). Similarly, the unnecessary use of blackouts to shorten natural daylengths in short day plants (SDP) during periods when flowering is insensitive to photoperiod, would reduce the light integral available to plants and might be detrimental to plant growth and quality attributes. However, an understanding of when plants are sensitive to photoperiod is essential if the timing of photoperiod treatments is to be optimized. While experiments to understand the phases of photoperiod sensitivity have been predominantly conducted on arable crops, the information is perhaps more valuable for protected crops where there is greater potential to manipulate the growing environment.

Assessing the phases of sensitivity to photoperiod can be done simply through the use of reciprocal transfer experiments where the flowering response of plants transferred from long to short photoperiods and vice versa at intervals during development is noted. The simplicity of these experiments enables their use on a wide range of species with comparative ease, including on very small seedlings and in species where grafting studies are impractical. However, grafting juvenile and mature apices onto mature trees can provide an indication as to whether the transition from juvenile to adult is controlled by the autonomous nature of the meristem or a signal reaching the meristem from the rest of the plant (Robinson and Wareing, 1969Go). This review aims to show the importance of considering the phases of photoperiod sensitivity and highlights how reciprocal transfer experiments can be used to quantify these phases.


    The flowering process
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
The flowering process can be divided into a sequence of phases. Seedlings are often incapable of flowering; they must first attain a given size or age before they can be induced to flower. This early phase of development has been termed the ‘juvenile’ phase (Thomas and Vince-Prue, 1997Go) or ‘pre-inductive’ phase (Roberts et al., 1986Go) and provides a mechanism by which plants are large enough to support the energetic demands of seed production before they flower (Thomas and Vince-Prue, 1984Go). For a photoperiod-sensitive plant to respond to an inductive floral stimulus, the leaves need to be ‘competent’ and produce a floral stimulus, and the meristem must have the capability to respond to such a stimulus. If either requirement is unfulfilled, the plant is unable to flower even under inductive conditions (McDaniel, 1984Go). It has been concluded that the distance between the apical meristem and the roots was the factor that governed when flower initiation occurred under inductive conditions in Ribes nigrum L. and Nicotiana tabacum L. (Schwabe and Al-Doori, 1973Go; McDaniel, 1980Go). For long day floral initiation in poinsettia, it was concluded that the time of floral initiation was a function of the age of the meristem (Evans et al., 1992Go), while for other herbaceous species juvenility seems to be due to incompetence in other plant parts, especially the leaves (Lang, 1965Go). Having completed the juvenile phase, plants can be described as ‘ripe to flower’ and capable of responding to inductive conditions. This mature adult condition is generally stable; reversion to the juvenile state is rare in most species (Thomas and Vince-Prue, 1984Go).

Once capable of being induced to flower, an inductive process can occur in the leaf (O'Neill, 1992Go) which results in a floral stimulus that acts to determine the fate of the meristem (McDaniel et al., 1992Go). To distinguish between changes taking place at the apex and the photoperiod induction occurring in the leaves, the term ‘evocation’ was proposed to describe the events occurring in the apex which lead to floral initiation (Evans, 1969Go). For many species, a point in time is reached when the fate of a meristem becomes irreversible. This was described as ‘flower commitment’ (Bernier, 1988Go) although some caution needs to be exercised in describing the point at which the fate of an apex becomes truly irreversible, as it is often a function of the severity of the treatment used for assessing it. Furthermore, some species never become irreversibly committed to flowering and can be made to revert from floral to vegetative growth (Battey and Lyndon, 1990Go). In other cases a single inductive cycle may be sufficient for flower commitment (e.g. Oryza sativa cv. Zuiho; Vince-Prue, 1975Go), although in chrysanthemum seven or eight consecutive SD may be needed to initiate flowers at the same leaf number as in plants grown in continuous SD (Cockshull, 1972Go). It has been shown that in Lolium temulentum L. commitment to floral differentiation occurs within a few hours of the estimated beginning of the arrival of the LD stimulus at the shoot apex and that evocation and floral determination occur well before any morphological changes appear (McDaniel et al., 1991Go). Furthermore, it has also been shown that wild-type Arabidopsis (a LDP) became committed to flower after 7 LD but took a further 2–3 d before the first floral meristems appeared in SEM studies (Bradley et al., 1997Go).

The mechanisms for photoperiod perception in SDP and LDP differ (Thomas and Vince-Prue, 1997Go). The responses of LDP are strongly influenced by light intensity, unlike those for SDP, and so to be effective night break treatments need to be much longer. There is evidence to suggest that phytochrome A is important in sensing daylength in LDP, and that there may be an interaction between phytochrome C and daylength sensitivity in SDP (Jackson and Thomas, 1997Go). While the underlying mechanisms in SDP and LDP differ, most quantitative models can be modified to predict flowering in both LDP and SDP.

Photoperiod has also been shown to affect the early phases of flower development. Some early work (Langton, 1977Go) showed that the buds of some early flowering chrysanthemums could reach anthesis in LD, but that the use of SD hastened flower development and it was also shown that 28 SD were needed before chrysanthemums could be exposed to LD without any further delay in time to anthesis (Ben-Jaacov and Langhans, 1969Go). However, after this time plants were effectively insensitive to photoperiod, especially if lateral buds were removed. Similarly, many other species have been shown to be insensitive to photoperiod during the final phase of flower development (Roberts et al., 1988Go; Collinson et al., 1993Go; Ellis et al., 1997Go; Wang et al., 1997Goa; Adams et al., 1998Go). However, the fact that the first flower has reached the point at which its development will proceed independently of photoperiod does not mean that the rate of development of subsequent flowers is similarly photoperiod-insensitive. Indeed it has been shown that the photoperiod sensitivity in soyabean continued after first flowering, but ended before the appearance of the last flower (Asumadu et al., 1998Go). Furthermore, other developmental processes may remain photoperiod sensitive. In peanut, while the time to first flower appearance was not greatly affected by photoperiod (Bagnall and King, 1991Goa), flower, peg and pod numbers were increased in short days (Bagnall and King, 1991Gob). For soybean, it was shown that photoperiod regulates not only flower induction, but also flower differentiation, pod lengthening, seed filling, and the partitioning of assimilates to seed (Morandi et al., 1988Go).


    Quantifying the phases of photoperiod sensitivity
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
The length of the phases of photoperiod sensitivity can be quantified by reciprocal transfer experiments, where plants are simply transferred at regular intervals between environments that are inductive and non-inductive for flowering (Wang et al., 1997Goa). Transfers normally commence soon after seed germination and continue until flowering. Caution is needed when conducting such experiments on plants that are vegetatively propagated; to reduce the chance of using pre-initiated plant material, and to minimize the variation, it may be beneficial to remove the terminal meristem and youngest leaves and collect data from a side shoot (Cockshull, 1976Go).

The durations of the phases of photoperiod sensitivity can be determined by examining data on the time to first flower opening of plants transferred between SD and LD at different times. Thus for example, SD will not delay flowering in a LDP if exposure is restricted to the photoperiod-insensitive juvenile phase or photoperiod-insensitive phase of flower development. However, exposure to SD during the photoperiod-sensitive phase would delay flowering (Fig. 1Go). Similarly, LD will only hasten flowering in a LDP if exposure takes place when plants are photoperiod-sensitive.



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Fig. 1. Schematic representation (as presented by Ellis et al., 1992Go) of the response of time from seedling emergence to first flowering (f) modified for LDPs transferred from LD to SD (—) and from SD to LD (.....) at various times from sowing if the period from sowing to first flowering comprises a photoperiod-sensitive phase (durations IL and IS in long- and short-days, respectively) sandwiched between two photoperiod-insensitive phases, namely a pre-inductive phase (duration a1) and a post-inductive phase (duration a3).

 
Reciprocal transfer experiments have been conducted on a number of photoperiod-sensitive plants to assess the phases of sensitivity to photoperiod (Kiniry et al., 1983Go; Roberts et al., 1988Go; Wilkerson et al., 1989Go; Mozley and Thomas, 1995Go; Patterson, 1995Go; Wang et al., 1997Goa). An analysis presented previously on lentil (Lens culinaris Medic.) identified three developmental phases, the pre-inductive (juvenile), inductive and post-inductive phases (Roberts et al., 1986Go). The first is insensitive to photoperiod, the inductive phase is a period during which plants are sensitive to photoperiod, whilst the post-inductive phase is a photoperiod-insensitive period during which flowers develop. The first period during which rice was insensitive to photoperiod was defined as the initial basic vegetative phase (BVP) which, together with the subsequent photoperiod-sensitive phase (PSP) ending at panicle initiation, was described as the vegetative phase (Vergara and Chang, 1985Go). However, the BVP has also been defined as the period from seedling emergence until floral initiation (Major and Kiniry, 1991Go). Therefore, there is a lack of consistency in the literature concerning the use of terminology for these phases. Furthermore, some of the terminology used may be misleading. For example, it may be inappropriate to describe the photoperiod-sensitive phase as the ‘inductive phase’ as both flower induction and the early phases of flower development may be sensitive to photoperiod.

For plants that develop a terminal flower or inflorescence, the leaf number below the flower can be used to provide additional information about the timing of developmental events. When plants are transferred from inductive to non-inductive conditions, the first time at which transferring plants subsequently results in a dramatic decrease in leaf number coincides with the time at which the meristem becomes committed to flowering (Bradley et al., 1997Go; Adams et al., 1998Go). The length of the juvenile phase can be determined by transferring plants from non-inductive to inductive conditions for flowering. Plants transferred during the juvenile phase will all have the same leaf number while plants transferred after the end of this phase will have an increasing leaf number due to delayed floral initiation (Cockshull, 1985Go; Adams et al., 1998Go).

The length of the phases of photoperiod sensitivity were originally determined graphically (Boyle and Stimart, 1983Go; Roberts et al., 1986Go; Patterson, 1995Go), although other studies have used regression analysis of partial data sets to estimate the length of the various phases of photoperiod sensitivity (Wilkerson et al., 1989Go; Wang et al., 1997Goa, bGo). To aid the analysis of complex data sets produced by transfer experiments, an holistic approach was presented (Fig. 1Go) where all data were combined and then analysed simultaneously in order to estimate the durations of the pre-inductive, inductive and post-inductive phases (Ellis et al., 1992Go). This analytical approach has subsequently been used (Collinson et al., 1992Go, 1993Go; Ellis et al., 1997Go; Yin et al., 1997Go; Bertero et al., 1999Go) to examine the phases of photoperiod sensitivity in rice (Oryza sativa L.), soya bean (Glycine max L.), sorghum (Sorghum bicolor L.), rice (Oryza sativa L.), and quinoa (Chenopodium quinoa Willd.), respectively. There is an obvious advantage of using an holistic analytical approach such as that presented by Ellis et al. where data from both transfers (LD to SD and SD to LD) can be combined in one analysis (Ellis et al., 1992Go). Furthermore, such an approach enables estimates of the error of the predictions of these phases to be determined.


    Quantifying flower commitment
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
The analytical approach presented by Ellis et al. assumes that at the end of the photoperiod-insensitive, pre-inductive (juvenile) phase an immediate change in time to flowering will be seen in plants transferred from both inductive to non-inductive and non-inductive to inductive conditions for flowering (Ellis et al., 1992Go). However, it has been shown that this approach does not consider any time lag from the onset of photoperiod sensitivity before an effect of photoperiod on the time to flowering can be observed in plants transferred from an inductive to a non-inductive environment (Adams et al., 1998Go). The duration of this phase, which can be determined provided a short transfer interval is used, coincides with the number of inductive cycles needed for flower commitment. It has also been shown in opium poppy (a LDP) that the minimum number of inductive cycles for flowering can be separated from the duration of the juvenile phase (Wang et al., 1997Goa). Therefore, the analytical approach (Ellis et al., 1992Go) can confound juvenility with the number of inductive cycles required for flower commitment after plants become sensitive to photoperiod, and so may be inaccurate where a large number of cycles are required for flower commitment. As a consequence, the Ellis model has been modified by dividing the photoperiod-sensitive phase into photoperiod-sensitive inductive and developmental phases (Fig. 2Go; see Appendix for details) (Adams et al., 1999Go).



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Fig. 2. Schematic representation (as presented by Adams et al., 1999Go) of the response of time from seedling emergence to first flowering (f) for LDPs transferred from LD to SD (—) and from SD to LD (.....) at various times from emergence. The response assumes that the period from emergence to flowering comprises of photoperiod-insensitive juvenile phase (a1), followed by photoperiod-sensitive flower induction (PI) and development (Pd) phases in LD or a photoperiod-sensitive phase for flowering in SD (IS). The final phase of flower development corresponds to the photoperiod-insensitive flower development phase (a3).

 
Thus, it is clear that at least four developmental phases need to be distinguished in reciprocal transfer experiments: (1) photoperiod-insensitive juvenile phase; (2) photoperiod-sensitive inductive phase, ending at flower commitment; (3) photoperiod-sensitive flower development phase, and (4) a photoperiod-insensitive flower development phase. However, these phases relate to the response of a given meristem and not the capability of plants to perceive photoperiod.


    Confounding of effects of light integral and photoperiod
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
All too often, photoperiod treatments between which plants are transferred are imposed by either the use of high intensity (photosynthetically active) day extension lighting, or a combination of natural LD and blackouts to give SD (Heide, 1963Go; Roberts et al., 1986Go; Collinson et al., 1992Go, 1993Go; Ellis et al., 1992Go; Wang et al., 1997Goa, bGo). This confounds the use of long days with high light integrals which is a particular concern considering the importance of light integral in the flowering process. Not only has light integral been shown to affect the time to flowering of a range of species (Cockshull, 1972Go; Kaczperski et al., 1991Go; Pearson et al., 1993Go; Adams et al., 1997Go), but flower development phases have also been shown to differ in their sensitivity to light integral. For example, in chrysanthemum, the time to inflorescence commitment was found to increase exponentially as the light integral fell below 1.0–1.5 MJ m-2 d-1 (PAR) (Langton, 1992Go).

The confounding between photoperiod and light integral may offer an explanation for the surprising results presented earlier for opium poppy (Wang et al., 1998Go). Plants were transferred from a 9 h d-1 photoperiod to either a 12, 14 or 16 h d-1 photoperiod and vice versa. The analysis showed the presence of a photoperiod-insensitive juvenile phase, but this was estimated to end after 7 d at 12 h d-1, 4 d at 14 h d-1 and 3 d at 16 h d-1, leading them to conclude that the length of this phase was affected by photoperiod. However, the photosynthetic photon flux density (PPFD) was maintained at 1100±100 µmol m-2 s-1 and so plants grown under a 12 h d-1 photoperiod received 47.5 mol m-2 d-1 compared with 63.4 mol m-2 d-1 at 16 h d-1. Consequently, the variation in the length of the juvenile phase may have been caused by the difference in the light integral, not photoperiod per se.


    The effect of light integral and temperature on the phases of photoperiod sensitivity
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
Very few studies have investigated the wider effects of the photo-thermal environment on the duration of the phases of photoperiod sensitivity, although such information is of fundamental importance in understanding the environmental regulation of flowering. Antirrhinum plants were shown to become sensitive to photoperiod after 22 d, but the late flowering cultivar ‘Orchid Rocket’ appeared to respond to LD photoperiodic stimuli only when the light intensity was maintained at a high level (Hedley, 1974Go). Furthermore, these data indicate that cultivar ‘Pink Ice’ became committed to flowering in LD earlier under high (~317 µmol m-2 s-1) rather than low (~73 µmol m-2 s-1) PPFD. A more recent study (Adams et al., 1999Go) showed for petunia that the juvenile phase was very sensitive to light integral; reducing light integrals (by shading) dramatically prolonged the length of this developmental phase. Similarly, temperature affected the length of the juvenile phase of development in petunia; it was prolonged by both high and low temperatures, with an optimum of approximately 21 °C. However, the reason why plants are incapable of floral induction during the juvenile phase is unclear. The hastening of the juvenile phase under high PPFD may have been due to increased assimilates, leaf area, or the plants more rapidly attaining a critical node number or distance between the meristem roots; further work is needed to explore the physiological basis of this lack of response. Furthermore, it was found that in quinoa (Chenopodium quinoa Willd.) species the duration of the juvenile phase was longer in cultivars originating from lower latitudes (Bertero et al., 1999Go) and it has been suggested that a long juvenile phase may improve adaptation to low latitudes (Lawn, 1989Go; Tomkins and Shipe, 1997Go).

The length of the final phase of flower development in petunia, when plants were again insensitive to photoperiod, was controlled primarily by temperature. Plants were relatively insensitive to light integral at this time, and the optimum temperature for this phase was higher than that for the juvenile phase of development (Adams et al., 1999Go). The effects of two temperature regimes on the phases of photoperiod sensitivity were investigated in four rice cultivars (Collinson et al., 1992Go). They found that the photoperiod-insensitive juvenile and flower development phases were shorter at 28.7 °C than at 23.8 °C, although the effect of temperature on the photoperiod-sensitive phases for flowering was cultivar-dependent. However, it was suggested that, in sorghum, only the photoperiod-insensitive juvenile phase was sensitive to temperature (Ellis et al., 1997Go). In contrast, it was found that, for opium poppy, the photoperiod-insensitive juvenile and photoperiod-sensitive induction phases were insensitive to temperature (Wang et al., 1997Gob). The photoperiod-sensitive flower developmental phase was most sensitive to temperature, whilst the effect of temperature on the duration of the photoperiod-insensitive flower development phase was slight. Therefore, at this stage, it can only be concluded that species vary in their sensitivity to environmental variables at different phases of flower development.


    Future developments
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
Although the role of certain genes and growth substances in the flowering process is becoming clearer (Coupland, 1997Go; Jackson and Thomas, 1997Go), the development of a truly mechanistic mathematical model of flowering is hindered by a lack of information on the underlying physiological processes governing flowering. However, there is potential to move away from simple quantitative models of flowering towards models where the effects of photo-thermal environment on the individual phases of flowering are quantified. Ideally, the effects of photo-thermal environment on flowering should be modelled at least on a daily basis. However, the rate of such developmental processes cannot be measured directly, hence the need for transfer experiments and dissections.

Although errors may be incurred when using flowering models that assume plants are equally sensitive to photo-thermal environment throughout development, in some situations their simplicity may be advantageous. However, these simple models cannot provide growers of protected crops with information for optimizing the timing of photoperiod treatments. A more physiologically-based quantitative model of flowering is needed if growers are to be able to predict not only the time of first flowering, but also the sensitivity of plants to the photo-thermal environment at any given time. The analytical approach described previously (Ellis et al., 1992Go; Adams et al., 1999Go) provides information on the phases of sensitivity to photo-thermal environment during the flowering process, which could provide the basis for such a model. However, these analytical approaches assume plants are equally sensitive to photoperiod during flower induction and the early phases of flower development; further development would be needed to enable the analyses of reciprocal transfer data from plants with differing photoperiod responses, particularly those with dual photoperiod requirements. Further work is needed before the effects of the photo-thermal environment on the individual phases of the flowering process can be fully modelled; a considerable amount of data would be needed to do this.

Many flowering models intrinsically assume independence of developmental phases, such that the rate of progress to first flowering is simply a function of instantaneous photo-thermal environment. However, it has been suggested that since ‘development is a progression of response to the environment, there must be historic as well as current effects of the environment on current development’ (Slafer and Rawson, 1994Go). These authors subsequently showed that the duration from terminal spikelet appearance (TSA) to anthesis in spring wheat was affected (although not significantly so) by the photoperiod to which plants were exposed prior to TSA (Slafer and Rawson, 1995Go). Similarly, it was shown in barley that exposing plants to LD between sowing and the double ridge stage hastened progress from the double ridge to awn primordia stage (Kernich et al., 1996Go). It was suggested that the ‘memorized’ response was interactive with the response of the plant to the current photoperiod, rather than additive. Therefore, further studies are needed to test the independence of developmental phases.

An additional factor that could be incorporated into flowering models is plant variability. A stochastic flowering model would enable an estimate to be made of the proportion of plants in a particular developmental phase at any time. This would have great commercial benefit when scheduling crop production and predicting when, for example, a night break treatment should be given for maximum benefit. Furthermore, for maximum commercial benefit, it would also be advantageous to develop flowering models that predict the development of not only the first flower, but also of subsequent flowers.


    Appendix
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
Analytical approach (Adams et al., 1999Go)
The model presented earlier (Adams et al., 1999Go) quantifies the effect of the different times from sowing to transfer (tc), both from SD to LD and from LD to SD, on the durations from sowing to flowering (f). The model analyses reciprocal transfer experiments in terms of the following parameters: a1 the photoperiod-insensitive juvenile phase, IS and IL the photoperiod-sensitive phases for flowering in short and long days, respectively, and a3 the photoperiod-insensitive flower development phase. For long-day plants, the photoperiod-sensitive phase for flowering in long days (IL) is then subdivided into a photoperiod-sensitive flower induction phase (PI), and a photoperiod-sensitive flower development phase (Pd). While both flower induction and flower development will take place in SD, albeit at a slower rate, the durations of these phases in SD are not separated in this analysis.

For LDP, Fig. 2Go shows that in continuous LD the number of days from emergence to first flowering (f) is determined by the durations (d) of the phases of photoperiod-sensitivity:

(1)

This will also apply if plants are transferred from SD to LD before the end of the juvenile phase (a1), i.e. the day of transfer (tc) from SD to LD<=a1, or if plants are transferred from LD to SD during the photoperiod-insensitive flower development phase (a3), i.e. tc>=a1+PI+Pd. Similarly, for LDP growing in continuous SD:

(2)
which will also apply if plants are transferred from LD to SD before the end of the photoperiod-sensitive flower induction phase (PI), i.e. tc<=a1+PI, or if plants are transferred from SD to LD during the photoperiod-insensitive flower development phase (a3), i.e. tc>=a1+IS. By analogy with the approach of Ellis et al. (Ellis et al., 1992Go), the time to first flowering of plants transferred from LD to SD during the photoperiod-sensitive flower development phase (Pd), i.e. a1+PI<=tc<=a1+PI+Pd, can be calculated as:

(3)
and, finally, for plants transferred from SD to LD during the photoperiod-sensitive phase for flowering in short days (IS), i.e. a1<=tc<=a1+IS, the time to first flowering can be calculated as:

(4)

From these equations, it is possible to quantify the time to first flowering from emergence using the five parameters a1, PI, Pd, IS, and a3 for a LDP. Furthermore, a simple modification (substituting IL for IS and then dividing IS into PI and Pd) would enable the model to describe the phases of flowering in a SDP. These parameters can be fitted using an iterative procedure, although Mead suggests that continuous variables, such as time to flowering, should first be log transformed unless there is a good reason to believe this is not necessary (Mead, 1988Go).


    Acknowledgments
 
We wish to thank Dr FA Langton and Dr LR Benjamin for their useful comments and the Ministry of Agriculture, Fisheries and Food for funding this review (HH1318 SPC).


    Notes
 
3 To whom correspondence should be addressed. Fax: +44 1789 470552. E-mail: steven.adams{at}hri.ac.uk Back


    References
 Top
 Abstract
 Introduction
 The flowering process
 Quantifying the phases of...
 Quantifying flower commitment
 Confounding of effects of...
 The effect of light...
 Future developments
 Appendix
 References
 
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