Predicting the effects of environment and management on cotton fibre growth and quality: a functional–structural plant modelling approach

Fruit quality and more specifically quality of the fiber in the fruit of cotton, depends on interactions between fruit position in the plant architecture, temperature and agronomical practices, such as sowing time, mulching with plastic film, and topping of the plant's main stem and branches. A functional and structural cotton model CottonXL for fiber quality (strength, length and micronaire) was implemented at the level of each individual fruit in relation to thermal time for optimizing cotton fiber quality by matching cotton management to the environment. The model may be used to address climate and land use change scenarios.


Introduction
In many plant species, fruit quality ultimately depends on local conditions experienced by the fruit during its development. In cotton (Gossypium hirsutum), fruit quality and more specifically the quality of the fibre is the result of an interaction between genetic (Richard et al. 2006), environmental (Liakatas et al. 1998;Zhao and Oosterhuis 2000;Pettigrew 2001;Yeates et al. 2010) and management factors (Pettigrew and Adamczyk 2006;Read et al. 2006;Girma et al. 2007), and is determined by the position of, and the resources captured by each fruit. Fibre quality of the crop also depends on agronomic practices such as sowing date, shoot topping (removal of main stem and branch apices) and film mulching. Fibre quality is a key factor determining fibre price and quality of cotton textile products. Fibre quality is characterized by fibre length (mm), strength (cN tex 21 ) and micronaire (unitless), and the textile industry has a preference for long and strong fibres of moderate micronaire for producing high-quality yarns (Long et al. 2010). Fibre strength is measured by assessing the force at which a standard fibre sample will break into units of cN (centiNewton) per tex (ICC standard). Micronaire measures fibre fineness and maturity (Saville 2004;Ren et al. 2013). Although previous studies addressed the formation of fibre, fibre quality of a plant or population at the field level as a whole remains difficult to predict.
Fibre quality of a cultivar may differ substantially between different environments (Bradow et al. 1997;Davidonis et al. 2004;Campbell and Jones 2005). In China, there are considerable differences in the quality of cotton fibre between the three most important cotton growing regions, Xinjiang, the Yellow River basin and the Yangtze River basin (Fig. 1). These quality differences are associated with meteorological differences (e.g. temperature, light and precipitation) and soil factors (e.g. texture and fertility). Especially, temperature is a major determinant of fibre quality due to its effect on fibre elongation and secondary cell wall thickening. Low temperatures result in decreased fibre length (Zheng et al. 2012). The cotton boll maturation period is prolonged with the progression of the growing season due to decreasing temperatures (Anderson and Kerr 1938). The maximum elongation rate and duration of fibre growth depend on the variety and on environmental factors (Gipson and Ray 1969). Optimum temperature for fibre elongation is slightly lower than optimum temperature for boll development (Pettigrew 2001). Decreasing the night-time temperature prolongs fibre elongation duration and decreases elongation rate (Gipson and Ray 1969). However, effect of temperature on secondary cell wall thickening is debated (Gipson and Ray 1969;Zhao et al. 2013). Fibre quality is also reduced by drought (Nehra and Yadav 2013) and insufficient nitrogen (N) supply (Zhao et al. 2012).
Models have been widely developed and used to explore and predict relationships between fibre quality and environmental factors. Statistical models have been developed based on regressions between fibre quality indices and temperature or radiation (Heskenth and Low 1968;Wanjura and Barker 1985;Sequeira et al. 1994). Also, a process-based model simulating fibre quality for individual fruits in response to temperature and N supply has been developed (Zhao et al. 2012). Models with complex parameters often require local calibration before they are applied at different regions (Baker et al. 1983;Hearn 1994). A generic cotton model SUCROS-Cotton  simulates cotton growth and development based on a physiological day approach (Soltani et al. 2006), which is the days required for crop growth and development under optimal temperature. However, these models consider the fruit only and therefore cannot be applied to the analysis of fibre quality at plant or crop level because a cotton plant carries multiple fruits of different ages and developmental stages, with differences in accumulated thermal time in relation to position on the plant and in the canopy. The factors that affect fibre quality (notably temperature) are thus different for each single fruit, which needs to be taken into consideration for proper quantification of fibre quality. The models reported until now are not qualified for predicting fibre quality difference at both organ and crop levels. A model with detailed representation of the age and stage distribution of the fruit on the plant and in the canopy is therefore needed.
Scaling up fibre quality of individual fruits as determined by their local conditions to the plant and canopy levels is possible using the methodology of functionalstructural plant modelling (FSPM) (Vos et al. 2010). In FSPM plant physiological processes and environmental factors can be integrated in representations of plant development. This enables simulation and analysis of the interactions between plant architecture and functioning. Functional -structural plant modelling is a versatile tool to simulate plant development, reproducing plant topology and geometry in response to environmental and internal factors. Linking physiological and architectural models, virtual cotton models have been developed to assist in interpretation of the plant maps (distribution of organs within the plant) for helping crop management (Jallas et al. 2000;Hanan and Hearn 2003). However, these models do not include fibre quality and the effects of manipulation of plant structure, such as branch topping and removal of vegetative branches. An FSP model of cotton development, CottonXL, has been designed and calibrated to simulate development of leaf and fruits (square, flower and boll), plant height and branching (Gu et al. 2014). Crop development in CottonXL is driven by thermal time, population density, application of growth regulator mepiquat chloride (MC) and topping of the main stem and branches. This model allows to simulate cotton fibre development in relation to the temporal and spatial distribution of retained fruits.
The main objective of this study was to assess cotton fibre quality in response to temperature regimes and agronomic practices (sowing date, main stem and branch topping, film mulching), in order to understand how the fibre quality of individual bolls is determined by the environmental conditions experienced by each boll during boll development, in relation to overall plant architectural development, and thus how high-quality cotton production can be optimized. For this purpose, routines calculating fibre quality were integrated in CottonXL using concepts from a process-based cotton model SUCROS-Cotton . This yielded a model that simulates fibre quality determined by the conditions experienced by the individual fruits during their development on the plant. The model was subsequently calibrated and validated for fibre quality using experimental data. Finally, scenario studies were carried out to assess the effect of sowing date, main stem and branch topping, and film mulching.

Field experiments
Field experiments were conducted to determine fibre quality of individual fruits in Anyang (114813 ′ E, 36804 ′ N), Henan, China in 2007. The experiments included two cotton (Gossypium hirsutum) cultivars (Kemian 1 and NuCOTN 33B) grown under nonlimiting N supply (480 kg total N ha 21 ). Kemian 1 is a local bred Bt cotton which is popularly used in south China, and NuCOTN 33B is a Bt cotton from Monsanto, USA, which is popularly used in north China. The two cultivars both are middle matured cotton. The soil type was a sandy loam with 14.7 g kg 21 of organic matter content, 9.4 mg kg 21 of total N, 23.6 mg kg 21 of available P and 71.3 mg kg 21 of available K. Cotton was sown on 25 April. Half of the N fertilizer was applied before sowing and the rest was top-dressed on 15 July. Potassium chloride of 225 kg ha 21 and super phosphate of 750 kg ha 21 were applied basally. The experiments were designed as randomized complete blocks with three replicates. Each plot was 54 m 2 (9 × 6 m) with 0.75 m row spacing and 0.25 m plant distance. All plants at middle four rows in each plot were observed per plot. This experiment partially overlapped with the one described in Zhao et al. (2012) and gathered independent experimental data for unlimited water and N treatments at Anyang in 2007.
Weather data were obtained from the national meteorological information centre (www.cma.gov.cn/ 2011qxfw/2011qsjcx). Accumulated thermal time, total precipitation and sunshine hours during the cotton growing season (April to October) at the sites for calibration, validation and scenario analyses are shown in Table 1

Data for model parameterization
Observations on fibre length, strength and micronaire of individual fruits of the same developmental age for both cultivars combined, under sufficient water and nutrient supply, were used to determine potential fibre quality for individual fruits. To collect these data, fruits at the first and second node positions of each fruit branch on randomly selected cotton plants were tagged on 18 and 27 July, and 15 August. The age of each tagged fruit, expressed in days after squaring (a square, or flower bud, was counted when the bud was larger than 3 mm in diameter), was recorded. Twenty tagged fruits or open bolls were picked at an age of 28, 33, 40, 47, 54, 61, 68 and 75 days after squaring. The sampled fruits were used for measurement of cotton fibre quality. The immature cotton fibres were hand-ginned and allowed to dry at room temperature. The fibres for immature or mature bolls were prepared before the measurements under the same humidity and temperature conditions. Fibre length was measured using the water washing method (Thaker et al. 1989) for young bolls (,53 days after squaring), and with a Y-146 cotton fibre photodometer (Taicang Electron Apparatus Co. Ltd, China) for older bolls (Zhao et al. 2012). Cotton fibre strength and micronaire were determined with an Uster High Volume Instrument 900 (HVI 900; Uster Technologies Ltd, Switzerland) fibre testing system (Anonymous 2001) at the Cotton Quality Supervision, Inspection, and Testing Center of China Ministry of Agriculture, Anyang, China. Since fibre strength and micronaire can only be measured for relatively mature bolls, fewer data on strength and micronaire were available compared with fibre length.
To determine the effect of temperatures on fibre length, strength and micronaire, previously published data (Ma et al. 2006) were reanalysed. The experiments were conducted in Nanjing 118847 ′ E, 32803 ′ N), Anyang, Baoding (115847 ′ E, 39805 ′ N) and Shihezi (86801 ′ E, 44826 ′ N) in 2002 -03. Three different sowing dates in each site and year were compared with three replicates. All flowers at the third fruit branch in Shihezi and the fifth fruit branch in the other sites in each plot were labelled and harvested to measure fibre length, strength and micronaire. The relationship between the relative fibre quality (actual fibre quality divided by maximum fibre quality) for all individual fruits and temperature factors (daily average, minimum, maximum and the difference between minimum and maximum) was regressed using appropriate quadratic or linear models (see the Results section).

Development of an FSP cotton model for fibre quality
Cotton development and fibre quality were simulated using CottonXL (Gu et al. 2014), which is based on the principles of FSPM (Vos et al. 2010), and is developed using the GroIMP platform (available for free on www. sourceforge.net/projects/groimp) (Hemmerling et al. 2008).
Physiological days. Crop development in CottonXL is driven by thermal time, expressed as physiological days, i.e. the number of days required for growth and development of an organ under optimal temperature . Physiological days take the effects of both base and optimal temperatures into account. The physiological age of an organ is the sum of daily temperature effect (E(T )): where T is the daily mean temperature calculated by averaging minimum and maximum temperatures. T b is the base temperature and T o is the optimal temperature. Temperatures between 21.9 and 29.7 8C are optimal for cotton boll development, which determines fibre quality; however, temperatures as low as 15 8C still do not arrest cotton boll development (Gipson and Ray 1969;Dusserre et al. 2002). Therefore we used 12 8C for T b and 25 8C for T o . Additionally, the daily E(T ) was set to zero when T was smaller than T b and to 1 when T was greater than T o . The effect of film cover on physiological age was simulated by adding an increment of air temperature estimated based on soil temperature increased by plastic film and crop response .
Simulation of plant structure and organs. CottonXL simulates development of cotton plant architecture at the level of the phytomer (Fig. 3) and its organs, explicitly taking into account organ appearance, extension, final size, location and orientation. The rate of organ appearance is determined by the plastochron. The value of the plastochron is fixed throughout plant development and expressed in thermal time.
Organ development is calculated based on organ age, which itself is expressed in thermal time since organ appearance. Organs that have the same cumulative phytomer number (CPN, the phytomer rank of a fruit counted from the cotyledon node; Fig. 3) appear simultaneously and therefore have the same age. In the model, new phytomers appear at a plastochron of 3 -3.5 physiological days. The value of the plastochron is a function of population density and the application of plant growth regulator MC. Topping of main stem and branches was simulated by removal of the apex and the top two phytomers (according to farmer's practice), resulting in termination of the appearance of new phytomers. Parameters for temperature-dependent growth and development rates of organs, fruit formation and abscission, and the effect of film mulching were taken from a process-based cotton growth model SUCROS-Cotton . Fruits (square, flower and boll) appeared on each phytomer on fruiting branches. The fruit abscission rate depended on fruit age , expressed in physiological days, which allows comparison of all the fruits at different positions. A full account of model parameterization can be found in Gu et al. (2014). We incorporated routines for the simulation of fibre quality in relation to temperature and individual fruit age in CottonXL. Fibre length, strength and micronaire of all individual bolls growing on the plant throughout the season were calculated on a daily basis taking into account the physiological time, the prevailing temperature and agronomic practices under sufficient water and N supply (Fig. 4).
Simulation of fibre quality. We assumed that fibre quality can be modelled as a growth process with physiological age after the emergence of a square. Accordingly, we described a potential fibre quality index under optimal conditions as a logistic equation against physiological days: where Q i represents the thermal time-dependent potential fibre quality; i represents the different quality index, i.e. fibre length (mm), strength (cN tex 21 ) and micronaire. Q max,i is the maximum value of a potential fibre quality index i of given cultivar; K i is the relative growth rate (day 21 ), a constant that determines the curvature of the growth pattern; t is the physiological days and t m is the inflection point at which the growth rate reaches its maximum value. Under actual ambient conditions, growth will be less than the potential. Thus, the actual fibre quality is simulated by multiplying potential growth and reduction factors. The reduction factors are used to adjust actual growth rate according to the effect of temperatures, i.e. f ( T) i , the effect of daily mean temperature ( T) on index i; f (T min ) i , the effect of minimum temperature (T min ) on index i; and f (TD) i , the effect of the difference between maximum (T max ) and minimum temperatures (TD) on index i. Actual fibre quality of index i, DQ a,i , is then calculated as the product of the potential increment DQ i (Eq. (3)) and the reduction factors: For different fibre quality indices, the effect of reduction factors differed. Fibre length was only affected by daily mean temperature. Fibre strength is the fibre's resistance to stretching, and is determined by fibre extension and duration of fibre thickening. Moreover, fibre strength is determined by environmental conditions and variety traits (Zhou et al. 2011). There is a significant positive correlation between cotton fibre strength and daily mean temperature during the formation of the fibre (Wang et al. 2009). Fibre strength increased linearly with daily mean temperature and decreased linearly with diurnal temperature difference between maximum and minimum (Ma et al. 2006).
Micronaire is a comprehensive fibre quality index that represents cotton fibre fineness and maturity (Rodgers et al. 2013). Micronaire increases with cotton fibre thickening . Daily minimum temperature greatly affects fibre micronaire (Ma et al. 2006). Higher daily minimum temperature could promote micronaire (Gipson and Ray 1969;Davidonis et al. 2004). Model evaluation. To determine model performance, the root mean square error (RMSE) was used. RMSE quantifies the difference between observed and simulated results: The relative error (RE) was used to determine the accuracy of the simulations: where Y i and X i are the observed and simulated results, respectively. N is the number of observations. Data analysis was conducted using Microsoft Excel.
The effects of sowing dates, main stem and branch topping, and film cover on cotton fibre length, strength and micronaire in different scenarios were analysed using general linear model procedure (GLM) in SPSS 17 (IBM Corporation, New York, NY, USA).

Simulations
To relate fibre quality to plant architecture, fibre length, strength and micronaire were expressed in relation to CPN (Fig. 3). Fruits of similar CPN can be regarded as being in the same cohort of fruits and therefore having experienced the same temperature regimes during their development. Moreover, the CPN is a useful measure for expressing the hierarchical position of a fruit with respect to the base of the plant, because the fruits at the same CPN number were formed around the same thermal time. This position affects the time of the formation of the fruit and its position in the canopy. Topping means removal of apical buds with two phytomers. In Xinjiang, mulching using plastic film cover is widely used to increase soil temperature and protect the seedlings against low night-time temperatures. Mulching is not a standard practice in the other two regions. Hence, the effect of plastic film mulch on temperature was included in the simulations for Xinjiang only, and algorithms for the effect of film mulching are given by Zhang et al. (2008). Although film mulching does not directly affect fibre quality, it may modify fibre by an influence of plant growth and development by increasing soil temperature. Thus, the film mulching effects on fibre quality at different regions were also put into scenario treatments.
Since fibre quality is mainly affected by temperature, the fruit growing duration and spatial distribution of fruit are considered as major causes to the formation of fibre quality. Agronomy practices, e.g. sowing date, branch topping and film cover might have great influences on fibre quality. Thus, four scenarios for different sowing dates, main stem and branch topping dates, and film mulching were designed to explore their effect on fibre quality (Table 2). Simulations were run for three sites: Aksu in south Xinjiang (Xinjiang region), Huimin in Shandong (Yellow River region) and Yueyang in Hunan (Yangtze River region), for the years 1981 -2010. Each simulation was run once using 6 plants for each year. The plant densities in the scenario studies were the same as in those used in model parameterization and validation.

Calibration of potential fibre quality increase rates
Parameter values were obtained through fitting the relationship of potential quality indices, i.e. length, strength and micronaire, and showed a good fitness with observed values under unlimited water and N conditions (Fig. 5). The two testing cultivars showed no difference. The R 2 of curve fitting ranged from 0.992 to 0.989, the RMSE between estimated and observed values was 1.07 mm for length, 1.43 cN tex 21 for strength and 0.19 for micronaire. The time that a fruit reached its maximum increase rate for length was at 34 physiological days after squaring (fruit age), for strength at 40 days and for micronaire at 47 days (Table 3).

Effect of temperature on fibre quality
Quadratic regression between mean temperature and effect on fibre length f ( T) L is given in Eq. (6), R 2 ¼ 0.67. Effect of mean temperature on fibre length had a maximum of 1 near the optimum temperature of 25 8C, and zero at the lower and upper temperature thresholds for fibre growth of 9 and 42 8C, respectively: The effect of mean temperature on fibre strength (f ( T) S , Eq. (7)) ranged between 0 and 1. Parameter values were obtained through fitting experimental data, R 2 ¼ 0.55. When daily average temperature was over 30 8C, the value equalled 1: The effect of the difference between minimum and maximum daily temperature on fibre strength ( f(TD) S , Eq. (8) Micronaire was only affected by daily minimum temperature. The effect of minimum temperature on fibre micronaire ( f (T min ) M , Eq. (9)) was described as a linear regression and R 2 of the fitted equation was 0.67. When minimum temperature was over 25 8C, the value of the reduction factor was 1: Simulations of cotton and fibre growth Fruits at CPN values lower than 20 showed comparable values for all three aspects of fibre quality, although micronaire showed a decreasing trend with increasing CPN over the whole range of CPN values (Fig. 6). Fruits that developed at high ranks, especially above a CPN value of 25, showed very low fibre quality in every aspect.

Scenarios studies
Sowing date. Delaying the sowing date significantly (P . 0.01) increased fibre length in the Yangtze River valley, but significantly (P , 0.05) decreased fibre length in the Xinjiang when sowing date was postponed by 20 days. It had no significant (P ¼ 0.225) influence on fibre length in the Yellow River valley. Over 30 years and three regions, cotton fibre strength was not significantly (P ¼ 0.393) decreased by delaying sowing date; however, fibre micronaire was significantly (P ¼ 0.023) decreased.
Here, the variation of fibre length (as represented by the size of the error bars in Fig. 8) due to climate variation (i.e. the crop experiencing a different climate over the years) was much greater compared with the other  The results from scenario analysis based on regional temperature for cotton fibre quality showed good agreement with the actual distribution of fibre quality (Fig. 1).
Topping. The times of main stem and branch topping determine the final number of fruits on a plant. Early topping practice resulted in all the fruits of high quality. Over 30 years and three sites, simulated fibre length, strength and micronaire were significantly (P , 0.01) decreased with later timing of main stem topping; however, delaying topping main stem time significantly increased fibre length in the warm and humid region of Yangtze River (Fig. 9). This effect was greatest for the Xinjiang region and the Yellow River region. The effect of topping was smallest in the Yangtze River region. The percentage of fruits (frequency) of high quality was greatly affected by the time of main stem topping (Fig. 10). As topping time was delayed, the number of fruits with high length, strength and micronaire decreased significantly (P , 0.01). Early topping of main stems significantly (P , 0.01) increased the frequency of fruits with longer fibre length (30 -35 mm) in the Xinjiang and Yellow River regions, but there was no effect on the frequency distribution of fibre length in the Yangtze River region. Earliest time for topping main stem (10 days earlier than traditional time) significantly (P , 0.001) increased the percentage of fruits with higher fibre strength (30 -35 cN tex 21 ) and micronaire (4.5 -5.25), especially in Xinjiang (Fig. 10). Delaying topping time (10 -15 days) significantly (P , 0.01) increased the percentage of fruits with lower length, strength and micronaire (Fig. 10) in all regions, thus the overall fibre qualities were significantly (P , 0.05) decreased. Delaying branch topping time resulted in a significant (P , 0.001) decrease in fibre length, strength and micronaire in all regions simulated (Fig. 11), especially in Xinjiang and the Yellow River region. Delaying branch topping time also caused a significantly (P , 0.001) high distribution frequency of fruits with low fibre length, strength and micronaire. Current time for branch topping (5 August in Xinjiang, 15 August in Yellow and Yangtze River regions) showed a significantly higher percentage of fruits with high length, strength and micronaire than delayed topping branch time, except for a lower value in length in the warmer Yangtze River region [see Supporting Information].
Film mulching. The results of Scenario 4 (with and without film mulching) at the three regions did not show a significant effect on fibre length (P ¼ 0.794), strength (P ¼ 0.570) and micronaire (P ¼ 0.559), and also did not affect the distribution of fruit frequency in fibre length, strength and micronaire. However, applying film cover in the Yellow River region slightly decreased the percentage of fruits with a high strength (25.0 -35.0 cN tex 21 ) value [see Supporting Information]. Although film mulching plays an important role in improving cotton yield in Xinjiang, its effect on fibre quality and its distribution is less important when a proper topping time is practiced according to the heat resources available.

Discussion
The extended version of CottonXL presented here gave good predictions of fibre length, strength and micronaire in relation to boll age and prevailing temperatures during boll development. Model output corresponded well with independent experimental data. The observation that fibre quality decreases severely for fruits of a high CPN, was consistent with results from previous studies (Davidonis et al. 2004;Zhou et al. 2011), showing late-formed fruits had rather low fibre quality due to low temperatures. Fibre strength was underestimated by the model in the Yellow River and Xinjiang regions. This was probably due to water shortage which often occurs in these regions, whereas the model was calibrated for optimal water supply. Water shortage results in stronger fibres, but the current version of CottonXL does not account for this effect. The advantage of this model over the model of Zhao et al. (2012) was the calculation of fibre quality model at individual single boll level and the upscaling to plant and crop level, which made analysis of effects of regional conditions on fibre quality possible.  Controlling the effect of temperature by sowing date and mulching Sowing date did not significantly change fibre quality in the Yellow and Yangtze River regions. However, in Xinjiang, where the temperature is relatively low during the early cotton growing period, delay of sowing date decreased fibre quality because low temperatures at the end of growing period could prevent bolls from reaching full maturity. This effect was most prominent for fibre length which also showed considerable variation over the years (1981 -2010) due to the effects of changing weather conditions. Later sowing negatively impacts cotton yield (Cathey and Meredith 1988;Bozbek et al. 2006), but does not influence boll numbers (Barradas and Lopez-Bellido 2009). Therefore, breeding strategies that provide low-temperature tolerance might increase flexibility for planting times especially in cooler regions (Tan et al. 2011). We conclude that the effect of sowing date on cotton yield and quality depends on heat resource availability. Film mulching could increase soil temperature, soil moisture content and yield (Dong et al. 2008), and therefore it could play an important role in improving yields in the Xinjiang region. The limitation for heat resource can only be overcome by film mulching at the beginning, when the sun can reach the soil, and generate very high temperatures under the plastic and in the soil. Our simulations found no significant effect of film mulching on fibre quality for this region because the film effects mainly occurred at an early stage and appearance of late fruits which have no sufficient heat to be matured was stopped by topping, although it is considered a useful agronomic practice to enhance cotton yield (Dong et al. 2008).

Main stem and branch topping
For optimizing topping time, farmers in China usually use the number of fruit branches as an indicator while the number of nodes above the first white flower is used in the USA (Bynum and Cothren 2008). Our simulation of delaying main shoot topping, which results in a greater number of fruit branches and fruits on the plant, predicted a substantially reduced cotton fibre quality due to the increase of late-formed bolls. This was especially the case in Xinjiang and Yellow River valley cotton producing regions, whereas it did not greatly affect fibre quality in the Yangtze River valley due to the longer growing season. Topping earlier than the reference time greatly increases fibre quality especially in the Xinjiang region, but also leads to a reduction of total boll number and yield due to removal of new fruiting branch sites on the plant (Teague et al. 2011). Increasing population density and application of MC could improve cotton fibre quality (Ren et al. 2013). According to our simulations, combining high density and MC with early topping would be practical, since the late-formed fruits that may not be mature at the time of harvest will be prevented from appearing (Siddique et al. 2002;Ren et al. 2013).
Fruits that are initiated ,60 -70 calendar days before final harvesting do not contribute to yield . Therefore, proper timing of topping or other measures to prevent useless fruits from forming is important for increasing yield and quality of the yield. From our scenario analysis, we conclude that delaying branch topping after main stem topping would greatly decrease fibre quality, especially in the Yellow River valley and Xinjiang regions. Delaying branch topping to 25 days after main stem topping decreased fibre quality by 9 % (length: 11 %, strength: 6 %, micronaire: 11 %) compared with 15 days after main stem topping. Branch topping 15 -25 days after main shoot topping is a common practice for Chinese farmers in order to increase yields at the expense of fibre quality. Our simulation results showed that branch topping should be done at same time or no later than 15 days after main shoot topping, otherwise, acceptable fibre quality is unlikely to be reached.

Conclusions
CottonXL was capable of simulating cotton fibre quality under various conditions such as climate, cultivar, sowing date and topping time, by taking into account the variation in temperature regimes experienced by the developing fruits. The model is therefore a useful tool to explore cotton fibre quality, and is especially suitable to explicitly predict the variation of quality aspects within a plant as a result of differential periods of development of the fruits. Also it can be used to optimize plant architecture in order to get high fibre quality in given environmental conditions and management scenarios by manipulating plant architecture in the model, as well as to help farmers understand how the plant architecture determines crop development and quality. Since cotton fibre quality can be improved by a proper combination of MC application and population density (Ren et al. 2013), optimal management taking into account density, MC, sowing date and topping times for both high yield and quality can be explored and predicted using the current model.

Contributions by the Authors
L.Z., Z.L., X.P. and X.W. conceived and designed the experiments; L.M., X.W., X.Z. and S.W. performed the experiments; X.W. and L.Z. analysed the data; L.Z. and J.E. developed the model; and X.W., L.Z., J.E. and W.W. wrote the paper.

Conflicts of Interest Statement
None declared.
The following Supporting Information is available in the online version of this article -   and micronaire (C) affected by branch topping for three sites located in northwest (Aksu), Yellow River (Huimin) and Yangtze River (Yueyang) cotton producing regions in China averaged over the period 1981 -2010. The arrow points to traditional branch topping time.