Received for publication: 28 March, 2014. Accepted for publication: 30 July, 2014. 1 Program of Agronomy, Centro de Investigacion de la Caña de Azucar de Colombia (Cenicaña). Cali (Colombia). malopez@cenicana.org 2 AgWeatherNet, Washington State University. Prosser, WA (USA). 3 Department of Agronomy, Faculty of Agricultural Sciences, Universidad Nacional de Colombia. Bogota (Colombia). Agronomía Colombiana 32(2), 196-204, 2014 Potential growing model for the standard carnation cv. Delphi Modelo del crecimiento potencial de clavel estándar cv. Delphi Miguel Ángel López M.1, Bernardo Chaves C.2, and Víctor Julio Flórez R.3 ABSTRACT RESUMEN The cut f lower business requires exact synchronicity between product offer and demand in consumer countries. Having tools that help to improve this synchronicity through predictions or crop growth monitoring could provide an important advantage to program standards and corrective agronomic practices. At the Centro de Biotecnología Agropecuaria, SENA (SENA’s Biotechnology, Agricultural and Livestock Center), located in Mosquera, Cundinamarca, a trial with standard carnation cv. Delphi grown under greenhouse conditions was carried out. The objective of this study was to build a simple model of dry matter (DM) production and partition of on-carnation f lower stems. The model was based on the photosynthetically active radiation (PAR) MJ m-2 d-1 and temperature as exogenous vari- ables and assumed no water or nutrient limitations or damage caused by pests, disease or weeds. In this model, the daily DM increase depended on the PAR, the light fraction intercepted by the foliage (FLINT) and the light use efficiency (LUE) g MJ-1. The LUE in the vegetative and reproductive stages reached values of 1.31 and 0.74 g MJ-1, respectively. The estimated extinction coefficient (k) value corresponded to 0.53 and the maximum FLINT was between 0.79 and 0.82. Partitioning between the plant vegetative and reproductive stages was modeled based on the hypothesis that the partition is regulated by the source sink relationship. The estimated partition coefficient for the vegeta- tive stage of the leaves was 0.63 and 0.37 for the stems. During the reproductive stage, the partitioning coefficients of leaves, stems and f lower buds were 0.05, 0.74, and 0.21, respectively. El negocio de las f lores de corte requiere una estricta sin- cronía entre la oferta del producto y la demanda en los sitios de consumo. Contar con herramientas que ayuden a mejorar esta sincronía mediante predicciones o monitoreo del cultivo puede significar una ventaja importante a la hora programar prácticas de manejo rutinarias o correctivas. En el Centro de Biotecnología Agropecuaria del SENA, ubicado en Mosquera, Cundinamarca, se estableció un ensayo en clavel estándar cv. Delphi en condiciones de invernadero. El objetivo del estudio fue construir un modelo simple de producción y distribución de masa seca en tallos f lorales de clavel. El modelo se basó en la radiación fotosintéticamente activa (PAR) MJ m-2 d-1 y la temperatura como variables exógenas y asume que no hay limitantes de agua, nutrientes o daño por plagas, enfermedades o malezas. En este modelo el incremento diario de masa seca dependió de la PAR, la fracción de luz interceptada por el fol- laje (FLINT) y la eficiencia en el uso de la luz (LUE) g MJ-1. El LUE para la etapa vegetativa y reproductiva alcanzó valores de 1.31 y 0.74 g MJ-1, respectivamente. El valor estimado de k correspondió a 0,53 y la máxima FLINT estuvo entre 0,79 y 0,82. La distribución entre las etapas vegetativa y reproductiva de la planta se modeló basada en la hipótesis de que la partición está regulada por la relación fuente vertedero. El coeficiente de distribución estimado para la etapa vegetativa para las hojas fue 0,63 y para el tallo 0,37. Los coeficientes de distribución en la etapa reproductiva fueron para hojas 0,05; tallos 0,74 y botón f loral 0,21. Key words: Dianthus caryophyllus, prediction, dry matter, partition coefficient, stems. Palabras clave: Dianthus caryophyllus, predicción, materia seca, coeficiente de partición, tallos. Introduction Colombia is the main provider of cut f lowers in the United States and the second exporter in the world with 205,407 t of fresh f lowers, which have all been produced in an area of 7,200 ha, employing about 220,000 persons, directly and indirectly (Asocolf lores, 2009). The standard carnation and mini carnation are the most important f lower crops in the country, after roses, accounting for 18% of the cultivated area and with an export of 37,855 t (Asocolf lores, 2009). The demand for f lowers in North America, Europe and Asia is closely linked to special celebrations; a market characteristic that forces a special coordination between the national supply and international demand. In order to maintain this synchronicity, it is necessary to have a deep knowledge of the growth and development dynamics of the 197López M., Chaves C., and Flórez R.: Potential growing model for the standard carnation cv. Delphi species of interest as well as on the use of different tools that are intended for monitoring the production related physiological processes and for collaborating with making agronomic and administrative decisions. Crop modelling gives quantitative information for the decision making of, for example, sowing season, irriga- tion, fertilizing, and pest and disease management, among others. In addition, it serves as a tool for estimating yield potential, water needs, fertilizer losses and other factors (Penning de Vries et al., 1989; Gary et al., 1998; Meira and Guevara, 2000). Models are tools used to summarize knowledge, test hy- pothesis, describe and understand complex systems, and compare different situations; they are used as support for making decisions concerning production management and planning (Lentz, 1998; Marcelis and Gijzen, 1998). Modelling simplifies, as much as possible, a situation that is being studied (Monteith, 1969) by representing, generally in a mathematical way, the system of interest (Goudriaan and Van Laar, 1994). The objective of modelling is to create a model that can work and imitate, as closely as possible, the real world or a real situation by means of a process known as simulation (Salazar, 2006). A crop model predicts the final biomass production or the harvestable yield and facilitates the processes involved in plant growth and development (Jame and Cutforth, 1996), including phenology (Jones and Ritchie, 1990). Accumulation of dry matter (DM) or crop growth can be modeled as a function of the photosynthetically active ra- diation (PAR), light use efficiency (LUE) and the extinction coefficient of light (k) (Tsubo et al., 2005). The objective of this study was to generate a model that simulates the potential yield and the total dry matter ac- cumulation as well as per organ (stem, leaves and buds) of the f loral stems of the carnation cv. Delphi. Materials and methods The investigation was carried out in the greenhouses of the Centro de Biotecnologia Agropecuaria of SENA in the municipality of Mosquera (Colombia). The geographical coordinates are 74.2° W, 4.7° N, with an altitude of 2,556 m a.s.l., mean annual precipitation of 645 mm, mean annual temperature of 14.7°C and 80% relative humidity. The data used in this research was gathered between June 28th and November 15th, 2008. Rooted cuttings of standard carnation (Dianthus caryophyl- lus L.) variety Delphi (white color flowers) were used, which were donated by Suata Plants in Bogota. Sowing took place on May 15th on elevated beds measuring 15.00 x 0.85 m. Each bed consisted of two plastic containers. In this way, each bed was sown with 540 plants giving a sowing density of 24.7 plants/m2 per greenhouse. Pinching was done on June 25th upon the 6th node, when the central lateral stems showed approximately four nodes. These results come from a trial where the effect in growth and production of carnation were evaluated using three differences substrates: 1) 100% burned rice husk (100BRH); 2) mixture of 65% burned rice husk - 35% coconut fiber (65BRH); and 3) mixture of 35% burned rice husk - 65% coconut fiber (35BRH). Since no statistical differences between the substrates were found, the information from all the treatments was compiled into a unique data base with nine replications. The experimental unit was 12.8 m2. Fertigation was applied using an automatized irrigation equipment with four drip lines of 17 mm of diameter on each bed and type Hydro PCAD drippers incorporated every 20 cm and a f low rate of 1.2 L h-1. The climate variables were obtained from the agroclima- tological station HOBO (Onset Computer Corporation, Bourne MA) located at the experimental site (in the green- house). The photosynthetically active radiation (PAR) was used for building the DM production and partition model. The PAR data were registered every 30 min obtaining 48 readings per day, of which 24 (light hours) were used to calculate the average and obtain the daily PAR value. The sampling method applied to the research was of a destructive nature and each experimental unit was sub- divided into 15 squares. Therefore, in each sampling, one square was randomly selected and two plants under perfect competition where plucked (central line and central row). Samplings were carried out every 15 d. From the sampled plants the variables total DM and DM per organ was deter- mined (stem, leaves, bud). The obtained data were used to generate the DM production and partition model. A total of 11 destructive samplings were performed during the whole growing cycle until the first harvest peak. These variables were determined after separating the dif- ferent organs (leaves, stem and bud) from the f lower stems: Leaf area: obtained through direct measurement from the planimeter. A LICOR LI - 3100 leaf area meter (Licor, Lin- coln, NE) was used. The obtained readings were expressed as cm2 of leaf blade. 198 Agron. Colomb. 32(2) 2014 Dry matter: the different organs of the f lower stem were dried in oven at 80°C until reaching constant weight (96 h). Once dry, the stems, leaves and f lowers were weighed using a precision scale, determining the DM by organ and the total DM for each of the sampled plants according to the treatment. Model description For the development of the DM production and partition model data for the leaf area index (LAI) and photosynthe- tically active radiation (PAR) in MJ m-2 d-1 was used. The average daily data (12 h) were used for the PAR. Daily growth rate According to Tsubo et al. (2005), the daily increase in DM on a potential growth model can be directly calculated out of the received PAR, the fraction of intercepted light by the foliage (FLINT) and the light use efficiency (LUE) (Eq. 1). δWt = LUE FLINTPARt (1) Where, δWt is the daily growth increase expressed as g m-2 d-1, LUE is the light use efficiency in g MJ-1, FLINT is the fraction of light intercepted by the crop and PAR is the photosynthetically active radiation expressed as MJ m-2 d-1 (Monteith, 1969; Gosse et al., 1986; Kooman and Jones, 1995; Salazar et al., 2007). Equation 1 includes two estimated parameters, LUE and FLINT, since the PAR was a direct measuring variable obtained from the HOBO station. LUE is an important parameter in crop development because it represents the balance between photosynthesis and respiration. Factors affecting these processes also af- fect LUE and, hence, crop growth and development. LUE changes according to crop development (Kooman and Spitters, 1995). Equation 2 was used for calculating FLINT, since light in- terception by the foliage can be described as a function of the leaf area index (LAI) increase (Kooman and Spitters, 1995; Salazar et al., 2007). FLINT = 1–e–kLAI (2) Where k is the extinction coefficient of the light and LAI is the leaf area index. Estimation of the parameters k and LUE was performed us- ing a non-lineal iterative procedure that minimized the sum of squares between the observed values and the simulated values using the Solver tool of Microsoft Excel®. Using the NLIN procedure of the SAS statistical package, the variable LAI was modeled from the leaf area (LA) data, which were obtained directly from the destructive sampling. The adjusted model was logistic, Y=α/1+e-β(t-γ), where α is the maximum leaf area value, β is the parameter determining the slope of the growth curve, and γ is the moment at which maximum growth rate was achieved (SAS Institute, 2003). Dry matter simulation Once the daily DM growth rate model was developed (Eq. 1), the simulation of total daily DM was carried out (Eq. 3) using the Euler method: Wt = Wt–1 + δWt Δt (3) Where, Wt is the total DM at time t (g m-2), Wt-1 is the total DM at time t-1 (g m-2), δWt is the daily DM growth rate at time t (g m-2 d-1), and Δt is the increase over time (1 d) (Van Kraalingen, 1991; Salazar et al., 2007). Dry matter partitioning The total DM was distributed among the different organs of the f lower stem according to the vegetative (before onset of f lower bud) and reproductive (from onset of f lower bud until harvest) stages. The biomass partitioning was cal- culated on the supposition of competition for assimilates between the different plant organs in a way in which each organ receives a proportion of the total DM. Partitioning varies according to the developmental stage of the crop (Marcelis, 1994). The partitioning coefficients αo were the proportions of the total dry matter that were assigned to the stems, leaves and buds. Estimation of the αo values was performed using a non-lineal iterative procedure that minimized the sum of squares between the observed values and the simulated values using the Solver. The simulation of DM partitioning on the different plant organs was carried out applying the Euler method through Eq. 4. Wot = Wo(t–1) + αo δWt Δt (4) Where, Wot is the total DM of an organ: stems (Wst), leaves (Wsh) or buds (Wsb), at day t (g m-2 d-1); Wo(t-1) is the DM of each organ as follows: stems (Wst-1), leaves (Wsh-1) or buds (Wsb-1) at day t-1 (g m-2 d-1), αo is the partitioning coefficient in stems (αt), leaves (αh) or buds (αb); δWt is the total daily DM growth rate (g m-2 d-1) and Δt is the growth over time (1 d). 199López M., Chaves C., and Flórez R.: Potential growing model for the standard carnation cv. Delphi Results Leaf area The leaf area (LA) of the carnation f lower stems was ad- justed to a logistic growth model using a general formula: Y=α/1+e-β(t-γ). Tab. 1 and Fig. 1 show the estimated values of the parameters α, β and γ as well as the behavior of LA over time. TABLE 1. Estimated values for the logistical model parameters regar- ding the variable leaf area of flower stems of the standard carnation cv. Delphi. Parameter Estimated UL LL α 232.4 226.0 238.7 β 0.061 0.054 0.069 γ 47.6 45.3 50.0 α = maximum value of leaf area; β = curve slope; γ = DAP, when maximum AGR (absolute growth rate) is achieved. UL, upper limit (95% confidence interval); LL, lower limit. The maximum LA of the f lower stems was 232.4 cm2, with a critical period for growth at around 48 DAP, where the highest absolute growth rate (AGR) of leaf expansion was reached. On the other hand, the leaf area index (LAI) and (LA) presented similar behaviors with maximum LAI values of 3.14, which were reached around 90 DAP. This LAI level was maintained until the f lowers stems were cut. Photosynthetically active radiation and fraction of intercepted light The photosynthetically active radiation (PAR) received in the greenhouse showed a f luctuation between 2.46 and 13.99 MJ m-2 d-1 (Fig. 2). During the production cycle, the crop received 989.18 MJ m-2 PAR with a daily average of 7.01 MJ m-2 d-1. In turn, LA ( cm 2 ) A B 0 50 100 150 200 250 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 LA I 0 30 60 90 120 150 0 30 60 90 120 150 Days after pinchingDays after pinching FIGURE 1. Behavior of leaf area (LA) and leaf area index (LAI) of flower stems of the standard carnation cv. Delphi as a function of the days after pinching. PA R ( M J m -2 d -1 ) Days after pinching 0 30 60 90 120 150 0 2 4 6 8 10 12 14 16 FIGURE 2. Behavior of the photosynthetically active radiation (PAR) du- ring the months of June and November 2008 at the Centro de Biotecno- logía Agropecuaria of SENA in Mosquera, Cundinamarca. F L IN T Days after pinching 0 30 60 90 120 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 FIGURE 3. Behavior of the fraction of intercepted light (FLINt) by flower stems of the standard carnation cv. Delphi. the fraction of intercepted light FLINT (Fig. 3), calculated according to Eq.2, showed a similar behavior as that of the LAI (Fig. 2), with maximum values of 0.80, which were reached around 80 DAP. 200 Agron. Colomb. 32(2) 2014 Extinction coefficient (k) and light use efficiency (LUE) In this study, k was determined through the iterative minimization method using the Solver, which reported a value of 0.53 (Tab. 2). TABLE 2. Values of the extinction coefficient of the light (k) and light use efficiency (LUE) for the carnation crop. Developmental stage Parameter k LUE (g MJ-1) Vegetative 0.53 1.31 Reproductive 0.53 0.71 Under this research, the growing cycle was divided into two stages and a LUE value was calculated for each of them. However, the two stages do not correspond to the vegetative and reproductive phases but to the initial and lineal growth phases on the curve (LUE1) and to the main- tenance phase (LUE2). This division was done in order to determine the DM production in a more fitted way through the simulation model. Therefore, the values of LUE1 and LUE2 determined in this research correspond to 1.31 and 0.71 g MJ-1, respectively (Tab. 2). Dry matter growth, production and partitioning The total DM growth rate was calculated from Eq. 1. The average rate during this trial was 4.96 g m-2 d-1, showing maximum and minimum values of 12.70 and 0.68 g m-2 d-1. During the vegetative stage (71 d), the rate reached average values of 4.31 g m-2 d-1; whereas, during the reproductive stage (70 d), it reached 5.63 g m-2 d-1. Both absolute maxi- mum and minimum levels in the growth rate were achieved during the vegetative stage of the crop. In turn, the values of the minimum and maximum growth rate during the reproductive stage corresponded to 1.40 and 12.10 g m-2 d-1, respectively. Total DM partitioning was carried out for both the vegeta- tive and reproductive stages. During the vegetative stage, the DM of the leaves and stem was considered; while dur- ing the reproductive stage leaves, the stem and f lower bud were considered. Figure 4 shows the observed and simulated total DM values of the carnation f lower stems as well as their different con- stituent organs (stems, leaves and f lower buds). Regarding DM accumulation in the leaves, a constant biomass can be observed after 80 DAP. Table 3 shows the estimated values for the main parameters of the DM production and partitioning model. During the vegetative stage (71 d), 37% of the DM produced by the plant was assigned to stem growth, while the remaining 63% was directed to leaf growth. TABLE 3. Estimated values of dry matter partitioning coefficients in the standard carnation cv. Delphi. Developmental stage Parameter αt αh αb Vegetative 0.37 0.63 --- Reproductive 0.74 0.05 0.21 αt: partitioning coefficient for the stem; αh: partitioning coefficient for leaves; αb: partitioning coefficient for the flower bud. Seventy days after pinching, the f lower bud appeared as a new sink organ on the stem, a phenomenon that modifies the DM partitioning on the inside of the plant and, thus, the partition coefficients varied. Therefore, during the vegetative stage, 74% of the produced DM was assigned to the stem, with 5% to the leaves and the remaining 21% was directed to the f lower bud (Tab. 3). Finally, Fig. 4E shows the integrated models (DM of stems, leaves, f lower buds and total DM). The observed and simu- lated values are presented in an integrated manner for the different organs of the carnation f lower stem. The simu- lated values show the same trend as the observed values. In the same way, Fig. 4 shows the root square mean error for each case (RSME), a statistical parameter with values considered low since their size was generally below 10% of the variable’s maximum value. Discussion Leaf area The maximum LA value in the stems that was determined in this research is comparable with the values obtained by Cárdenas et al. (2006), who reported maximum leaf areas in whole plants of the carnation cv. Nelson (five f lower stems) ranging from 995.9 to 1172.0 cm2, which means between 199.2 and 234.4 cm2 per f lower stem. From the LAI values, it is possible to state that, in a carna- tion crop for each m2 of sown soil or area, there are 3.14 m2 of leaves responsible of taking part in the photosynthetic process. The observed LAI values are lower than the value of 6.0 determined by Partridge et al. (1983) for carnations grown in California and the LAI values between 4.0 and 5.0 reported by Cárdenas et al. (2006) in the carnation cv. Nelson grown with the same types of substrate. Likewise, these LAI values are lower than the ones re- ported by Lee et al. (2002) for other ornamental species, such as the chrysanthemum, who determined LAI values from 4-8 using plant densities of 32-64 plants/m2. Dennett and Ishag (1998), working with the pea (Pisum sativum) 201López M., Chaves C., and Flórez R.: Potential growing model for the standard carnation cv. Delphi RSME=23.9 RSME=15.1 RSME=19.5 RSME=12.1 D ry m at te r (g m -2 ) E 0 400 300 200 100 500 600 700 800 0 80604020 100 120 140 160 Days after pinch oDMf sDMf oDMl sDMl oDMs sDMs oDMt sDMt D ry m at te r (g m -2 ) D ry m at te r (g m -2 ) C D 0 250 200 150 100 50 300 350 400 450 0 80604020 100 120 140 160 0 80604020 100 120 140 160 Days after pinchDays after pinch Obs Sim 0 50 40 30 20 10 60 70 80 90 D ry m at te r (g m -2 ) D ry m at te r (g m -2 ) A B 0 400 300 200 100 500 600 700 800 0 80604020 100 120 140 160 0 80604020 100 120 140 160 Days after pinchDays after pinch 0 50 100 150 200 250 FIGURE 4. Observed and simulated values of total dry matter of complete flower stems. A, stem dry matter; B, dry matter of leaves; C, dry matter of flower buds; D, whole dynamic; E, as a function of days after pinching (DAP). Obs, observed values; Sim, simulated values; t, total; s, stems; l, leaves; f, flower buds. and broad bean (Vicia faba), reported maximum indexes of 6.3 and 4.2, respectively, using plant densities of 80 plants/m2 in the pea and 20 plants/m2 in the broad bean. In horticultural species such as broccoli and cabbage, Carranza et al. (2008) showed maximum LAI values of 1.76 and 5.17, respectively. Photosynthetically active radiation and fraction of intercepted light The mean value for the PAR of 7.01 MJ m-2 d-1 determined in this research is similar to the 7.24 MJ m-2 d-1 found by Salazar (2006) in Chía, Cundinamarca, also under green- house conditions. 202 Agron. Colomb. 32(2) 2014 The fraction of intercepted light “FLINT” presented a similar behavior to LAI (Fig. 2), a response that can be attributed to the fact that the extinction coefficient of light (k) together with the LAI are the only variables that FLINT depends on. At the end of the growing cycle, the f lower stems of the carnation captured 80% of the incident PAR. The maxi- mum FLINT values in the carnation were higher than those found in species such as quinoa, where only values from 0.33 to 0.51 were achieved, with LAI values from 0.61 to 1.38 (Ruiz and Bertero, 2008). Extinction coefficient and light use efficiency The extinction coefficient k determines the rate at which solar radiation is absorbed by unit of leaf area and depends on the inclination angle of the incident rays and the position and orientation of the leaves. The extinction coefficient of the light of 0.53 determined for the carnation indicates that, for each LAI unit that is penetrated by PAR radiation in the canopy of carnation, 40.9% (1-e-k) of the light will be absorbed. The LUE values of 1.31 and 0.71 g MJ-1 indicate that, dur- ing the initial and lineal growth phases, the carnation f lower stems produced 1.31 g of DM for each MJ of light intercepted by their leaves. In the maintenance phase of the growth curve, these same stems produced 0.71 g of DM for each MJ of intercepted light. This response indicates that the DM production efficiency in the carnation stems was higher during the first growth phases, which explains the fast development of the leaves and stems, which were the only organs present at this stage. In the final stage of the cycle, the DM production efficiency decreased, consistent with the growth reduction of the leaves and stems, but in contrast to the accelerated growth of the f lower bud. It is worth noticing, that the LUE value determined here is lower than in other cut f lowers. This event is due to the fact that f lower stems of carnation do not show an elevated DM accumulation during their whole cycle. Therefore, the maximum DM values of 5.0 to 5.3 g were obtained after 144 d, while, in other species of f lowers such as chrysan- themum, Lee et al. (2003) reported DM accumulation of 500-600 g in approximately 80 days, with estimated LUE values at different light and plant density levels ranging from 3.47 and 6.91 g MJ-1. The maximum DM values in the stems found in this study are lower than the values of 10 g per stem that were published by Partridge et al. (1983) in the carnation variety Davies in the United States of America. The LUE value depends on the crop, management, sow- ing density and temperature. In this way, Haxeltine and Prentice (1996) stated that, as temperature increases, LUE decreases; a fact that is explained by the balance change between photosynthesis and respiration (decrease in pho- tosynthesis and increase in respiration). The LUE values estimated in this research are lower than those for other species of cut f lowers, such as the chrysanthemum, report- ing values of 3.4 (summer) and 5.3 (winter) g MJ-1 (Lee et al., 2002). In the cape gooseberry, Salazar et al. (2007) determined LUE values of 0.46 and 2.62 g MJ-1 for the vegetative and reproductive stage, which are much higher values than those found in the carnation cv. Delphi. These results, as well as those with chrysanthemum, broccoli and cabbage, are consistent with the elevated DM accumulation rates of 8,000-9,000 g in 400 d. The LUE levels in g MJ-1 reported for other species are di- verse. For example, in the potato, it is possible to find values between 2.1 and 3.2 (Kooman and Spitters, 1995), and at 1.6 and 1.25 in maize and sorghum, respectively (Muchow and Davies, 1988); 3.5 and 4.0 in barley and pea, respectively (Berntsen et al., 2004), 1.81±0.05 in wheat (O’Connell et al., 2004); between 1.98 and 5.03 for caulif lower (Kage and Stützel, 1999), 1.80 for sugar cane (Keating et al. 1999), and between 1.25±0.09 and 2.68±0.15 for quinoa (Ruiz and Bertero, 2008). According to the obtained results, it is possible to infer that either days with higher PAR levels or light management techniques could help increase biomass production in flower stems and, hence, favor the improvement of variables of agronomic interest, such as length, width, weight and postharvest life of stems. Dry matter growth, production and partition rate The total DM production and accumulation, as well as partitioning to the different constituent organs of the f lower stem (stem, leaves and f lower bud), presented a distinct equivalence between the simulated and observed values, which is a characteristic that, together with the low total and per organ values of the root square mean error (RSME), indicates a satisfactory adjustment of the model in all of the cases. The pattern of DM partitioning during the vegetative stage of the carnation crop indicates that, during the initial growth stages, matter increase is a priority and, hence, leaf area. This behavior can be attributed to the necessity of the crop to favor its growth by capturing the highest amount of PAR in the shortest time possible. Achieving the afore- mentioned guarantees that the crop can rapidly reach the 203López M., Chaves C., and Flórez R.: Potential growing model for the standard carnation cv. Delphi critical LAI or the LAI value by which 95% of the incident radiation is captured. For the reproductive stage the largest proportion of DM was assigned to the stems, a behavior indicating active growth that is mainly directed to increasing the length and diameter of this organ. Apart from that, the leaves drastically reduced the amount of DM received (63 to 5%), which indicates a reduced growth during this stage due to the accelerated DM accumulation that took place during the vegetative stage. On the carnation stems, the onset of nodes and, therefore, leaves stops when the f lower bud appears, i.e. after 18-19 nodes or 1363.2 degree day (López et al., 2010). Finally, the f lower bud is, after the stem, the biggest DM sink at this stage, which is an unexpected characteristic considering that the f lower is the reproductive organ of the plant and that its growth happens in a shorter period of time in rela- tion to the stem and leaves. The severe reduction in the proportion of DM distributed to the leaves has also been documented by authors such as Salazar et al. (2007) in the cape gooseberry, who showed a reduction from 72 to 9% of the distributed DM due to the shift from the vegetative to reproductive stage. A similar situation was also reported in broccoli with a reduction from 46.6 to 14.2% due to the same phenomenon (Car- ranza et al., 2008). The comparison between the simulated and observed val- ues as well as the low RSME values indicates a satisfactory adjustment of the simulation model for any of the studied organs. According to these results, the model developed in this research project could be a potentially useful tool for predicting DM production and partitioning in the carna- tion cv. Delphi. Conclusions The efficiency in DM production during the first devel- opment stages of the f lower stem was higher than in the final stages, which was verified by the higher LUE values during the first months of the growing cycle. In this way, during the first developmental stages, water management, nutrients and PAR radiation are factors that are especially critical in relation to the accumulation of high DM contents in f lower stems. In general, the simulated data in each of the models fol- lowed the same trend as the observed data, as supported by the low RSME values. In this way it can be concluded that the fit of all the models was satisfactory and, therefore, they can be used to predict DM production and partitioning in the standard carnation cv. Delphi under the prevail- ing conditions of the savanna of Bogota in the absence of limitations such as water, nutrients and biomass reduction caused by pests and diseases. Literature cited Asocolf lores, Asociación Colombiana de Productores de Flores. 2009. Colombian Floriculture: 2009 statistics. Bogota. Berntsen, J., H. Hauggard-Nielsenb, J.E. Olesena, B.M. Petersena, E.S. Jensenb, and A. Thomsena. 2004. Modelling dry matter production and resource use in intercrops of pea and barley. Field Crops Res. 88, 69-83. Cárdenas, C.A., I.F. Rivera, V.J. Flórez, W. Piedrahíta, and B. Chaves. 2006. Análisis de crecimiento en clavel estándar variedad ‘Nelson’ cultivado en sustratos. pp. 111-127. In: Flórez, V., A. De la C. Fernández, D. Miranda, B. Chaves, and J.M. Guzmán (eds.). Avances sobre fertirriego en la f loricultura colombiana. Universidad Nacional de Colombia, Bogota. Carranza, C., O. Lanchero, D. Miranda, M.R. Salazar, and B. Chaves. 2008. Modelo simple de simulación de distribución de masa seca en brócoli (Brassica sp.) variedad Coronado y repollo (Brassica oleracea) híbrido Delus cultivado en la Sabana de Bogotá. Agron. Colomb. 26, 23-31. Dennett, M.D and K.H.M. Ishag. 1998. Use of the expolinear growth model to analyse the growth of faba bean, peas and lentils at three densities: fitting the model. Ann. Bot. 82, 497-505. Gary, C., J.W. Jones and M. Tchamitchian. 1998. Crop modelling in horticulture: state of the art. Sci. Hortic. 74, 3-20. Gosse, G., C. Varlet-Grancher, R. Bonhomme, M. Chartier, J. Al- lirand, and G. Lemaire. 1986. Production maximale de matiere seche et rayonnement solaire intercepte par un couvert vegetal. Agronomie 6, 47-56. Goudriaan, J and H.H. Van Laar. 1994. Current issues in produc- tion ecology. Modelling potential growth processes. Kluwer Academic Publishers, London. Haxeltine, A. and I.C. Prentice. 1996. A general model for the light- use efficiency of primary production. Funct. Ecol. 10, 551-561. Jame, Y.W. and H.W. Cutforth. 1996. Crop growth models for deci- sion support systems. Can. J. Plant Sci. 76, 9-19. Jones, J.W. and J.T. Ritchie. 1990. Crop growth models. pp. 63-69. In: Hofman, G.J., T.A. Howell, and K.H. Solomon (eds.). Manage- ment of farm irrigation systems. ASAE, St. Joseph, MI. Kage, H. and H. Stützel. 1999. A simple empirical model for predict- ing development and dry matter partitioning in caulif lower (Brassica oleracea L. botrytis). Sci. Hortic. 80, 19-38. Keating, B.A., M.J. Robertson, R.C. Muchow, and N.I. Huth. 1999. Modelling sugarcane production systems I. Development and performance of the sugarcane module. Field Crops Res. 61, 253-271. 204 Agron. Colomb. 32(2) 2014 Kooman, P.L. and J.W. Jones. 1995. Report on theoretical studies with potencial yield and shooting models for banana. Florida University, Gainesville, FL. Kooman, P.L. and C.J.T. Spitters. 1995. Coherent set of models to simulate potato growth. pp. 253-274. In: Kaba, P., B. Marshall, B.J. Van den Broek, J. Vos, and H. Van Keulen (eds.). Modelling and parameterization of the soil-plant-atmosphere system. A comparison of potato growth models. Wageningen Press, Wageningen, The Netherlands. Lee, J.H., E. Heuvelink, and H. Challa. 2002. Effects of planting date and plant density on crop growth in cut chrysanthemum. J. Hort. Sci. Biotechnol. 77, 238-247. Lee, J.H., J. Goudriaan, and H. Challa. 2003. Using the expolinear growth equation for modelling crop growth in year-round cut chrysanthemum. Ann. Bot. 92, 697-708. Lentz, W. 1998. Model applications in horticulture: a review. Sci. Hortic. 74, 151-174. López, M.A., B. Chaves, V.J. Flórez, and M.R. Salazar. 2010. Modelo de aparición de nudos en clavel (Dianthus caryophyllus L.) cv. Delphi cultivado en sustratos. Agron. Colomb. 28, 47-54. Marcelis, L.F.M. 1994. A simulation model for dry matter partition- ing in cucumber. Ann. Bot. 74, 43-52. Marcelis, L.F.M. and H. Gijzen. 1998. Evaluation under commercial conditions of a model of prediction of the yield and quality of cucumber fruits. Sci. Hortic. 76, 171-181. Meira, S. and E. Guevara. 2000. Uso de modelos de simulación de cultivos como herramienta para la toma de decisiones en el cultivo de soja. INTA, Pergamino, Argentina. Monteith, J.L. 1969. The quest for balance in crop modelling. Agron. J. 88, 695-697. Muchow, R.C. and R. Davies. 1988. Effect of nitrogen supply on the comparative productivity of maize and sorghum in a semi-arid tropical environment. Radiation interception and biomass accumulation. Field Crops Res. 18, 17-30. O’Connell, M.G., G.J. O’Leary, D.M. Whitfield, and D.J. Connor. 2004. Interception of photosynthetically active radiation and radiation-use efficiency of wheat, field pea and mustard in a semi-arid environment. Field Crops Res. 85, 111-124. Partridge, P.L., M.S. Reid, and H.C. Kohl. 1983. A productivity and partitioning approach to carnation production. Acta Hort. 141, 173-180. Penning de Vries, F.W.T., D.M. Jansen, H.F.M. ten Berger, and A. Bakema. 1989. Simulation of ecophysiological processes of growth in several annual crops. Centre for Agricultural Publishing and Documentation-Pudoc, Wageningen, The Netherlands. Ruiz, R.A. and H.D. Bertero. 2008. Light interception and radia- tion use efficiency in temperate quinoa (Chenopodium quinoa Willd.) cultivars. Eur. J. Agron. 29, 144-152. Salazar, M.R. 2006. Un modelo simple de producción potencial de uchuva. Ph.D. thesis. Faculty of Agronomy, Universidad Nacional de Colombia, Bogota. Salazar, M.R., J.W. Jones, B. Chaves, and A. Cooman. 2007. A model for the potential production and dry matter distribution of cape gooseberry (Physalis peruviana L.) Sci. Hortic. 115, 142-148. SAS Institute. 2003. The NLIN procedure. SAS/STAT User’s quick start guide, Version 9.1. and Online Support. Cary, NC. Tsubo, M., S. Walker, and H.O. Ogindo. 2005. A simulation model of cereal-legume intercropping systems for semi-arid regions. I. Model development. Field Crops Res. 93, 10-22. Van Kraalingen, D.W.G. 1991. The FSE system for crop simulation. Centre for Agrobiological Research-CABO; Department of Theoretical Production Ecology-TPE, Wageningen Agricul- tural University. Wageningen, The Netherlands.