SIMULATING LEAF APPEARANCE IN A MAIZE VARIETY PAGE 384 Original Article SIMULATING LEAF APPEARANCE IN A MAIZE VARIETY SIMULAÇÃO DO APARECIMENTO DE FOLHAS EM UMA VARIEDADE DE MILHO Nereu Augusto STRECK1; Luana Fernandes GABRIEL2; Taise Cristine BUSKE2; Isabel LAGO3; Flávia Kaufmann SAMBORANHA4; Ana Paula SCHWANTES2 1. Professor, PhD, Departamento de Fitotecnia, Universidade Federal de Santa Maria – UFSM, Santa Maria, RS, Brasil, nstreck2@yahoo.com.br ; 2. Aluna do curso de graduação em Agronomia - UFSM; 3. Doutoranda do Programa de Pós-Graduação em Engenharia Agrícola - UFSM; 4. Mestranda do Programa de Pós-Graduação em Engenharia Agrícola - UFSM. ABSTRACT: The calculation of leaf appearance rate (LAR) is an important part of many crop simulation models. The objective of this study was to evaluate and compare a linear model (the Phyllochron model) with a non-linear model (the Wang and Engel, WE, model) for simulating LAR in a maize variety. A field experiment was done in Santa Maria, RS, Brazil, with seven sowing dates during two growing seasons (2005/2006 and 2006/2007). The maize variety BRS Missões was used in a randomized block design, with six replications. Plant spacing was 0.8 m x 0.21 m, and each plot had three 5 m rows. Three plants in the central row of each plot were tagged. The ligule (expanded) and tip leaf number was measured weekly on the tagged plants. The Phyllochron model, which assumes a linear response of LAR to temperature, and the WE model, which assumes a non-linear response of LAR to temperature, were used to calculate ligule and tip leaf number. Models coefficients were estimated using the data set collected in 2005/2006 and evaluation of the models was done with the data set collected in 2006/2007 using the statistics root mean square error (RMSE), index of agreement (d) and accuracy of WE model relative to the phyllochron model (E12). The WE model was superior to the Phyllochron model for predicting leaf number, with an overall RMSE of 0.80 leaves for ligule leaf number and 1.29 leaves for tip leaf number. KEY WORDS: Plant development. Modeling. Temperature. Phyllochron. Zea mays. INTRODUCTION One crop that is particularly important for small farmers in Brazil is maize (Zea mays L.), where this crop is grown for feeding animals (leaves, stalks and ears) or for grain production that can be used either also to feed animals and humans or to be sold in the market. Seeds of maize hybrids are expensive and can be used only for one growing season. Maize varieties that can be sown over several years play an important role in small farm sustainability, as farmers can produce their own seeds and thus reduce costs. The calculation of leaf appearance rate (LAR) is an important part of many crop simulation models (HODGES, 1991), including maize models (JONES; KINIRY, 1986; LÓPEZ-CEDRÓN et al., 2005). The integration of LAR over time gives the number of accumulated or emerged leaves on the main stem (LN), which is an excellent measure of plant development. The main stem LN in maize is related to the timing of some developmental stages such as ear and panicle initiation (RITCHIE et al., 1997; FORTSTHOFER et al., 2004) and vegetative development creates the structure (leaves, stems) to support (physically and physiologically) leaf area and grain growth, and to intercept solar radiation for canopy photosynthesis and accumulation of dry matter and commercial yield (WILHELM; MCMASTER, 1995; STRECK et al., 2003; SUBEDI; MA, 2005). Temperature is a major factor that drives leaf appearance in maize (JONES; KINIRY, 1986; HESKETH; WARRINGTON, 1989; WHITE, 2001). One approach to predict the appearance of individual leaves is the phyllochron concept, defined as the time interval between the appearances of successive leaves (KLEPPER et al, 1982; KIRBY, 1995; WILHELM; MCMASTER, 1995). Time is often expressed as thermal time (TT), with units of oC day, and in this case, the phyllochron has units of oC day leaf-1. However, the TT approach is open to criticism because there are different ways to calculate TT (MCMASTER; WILHELM, 1997), and because of the assumption of a linear response of development to temperature, which is not realistic in all situations where plants develop and grow (SHAYKEWICH, 1995; XUE et al., 2004). One way to overcome the disadvantages of the TT approach is to use non-linear temperature response functions and multiplicative models. The Wang and Engel (WE) model (WANG; ENGEL, 1998) is a an example of such models, and the WE model improved the predictions of leaf appearance compared to the Phyllochron model, which uses a linear response, in several crops such as winter wheat (XUE et al., 2004), muskmelon (STRECK et al., 2006), potato (STRECK et al., 2007) and eucaliptus seedlings (MARTINS; STRECK, 2007), but not in maize, which constituted the rationale for this scientific effort. The objective of this study was to evaluate and compare the Phyllochron model and the WE model for simulating LAR in a maize variety. MATERIAL AND METHODS The Phyllochron model (KLEPPER et al, 1982; KIRBY, 1995; WILHELM; MCMASTER, 1995) using the thermal time approach was used in this study as the linear model. This model is widely used to simulate leaf appearance is grasses (MCMASTER et al., 1991; AMIR; SINCLAIR, 1991; MCMASTER, 2005). Daily values of thermal time (TT, oC day) were calculated as (GILMORE; ROGERS, 1958; ARNOLD, 1960; MATTHEWS; HUNT, 1994): TT=(T–Tmin) . 1 day (1) when TminTmax then T=Tmax where Tmin, Topt, Tmax are the cardinal (minimum, optimum, and maximum) temperatures for maize and T is the daily air temperature. SEQ CHAPTER \h \r 1The cardinal temperatures for LAR in maize were 8°C, 31°C, and 41°C (YAN; HUNT, 1999; WHITE, 2001). TT was calculated using daily minimum (TN) and daily maximum (TX) air temperature, and then averaged. The schematic representation of the thermal time method is presented in Figure 1. Figure 1. Method of calculating daily values of thermal time (equations 1 and 2) and the temperature response function [f(T), equations 4 to 6] of the WE leaf appearance model with cardinal temperatures for leaf appearance in maize variety BRS Missões of 8°C for Tmin, 31°C for Topt, and 41°C for Tmax. The accumulated thermal time (ATT) from emergence was calculated by accumulating TT, i.e. ATT=∑TT. The phyllochron (oC day leaf-1) was estimated by the inverse of the slope of the linear regression of LN against ATT (KLEPPER et al, 1982; KIRBY, 1995; XUE et al., 2004). SEQ CHAPTER \h \r 1The main stem number of emerged leaves (LN) was calculated by LN=ATT/phyllochron. Because in maize LN is measured both as ligule leaf number and tip leaf number (JONES; KINIRY, 1986; HESKETH; WARRINGTON, 1989; BIRCH et al., 1998; LÓPEZ-CEDRÓN et al., 2005), phyllocron was expressed both on a ligule and on a tip leaf basis, i.e., ligule LN and tip LN. The WE model (WANG AND ENGEL, 1998) for LAR in maize has the general form: LAR = LARmax f(T) (3) where LAR is the daily leaf appearance rate (leaves day-1), LARmax is the maximum daily leaf appearance rate (leaves day-1), and f(T) is a dimensionless temperature response function (varying from 0 to 1) for LAR, respectively. The f(T) is a beta function: f(T) = [2(T-Tmin)((Topt-Tmin)(-(T-Tmin)2(]/(Topt-Tmin)2( for Tmin ( T ( Tmax (4) f(T) = 0 for T < Tmin or T > Tmax (5) ( = ln2/ln[(Tmax-Tmin)/(Topt-Tmin)] (6) where Tmin, Topt, and Tmax are the cardinal (minimum, optimum, and maximum) temperatures for LAR and T is the daily air temperature. Values of Tmin, Topt, and Tmax have been previously defined and are the same used in equations (1) and (2). The curve generated by equations (4) to (6) with these cardinal temperatures for LAR in maize is plotted in Figure 1. The f(T) was calculated using daily TN and TX, and then the resulting daily values of f(T) were averaged, corresponding to the daily average f(T). This approach was used since in a non-linear function, averaging the minimum and the maximum daily temperature first, and then calculating the f(T) with the average daily temperature is incorrect (XUE et al., 2004). SEQ CHAPTER \h \r 1The main stem number of emerged leaves (LN), was calculated by accumulating daily LAR values (i.e. at a one day time step) starting at emergence, i.e., LN=∑LAR. LN, LAR and LARmax were also expressed both on a ligule and a tip leaf basis. Data from a two-year (2005/2006 and 2006/2007) field experiment done at the research area, Plant Science Department, Federal University of Santa Maria, Santa Maria, RS, Brazil (29°43’ S; 53º43’ W; 95 m a.s.l.) were used in this study. This location is representative of maize growing conditions in a large portion of southern Brazil. The region has a sub-tropical climate Cfa according to Köppen’s climate system, with warm summer and well distributed rainfall throughout the year (MORENO, 1961). Soil type at the experimental site was a Rhodic Paleudalf (USDA Taxonomy). The maize variety BRS-Missões was sown on seven dates in each year. During the 2005/2006 growing season, sowing dates (day/month/year) were 21/09/2005, 20/10/2005, 29/11/2005, 04/01/2006, 07/02/2006, 16/03/2006 and 12/04/2006, and during the 2006/2007 growing season, sowing dates were: 23/08/2006, 27/09/2006, 30/10/2006, 30/11/2006, 08/01/2007, 13/02/2007 and 15/03/2007. BRS-Missões is a synthetic variety development by Embrapa Trigo and recommended for southern Brazil States (Rio Grande do Sul, Santa Catarina, and Paraná) (EMBRAPA, 2006). This variety was used because it has greater yield potential than local varieties, low seed cost, seeds can be produced by the farmers, and it has good yield stability under low soil water stress, all desired advantages for small farmers (EMBRAPA, 2006). The wide range of sowing dates used in this study are in part within and in part out of the recommended sowing period for this region which is from 11/08 to 20/01 (REUNIÃO TÉCNICA ANUAL DE PESQUISA DE MILHO E SORGO DO RS, 2005) and represents the range of sowing dates that local small formers grow maize for different uses (forage and grain). Plant density was 6 plants m-2 and plant spacing was 0.8 m among rows and 0.21 m among plants within rows. The experimental design was a randomized block, with seven treatments (sowing dates) and six replications. Each replication was a plot with three 5m rows. Sprinkler irrigation was applied as needed to avoid stress due to low soil water content. Insects were controlled by spraying insecticides as needed and weeds were hand controlled. Fertilization rates at sowing were 700 kg ha-1 of a commercial 07-11-09 (NPK) fertilizer. Additional nitrogen was added as a side-dress application at V4, V7, V11, and VT (FORTSTHOFER et al., 2004) with urea at a rate of 89 kg of urea ha-1. Emergence was measured by counting the number of plants visible above soil surface in all plots on a daily basis. The date of 50% emergence was calculated for each plot and averaged for each sowing date. One week after emergence, three plants in the center row of each plot were arbitrarily selected and tagged with colored wires. The number of fully expanded leaves (ligule LN) and the number of leaf tips (tip LN) on the tagged plants were counted once a week until flag leaf appearance. Daily minimum (TN) and maximum (TX) air temperature were measured by a standard meteorological station located at about 200 m from the plots. The coefficients phyllochron and LARmax (equation 3) were estimated using the NL data collected in the seven sowing dates of the 2005/2006 growing season. The phyllochron was estimated by the inverse of the slope of the linear regression of LN against ATT (KLEPPER et al, 1982; KIRBY, 1995; XUE et al., 2004). The coefficient LARmax was estimated by changing (increasing and decreasing) an initial value (0.3 leaves day-1) by a 1% step until obtaining the best fit between observed and estimated values (least square method, XUE et al., 2004) with an algorithm in MS Excel. The phyllochron and LARmax estimates were the average of the seven sowing dates. The values of LN (ligule LN and tip LN) predicted with the Phyllochron model and with the WE model were compared with the observed LN values during the seven sowing dates of the 2006/2007 growing season, which are independent data sets. The statistics used to evaluate model performance were the root mean square error (RMSE), the index of agreement (d), and the accuracy of model 1 relative to model 2 (E12). The RMSE was calculated as (JANSSEN; HEUBERGER, 1995): RMSE = [Σ(Pi-Oi)2/ N]0.5 (7) where Pi = predicted LN values, Oi = observed LN values, and N = number of observations. The unit of RMSE is the same as P and O, i.e., leaves. The smaller the RMSE the better the prediction. Systematic and unsystematic errors of model predictions were calculated for each model by taking the mean square error (MSE), i.e (RMSE)2, and decomposing the MSE into systematic (MSEs) and unsystematic or random (MSEu) components (MSEs + MSEu = 100%) according to Willmott (1981): MSEs= [Σ( -Oi)2]/N (8) MSEu= [Σ(Pi- )2]/N (9) where = a + bOi; a is the intercept and b is the slope of the scatterplot between P and O. The lower the MSE the better the model. The d index measures the degree to which the predictions of a model are error free, and is dimensionless (WILLMOTT, 1981). The values of d range from 0, for complete disagreement, to 1, for perfect agreement between the observed and predicted values. The d index was calculated as (WILLMOTT, 1981): d = 1 - [((Pi-Oi)2]/ ([(|Pi-Ō)+(|Oi- Ō|)]2 (10) where Ō is the average of the observed values. The accuracy of model 1 relative to model 2 (E12) was calculated as (ALLEN; RAKTOE, 1981): E12 = MSE1/MSE2 (11) where MSE1 and MSE2 are the mean square error of the predictions by model 1 and 2, respectively: MSE1 = ((P1i - Oi)2 (12) MSE2 = ((P2i - Oi)2 (13) The E12 index is dimensionless and varies from 0 to infinity. A value of E12 between 0 and 1 implies that model 1 is superior to model 2. If E12 is greater than 1 then model 2 is better. For the purpose of calculating E12, in this study the WE model was considered model 1 and the Phyllochron model was model 2. RESULTS AND DISCUSSION Air temperature varied widely during the two growing seasons (Figure 2). Minimum temperature varied from -0.2°C to 25°C and from 0.8°C to 25.8°C, and maximum temperature varied from 12°C to 38.6°C and from 12.4°C to 37.4°C in the 2005/2006 and 2006/2007 growing seasons, respectively. Fall 2006 was warm (above normal temperatures), allowing unusual plant growth and development during May, June and early July. Fall 2007, on the other hand, was cold, which led plants to die due to low temperatures and frost by the end of April 2007. This wide variation in air temperature during the maize developmental cycle provided a rich data set to estimate model coefficients and evaluate the two models. Figure 2. Daily minimum (TN) and maximum (TX) air temperature throughout the experimental period during the two growing seasons (from emergence of the first sowing date to the last day of measurement). Arrows indicate the date of emergence for the seven sowing dates within each year. Santa Maria. RS. Brazil. 2005-2007. The estimates (average of seven sowing dates in the 2005/2006 growing season) of the phyllochron were 51.2 and 42.7°C day leaf –1 and the estimates of the LARmax were 0.452 and 0.626 leaves day–1, for ligule LN and tip LN, respectively. The results of these estimates indicate a greater rate of tip leaf appearance than ligule leaf appearance, which lead to an accumulation of the number of leaf tips at the whorl as plant developed until flag leaf appearance. When the first ligule was visible, there were about two leaf tips at the whorl, whereas when there were 15 leaf ligules there were 5-6 leaf tips at the whorl. Predictions of ligule LN were very good with both models, mainly up to about 10 leaves (Figure 3a,c). The overall RMSE (pooling data of all sowing dates) was smaller than one leaf and slightly lower with the WE model (0.80 leaves) than with de Phylochron model (0.84 leaves). Among sowing dates, predictions with the Phyllochron model were the worst (underpredictions) for sowings on 30/10/2006 and 30/11/2006 whereas with the WE model, predictions were the worst (overpredictions) for sowings on 13/02/2007 and 15/03/2007. The lowest RMSE was 0.61 leaves (sowing date: 30/10/2006) and 0.23 leaves (sowing date: 08/01/2006) with the Phyllochron and the WE model, respectively (Table 1). Figure 3. Predicted versus observed ligule and tip leaf number of maize variety BRS Missões in seven sowing dates (day/month/year). using the Phyllochron model (a) and (b). and the WE model (c) and (d). Predictions of tip LN had slightly greater error compared to the ligule LN with both models, mainly for LN greater than 15, with the Phyllochron model underpredicting all data (Figure 3b,d). The overall RMSE was one leaf lower with the WE model (1.29 leaves) than with the Phyllochron model (2.32 leaves). Among sowing dates, underpredictions were greater with the Phyllochron model for sowings on 30/10/2006, 30/11/2006 and 08/01/2007, whereas the greatest overpredictions with the WE model were obtained for sowings on 13/02/2007 and 15/03/2007. The lowest RMSE with the Phyllochron model was 1.10 leaves (sowing date: 15/03/2007) and the lowest RMSE with the WE model was 0.67 leaves (sowing date: 23/08/2006) (Table 1). Table 1. Root mean square error (RMSE), total mean square error (MSE), systematic MSE (MSES), and unsystematic MSE (MSEu) using the Phyllochron model and the WE model to predicted the ligule leaf number (LN) and the tip LN in the maize variety BRS Missões in seven sowing dates (day/month/year) during the 2006/2007 growing season. Santa Maria, RS, Brazil. Numbers in parenthesis are the percentage of MSEs and MSEu. Sowing date Statistic Phyllochron model WE model Ligule LN Tip LN Ligule LN Tip LN 23/08/2006 RMSE 0.82 1.59 0.57 0.67 MSE 6.08 22.66 2.89 4.01 MSES 0.52 (8.6%) 2.45 (10.8%) 0.19 (6.5%) 0.35 (8.7%) MSEu 5.56(91.4%) 20.21(89.2%) 2.70 (93.5%) 3.66 (91.3%) 27/09/2006 RMSE 0.66 1.77 0.59 0.85 MSE 3.96 28.17 3.10 6.43 MSES 0.20 (5.1%) 2.95 (10.5%) 0.15 (4.9%) 0.41 (6.3%) MSEu 3.76(94.9%) 25.22(89.5%) 2.95 (95.1%) 6.02 (93.7%) 30/10/2006 RMSE 0.61 3.09 0.35 1.43 MSE 2.64 66.94 0.85 14.32 MSES 0.33 (12.5%) 9.53 (14.2%) 0.10 (11.7%) 2.01 (14.1%) MSEu 2.31(87.5%) 57.41(85.8%) 0.75 (88.3%) 12.31(85.9%) 30/11/2006 RMSE 1.37 3.37 0.67 0.87 MSE 13.19 79.65 3.11 5.32 MSES 1.81 (13.7%) 11.16(14.0%) 0.33 (10.5%) 0.49 (9.2%) MSEu 11.37 (86.3%) 68.49 (86.0%) 2.78 (89.5%) 4.83 (90.8%) 08/01/2007 RMSE 0.68 3.26 0.23 1.36 MSE 3.26 74.57 0.36 12.90 MSES 0.43 (13.3%) 10.42(14.0%) 0.02 (6.2%) 1.45 (11.3%) MSEu 2.83 (86.7%) 64.15 (86.0%) 0.34 (93.8%) 11.45 (88.7%) 12/02/2007 RMSE 0.71 1.16 1.31 1.67 MSE 3.00 8.14 10.37 16.66 MSES 0.45(14.9%) 1.32 (16.3%) 1.68(16.2%) 2.71 (16.3%) MSEu 2.55(85.1%) 6.81 (83.7%) 8.68 (83.8%) 13.95 (83.7%) 15/03/2007 RMSE 0.84 1.10 1.23 1.85 MSE 6.42 10.91 13.52 30.69 MSES 0.62 (9.6%) 1.12 (10.3%) 1.33 (9.8%) 3.36(10.9%) MSEu 5.80(90.4%) 9.79 (89.7%) 12.19(90.2%) 27.33(89.1%) Other statistics also showed that the WE model is superior to the Phyllochron model in the earlier five out of the seven sowing dates (Table 2 and 3). The d index varied from 0.97 to 1.0 with the WE model and from 0.91 to 1.0 with the Phyllochron model (Table 2). The E12 index was smaller than 1 (0.07-0.78) in the first five sowing dates and greater than 1 (2.05-3.42) in the two latest sowing dates (Table 3). Decomposing the MSE into systematic (MSEs) and unsystematic (MSEu) components (Table 1), indicated that the MSEu dominated the errors of predictions with both models (greater than 83%), which is desirable from a modeling perspective. One of the objectives of modeling is to minimize the MSEs, and in five out seven sowing dates, the MSEs was smaller with the WE model (Table 1). The MSEs for ligule LN varied from 5.1 to 14.9% with the Phyllochron model and from 4.9 to 16.2% with the WE model, and for tip LN the MSEs varied from 10.3 to 16.3% with the Phyllochron model and from 6.3 to 16.3% with the WE model. Table 2. The index of agreement using the Phyllochron model and the WE model to predict the ligule leaf number (LN). and the tip LN in the maize variety BRS Missões in seven sowing dates (day/month/year) during the 2006/2007 growing season. Santa Maria. RS. Brazil. Sowing date Phyllochron model WE model Ligule LN Tip LN Ligule LN Tip LN 23/08/2006 0.99 0.98 1.00 1.00 27/09/2006 1.00 0.98 1.00 1.00 30/10/2006 1.00 0.92 1.00 0.98 30/11/2006 0.98 0.91 1.00 0.99 08/01/2007 0.99 0.91 1.00 0.99 12/02/2007 0.99 0.98 0.98 0.97 15/03/2007 0.99 0.99 0.97 0.97 Table 3. The accuracy of the WE model relative to the phyllochron model (E12) using the Phyllochron model and the WE model to predict the ligule leaf number (LN) and the tip LN in the maize variety BRS Missões in seven sowing dates (day/month/year) during the 2006/2007 growing season. Santa Maria. RS. Brazil. Sowing date WE / Phyllochron Ligule LN Tip LN 23/08/2006 27/09/2006 30/10/2006 30/11/2006 08/01/2007 13/02/2007 15/03/2007 0.47 0.78 0.32 0.24 0.11 3.46 2.11 0.18 0.23 0.21 0.07 0.17 2.05 2.81 These results suggest that the WE model should be preferred to the Phyllochron model for predicting ligule and tip LN in maize. Even though the predictions of LN were better with the Phyllochron model in the two latest sowing dates of the 2006/2007 growing season, the WE model has advantages compared to the Phyllochron model. First, the WE model uses a non-linear temperature response function, which is more biologically sound to represent the LAR response to temperature than a linear response (XUE et al., 2004; STRECK et al., 2006, 2007). Second, the coefficients of the WE model LARmax and cardinal temperatures (minimum, optimum, and maximum) have biological meaning and operational definition. Third, the non-linear effects of temperature on LAR combined in a multiplicative fashion are also biologically sound to represent the interaction of environmental factors on plant development observed in the field. The fact that the WE model did not give the best predictions in the two latest sowing dates (12/02/2007 and 15/03/2007) is of minor concern from a pratical vewpoint for two seasons. First, these two sowing dates were out of the recommended sowing period for this location (11/08-20/01). Second, if Global Warming takes places in the near future, it is expected that maize plants will be exposed to higher temperatures than the current temperatures observed in April and May for this location. Furthermore, in a warmer climate, maize plants will be exposed to high temperatures that often will be higher than Topt, as currently occurs with maize plants grown in December and January of the 2006/2007 growing season in this location, where the WE model predicted LN better than the Phyllochron model. Therefore, the WE model is expected to capture the non-linear effects of supra optimum temperatures better than the Phyllochron model in future climates. These advantages of the WE model over the Phyllochron model highlight two important features of the WE model that are sought for any crop simulation model: robustness while maintaining accurate predictions. Better predictions of leaf appearance with the WE model compared to the Phyllochron model have also been reported for other crops such as winter wheat (XUE et al., 2004), muskmelon (STRECK et al., 2006), African violet (STRECK, 2004), potato (STRECK et al., 2007), and eucaliptus seedlings (MARTINS; STRECK, 2007). Errors in the predictions of ligule LN with the WE model were lower than one leaf in most of the sowing dates (Table 1). An error lower than one leaf is acceptable for many practical applications. The predictions of tip LN were with an error of about one leaf in most of the sowing dates (Table1). An error of one leaf for tip LN has less impact than an error of one leaf for ligule LN, because there are two to five leaves unfolding and expanding at the whorl of a maize plant, and the uppermost visible leaf is small and has a minor contribution to the whole plant leaf area. Therefore, from a practical view point, the greater error for tip LN is of no concern. CONCLUSIONS The WE model is superior to the Phyllochron model to predict ligule and tip leaf number in maize. Better predictions of leaf number with the WE model are mainly due to more biologically sound representation of non-linear effects of temperature on LAR when air temperature is near and beyond the optimum temperatures for LAR. ACKNOWLEDGEMENTS To Alfredo Schons for his assistance in collecting data during the first year of experiment, and to Embrapa Trigo for providing the seeds. Funding for N.A. Streck (Bolsa de Produtividade) and L.F. Gabriel (Bolsa de Iniciação Científica) by Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq at the Ministry of Science and Technology of Brazil, for T.C. Buske (Bolsa FIPE) and A.P. Schwantes (Bolsa FIEX) by UFSM, for F.K. Samboranha (Bolsa de Iniciação Científica) by Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul, and for I. Lago (Bolsa de Mestrado) by Fundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES (Bolsa de Mestrado) at the Ministry of Education of Brazil are greatly acknowledged. RESUMO: O cálculo da taxa de aparecimento de folhas (TAF) é uma parte importante em modelos de simulação de culturas. O objetivo deste trabalho foi avaliar e comparar um modelo linear (o modelo Filocrono) e um modelo não linear (o modelo Wang e Engel - WE) para a simulação da TAF em uma variedade de milho. Um experimento foi realizado em Santa Maria, RS, com sete datas de semeadura em dois anos agrícolas (2005/2006 e 2006/2007). A variedade de milho usada foi BRS Missões, no delineamento experimental blocos ao acaso, com seis repetições. O espaçamento foi 0,8 m x 0,21 m e a parcela tinha três linhas de 5 m de comprimento. Em cada parcela foram marcadas três plantas na linha central nas quais se realizou semanalmente a contagem do número de folhas expandidas e totais. Os modelos usados foram o Filocrono, que usa uma relação linear entre taxa de aparecimento de folhas e temperatura, e o modelo WE que utiliza uma função de resposta não-linear de temperatura [f(T)]. 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J., Uberlândia, v. 26, n. 3, p. 384-393, May/June 2010 _1252059177.unknown 0 5 10 15 20 25 30 35 40 45 272292312332352727476787107127147167187207 Day of the year Temperature (°C) TN TX 2005-2006 growing season 0 5 10 15 20 25 30 35 40 45 247267287307327347222426282102122142 Day of the year Tempearture (°C) TN TX 2006-2007 growing season 0 3 6 9 12 15 18 21 051015202530354045 Temperature (°C) Thermal time (°C day) 0 0.2 0.4 0.6 0.8 1 Response function, f(T) Thermal time f(T) ^ Pi ^ Pi ^ Pi 0 5 10 15 20 25 0510152025 Observed tip LN Predicted tip LN (b) RMSE = 2.32 leaves 0 5 10 15 20 25 0510152025 Observed ligule LN Predicted ligule LN RMSE = 0.80 leaves (c) 0 5 10 15 20 25 0510152025 Observed tip LN Predicted tip LN RMSE = 1.29 leaves (d) 0 5 10 15 20 25 0510152025 Observed ligule LN Predicted ligule LN 23/08/2006 27/09/2006 30/10/2006 30/11/2006 8/01/2007 13/02/2007 15/03/2007 (a) RMSE = 0.84 leaves