A Growth Curve Application to Compare Plant Heights and Dry Weights of Some Wheat Varieties

Transcription

1 American-Eurasian J. Agric. & Environ. Sci., 3 (6): , 2008 ISSN IDOSI Publications, 2008 A Grow Curve Application to Compare Plant Heights and Dry Weights of Some Wheat Varieties U. Karadavut, S.A. kayi, Ç. Palta and O. Okur 1 Soil and Water Sourches Research Institute, Konya, Turkey 2 Biometry and Genetics, Agricultural Faculty, University of Selçuk, Konya, Turkey Abstract: In is study, plant height and plant dry weight of five wheat varieties (namely Da da 94, K nac 97,, Karahan 99 and Ahmeta a), collected for 20 weeks, were modeled via fitting generalized logistic (GLC), logistic (LC) and Gompertz (GC) grow curves. Grow curve selection was based on residual sum of square (RSS) and mean square error (MSE). Following grow curve selection, grow curves of wheat varieties and eir parameter estimates were compared via a sum of square reduction test. Results from grow curve fitting show at GLC and LC produced similar RSS and MSE values while GC resulted in higher RSS and MSE values bo for plant height and dry weight. Since parameters of LC have meaningful biological interpretation, it was chosen for plant height and dry weight modeling. Results from e sum of square reduction test show at Ahmeta a has e highest plant height potential (124.3 cm) while e varieties and Karahan 99 have e smallest (102.6 cm). is e variety at reaches maximum absolute grow rate earliest (9.29 weeks) while Karahan 99 reaches it latest (10.37 weeks). Asymptotic dry weight of all wheat varieties was found to be g. Results also show at all varieties reaches to maximum grow rate at weeks, except e variety at reaches e same stage at weeks. Key words: Logistic curve Gompertz curve Generalized logistic curve Comparison of grow curves of wheat varieties Sum of square reduction test INTRODUCTION Karadavut [14] used e Richards, logistic, Gompertz and Weibull grow curves for fresh weight of rye Grow is one of e important properties of living plant which was grown in e Konya conditions. organisms. Changes in a phenotype during e grow Karadavut et al. [15] used 10 different models in a study period can be modeled via grow curves, such as to evaluate grow of Dagda wheat plant in different generalized logistic, logistic or Gompertz grow curves. -2 sowing frequencies (450, 550 and 650 plants m ). Behavior of e grow curves can change according to Karadavut and Kay [16] used a Gompertz grow curve living organisms, e phenotype to be studied and to compare fresh weight of some wheat varieties. environment to which it is exposed. To be able to evaluate This study reports on a comparison of grow curves grow data properly, it is required to select a suitable of plant height and plant dry weight of five wheat grow curve and its parameters should be able to be varieties at are commonly grow in Konya area. The interpreted biologically. aims of is study are: 1) to determine a suitable grow In e past, models have been developed to curve for plant height and plant dry weight data; and 2) to describe and explain e grow and yield of plants compare plant height and plant dry weight of wheat bo for glasshouse conditions [1-4] and for field varieties via e selected grow curve. experiments [5-10]. Von Fircks and Verwst [11] used e logistic and e MATERIALS AND METHODS Richards functions to model frost resistance of plant shoots. Tadesse et al. [12] used e logistic grow curve In is study was carried out in years. to model leaf area development of potato plants. Hara Plant height and dry weight of five wheat varieties [13] used e Richards and logistic functions to model (namely Da da 94, K nac 97,, Karahan 99 germination data of several rice varieties. and Ahmeta a), which are widely grow in Konya region, Corresponding Auor: U. Karadavut, Soil and Water Sourches Research Institute, Konya, Turkey 888

2 Am-Euras. J. Agric. & Environ. Sci., 3 (6): , 2008 Turkey, were used. Phenotypes were recorded in weekly Of ese curves, e parameters of LC and GC have for twenty weeks starting from emergence. Measurements a simple biological interpretation. On e oer hand, GLC were used 5 plants given each plot and each variety. has an additional parameter (T) which makes it more The experiment was conducted at e Bahri Da da flexible. Unfortunately, e addition of e parameter International Agricultural Research Institute and Soil and T affects e simple biological interpretability of e Water Research Institute as two locations in Konya, parameters of e model [18]. Turkey. The field plots used was allocated in a complete Model fitting and parameter estimation were randomized design (CRD) wi five replicate plots per performed via e PROC NLIN procedure of SAS [19]. variety [17]. In order to determine e best fitting grow curve, Changes in e plant height and dry weight of models were wi separate parameters for each e five wheat varieties were modeled via generalized variety and common parameters for all varieties via GLC, logistic (GLC), Gompertz (GC) and logistic curves (LC). LC and GC. Selection of e best fitting grow curve was The functions of GLC, GC and LC are given in (1), (2) and done based on e residual sum of square (RSS) and e (3), respectively. mean square error (MSE). However, when e comparison is made between GLC versus LC or GC, results of MSEs C were primarily considered since it takes into account e Y = A+ + e ( ) ( 1+ ) 1 T B Xi M Te (1) number of parameters in e model as well. Following determination of e suitable grow where curve, a full model, which has different parameters set for Y = Phenotype of j experimental unit in e i each variety and a reduced model, which has common recording time, parameters for varieties were. Full and reduced A = Constant (in is study, it is set to 0, A = 0), models were compared via a sum of square reduction test C = Final or potential yield, (4) according to Draper and Smi [20]. T = Near which asymptote maximum grow occurs (T > 1 near top, T < 1 near bottom, T = 1 normal), RSS RSS D ( ) R F D, RdfF B = Relative grow rate, MSE (4) F X i = i recording time, M = Time at which absolute grow rate is maximum, where, e = Residual term for j experimental unit at i recording RSS R = Residual sum of square for reduced model, time. RSS F = Residual sum of square for full model, D = Rdf R - Rdf F, where B( X M) e i Y = A + Ce + e (2) Rdf R = Residual degrees of freedom for reduced model, Rdf F = Residual degrees of freedom for full model, where, Y, X i, A, C, e and e are as in (1), MSE F = Mean square error for full model, M = Time at which absolute grow rate is maximum; is F D,RdfF = F value wi D and Rdf F degrees of freedom. is also e time at which e relative grow rate is B -1 and e time at which grow has reached ec; note RESULTS AND DISCUSSION -1 at e = /3, B = Relative grow rate at time = M, Grow Curve Selection: Results from grow curve fitting of GLC, LC and GC to plant height data are = + C Y ( ) 1+ summarized in Table 1. As it can be seen from A e B X i M e (3) Table 1, GLC has e smallest RSS for grow curve fitting via bo common and separate parameters ( where, Y, X i, A, C, e and e are as in (1). and , respectively) while e GC has e largest M = Time at which absolute grow rate is maximum; RSS for grow curve fitting via bo common and Time at which relative grow rate is ½B; Time at separate parameters ( and , respectively). which grow has reached ½C, On e oer hand, e RSS of LC for common and B = Twice e relative grow rate at time = M; separate parameters ( and , respectively) Approximately e relative grow rate at time = 0 were close to ose of GLC. F = 889

3 Table 1: Am-Euras. J. Agric. & Environ. Sci., 3 (6): , 2008 Results from grow curve fitting of GLC, LC and GC to plant height data Grow curve fitting via No. of Common parameters Separate parameters Grow parameters Curve in curve RSS MSE RSS MSE GLC LC GC fitting ( and 2.25, respectively). However, MSEs of LC for common and separate parameters model fitting (2.87 and 2.15, respectively) were similar to ose of GLC. Therefore, LC was chosen for e comparison of plant dry weight of wheat varieties. Variety Comparison: Height: Comparison of full and reduced models for plant height of wheat varieties via e sum of square reduction test showed at it is not possible to express e grow curve of plant height for Table 2: Results from grow curve fitting of GLC, LC and GC to plant dry weight data Grow curve fitting via e five wheat varieties via a single parameters set (P < 0.01), but can be modeled via sharing some of e parameters (Table 3). Results show at Da da 94, K nac 97, and Ahmeta a varieties can be No. of Common parameters Separate parameters modeled wi e same B (0.37 weeks). However, e Grow parameters estimated parameter B of e variety Karahan 99 Curve in curve RSS MSE RSS MSE (0.34 weeks) was found to be statistically significant GLC from e estimated Bs of oer varieties. LC and Karahan 99 varieties have e same estimated GC C (102.6 cm) parameters. Da da 94 and K nac 97 have e same estimated parameter M (9.63 weeks). It can be Table 3: Comparison of full and reduced models for plant height of wheat seen from Table 3 at e variety Ahmeta a has e varieties via e sum of square reduction test highest height potential (124.3 cm) while e varieties Parameters and Karahan 99 have e smallest height Variety B±S.E. C±S.E. M±S.E. potential. is e first variety at reaches Da da ± ± ± maximum absolute grow rate (9.29 weeks) while Karahan K nac ± ± ± reaches is latest (10.37 weeks). These are also e 0.37± ± ± time at which varieties have reached half of eir final Karahan ± ± ± yield. Observed plant height and values via LC for Ahmeta a 0.37± ± ± wheat varieties are shown in Figure 1. When e grow curves were compared using MSE for e common parameters, it is seen (Table 1) at LC has e lowest value (35.59) while e GC has e largest value (39.73). However, when a comparison was made according to separate parameters for each variety, GLC has e lowest MSE (6.29) while GC has e highest MSE (10.78). Since LC fits as well as GLC and its parameters have a simple biological interpretation, it was chosen for e comparison of plant height of wheat varieties. Results from grow curve fitting of GLC, LC and GC to plant dry weight data are summarized in Table 2. Evaluation of Table 2 shows at GLC has e smallest RSS and MSE in fitting common parameters across all varieties ( and 2.83, respectively) and in separate parameter fitting ( and 2.13, respectively) while GC has e largest RSS and MSE in common parameter fitting ( and 2.96, respectively) and in separate parameter Variety Comparison: Dry Weight: Comparison of full and reduced models, for plant dry weight of wheat varieties, via a sum of square reduction test showed at it possible to express e grow curve of plant dry weight of all varieties via a single parameter set except e variety Karahan 99. Karahan 99 differs from oer varieties only wi e parameter M (estimated at weeks). Parameter estimates are summarized in Table 4. Results show at asymptotic dry weight of wheat varieties found to be g. Results also show at all varieties reach maximum grow rate at weeks, except e variety at reaches is at weeks. Observed plant dry weight and values via LC for wheat varieties are given in Figure 2. According to our best knowledge, ere are no oer studies on ese wheat varieties which have investigated eir grow curves. Therefore, it is not possible to compare our results wi anoer study. 890

4 Plant height (cm) Am-Euras. J. Agric. & Environ. Sci., 3 (6): , 2008 Karahan 99 Ahmetaga Time (week) Fig. 1: Observed plant height and values via LC for wheat varieties Plant dry weight (gr) Karahan 99 Ahmetaga Oer varieties Time (week) Fig. 2: Observed plant dry weight and values via LC for wheat varieties Table 4: Comparison of full and reduced models, for plant dry weight of wheat varieties, via a sum of square reduction Parameters Variety B±S.E. C±S.E. M±S.E. Da da ± ± ± K nac ± ± ± ± ± ± Karahan ± ± ± Ahmeta a 0.40± ± ± Grow curves show e changes in e grow according to time. In is study, grow curves for wheat varieties were evaluated. It is known at e fast growing period is e time at e formation of a plant s tillers and bolting occur. During is period, plants require more nutrients. In practice, knowing is period in advance is vitally important since it is e time for some management such as irrigation and fertilization application. In addition, results from well-fitting grow curves for wheat varieties allows estimating critical time points. Consequently, farmers can perform e necessary management at e optimally chosen time. Therefore, results from is study would be helpful to farmers for is type of application. CONCLUSION In is study, grow curves were to plant height and plant dry weight data and it was found at bo phenotypes could be modeled via LC. In terms of plant height, most of e wheat varieties were statistically 891

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