Europ. J. Agronomy 48 (2013) 12–18 Contents lists available at SciVerse ScienceDirect European Journal of Agronomy jo u r nal homep age: www.elsevier.com/locate/eja Sample size for estimation of the plastochron in pigeonpea Alberto Cargnelutti Filho ∗ , Marcos Toebe, Giovani Facco, Gustavo Oliveira dos Santos, Bruna Mendonc ¸ a Alves, Anderson Bolzan Department of Plant Science, Federal University of Santa Maria (UFSM), Santa Maria, RS, Brazil a r t i c l e i n f o Article history: Received 24 October 2012 Received in revised form 6 February 2013 Accepted 7 February 2013 Keywords: Cajanus cajan (L.) Millsp. Experimental planning Linear models Resampling a b s t r a c t The objectives of this study were to estimate the plastochron in pigeonpea (Cajanus cajan (L.) Millsp.) during the period between emergence and flowering using three methods of calculating the average daily air temperature and to determine the sample size (number of plants) needed to estimate the plastochron. A uniformity test (blank experiment) was conducted in an area of 1440 m 2 containing a pigeonpea crop. The area was divided into 360 plots of 2 m × 2 m, and 1 plant per plot was marked at random. In each of these 360 plants, the number of nodes on the main stem was counted at 37, 43, 50, 57, 64, 71, 78, 85, 93, 99, 106, 114 and 120 days after emergence (DAE). The average daily air temper- ature (T average ) was calculated using three methods: method 1: T average = (T minimum + T maximum )/2; method 2: T average = (T 0 h + T 1 h + T 2 h + · · · + T 23 h )/24; and method 3: T average = (T minimum + T maximum + T 9 h + 2T 21 h )/5. For the three methods, the daily and cumulative thermal times were calculated from the date of emergence to early flowering and fitted to a linear regression of the average number of nodes on the main stem as a function of the accumulated thermal time. The plastochron was then calculated under each method as the inverse of the slope of the linear regression, and the required sample size (number of plants) to estimate the plastochron was determined by resampling with replacement. Plastochron values deter- mined from the average daily air temperature calculated based on the three methods are different, and the use of the arithmetic mean of the hourly temperatures (method 2) should be favoured. Under method 2, the plastochron for pigeonpea was determined to be 21.34 ◦ C day node -1 . To estimate the plastochron with 95% confidence interval amplitudes equal to 1, 2 and 3 ◦ C day node -1 , it was necessary to count the number of nodes in 194, 50 and 24 pigeonpea plants, respectively. © 2013 Elsevier B.V. All rights reserved. 1. Introduction The pigeonpea (Cajanus cajan (L.) Millsp.) is one of the most important legumes in the world (Rao et al., 2002). It can be used as a soil enhancer, as a phytoremediation plant, for the recovery of pastures and degraded areas, in the management of soil nema- todes, as human food and as animal feed (Azevedo et al., 2007; Rao et al., 2002; Sheldrake and Narayanan, 1979). Studies on the growth and development of pigeonpea have been conducted, involving aspects related to leaf area (Ranganathan et al., 2001), the accumulation and partitioning of biomass (Robertson et al., 2001), the crop response to the photoperiod (Carberry et al., 2001; Chauhan et al., 2002; Silim et al., 2007) and the response to temperature variation (Ranganathan et al., 2001; ∗ Corresponding author at: Avenida Roraima, n ◦ 1000, Bairro Camobi, CEP 97105- 900, Santa Maria, RS, Brazil. Tel.: +55 55 3220 8899; fax: +55 55 3220 8899. E-mail addresses: alberto.cargnelutti.filho@gmail.com (A. Cargnelutti Filho), m.toebe@gmail.com (M. Toebe), giovanifacco@hotmail.com (G. Facco), gustavo santos rs@hotmail.com (G.O.d. Santos), brunamalves 11@hotmail.com (B.M. Alves), ander bolzan@hotmail.com (A. Bolzan). Silim and Omanga, 2001; Silim et al., 2007). While pigeonpea is sensitive to the photoperiod, some stages between emergence and flowering have proven insensitive to this parameter, which enables the modelling of crop development based on thermal units ( ◦ C day) for different sowing seasons and growing regions (Carberry et al., 2001). One important indicator of crop development is the plastochron, which is defined as the time interval between the appearance of two successive nodes in a plant (Baker and Reddy, 2001). The plastochron can be obtained from the inverse slope of the linear regression of the number of nodes developed by the plant during a certain period, according to the accumulated thermal time (Baker and Reddy, 2001; Sinclair et al., 2005). The number of nodes is obtained through periodic counts performed in previously marked plants, and the daily thermal time ( ◦ C day) is calculated based on the difference between the average daily air temperature and the crop’s base temperature. The daily thermal time is generally calculated from the arith- metic mean between the minimum and maximum temperatures. However, according to Jerszurki and Souza (2010), this method has shown limitations with respect to estimating the average daily tem- perature of the air in Brazil, especially in the summer and spring. 1161-0301/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.eja.2013.02.003