Accuracy of Equations Predicting the Phyllochron of Wheat

Predicting the rate of leaf appearance, or phyllochron, aids in understanding and modeling grass development and growth. Nine equations predicting the phyllochron of wheat (Tria'cum aesfivurn L.) were evaluated using field data from a variety of locations, cultivars, and management practices. Each equation is referred to by the last name of the first author; if there is more than one equation by the first author, additional descriptors were included. The BAKER and KIRBY equations predict the phyllochron based on changes in daylength following seedling emergence; CAO-TEMP and CAO-DAY use a curvilinear relationship with temperature and daylength, respectively; CAO-T&D uses the ratio of temperature to daylength; VOLK mathematically refines CAO-T&D; MIGLIETTA uses an ontogenetic decline in the rate of leaf appearance; and MIGLIETTA-DAY adds photoperiod effects to MIGLIETTA. No equation adequately predicted the phyllochron. The r2 values between predicted and measured phyllochron for winter wheat and spring wheat cultivars, respectively, were BAKER (0.001,0.486), KIRBY (0.002,0.487), CAO-DAY (0.000, 0.174), MIGLIETTA-DAY (0.013, 0.008), MIGLIETTA (0.002, 0.405), CAO-TEMP (0.100,0.190), CAO-FIELD (0.@78,0.036), CAOT&D (0.066,0.030), and VOLK (0.119,0.043). AU equations predicted the phyllochron for spring wheat cultivars better than winter wheat cultivars. BAKER and MIGLIETTA showed no bias towards either over or underestimating the phyllochron; KIRBY tended to overestimate the phyllochron; and the remaining equations were biased towards underestimating the phyllochron. Equations developed from field data had the greatest range of predicted phyllochrons. Based on multiple criteria, the BAKER equation best predicted the phyllochron for the experimental data set. Other factors must be added to the equations to improve predictions. Much opportunity exists to improve our ability to predict the phyllochron. T HE NOTION of pattern and orderliness in plant development and leaf appearance, the importance of understanding the role of leaf appearance in grass development and growth (Klepper et al., 1984), and attempts to model grass development and growth (e.g., McMaster et al., 1992a; Waldman et al., 1991; Weir et al., 1984) have fostered efforts to predict leaf appearance. The phyllochron, or rate of leaf appearance, is defined as the time between the appearance of successive leaves on a shoot and is usually expressed in units of growing degree-days (GDD) per leaf. The earliest work on leaf appearance was largely descriptive, concentrating on location in the leaf where growth occurs, rate of elongation, and total number of leaves produced. Crop modeling has spurred interest in deriving equations to predict the phyllochron. Starting in 1980, nine equations have been published to predict the phyllochron of wheat (Table 1). In 1980, Baker and others published an equation for calculating the phyllochron of winter wheat as a function of the change in daylength immediately following seedG. S. McMaster, USDA-ARS, Great Plains Systems Research Unit, P.O. Box E, Fort Collins, CO 80522; and W.W. Wilhelm, USDA-ARS, Soil and Water Conservation Research Unit, 119 Keim Hall, Univ. of Nebraska, Lincoln, NE 68583. Received 11 Mar. 1994. *Corresponding author (gregQgpsrv 1 .gpsr.colostate.edu). Published in Crop Sci. 35:30-36 (1995). ling emergence based on one cultivar (Maris Huntsman) grown in England. Two assumptions are that the phyllochron is determined at the time of seedling emergence and that it remains relatively constant during the growing season. Many studies support these assumptions (e.g., Belford et al., 1987; Delkolle et al., 1989; Kirby and Eisenberg, 1966; Malvoisin, 1984; Masle et al., 1989); other studies, primarily growth chamber work, present conflicting results (Baker et al., 1986; Boone and Wall, 1990; Cao and Moss, 1991; Hay and DelCcolle, 1989). Experimental results show that as planting date is delayed, the phyllochron decreases (Baker et al., 1980; Jones and Allen, 1986; Kirby and Perry, 1987; Kirby et al., 1982, 1985). Because daylength changes with planting date, this equation changes the predicted phyllochron so that planting date effects are incorporated. In 1987, Kirby and Perry published a similar equation to Baker et al. (1980) but based their equation on Australian cultivars. Cao and Moss (1989a,b,c) conducted a series of growth chamber experiments examining the detailed phyllochron response of four winter wheat and four spring barley cultivars to different temperatures, daylengths, and their interactions. Equations were derived for each cultivar and across cultivars. The experiment followed the first four leaves, which may have impacted the observed rates because the seed embryo typically has 3 to 4 leaf primordia (Baker and Gallagher, 1983; B o ~ e t t , 1966; Lersten, 1987; Malvoisin, 1984) and early leaves may appear at a faster rate than those leaves whose primordia have not been initiated in the embryo. The intention of their experiment was not to predict the phyllochron under field conditions but rather to understand the effects of temperature and daylength on the phyllochron (W. Cao, 1992, personal communication). The Cao and Moss (1989a) equation assumes a curvilinear relationship with temperature. This is an important departure from the assumption of Baker et al. (1980) and Kirby and Perry (1987) of a linear relationship with temperature. This approach allows the phyllochron to vary through time as temperature varies, and therefore does not assume a relatively constant phyllochron that is set early in plant development. The phyllochron increases with temperature up to a maximum of ~ 2 0 ° C . There. fore, under many field conditions in the northern hemisphere, the phyllochron will decrease with later fall planting dates for winter wheat, but for spring plantings, the phyllochron will increase with later planting dates. The Abbreviations: BAKER, Equation from Baker et al., 1980; CAO-DAY, Equation from Cao and Moss (1989b); CAO-FIELD, Equation from Cao and Moss (1991); CAO-T&D, Equation from Cao and Moss (1989~); CAO-TEMP, Equation from Cao and Moss (1989a); GDD, growing degree-days; KIRBY, Equation from Kirby and Perry (1987); LER, leaf emergence rate; MIGLIETTA, Equation from Miglietta (1991a); MIGLIETTA-DAY, Equation from Miglietta (1991b); RMSE, root mean square error; SARES, sum of the absolute residuals; SRES, sum of the residuals; VOLK, Equation from Volk and Bugbee (1991); CV, coefficient of variation.