The ratio of labeled fertilizer nitrogen (N) divided by the amount of total N is a convenient expression for evaluating the amount of N that is derived from fertilizer. The slope of the regression line for the relationship between total N and labeled fertilizer N is also a measure of fertilizer contribution to N uptake because it represents the incremental increase in fertilizer N for each unit increase in total N. This article compares slope-based and ratio-based approaches to determine the amount of N in plants and plant tissues that is derived from labeled N fertilizer. Mathematical principles inherent in any ratio-based efficiency assessment (Atchley et al., 1976; Packard and Boardman, 1988; Pearson, 1897; Righetti et al., 2007; Tanner, 1949) were evaluated to demonstrate how ratio-based assessments of the amount of N derived from the fertilizer (NDFF) could be misleading.
Researchers commonly conduct 15N studies to determine how multiple N sources (fertilizer, soil, and plant reserves), tissue type, and applied treatments alter the portion of N that is fertilizer-derived in perennial plant tissues. Atom percentage values obtained by mass spectrometry can be converted to the portion of NDFF using standard conversions (Hauck and Bremner, 1976). The NDFF values for different treatments or genera for either entire plants or individual tissues are commonly compared. When we evaluated citations in the Journal of the American Society for Horticultural Science that dealt with 15N studies for 2000–2005, we found that more than 85% of the published papers presented ratio-based NDFF values in tables or figures. Statistically evaluating ratio-based NDFF values has become standard in the N nutrition literature.
Values of ratio-based expressions are dependent on the value of the denominator if a plot of the denominator versus the numerator of ratio components produces a linear function with a nonzero intercept (Atchley et al., 1976; Packard and Boardman, 1988; Pearson, 1897; Righetti et al., 2007; Tanner, 1949). A ratio-based expression is also mathematically dependent on its denominator if a plot of the log denominator versus log numerator has a slope that does not equal 1.0 (Brown and West, 2000; Kleiber, 1932; Reich et al., 2006). Packard and Boardman (1988) suggested that ecological physiologists discontinue using ratios to scale data. They proposed using the denominator of a ratio-based expression as a covariate when analyzing the numerator to eliminate indirect effects associated with different sized denominators.
Difficulties in interpreting ratio-based expressions have also been demonstrated in the plant science literature (Meinzer and Zhu, 1998; Ranjith and Meinzer, 1997; Righetti et al., 2007; Sage and Pearcy, 1987; Sandrock et al., 2005). Covariate approaches similar to what Packard and Boardman (1988) suggested have been applied to N concentration data (Righetti et al., 2007). The inverse of the denominator can also be used as a covariate when a ratio-based expression is evaluated (Righetti et al., 2007).
Sage and Pearcy (1987) proposed evaluating the relationship of the slope of leaf N content versus total CO2-assimilation regression equation as an alternate measure to traditional ratio-based photosynthetic N use efficiency (PNUE) evaluations. Slope-based approaches for evaluating PNUE have also been used by other plant researchers to avoid biases in ratio-based expressions (Meinzer and Zhu, 1998; Ranjith and Meinzer, 1997). We suspect that similar issues are important in evaluating NDFF, a ratio between labeled fertilizer N and total N. It is possible that plots of total N versus labeled fertilizer N have nonzero intercepts or the slopes of log total N versus log fertilizer N do not equal one.
We hypothesize that the ratio-based NDFF will often be dependent on the size (dry weight and total N) of the tissues or plants that are compared. There are likely to be many statistical differences in mean NDFF and treatment interactions, but it may be difficult to distinguish between size-related differences (indirect) and other physiological differences among treatments, genera, and tissues (direct). Our goal is to demonstrate how graphical observations, regression analyses, and covariate approaches that account for different total N content among treatments or genera can be helpful tools in discerning the difference between direct and indirect effects.
Horneck, D.A., Hart, J.M., Topper, K. & Kopsell, B. 1989 Methods of soil analysis used in the soil testing laboratory at Oregon State University Agricultural Experiment Station, Oregon State University Corvallis
Meinzer, F.C. & Zhu, J. 1998 Nitrogen stress reduces efficiency of the C4 CO2 concentrating system, and therefore quantum yield, in Saccharum (sugarcane) species J. Expt. Bot. 49 1227 1234
Pearson, K. 1897 On a form of spurious correlation which may arise when indices are used in the measurement of organs Proc. Royal Soc. London 60 489 502
Ranjith, S.A. & Meinzer, F.C. 1997 Physiological correlates of variation in nitrogen-use efficiency in two contrasting sugarcane cultivars Crop Sci. 37 818 825
Reich, P.B., Tjoelker, M.G., Machado, J.L. & Oleksyn, J. 2006 Universal scaling of respiratory metabolism, size and nitrogen in plants Nature 439 457 461
Righetti, T.L., Sandrock, D.R., Strik, B., Vasconcelos, C., Banados, P., Ortega-Faris, S. & Moreno, Y. 2007 Analysis of ratio-based responses J. Amer. Soc. Hort. Sci. 132 3 13
Sandrock, D.R., Righetti, T.L. & Azarenko, A.N. 2005 Isotopic and nonisotopic estimation of nitrogen uptake efficiency in container-grown woody ornamentals HortScience 40 665 669
Tanner, J.M. 1949 Fallacy of per-weight and per-surface area standards and their relation to spurious correlation J. Appl. Physiol. 2 1 15
Thomson, J.D., Weiblen, G., Thomson, B.A., Alfaro, S. & Legendre, P. 1996 Untangling multiple factors in spatial distributions: Lilies, gophers, and rocks Ecology 77 1698 1715