Use of Stability Analysis for Long-Term Soil Fertility Experiments

Long-term fertility experiments with replications are often statistically analyzed as split plots in time. Years are often shown to be significantly different and the inconsistency of treatment effects over years enters into significant year-by-treatment interactions which are difficult to interpret. The objectives of this study were to evaluate long-term fertility experiments by stability analysis and relative stability and to observe possible benefits of these analyses to complement conventional analysis of variance procedures. Stability analysis which is the linear regression of treatment yield on the location/year environment mean yield was performed on long-term wheat (Triticum aestimm) and corn (Zea mays L.) fertility trials. Stability analysis on wheat data from the Magmder Plots, indicated that beef manure applications (269 kg N ha~') responded poorly compared to the NPK treatment when environment means were low (<2.0 Mg ha-) and visa versa when environment means were high (>2.0 Mg ha~')Similarly, anhydrous ammonia applied as sidedressing in an irrigated corn experiment at Mead, NE, was found to be superior to ureaammonium nitrate applied either pre-piant or sidedressed when environment means were less than 8.0 Mg ha-. Stability analysis provided a simple method of interpreting significant year-by-treatment interactions detected in analysis of variance models from these longterm experiments. Stability analysis may also be useful for multilocation experiments and continuous site experiments where treatments are applied to the same plot year to year. However, stability analysis may be misleading when employed on continuous site experiments where autocorrelations are present year to year. A MAJOR PURPOSE of long-term fertility trials is to provide a measure of the effect of the environment over time on the consistency of treatment effects. Assessing year-by-treatment interactions in longW.R. Raun and R.L. Westerman, Dep. of Agronomy, Oklahoma State Univ., Stillwater, OK 74078; and H.J. Barreto, CIMMYT, Apdo. Postal 6-641, Mexico D.F. 06600. Contribution from the Oklahoma Agric. Exp. Stn. as journal no. 5707. Received 25 June 1990. * Corresponding author. Published in Agron. J. 85:159-167 (1993). term fertility experiments is an issue when more than 2 or 3 yr of data are present. However, interpretation of year-by-treatment interactions by conventional analysis of variance is difficult because of the complexity of factors affecting environment. Initial use of regression to assess yield stability of genotypes across a wide range of environments was originally presented by Yates and Cochran (1938) and later followed by Finlay and Wilkinson (1963) and Eberhart and Russell (1966). The technique is useful in relating a measurement of environment, which is usually the mean yield across all genotypes for each environment, to performance of different genotypes tested. Work by Crossa (1988) has addressed other methods used in determining yield stability of genotypes over environments. Measurement of yield stability over time involves the evaluation of at least three distinct components: (i) relationship of yield with local environment, (ii) average yield level, and (iii) variability of yield (R. Mead, University of Reading, UK, 1989, personal communication). A stable system has been defined as one that changes least in response to changes in environment (Lightfoot et al., 1987). Eberhart and Russell (1966) characterize a stable genotype as having a linear regression coefficient of one and deviations from regression equal to zero. Other measures of yield stability include the use of relative stability, which is the analysis of functional linear relationships between pairs of varieties or cropping systems (Mead et al., 1986, Lightfoot et al., 1987). Although this technique was originally introduced to compare stability of intercropped versus monocropped systems, it can also be used for comparisons among agronomic treatments. The extrapolation of some of these concepts to characterize the stability of agronomic treatments instead of genotypes seems to be a practical application in separating the response of treatments as a function of environment over time. This assumes that the lack of 160 AGRONOMY JOURNAL, VOL. 85, JANUARY-FEBRUARY 1993 consistency of treatment effects over time (a treatment-by-year interaction) can be interpreted as a linear function of the environment mean on the mean yield for’ a given treatment. The use of regression on the environment mean to assess stability of genotypes as affected by fertilizer treatment on 14 unreplicated trims has been presented by Hildebrand (1984). Hildebrand (1984) stated that it is visually possible to compare treatments and to generalize these equation sets for various kinds of management practices; he further stated that the environment mean measures treatment response to good or poor environments regardless of the reasons these environments are good or bad. However, a major criticism of the technique for use in agronomic trials with few treatments lies in the nonindepende~nce of the individual values used in regressing the environment mean on treatment mean yields (Lightfoot et al., 1987). Non-independence of variables used in regression as well as potential interdependence of the different linear equations to be compared become critical considerations when one uses stability analysis to separate treatment response as a function of the environment mean. However, such problems are largely overcome as the number of treatments used in calculating the environment mean is increased (R. Mead, University of Reading, UK, 1989, personal communication). In the case of agronomic experiments with a few treatments, the amount of bias caused by large interdependence of regression equations can be avoided by use of relative stability which uses independent values. Another approach to express stability is the evaluation of relative risk when two treatments are compared (Mead et al., 1986). Various other aspects have recently been investigated relative to proper analysis procedures for fertilizer response experiments, specificadly the use of differential equations (Cochrane, 1988) and trend analysis (Tamura et al., 1988). The objectives of this manuscript were to evaluate various long-term fertility experiments by stability analysis by means of regression of treatment yield on the location/year mean yield and relative stability among selected treatment pairs to assess treatment response as a function of environment and to detect the benefits of these analyses to complement conventional analysis of variance. MATERIALS AND METHODS Two long-term wheat fertility studies at Stillwater, OK (Experiment #222 and Magruder Plots) and one long-term corn fertility study at Mead, NE that had treatments applied to the same plots year after year were analyzed by conventional analysis of variance procedures, stability analysis (Finlay and Wilkinson, 1963, without the use of data transformations), and relative stability (Mead et al., 1986, and Lightfoot et al., 1987). Conventional analysis of variance was performed by the design structure for each individual long-term trial. Because the Magruder plots did not employ replications, the only possible combined analysis included only sources of variation for year and treatment, with the interaction (year by treatment) as the error term. This analysis, although restrictive, does provide a measure of the consistency of treatment effects over time. Conventional analysis over years of Experiment #222 and the Mead, NE experiment employed split-plot-in-time designs since the same fertilizer treatments were applied each year to the same plots. Consistent with Mclntosh (1983), considering year and treatments as random and fixed effects, respectively, in Experiment #222, the appropriate tests of hypothesis were made. Stability analysis is the linear regression of treatment yield on the location/year environment mean yield (average yield of all treatments in a given year). Steps to determine differences in slope and intercept components for linear equations from the stability analysis were derived from Steel and Torrie (1980) and Cochran and COx (1957). Relative stability is assessed by studying the joint distribution of data pairs (mean for Treatments A and B in a given year) and by comparing slopes of the regression line when the average yield of the pair (A +B)/2 is regressed on the yield difference (A-B) between the two treatments. A slope close to zero would indicate that the two treatments change similarly and are equally stable. A positive slope indicates that B is more stable than A since there is more variability in A. A strongly negative slope indicates that A is more stable than B. A probability level ofP < 0.05 for the slope from the relative stability equation indicates that the slope is significantly different from zero. These probability levels are listed on each of the relative stability graphs discussed. Due to various treatment changes in the Magruder plots over the past 90 yr, analyses on these plots were restricted to the last 31 yr where constant P-K-Lime rates were employed. Nitrogen was applied at 37 kg ha-1 prior to 1968 while plots receiving N since that date have received 67 kg ha-1. Treatments analyzed in this experiment are defined in Table 1. The use of N, P, K and lime (L) as related to treatment comparisons are explained in Table 1. Further information relative to the Magruder Plots can be found in Webb et al. (1980). Treatment structure for the Mead, NE experiment which was conducted for 15 yr is discussed in Olson et al. (1986). A split-block design for individual year analysis was employed with four replications at this site. The three treatments from that corn experiment discussed in this manuscript were anhydrous ammonia injected sidedress at the 11 to 12 leaf stage (AA-IS), urea-ammonium nitrate sidedressed at the eight-leaf stage (UANSD) and urea-ammonium nitrate band applied at planting 0dANPL), all at the 90 kg N ha-1 rate. Treatment structure for Experiment #222 which was established in 1969 is found in Table 2. This experiment used a randomized complete block design with four replications. Treatment means from all three experiments were compared by Fisher’s Least Significant Differences (LSD) at P = 0.05. Given the limitations of the LSD test (prone to Type I errors and limitations of two mean comparisons, Swallow, 1984), non-orthogonal contrasts were also performed on selected treatment comparisons from the Magruder and #222 experiments. Contrasts of treatments receiving no N versus manure or other treatments receiving N were not targeted for discussion because of the distinct differences noted at these two locations. Only treatment mean data by year could be obtained for the Mead, NE experiment thus restricting further mean separation and related data analysis.