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Many agronomic experiments with complete factorial treatment designs are conducted in two or more environments. If at least one of the treatment factors is qualitative, the combined analysis may appropriately include pairwise comparisons of various treatment means averaged over environments. Heretofore, however, formulae for estimation of the variances of pairwise mean differences, which are needed for the calculation of least significant differences (or other mean separation procedures), have not been available in either the agronomic or statistical literature. The main purpose of this paper is to provide the formulae for estimation of these variances so that researchers can use them in testing the significance of differences among various treatment means averaged over environments. Emphasis is given to combined analyses of series of experiments in which the effects of experiments are considered to be random; individual experiments are assumed to have complete factorial treatment designs involving either two or three factors of which at least one is qualitative. All treatment effects, including main effects and interactions, are considered to be fixed effects. Formulae applicable to commonly used experimental designs are presented for the estimation of variances for the five categories of pairprise mean differences in two‐factor treatment designs and the 19 categories of pairwise mean differences in three‐factor treatment designs. Experimental design considerations and the implications of assuming random (versus fixed) experiment effects as well as the structure of the treatment × experiment interactions are studied. Pooling portions of the treatment × experiment interaction with error mean squares are considered, and suggestions are given for cases where some of the treatment factors are quantitative rather than qualitative.

Corn (Zea mays L.) grown in an equidistant plant‐spacing pattern (EPS) often yields more grain per unit area of land than that grown in conventional plant‐spacing patterns (CPS). The objective of this study was to determine the effect of equidistant plant spacing on aboveground dry matter production in corn. Two hybrids (‘Pioneer brand 3732’ and ‘B73 ✕ LH58’) were grown in two planting patterns (EPS and CPS) in field studies on a Chalmers silty clay loam soil (Typic Haplaquoll) near West Lafayette, IN, in 1983 and 1984. Measurements of plant dry matter accumulation and leaf area development began at growth stage V4 and continued weekly through R6. Growth analysis components were estimated from growth curves fitted to the relationships between the measured plant variables (dry weight per plant and dry weight per leaf) and a temperature index measured in growing degree days (GDD). Crop growth rate was greater for EPS than for CPS early in the growing season for both hybrids. An increase in plant biomass was primarily responsible. Although relative growth rate (RGR) tended to be smaller for EPS compared to CPS, the data suggested that the increase in plant biomass caused by EPS may be related to an increased RGR prior to 400 to 500 GDD after planting. Net assimilation rate was not significantly increased by EPS early in the season. Early and mid‐season leaf area indexes, however, were greater for EPS for both hybrids.

Breeding procedures used in pearl millet [Pennisetum glaucum (L.) R. Br.] improvement in India and the USA are aimed at exploitation of hybrid vigor for both grain and forage yields. Selection efforts in Africa have been limited to intrapopulation improvement for grain yield. Knowledge of heterotic patterns and combining ability of the widely cultivated African landraces would be useful in the development of a sound breeding program in Africa. The objectives of this study were to evaluate the combining ability and heterosis among African pearl millet populations and to explore the utility of inter‐population improvement for the development of high yielding varieties and hybrids. Five populations and their 10 interpopulation crosses were evaluated in a randomized complete‐block design with six replications at two locations in Niger during the 1989 and 1990 rainy seasons. Plant height, flowering time, natural incidence of downy mildew, spike length, grain yield, and 1000‐seed weight were measured in different populations. Significant differences among entries for most of the traits were observed. Better‐parent heterosis for grain yield ranged from 25 (Iniari × Ugandi) to 81% (Mansori × Ex.Bornu). Six of the crosses showed significant heterosis and gave 36 to 81% more grain yield than their better parent. All crosses except one were significantly more tolerant to downy mildew than their better parent. Mean squares for general combining ability were significant (P < 0.05) for most traits indicating the importance of additive gene effects for these traits. The large heterotic effects and the magnitude of the additive effects observed in the experiment should be useful in choosing pearl millet landraces for intercrossing in the development of cultivars with improved grain yield.