1.5.1 Heterosis
The term heterosis was coined by Shull (1952). It is defined as “the difference between the hybrid value for one trait and the mean value of the two parents for the same trait” (Falconer and Mackay, 1996). According to Miranda (1999), heterosis is the genetic expression of the superiority of a hybrid in relation to its parents. Two definitions of heterosis are reported in literature; namely, mid-parent or average heterosis, which is the increased vigour of the F1 over the mean of two parents; and high-parent or better parent heterosis, which is the increased vigour of the F1 over the better parent (Sinha and Khanna, 1975; Jinks, 1983). Assigning of maize inbred lines into heterotic groups is helpful to exploit heterosis or hybrid vigour (Stuber, 1994; Troyer, 2006; Flint-Garcia et al., 2009) particularly for grain yield (Osorno and Carena, 2008). Although several economically important crops benefit from the manifestation of heterosis, both the genetic and physiological mechanisms underlying this phenomenon are still unexplained (Hallauer and Miranda, 1988;
Tollenaar et al., 2004; Osorno and Carena, 2008; Hallauer et al., 2010). Three major theories have been proposed including dominance, over-dominance and epistasis, to explain mechanisms underlying the phenomena of heterosis (Hallauer and Miranda, 1988; Singh, 2005). However, it is generally accepted that heterosis, to a large extent, is due to dominance gene action (Singh, 2005). To overcome many of the difficulties that are encountered in the interpretation of heterosis for complex traits, yield component analysis approaches have been applied used to study the effect of heterosis on grain yield (Sinha and Khanna, 1975). Grain yield has several components, for instance, number of ears per plant, number of kernels per cob, and kernel weight in an attempt to understand how heterosis influences grain yield (Sinha and Khanna, 1975).
Heterosis is dependent on level of dominance and differences in gene frequency. It has been extensively exploited in maize breeding (Troyer, 2004). The manifestation of heterosis depends on genetic divergence of the two parents (Hallauer and Miranda, 1988). Low grain yield heterosis is observed for crosses among genetically similar germplasm and for crosses among broad genetic base germplasm (Hallauer
and Miranda, 1981; Beck et al., 1991; Vasal et al., 1993a). High-level of heterosis was observed with increased divergence within a certain range, but that heterosis declined in extremely divergent crosses (Moll et al., 1965; Prasad and Singh, 1986;
Melchinger, 1999; Hallauer et al., 2010). Genetic divergence of the parents is inferred from the heterotic patterns manifested in a series of crosses (Moll et al., 1965; Hallauer and Miranda, 1988; Miranda, 1999).
1.5.2 Combining ability
The concept of general combining ability (GCA) and specific combining ability (SCA) was first introduced by Sprague and Tatum (1942), and later elaborated by Hallauer and Miranda (1988). GCA refers to the average performances of parents in cross combinations and SCA is the deviation of individual crosses from the average performance of the parents involved. The additive portion of genotypic variance is related to the general combining ability (GCA), determined by mean hybrid performance of a line. The non-additive portions such as dominance and epistasis relate to the specific combining ability (SCA), a measure for cases where some hybrid combinations are better, or worse, than expected based on mean performance of the lines involved. The diallel mating design is among the most widely used genetic designs appropriate to estimate the magnitude of the GCA effects of parents and the SCA effects of their crosses for yield and yield components (Griffing, 1956; Hallauer and Miranda, 1988; Hallauer et al., 2010). In this design, a set of lines are crossed pair-wise in all possible combinations, providing an assessment of their relative merits to guide selection and testing schemes for the trait under consideration.
Information on the combining ability of maize germplasm is of great value to maize breeders. GCA and SCA effects are important indicators of the potential value of inbred lines in hybrid combinations (Sprague and Tatum, 1942). Combining ability of inbred lines is the ultimate factor determining future usefulness of the lines for hybrid development (Hallauer and Miranda, 1988; Hallauer et al., 2010). Besides, combining ability studies allow classification of selected parental materials with respect to breeding behaviour (Hallauer and Miranda, 1988; Sleper and Poehlman, 2006). Using the concept of combining ability, genetic variance is partitioned into two
components: variance due to GCA and variance due to SCA (Hallauer and Miranda, 1988; Hallauer et al., 2010). The relative importance of additive versus non-additive effects in diallel crosses is an indication of the type of gene action (Baker, 1978;
Hallauer et al., 2010). The greatest proportion of total genetic variance can be attributed to additive effects for most agronomic traits in maize (Hallauer et al., 2010).
1.5.3 Genotype-by-environment interaction (GEI)
The performance of a cultivar is a function of the genotype and the nature of the production environment (Cooper and Byth, 1996). Environmental factors have greater effect on quantitative traits than on qualitative traits, as a result of which performance evaluations of potential cultivars are conducted in multiple seasons/years and locations (Bernardo, 2002). In addition to genotype and environment main effects, performance of cultivars is largely influenced by the genotype-by-environment interaction (GEI). GEI is the differential response of cultivars to environmental changes (Hallauer and Miranda, 1988; Crossa et al., 1990;
Vargas et al., 1999). Various biotic and abiotic stresses have been implicated as causes of GEI. Fluctuation in growing temperatures, seasonal rainfall amount and distribution, length of growing season, within-season drought, sub-soil pH and socio- economic factors that result in sub-optimal input use are often the causes of GEI in maize production in Africa (Banziger et al., 2006). Multi-environment trials (METs) are systematic approaches exploited to identify promising new cultivars with average yield stability in representative growing or test environments (Shakhatreh et al., 2001; Yan et al., 2007). GEI is complex and often it represents a significant impediment to genetic improvement in crop breeding programs (Basford and Cooper, 1998).
The relative magnitude of genotype x environment provides information concerning the likely area of adaptation of a given genotype. It is also useful in determining efficient methods of using time and resources in a breeding program (Ceccarelli, 1989; Yan and Kang, 2003). Consequently, improving a resistance or tolerance of a given genotype to different stresses to which it would likely be exposed may
a wide range of environments and outside their normal zone of adaptation (Beck et al., 1991). Selection of multi-environment sites to sample stresses adequately, where GE interaction are major sources of variation, is a critical step in a successful breeding program (Edmeades et al., 2006; Yan and Holland, 2010). The existence of GEI thus necessitates breeders to evaluate genotypes in more than one environment in order to obtain repeatable rankings of genotypes with average yield stability (Hallauer and Miranda, 1988; Yan and Kang, 2003). However, GEI becomes of practical significance only when crossover interactions occur (Crossa and Cornelius, 1997). Crossover interactions occur in evaluation trials when ranks of cultivars change across environments (Russel et al., 2003; Frashadfar et al., 2012; Nzuve et al., 2013). The Additive Main Effect and Multiplicative Interaction (AMMI) (Zobel et al., 1988) and genotype and genotype-by-environment interaction (GGE) biplot (Gabriel, 1971) are multivariate methods which are widely applied to analyze complex set of GE data obtained from METs (Gauch and Zobel, 1996; Yan et al., 2000).