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activities at various stages of plant growth and development is another challenge to the maize breeder. Hageman and Lambert (1996) questioned the effect, role and interaction of N metabolism on the size of the plant in lengthening photosynthetic activity of leaves. It has also been difficult to associate physiological traits such as LCC and DMA with final yield.
Experiments to address these challenges may be costly and so require precise yet economical equipment to quantify the LCC character over grain filling stages under low and high soil N. In addition to this, combining knowledge on other traits related to yield and calendar physiological maturity may help to address these challenges. Since yield is the ultimate product of many processes, yield would be the best estimate for superior physiological processes.
1.3 Generation mean analysis and transgressive segregation
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are statistically significant (Mather and Jinks, 1982, 1977; Kearsey and Pooni, 1996; Azizi et al., 2006; Shashkumar et al., 2010). These authors have provided the importance of the signs and magnitudes of genetic effects under the GMA. The type of epistasis, whether complementary and/or duplicative, could be identified in the cross where they occur.
However, in terms of the importance of epistasis in maize, Rahman et al. (1994) reported on the descending order from dominance, additive; and dominance x dominance, additive x dominance, to additive x additive. The sign and magnitude count and they may vary per this trend, depending on the trait and environment. Factors other than digenic epistasis, such as high order epistasis, linkage and G x E interaction, could be inferred within the limits of the study at hand.
However, the limitations of GMA are that heritability and response to selection become difficult to compute due to lack of variances (Kang, 1994), because the GMA confounds the genetic effects (Mather and Jinks, 1982). This could be counter-argued because variances within and between the generations of GMA have been used to estimate heritable and non- heritable genetic parameters; and this is consistent with the literature (Shashkumar et al., 2010; Smith et al., 2009; Azizi et al., 2006; Kearsey and Pooni, 1996; Dabholkar, 1992).
Mather and Jinks (1982) concluded that neither method nor mating design is satisfactory in genetic and breeding experiments but the methods should be complementary.
The genotypes under GMA would help to infer and utilise the phenomenon of transgressive segregation. Transgressive segregation is ubiquitous in plants and this phenomenon creates superior phenotypes and, as a consequence, hybrids that are adapted to local stresses (Falconer and Mackay, 1996; Rieseberg et al., 1999). Rieseberg et al. (1999) reported that 65% of transgressive segregation in plants affects morphological traits and the rest are on the fecundity, biochemical compounds, physiology, life history and tolerance to local stresses. However, important questions have not been cleared regarding transgression.
First, how frequent is transgression in crosses due to genetic distances (narrow vs. wide crosses)? Secondly, is transgressive segregation for a given cross or a given character predictable? Thirdly, since Rieseberg et al. (1999) reported that transgressive segregants are heritable, the magnitudes of this heritability are not clear across environments, particularly those under low N, as maize in SSA is produced under low N conditions. Generally, visual
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illustration of transgressive segregation for the point of inferring inheritance of the secondary traits in tropical maize under high and low N conditions has not been established. Frequency distributions observed by plotting P1 and P2 against their segregating generations (i.e. F2, BCP1 and BCP2) may help to express comprehensive understanding into the phenomenon of transgressive segregation (Braden, 2005; Smith et al., 2009). Skewness of the distribution curve of the segregating generation towards either parent may indicate the parent which provided dominant genes. High population means and variances may warrant selection from either positive or negative segregants depending on the trait of interest as Lamkey et al.
(1995), Smith et al. (2009) and Shashkumar et al. (2010) suggested. When transgression is implied in an experiment, Carson and Hooker (1981) working with phytopathology in maize asserted that selection could be done from the intermediate x intermediate in the F2, whereas Lamkey et al. (1995) reported that F2 and backcrossed generations had been used in the United States of America (USA) to develop inbred lines. Furthermore, Shashkumar et al.
(2010) asserted that diallel mating or biparental mating designs could be used directly on the segregants or, the segregants could first be selfed or randomly mated. This would break linkage blocks to release the genetic variance that is embedded in the segregants and then selection done at later stages. This may suggest the need to investigate and use various statistical tools to infer and design breeding strategies, particularly in SSA, where genetic effects are compromised by many environmental factors such that breeders very often select under ideal and no-ideal conditions.
1.3.2 Assumptions of a generation mean analysis and their critique
According to Wright (1968), Mather and Jinks (1977) and Lande (1981), certain basic assumptions could be made when undertaking GMA experiments. These included:
i) all segregating genes are located in one parent, i) responsible genes are not linked,
ii) all responsible genes have equal effects with respect to the character under study,
iii) there is no epistasis, iv) there is no dominance, and
v) there is no genotype x environment interaction.
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However, these assumptions have been falsified in the literature, as reported below:
i) the differences between F1 and mid parents indicates dominance (Mather and Jinks, 1977, 1982; Fehr, 1991; Hill et al., 1998),
ii) skewness in the back-crossed progenies shows dominance (Shashkumar et al. 2010;
Smith et al, 2009; Braden, 2005), in other words, this occurs when BCP1 ≠ BCP2 implies presence of epistasis (Melchinger et al., 1988; Hill et al., 1998),
iii) transgressive segregation in F2 denies the assumption of isodirection (Carson and Hooker1981), Kearsey and Pooni (1996) indicated transgression when F2, BCP1 and BCP2 exceeded or were below the mid-parents or F1,
iv) very wide crosses lead to a preponderance of dominance effects at the expense of additive effects (Kearsey and Pooni, 1996; Braden, 2005; Checa et al., 2006; Azizi et al., 2006), while much earlier, and to the contrary, Kelly and Bliss (1975) reported that lower differences between parents may result in low broad sense heritability.
However, Kearsey and Pooni (1996) added that the means and dominance remain independent of dispersion effects.
v) dispersion and association affects the detection and estimation of genetic effects (Mather and Jinks, 1977, 1982; Kearsey and Pooni, 1996; Braden 2005), and
vi) standard errors reduce the size of estimated genetic effects such that the effects with low errors occur significantly more frequently in the model or experiment regardless of the magnitude of genetic effects (Braden, 2005; Smith et al., 2009). Under non- ideal experimental conditions, standard errors increase, whereby epistatic interactions increase relative to additive and dominance effects (Rahman et al., 1994;
Ceballos et a., 1998). This increase of experimental errors may deny the assumption of lack genotype x environment interaction.
In the light of the above, according to Smith et al. (2009), the challenge to breeders has been lack of consistency in detecting and estimating genetic effects from GMA studies. For instance, heritability estimates and number of genes have not been measured precisely enough in GMA or other breeding and genetic studies. Ceballos et al. (1998) suggested use of the criterion of minimum standard error, while Melchinger et al. (1988) recommended use of experiments with high confidence interval and high R2 values as an alternative to heritability estimates. Sources of errors are not necessarily environmental, as Mather and
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Jinks (1977) reported that use of inappropriate germplasm for traits of interest may also be a source of error. Furthermore, experimental conditions may have different effects on segregating and non-segregating generations (Gomez and Gomez, 1984).