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The analysis of quantitative and qualitative traits has established the inheritance and genetic diversity of the traits in crop plants. The use of heritability, general and specific combining ability has explored the inheritance of traits within Musa. On the other hand morphological and molecular qualitative traits have been used for determining variation and genetic diversity in bananas.

24 1.5.1 Analysis of quantitative traits

Genetic analysis of quantitative traits uses mating designs to understand relationships between individuals through estimates of variance and covariance. However, the mating design approach is difficult to use in genetic studies of bananas because of incompatibilities, difficulty in making reciprocal crosses, female sterility, limited genetic variation, and the few numbers normally generated from banana crosses.

The ratio of genotypic to phenotypic variance is known as heritability (Wrickle and Weber, 1986; Fehr, 1987). There are two types of heritability, broad sense and narrow sense heritability. Broad sense heritability, expressed as the proportion of genetic variance to the total phenotypic variance, is useful in indicating the presence of variation in a population but its predictive role in progeny performance is limited (Wrickle and Weber, 1986). Narrow sense heritability is expressed as the proportion of additive genetic variance to the total phenotypic variation. Narrow sense heritability is useful in predicting the performance of progenies based on parental performance.

In Musa breeding heritability estimates have been used quite often. Broad sense heritability estimates were determined in 4x by 2x plantain hybrids; the heritability estimates for disease traits ranged between 43%-69%; plant height ranged between 70-85%; bunch weight ranged between 84-94% (Ortiz and Vuylsteke, 1994c; Craenen and Ortiz, 1997). Ortiz (2000) calculated narrow sense heritability by regressing 3x parents against 4x offspring; heritability estimates for plant height, bunch weight, number of fruits, and fruit length had intermediate to low heritability estimates (0.20- 0.55). From this study, it was observed that many of the traits such as short plant height and heavy bunches with many fruits in tetraploid progenies from 3x by 2x crosses could not be predicted using the phenotype of the triploid parent. It was also observed that fruit weight and circumference with heritability estimates above 0.5 could be predicted on the basis of the triploid parental phenotype. The predictive role of narrow sense heritability can be limited depending on the experimental conditions and genetic nature of parents. For example, Ortiz (2000) reported that days to flowering had a high heritability estimate of 0.8 but only 19% of the total variation was explained by the genotype of the parent, implying the heritability estimate could have been inflated by non-additive gene action.

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Tenkouano et al. (1998) analysed 4x by 2x progenies and calculated general and specific combining abilities, observing little heterosis in these crosses. They concluded that 4x by 2x crosses were essential only in restoring female sterility in bananas.

Compared to tetraploid females, diploid males made a relatively larger contribution to yield in 4x by 2x crosses and the conclusion was that the male phenotype was more predictive of offspring performance than the female phenotype; this suggested that greater yield gains could be achieved by increasing the frequency of these alleles in the diploid male background through recurrent selection procedures before crossing with tetraploids. However, there is still little knowledge on how black Sigatoka resistance and yield traits such as bunch weight are inherited in 2x by 2x crosses.

1.5.2 Analysis of qualitative traits

Quantitative traits have been useful in establishing the nature of inheritance of traits within crop species. On the other hand, plant taxonomists prefer qualitative traits in diversity studies because they are not affected by environment (Ortiz and Vuylsteke, 1998). These diversity studies group individuals into uniform subgroups which may be according to either the individual’s origin or evolutionary development process.

Morphological and genomic differences are important in understanding the genetic diversity of crop species. Karamura (1998), after the analysis of morphological differences between East African highland bananas, was able to classify them into different banana clones. These clones were Musakala, Nfuuka, Nakabululu, Nakitembe, and Mbidde. Later, Tugume et al. (2002) used Amplified Fragment Length Polymorphic (AFLP) molecular markers to study genetic diversity among East African highland bananas and the results agreed with the morphological classification by Karamura (1998). Random Amplified Polymorphic DNA (RAPDs) markers are preferred to AFLPs, because RAPD markers require small amounts of DNA, are quick, and are not expensive. Although the reproducibility of RAPDs has been doubted (Collard et al., 2005), they have been used to study diversity among Musa species. For example, Jain et al. (2007) used randomly amplified DNA markers to determine the genetic diversity of materials from Indian banana germplasm. Similarly, Agoreyo et al. (2008) used RAPD markers to classify plantains into groups according to their origin. In a study by Ferreira et al. (2004), genetic diversity of banana diploids with molecular markers

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established that individuals, which were closer to each other in terms of genetic distances had similar response to Sigatoka. Pillay et al. (2001) used RAPDs to analyse genetic diversity and relationships in East African highland banana germplasm. They reported a similarity range of 95.5% to 97.8% among the East African highland banana varieties. These research findings highlight the importance of molecular markers to estimate genetic diversity of banana genotypes. The genetic diversity will be important in selecting materials to constitute a population to be improved for black Sigatoka resistance and other traits.