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Plant breeders need to quantify additive and non-additive components of genetic variance in order to determine appropriate selection methods to improve quantitative characteristics. Hierarchical and factorial mating designs (also known as North Carolina mating designs I and II, respectively) allow one to determine these variance components. The relative advantages of these two designs in the quantitative genetics of tuber yield in tetrasomic potato were investigated. Likewise, the number of female parents to include in design I was also investigated. Data were collected from two independent experiments at two contrasting Peruvian locations: La Molina in the dry coast and San Ramon in the humid mid-altitude. In the first experiment, although design I gave a negative digenic variance (sigma(2)(D)), this design provided almost the same estimate of narrow-sense heritability (h(2)) for tuber yield as that obtained in design II (0.291 and 0.260, respectively). Therefore, design I appears to be appropriate for quantitative genetics research in tetrasomic potato, a crop in which some clones are male sterile. The easy handling of crosses (distinct random females included in the crossing scheme) is another advantage of design I relative to design II. In the second experiment, 12 males were crossed with either two or four females following a design-I mating scheme. The additive genetic variance (sigma(2)(A)) was zero (or negative) when two females per male were included but was positive with four females. These results suggest that two females per male may not be enough for design I in tetrasomic potato. Four females per male are preferable to determine sigma(2)(A) in design I for this tetrasomic crop.

The original variation in the source population as well as the selection method may influence the genetic variation in further cycles of genetic improvement. Therefore, the objectives of this research were to determine genetic parameters (variance components and heritability) in source and intermediate stages of a true potato seed (TPS) breeding population and to calculate the genetic and phenotypic correlations in this breeding material developed by the Centro Internacional de la Papa (CIP). The intermediate stage was derived from a source population adapted to the warm lowland tropics plus introduction of exotic germplasm from North America and Europe. Non-additive genetic variation was almost nil for plant survival, tuber yield and tuber shape uniformity in both stages of the breeding population and no quantitative genetic variation for uniformity of tuber color was observed in both source and intermediate breeding materials. Heritability was higher in the intermediate stage than in the source population for plant survival (0.86 vs 0.66), tuber yield (0.30 vs 0.14) and tuber shape (0.77 vs 0.51), but it was the reverse for tuber uniformity (0.11 vs 0.72). These results suggest that potato breeders at CIP were able to keep enough genetic variation for most important characteristics for potato production from true seed in their intermediate breeding materials by adding new sources of variation to the original breeding population. Additive genetic and phenotypic correlations were significant and positive between plant vigor after transplanting and tuber yield, and tuber shape and tuber uniformity, which suggest that high yielding offspring result from early vigorous growth, and that tuber uniformity could depend on tuber shape uniformity in this breeding material.

True potato seed (TPS) requires the selection of appropriate parents for developing hybrid offspring. Parents for routine crossing schemes need to be selected according to their combining ability. Hierarchical and factorial mating designs provide a mean values to assess the general combining ability (GCA) of clones included in crossing schemes. Furthermore, specific combining ability (SCA) may be investigated using the factorial mating design. The aim of this research was to determine the combining ability of clones included in early and intermediate TPS breeding populations developed by the Centro Internacional de la Papa (CIP). Likewise, correlations between breeding values (or additive genetic correlation, q A ) were calculated. Two hierarchical mating designs (in both the early and intermediate populations) and one factorial mating design (in the intermediate population) were evaluated in two contrasting Peruvian locations (La Molina -coastal desert, and San Ramon, warm humid tropics). Plant and tuber characteristics were recorded in these experiments. Significant GCA was observed for tuber yield in all experiments. The male's q A between plant vigour after transplanting and tuber yield was significant, thereby suggesting that offspring with early vigorous growth are high yielding. Plant vigour was also correlated with tuber set, but only among the breeding value of female parents, which suggests that high tuber yield could be achieved because offspring with early, vigorous growth have many tubers. High tuber yielding hybrids can be obtained by choosing parents with significant GCA, whose tuber yield can also be further enhanced if the crosses have a significant SCA.

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