Abstracts

Multivariate genetic divergence and hybrid performance of cacao ( Theobroma cacao L.)*

Luiz Antônio dos Santos Dias ¹ and Paulo Yoshio Kageyama ²

*Part of a thesis presented by L.A.S.D. to ESALQ, USP, in partial fulfillment of the requirements for the Doctoral degree.

¹Estação Experimental "Filogônio Peixoto", Centro de Pesquisas do Cacau.

Present address: Departamento de Biologia Geral, Universidade Federal de Viçosa, 36571-000 Viçosa, MG, Brasil.

Send correspondence to L.A.S.D.

²Departamento de Ciências Florestais, Escola Superior de Agricultura" Luiz de Queiroz" (ESALQ),

Universidade de São Paulo (USP), Caixa Postal 9, 13418-900 Piracicaba, SP, Brasil.

ABSTRACT

Genetic distances among cacao cultivars were calculated through multivariate analysis, using the D² statistic, to examine racial group classification and to assess heterotic hybrids. A 5 x 5 complete diallel was evaluated. Over a five-year period (1986-1990), five cultivars of the S₁ generation, pertaining to the Lower Amazon Forastero and Trinitario racial groups and 20 crosses between the corresponding S₀ parents were analyzed, based upon five yield components - number of healthy and collected fruits per plant (NHFP and NCFP), wet seed weight per plant and per fruit (WSWP and WSWF), and percentage of diseased fruits per plant (PDFP). The diversity analysis suggested a close relationship between the Trinitario and Lower Amazon Forastero groups. A correlation coefficient (r) was calculated to determine the association between genetic diversity and heterosis. Genetic distance of parents by D² was found to be linearly related to average performance of hybrids for WSWP and WSWF (r = 0.68, P < 0.05 and r = 0.76, P < 0.05, respectively). The heterotic performance for the same components was also correlated with D², both with r = 0.66 (P < 0.05). A relationship between genetic divergence and combining ability effects was suggested because the most divergent cultivar exhibited a high general combining ability, generating the best performing hybrids. Results indicated that genetic diversity estimates can be useful in selecting parents for crosses and in assessing relationships among cacao racial groups.

INTRODUCTION

Cacao (Theobroma cacao L.) is a species recently domesticated by the Aztecs and Mayas. The first cultivated trees belonged to the Criollo racial group.‘ Non- Criollo’ groups of cacao trees exist in the wild state in South America, in the Amazon basin - supposedly the cacao center of origin - and constitute the Forastero racial group, which has been cultivated only during the last two or three centuries. These racial groups are distinguished basically by fruit and seed characteristics. Trinitario is a hybrid group between the two, formed by natural hybridization that took place in Trinidad, when the Criollo plantations were ravaged by disease in the mid-18th century and the trees that were lost were replaced by Forastero, interplanted with the remaining Criollo. There are subdivisions in these groups. Among the Criollo, one can find the population from Central America and that from northern South America. Among the Forastero there are populations from the Lower and Upper Amazon (Cheesman, 1944; Lanaud, 1986).

Utilization of geographic divergence as a measure for evaluating genetic divergence is a common practice in hybridization programs of several crops, such as corn (Zea mays L.) (Moll et al., 1962). Hybridization of cacao is no exception to this practice. Cacao hybrids between parent clones of different geographic origin are common. Frequently the crossing strategy adopted aims at complementation of traits, with the purpose of correcting faults. Crosses are also conducted randomly, primarily when information on parent clones is not available. Lately, species diversity has been investigated through multivariate methods applied to morphological (Engels, 1983; Raboin et al., 1993; Bekele et al., 1994), enzymatic (Lanaud, 1986; Ronning and Schnell, 1994), and DNA-based molecular markers (Lanaud et al., 1993; Laurent, 1993; N’Goran et al., 1994). Restriction fragment length polymorphisms (RFLP) and random amplified polymorphic DNA (RAPD) are used as markers. Advances in cacao breeding due to introduction of these DNA markers have been examined (Dias, 1995). However, multivariate methods have not yet been applied to cacao with the objective of estimating genetic divergence, associating it with heterotic parental combinations.

Diallel crosses are frequently utilized in selecting parents for synthesis of hybrids. Parents with a high general combining ability are expected to produce superior hybrids. However, selection of superior hybrid combinations based on per se performance and on parental divergence is possible. The latter strategy has a predictive nature and it avoids making and evaluating hundreds of undesirable crosses. The association between heterosis in hybrids and genetic divergence of parents has been established in theory (Falconer, 1960; Cress, 1966), and confirmed in practice (Ramanujam et al., 1974; Arunachalam and Bandyopadhyay, 1984; Arunachalam et al., 1984; Ghaderi et al., 1984; Shamsuddin, 1985; Prasad and Singh, 1986; Cruz, 1990; Ali et al., 1995) using multivariate analysis from yield and its components. If this association occurs to a high degree, it should be possible to utilize an estimate of divergence as a criterion for selecting parents and subsequent production of high combining hybrids. Multivariate methods have contributed to the estimation of genetic divergence between populations in various crops. Such methods have proven to be more efficient than the criterion of geographic diversity in predicting superior hybrid combinations (Bhatt, 1973). The objectives of the present study were: 1) to investigate the extent of genetic divergence among five cacao cultivars (selfs), pertaining to different racial groups, by using multivariate analysis and 2) to determine the degree of association between genetic divergence in this set of cultivars and the mean and heterotic performance in their hybrids.

MATERIAL AND METHODS

Genetic materials

The present study employed data from cacao cultivars and hybrids obtained from a 5 x 5 complete diallel. A detailed combining ability analysis of this diallel was made by Dias and Kageyama (1995). Five non-commercial cacao cultivars were tested together with their 20 possible hybrids. Thus, it was possible to associate the performance of the hybrids with the divergence between parents. These cultivars, racial groups and their origins are described below:

Field evaluation

Seeds of the crosses were obtained by controlled pollination of clonal parents. Seeds of parental clones were produced by selfing corresponding clones. All cultivars involved in this study are self-compatible. These five cultivars and their 20 hybrids, including reciprocals, were planted in a randomized complete block design with four replications and 16-plant plots. Temporary shading involved planting bananas (Musa spp.) at a 3 x 3 m spacing, similar to the cacao trees. Erythrina spp. planted every 24 m provided definitive shading.

The trial was planted in 1975 at the CEPEC - Centro de Pesquisas do Cacau - in Itabuna, Bahia, Brazil. Effective yield was measured beginning in 1980. Yield components measured in monthly harvests in the crop years 1986 to 1990 were utilized for analysis. In assessing the cultivars and crosses, five characteristics were considered: number of healthy (NHFP) and collected fruits per plant (NCFP), wet seed weight per plant in kg (WSWP), and per fruit in g (WSWF), and the percentage of diseased fruits per plant (PDFP). Data on PDFP were transformed by adding 0.5 to the percent and taking the square root of the sum (Steel and Torrie, 1980).

Calculating multivariate genetic divergence

Initially, a joint univariate analysis of variance was calculated, using plot means. Next, multivariate analysis of variance was applied to all five characters. Thus, the matrices of sums of squares and products of treatments (H) and of pooled error (E) were obtained from the joint univariate analysis of variance. In order to test the significance of differences between treatment average vectors, Wilks’ statistic L, transformed into a value corresponding to F (Harris, 1975), was used. Wilks’ statistic L is defined as L = |E|/|H + E|. Divergence between S1 parents was quantified by determining the Mahalanobis’ generalized distance. The D2 statistic of Mahalanobis’ distance (see Rao, 1952) between two cultivars on p characters is defined as:

D2 = d’W-1 d

where d is a vector of differences between the cultivar averages for all p characters and d’ is its transpose. W is the p x p variance-covariance matrix of pooled error. Tocher’s method (Rao, 1952) applied to Mahalanobis’ distance matrix was used to determine cluster formation.

Degree of linear association between average and heterotic performance realized in hybrids with genetic divergence between five cacao parent cultivars was quantified using Spearman’s correlation (r). In this case, the 20 hybrids (10 F1s and the 10 reciprocal F1s) were averaged to give 10 F1s cross means, allowing the 10 D2 values obtained from five progenitors to be compared with an equal number of hybrids. This strategy avoided calculation from repeated values, since the distance between cultivars 1 and 5, for example, is the same as between 5 and 1. The lack of significance for reciprocal effects (Dias and Kageyama, 1995) supported this strategy. The heterosis of hybrids (h) was estimated on mid-S1 parental values, using the formula: h (%) = 100 (F1 - MP)/MP, where F1 is the hybrid mean and MP is the parental mean. The standard error for heterosis was used to determine the significance of the heterotic deviation for each mating. Least significant differences (LSD) were determined for cultivars and hybrids, for each character. In assessing an upper limit to the degree of genetic determination of each character, the repeatability coefficient (Falconer, 1960) was estimated, using the formula developed by Turner and Young (1969).

RESULTS AND DISCUSSION

Divergence among parental clones

The joint univariate analysis of variance involving only the parental cultivars showed significant differences between cultivar averages and years (P < 0.01) for all characters assessed. There was no significant cultivar-year interaction, except for PDFP (Table I). The coefficients of variation obtained were of the same order of magnitude as those obtained in cacao trials. The multivariate variance analysis based on the L statistic detected significant differences (P < 0.0001) between the cultivar average vectors (F = 19.37 for 20 and 186.68 d.f.). The diversity found among cultivars was predictable. Three out of five cultivars originated from populations of the Lower Amazon group from Bahia and two originated from Trinitario populations from Trinidad (ICS 1) and Costa Rica (CC 41). When the trial was designed it was expected that the combination of parents of distinct geographic origin and racial groups would generate heterotic hybrids.

The D2 Mahalanobis’ statistic quantified divergence between pairs of cacao cultivars (Table II). CC 41 and ICS 1 showed the most divergence, while CC 41 and SIC 19 were the most similar. Divergence, based on D2, was not in agreement with the classification of the cacao racial groups with regard to the most distant and to the most similar pair.

Using Tocher’s method (Rao, 1952), two divergent clusters were observed. Cluster 1 consisted of only ICS 1 while cluster 2 included the remaining cultivars. The Bahia selections (SIAL 169, CEPEC 1, and SIC 19), of the Lower Amazon group, were clustered with CC 41, classified as a Trinitario, by Engels (1983). CC 41 has been classified as a hybrid type, originating from open-pollinated progeny of ‘UF 676’. UF 676 is a Trinitario and its similarity to Lower Amazon cultivars of western Africa was recently detected by Raboin et al. (1993) based upon morphological characters, and by Laurent (1993) based upon RFLP markers. The cacao trees in western Africa originated from cacao populations in Brazil. The Trinitario complex, resulting from hybridization between Criollo and Amazon Forastero (Cheesman, 1944), combines the quality characteristics of the first with the hardiness of the latter. Therefore, the Trinitario complex actually includes a mixture of hybrid types, ranging from those similar to Criollo types, intermediate types, and types closely related to Amazonian. CC 41 was shown to be closely related to the Amazonian selections from Bahia SIAL 169, CEPEC 1 and SIC 19 (Table II), and very distant from ICS 1, which is also a Trinitario clone.

CC 41, SIAL 169, and SIC 19 were the highest yielding cultivars of wet cacao based on seed weight and number of fruits per plant, with similar yield values (Table III). It is possible that CC 41 received the greatest contribution from Amazonian genes and, as a result, became similar to the clones from that group. Assuming this hypothesis is true, Cheesman’s (1944) postulation that the Trinitario group consists of highly heterogeneous populations is confirmed, suggesting that classification of cacao racial groups is unreliable. Thus, a classification that considers the genetic relationships between cacao racial groups is required.

Association between heterosis and parental divergence

The divergence between parental cultivars should not be considered as the only criterion for making crossing decisions. The per se performance of such cultivars should also be considered, for characters of high economic importance. In cacao, a superior genotype is one having a high yield of dry beans per unit area, because dry beans constitute the commercial product. High yield should be combined with high seed weight per fruit to reduce harvesting cost. As a general rule, the commercial cultivars should produce beans of uniform weight, greater than 1 g.

Table IV reveals that the pairs of cultivars with highest distances, such as CC 41 and ICS 1, SIAL 169 and ICS 1, and ICS 1 and SIC 19 (Table II), generated the best hybrids for WSWP and WSWF. However, the SIAL 169 x ICS 1 hybrid, involving cultivars of the second most distant pair, was the best. Cultivar ICS 1, which had the greatest divergence from the others (Table II), showed the highest average for WSWF even though it ranked fourth best in production (Table III). Cultivar SIAL 169 had the second highest WSWF along with the highest production (Table III). Prasad and Singh (1986) have argued that, apparently, crosses between extremely divergent parents create a situation where the harmonious functioning of alleles is disturbed and consequently the physiological functions are not as efficient. For these authors, parents having a moderate genetic divergence and high per se performance can be more useful than those which have only high parental diversity. Arunachalam and Bandyopadhyay (1984) and Arunachalam et al. (1984), using mean and standard deviation from divergence values given by D2, delineated divergence classes demonstrating that the frequency of heterotic crosses and the magnitude of heterosis for yield and its components were higher in crosses between parents in intermediate divergence classes than in extreme ones.

The best performing hybrids with regard to WSWP and WSWF were those involving ICS 1, the most divergent cultivar of all (Table IV). ICS 1, according to Dias and Kageyama (1995), has a high general combining ability for WSWP and WSWF. This suggests a relationship between combining ability effects and genetic divergence of parents. Positive relationships between parental distance and combining ability effects has been found by Moll et al. (1962), in corn; by Gupta et al. (1991), in brown mustard [Brassica juncea L. (Czern and Coss)]; by Arunachalam et al. (1984) in groundnut (Arachis hipogaea L.), and by Shamsuddin (1985), in spring wheat (Triticum aestivum L.). Also, the cross of CEPEC 1 and SIC 19, the second most similar pair, produced F1 hybrids of mediocre performance (Table IV).

The relationship between divergence of S1 parents, expressed by D2, and average performance of crosses was quantified (Table IV). The correlations were high for characteristics which best reflect the commercial cacao yield, as for example WSWP and WSWF. The stability of yield components across years and the advanced age of cacao trees may reinforce this relationship. The notion of stability can be provided by the repeatability coefficient which reflects the consistency of the measurement of the components over the years. Repeatability estimates considering only cultivars, using mean squares values from Table I, were above 0.76 for all components, except PDFP. Smith and Smith (1989) chose morphological traits for multivariate genetic divergence studies which had repeatability estimates above 0.50. Also, the repeatability sets an upper limit to the degree of genetic determination and to the heritability (Falconer, 1960). Consequently, the estimated divergence between the pairs of parents in this study is due more to genetic than environmental differences. In addition, the cacao trees were 11 years old when this study started and 15 years old when it finished. Hence, it was evident that the yield stability had been already achieved, therefore allowing a consistency of performance over the years. Young cacao trees, under cultivation, begin to fruit about the 4th year. By the 8th or the 10th year of planting, the trees express all their productive potential. Hence, Bartley (1970) proposed starting the selection of cacao trees from the 8th year of planting.

The correlation of heterotic performance of hybrids with D2 and WSWP (Table V) was similar to the correlation between average performance of the same character and D2 (Table IV), and equal to WSWF (Table V). Wet seed weight per plant (WSWP) and per fruit (WSWF) are considered the best estimators of commercial cacao yield (Kuppers, 1953). Average performance and heterosis have been found to be associated with the genetic divergence by characteristics related to yield and its components, in several crop species (Moll et al., 1962; Ghaderi et al., 1984; Shamsuddin, 1985; Cruz, 1990; Ali et al., 1995).

The positive linear association between genetic distance and heterosis depends on the presence of dominance effects and/or of differences in the frequency of the alleles controlling the character considered (Ghaderi et al., 1984; Ali et al., 1995). This association is based on the biometrical concept of heterosis given by Falconer (1960), illustrated for a single gene case. An analysis for a single gene multiallelic case was provided by Cress (1966). However, an analysis involving two gene systems has shown the role of epistatic interactions in causing heterosis. Arunachalam (1977) demonstrated that for characters governed by more than one gene, it is possible to produce heterosis from pure additive gene action coupled with a favourable additive x additive interaction, since the gene frequency differences are ensured. In our case, for the same diallel, the relative importance of the non-additive genetic effects over the additive effects was shown for NHFP, NCFP and WSWP. On the other hand, additivity held for WSWF (Dias and Kageyama, 1995).

The term heterosis, as employed herein, refers to the difference between the F1 hybrid mean and the mid-S1 parent value. This is due to the structure of the cacao hybridization program. Although the parents of hybrids can be propagated clonally, the hybrids resulting from the crosses were multiplied by seed, so that comparisons were made among genotypes propagated only by seed, and hybrids were placed in trials with their selfed parents. In cacao, the phenomenon of heterosis for yield and its components has been demonstrated, based on comparison of hybrids over their selfed parents (Russel, 1952; Atanda, 1973).

Our S1 parental clones appear to have low or no inbreeding depression. Dias and Kageyama (1995) analyzed the same diallel over the same period with the inclusion of S1 parents and argued that the analysis using only hybrids, without parents, did not alter combining ability effects. We are able to use only self-compatible clones whose relative homozygosis makes them less depressive parents. This has been demonstrated in other studies reviewed by Dias and Kageyama (1995) involving ICS 1, SIAL and Catongo cultivars. Analysis of the stand is another means to assess inbreeding depression of S1 parents, since inbreeding depression is commonly expressed in cacao as low vigor and high mortality. In 1990, the last year of the study, the average stand ranged from 13.2 to 16.0-plant plots. Finally, if we were to adopt a wet to dry conversion rate of 40%, commonly done in the literature, we would have a yield of 1879.8 kg . ha-1 . year-1 for hybrids and 1208.8 kg . ha-1 . year-1 for S1 parents. This result means that parents yielded only 35.7% less than their hybrids and 61% more than the regional mean cacao yield.

CONCLUSIONS

The Trinitario group was shown to consist of highly heterogeneous populations, with close relationship to the Lower Amazon group, suggesting that a classification considering the genetic relationships between cacao racial groups is required. In addition, the association between average performance of hybrids and divergence between S1 parents expressed by D2 was high for several traits reflecting components of commercial cacao yield. High correlations were observed between D2 and WSWP and between D2 and WSWF. The heterotic performance of WSWP and WSWF was also correlated with D2.

Publication supported by FAPESP.

RESUMO

Distâncias genéticas entre cultivares de cacau foram calculadas através de análise multivariada, empregando-se a estatística D2, objetivando examinar a classificação dos grupos raciais e acessar híbridos heteróticos. Um dialelo completo 5 x 5 foi avaliado. Cinco cultivares da geração S1, pertencentes aos grupos Forasteiro do Baixo Amazonas e Trinitário, e os 20 híbridos entre os correspondentes cultivares S0 foram analisados com base em cinco componentes de produção - número de frutos sadios e colhidos por planta (NHFP e NCFP), peso de sementes úmidas por planta e por fruto (WSWP e WSWF) e percentagem de frutos doentes por planta (PDFP) - por cinco anos (1986-1990). A análise de diversidade sugeriu estreita relação entre Trinitários e Forasteiros do Baixo Amazonas. A associação entre diversidade genética e heterose dos híbridos foi avaliada pelo coeficiente de correlação (r). A distância genética entre os cultivares, dada por D2, mostrou-se linearmente associada com a performance média dos híbridos para WSWP e WSWF (r = 0,68; P < 0,05 e r = 0,76; P < 0,05, respectivamente) e com a performance heterótica para os mesmos componentes (r = 0,66; P < 0,05 em ambos os casos). Uma relação positiva entre distância genética dos cultivares e efeitos de capacidade de combinação foi sugerida. Os resultados indicaram que as estimativas de diversidade genética podem ser úteis na seleção de genitores para cruzamentos e no estabelecimento das relações entre grupos raciais de cacau.

REFERENCES

Ali, M., Copeland, L.O., Elias, S.G. and Kelly, J.D. (1995). Relationship between genetic distance and heterosis for yield and morphological traits in winter canola (Brassica napus L.). Theor. Appl. Genet. 91: 118-121.

Arunachalam, V. (1977). Heterosis for characters governed by two genes. J. Genet. 63: 15-24.

Arunachalam, V. and Bandyopadhyay, A. (1984). Limits to genetic divergence for occurrence of heterosis - experimental evidence from crop plants. Indian J. Genet. Plant Breed. 44: 548-554.

Arunachalam, V., Bandyopadhyay, A., Nigam, S.N. and Gibbons, R.W. (1984). Heterosis in relation to genetic divergence and specific combining ability in groundnut (Arachis hipogaea L.). Euphytica 33: 33-39.

Atanda, O.A. (1973). Heterosis in crosses of Theobroma cacao. Exp. Agricult. 9: 23-29.

Bartley, B.G.D. (1970). Yield variation in the early productive years in trials with cacao (Theobroma cacao L.). Euphytica 19: 199-206.

Bekele, F.L., Kennedy, A.J., McDavid, C., Lauckner, F.B. and Bekele, I. (1994). Numerical taxonomic studies on cacao (Theobroma cacao L.) in Trinidad. Euphytica 75: 231-240.

Bhatt, G.M. (1973). Comparison of various methods of selecting parents for hybridization in common bread wheat (Triticum aestivum L.). Aust. J. Agric. Res.24: 457-464.

Cheesman, E.E. (1944). Notes on the nomenclature, classification and possible relationships of cacao populations. Trop. Agric. 21: 144-159.

Cress, C.E. (1966). Heterosis of the hybrid related to gene frequency differences between two populations. Genetics 53: 269-274.

Cruz, C.D. (1990). Aplicação de algumas técnicas multivariadas no melhoramento de plantas. Doctoral thesis, ESALQ/USP, Piracicaba, SP.

Dias, L.A.S. (1995). Biotecnologia e melhoramento genético do cacaueiro (Theobroma cacao L.). Agrotrópica 7: 1-14.

Dias, L.A.S. and Kageyama, P.Y. (1995). Combining ability for cacao (Theobroma cacao L.) yield components under southern Bahia conditions. Theor. Appl. Genet. 90: 534-541.

Engels, J.M.M. (1983). A systematic description of cacao clones. III. Relationships between characteristics and some consequences for the cacao breeding. Euphytica 32: 719-733.

Falconer, D.S. (1960). Introduction to Quantitative Genetics. The Ronald Press, New York.

Ghaderi, A., Adams, M.W. and Nassib, A.M. (1984). Relationship between genetic distance and heterosis for yield and morphological traits in dry edible bean and faba bean. Crop Sci. 24: 37-42.

Gupta, V.P., Sekhon, M.S. and Satija, D.R. (1991). Studies on genetic diversity, heterosis and combining ability in Indian mustard [Brassica juncea L. (Czern & Coss)]. Indian J. Genet. Plant Breed. 51: 448-453.

Harris, R.J. (1975). A Primer of Multivariate Statistics. Academic Press, New York.

Kuppers, J.R. (1953). Some biometric observations on cacao fruit. Science 117: 354-355.

Lanaud, C. (1986). Utilisation des marqueurs enzymatiques pour l’etude génétique du cacaoyer: Theobroma cacao L. II. Etude du polymorphisme de six systèmes enzymatiques. Café Cacao Thé 30: 271-280.

Lanaud, C., Laurent, V., N’Goran, J., Risterucci, A.M., Bouet, A. and Sounigo, O. (1993). Assessment of the genetic diversity of cocoa using biochemical and molecular markers at CIRAD. In: International Workshop on Conservation, Characterisation and Utilization of Cocoa Genetic Resources in the 21st Century, CRU/University of West Indies, Port-of-Spain, Trinidad, pp. 163-175.

Laurent, V. (1993). Etude de la diversité génétique du cacaoyer (Theobroma cacao L.) basée sur le polymorphisme de la longueur des fragments de restriction (RFLP). Doctoral thesis, Université de Paris, Paris.

Moll, R.H., Salhuana, W.S. and Robinson, H.F. (1962). Heterosis and genetic diversity in variety crosses of maize. Crop Sci. 2: 197-198.

N’Goran, J.A.K., Laurent, V., Risterucci, A.M. and Lanaud, C. (1994). Comparative genetic diversity studies of Theobroma cacao L. using RFLP and RAPD markers. Heredity 73: 589-597.

Prasad, S.K. and Singh, T.P. (1986). Heterosis in relation to genetic divergence in maize (Zea mays L.). Euphytica 35: 919-924.

Raboin, L.M., Paulin, D., Cilas, C. and Eskes, A.B. (1993). Analyse génétique de quelques caractères quantitatifs des fleurs du cacaoyer (Theobroma cacao L.). Leur intérêt pour l’évaluation de la diversité de l’espèce. Café Cacao Thé 37: 273-282.

Ramanujam, S., Tiwari, A.S. and Mehra, R.B. (1974). Genetic divergence and hybrid performance in mung bean. Theor. Appl. Genet. 45: 211-214.

Rao, C.R. (1952). Advanced Statistical Methods in Biometric Research. John Wiley, New York.

Ronning, C.M. and Schnell, R.J. (1994). Allozyme diversity in a germplasm collection of Theobroma cacao L.. J. Heredity 85: 291-295.

Russel, T.A. (1952). The vigour of some cacao hybrids. Trop. Agric. 29: 102-106.

Shamsuddin, A.K.M. (1985). Genetic diversity in relation to heterosis and combining ability in spring wheat. Theor. Appl. Genet. 70: 306-308.

Smith, J.S.C. and Smith, O.S. (1989). The description and assessment of distances between inbred lines of maize. II. The utility of morphological, biochemical, and genetic descriptors and a scheme for the testing of distinctiveness between inbred lines. Maydica 34: 151-161.

Steel, R.G.D. and Torrie, J.H. (1980). Principles and Procedures of Statistics. McGraw-Hill, New York.

Turner, H.N. and Young, S.Y. (1969). Quantitative Genetics in Sheep Breeding. Cornell University Press, Ithaca.

(Received August 28, 1995)

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