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Published online 24 June 2005
Published in Crop Sci 45:1491-1496 (2005)
© 2005 Crop Science Society of America
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CROP BREEDING, GENETICS & CYTOLOGY

Epistasis in Cassava Adapted to Midaltitude Valley Environments

J. C. Péreza, H. Ceballosa,b,*, G. Jaramilloa, N. Morantea, F. Callea, B. Ariasa and A. C. Bellottia

a International Center for Tropical Agriculture (CIAT), Apartado Aéreo 6713, Cali, Colombia
b Univ. Nacional de Colombia, Carrera 32, Chapinero vía Candelaria, Palmira, Colombia

* Corresponding author (h.ceballos{at}cgiar.org)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Little is known about the inheritance of agronomic traits in cassava (Manihot esculenta Crantz). The vegetative multiplication of cassava allows cloning of individual genotypes, and separates environmental from genetic variation in the within-family variation. Knowing the magnitude of between- and within-family variation is important for defining breeding strategies and for measuring different components of genetic variances, particularly the seldom-estimated epistasis. A group of nine genotypes, adapted to midaltitude environments, was used for a diallel study. Thirty clones were obtained from every F1 cross (each clone was represented by six plants), and planted in three replications at two locations. Statistical differences among crosses were found for fresh-root yield, harvest index, root dry-matter content, and reaction to mites (Mononychellus tanajoa Bondar) and to whiteflies (Aleurotrachelus socialis Bondar). General combining ability (GCA) was significant for all traits except fresh-root yield and dry-matter content, and specific combining ability (SCA) was significant for all traits except whitefly damage score. Fresh-root yield was the only trait with significant epistatic effects, which, combined with a large dominance variance, suggested a prevalence of nonadditive effects. The introduction of inbreeding would be one approach for the efficient exploitation of these nonadditive effects found for fresh-root yield. For the remaining traits, epistasis was negligible and current schemes exploiting additive effects may suffice.

Abbreviations: GCA, general combining ability • SCA, specific combining ability


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
CASSAVA, ALONG WITH MAIZE (Zea mays L.), sugarcane (Saccharum spp.), and rice (Oryza sativa L.), constitutes the most important source of energy in the diet of most tropical countries of the world. Cassava is the fourth most important basic food after rice, wheat (Triticum aestivum L.), and maize, and is a fundamental component in the diet of millions of people (FAO/FIDA, 2000). Scott et al. (2000) estimated that for the 1995–1997 period, annual production of cassava was about 165.3 million Mg, with a value of approximately $8.8 billion (U.S.). Recent studies suggest that cassava is not only a reliable source of energy, but it can also be bred for enhanced nutritional quality, for example, for micronutrients and proteins (Chávez et al., 2005; CIAT, 2004, Chapter 9, p. 4–8).

Only a few articles relative to the inheritance of quantitative traits in cassava have been published (Easwari et al., 1995; Easwari and Sheela, 1998; Losada, 1990). Cassava's situation is unique in that, while a molecular map has already been developed (Fregene et al., 1997; Mba et al., 2001), knowledge on traditional genetics lags behind.

Cassava is an interesting crop because its vegetative propagation allows the estimation of within-family genetic variation and, indirectly, the relative importance of epistatic effects. Genetic studies analyzing the importance of epistatic effects are not very common, particularly in annual crops. Adequate measurement of epistatic effects for complex traits, such as yield, is difficult and expensive. Reports on the relevance of epistasis are infrequent and have generally taken advantage of the vegetative multiplication that some species offer (Comstock et al., 1958; Stonecypher and McCullough, 1986; Foster and Shaw, 1988; Rönnberg-Wästljung et al., 1994; Rönnberg-Wästljung and Gullberg, 1999; Isik et al., 2003). In many cases, these reports are on forest trees. Because of the complexities of these analyses and the costs involved, reports in the literature related to epistatic effects are frequently based on a limited sample of genotypes, which consequently may result in contradictory or unreliable results.

The objective of this study was to measure the within-family genetic variation in a diallel study conducted in two midaltitude valleys environments to determine the relative importance of epistatic and other genetic effects on the expression of several relevant traits of cassava.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
A diallel mating design was used to generate F1 crosses among nine parents. The analysis of between-family variation was published elsewhere (Jaramillo et al., 2005). The inbreeding level of parental lines was considered negligible because no self-pollination has been involved in cassava breeding, and crosses among related clones are generally avoided. Controlled pollinations were made following the standard procedures described by Kawano (1980).

Many parental clones were initially involved, but the parents ultimately used (as well as the number of parents involved) were those that allowed for a balanced set of crosses. MECU 72 (a landrace from Ecuador) was one of the parents and has host-plant resistance to the whitefly (Bellotti et al., 1999; Bellotti and Arias, 2001). Botanical or true seed obtained from the crosses made were germinated and grown in a screen house until the seedlings were 2 mo old, when they were transplanted to the field at CIAT experimental station in Palmira, Valle del Cauca, Colombia (Jaramillo et al., 2005). The F1 plants were grown in the field for 10 mo. Among the many genotypes (>30) from a given F1 cross, 30 were randomly chosen for this study based solely on their capacity to produce at least six good quality vegetative cuttings. This minor selection was unavoidable at this stage. These factors determined the group of genotypes representing each F1 cross in this study. Three stakes were planted in three replications at one location and the other three stakes were planted at the second location in three replications.

Trials were planted during August 2001 in two contrasting midaltitude valley locations in the Valle del Cauca Department, Colombia: Jamundí and Palmira (Jaramillo et al., 2005). The whitefly is a frequent problem for cassava fields in the Cauca and Valle del Cauca Departments. In the case of Jamundí, there was severe whitefly pressure during the evaluation of the diallel study. In the case of Palmira (CIAT Experimental Station), the life cycle of the fly was interrupted every year by eliminating cassava for a period of a month. As a result, very little A. socialis pressure existed during the evaluation of the diallel set at this station.

Plants were hand harvested individually. The roots produced by each plant, as well as the aboveground biomass (stem and foliage), were weighed. Harvest index was measured as the ratio between root weight and total biomass. Root dry-matter content was estimated using the specific gravity methodology (Kawano et al., 1987).

Reaction to mites, whiteflies, plant type or architecture, and general root appearance were scored using a 1-to-5 scale (1 = resistant or excellent and 5 = susceptible or very poor). The plant type score took into account several important characteristics, such as plant vigor, erectness with few branches and reduced branching angle, adequate capacity to produce vegetative cuttings, amount of foliage present at harvest time, and absence of foliar diseases (which in this particular environment were not frequent).

Statistical Model
An ANOVA was conducted following the expectations for each mean square (Table 1). The total genetic variance was partitioned into between-family variation and within-family variation . The between-family variation, in turn, was partitioned into the well-known variances related to general and specific combining ability, which allowed the estimation of {sigma}2A and {sigma}2D (Griffing, 1956; Hallauer and Miranda Fo, 1988, p. 45–114; Mullin and Park, 1992):

[1]
where Cov.HS = covariance of half sibs and Cov.FS = covariance of full sibs.


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  		Table 1. Analysis of variance and expected mean squares for a nine-parent diallel design in which the 30 cassava genotypes representing each F1 cross were clonally propagated.

 
Genetic parameters were estimated using the following mean squares (MS) from Table 1:

[2]
Variance for these estimates were calculated as follows (Becker, 1985, p. 95–96.; Vega, 1987):

[3]
In the above equations, r = number of replications; a = number of environments, k = number of genotypes per F1 cross; and p = number of progenitors in the diallel mating design. As is commonly the case, a few plants died or failed to develop normally to be harvested. Therefore, in a few F1 crosses, less than 30 clones were actually evaluated in the field in each of the three replications at the two locations. Venkovsky and Barriga (1992) suggested that, to take into consideration this lack of uniformity, the harmonic (not the arithmetic) mean should be used as k (number of clones representing each F1 cross).

In this evaluation, in addition to the usual between-family variation, the vegetative propagation of cassava allowed the analysis of the within-family variation. By cloning individual genotypes, they could be planted in two locations with three replications in each location, making it possible to partition the within-family variation into its genetic , genotype x environment , and the environmental error components, as illustrated in Table 1.

The within-family analysis allowed us to obtain information on the relative importance of epistatic effects. In the absence of epistasis, the equation is (Hallauer and Miranda Fo, 1988, p. 45–114; Mullin and Park, 1992)

[4]
The variance for this test is expected to be large (Hallauer and Miranda Fo, 1988, p. 45–114) because of the complexity of this linear function. The variance was estimated following the principles established in the literature (Lynch and Walsh, 1998, p. 558–563, 813–816; and Isik et al., 2003):

[5]
However, since Cov = 0 and 4 Cov = 0, the formula can be simplified as

[6]
The last term in the equation can be estimated as

In the above equation,

Therefore,

Equation [6] can now be written as follows:

The estimates of additive and dominance variances are overestimated because they contain portions of epistatic variances (Eq. [1]).

In the analysis of between-family variation (Jaramillo et al., 2005), genetic effects, rather than genetic variances, were of interest (fixed effects). In the present study, however, the analysis of within-family variance and the relative importance of epistatic effects are of prime interest. All effects, therefore, were considered random and normally distributed. The 30 genotypes representing each F1 cross were considered a random sample of all the possible genotypes that could be derived from the respective parents and account for most of the degrees of freedom in the analysis. The only criterion for including a genotype was its capacity to produce six stakes in environmental conditions that would be somewhat different from the target environment where the evaluation was to be conducted. The parents involved in this study came from a group of 25 to 30 clones; the actual nine parents eventually used were those that allowed for a balanced set of progenies for the study. Therefore, the main criterion for the selection of the parental lines was their capacity to flower and produce adequate samples of botanical seed from many different crosses. The ANOVA for the between-family variation followed Griffing's Method 4 (only one set of F1 crosses evaluated; no reciprocals) (Griffing, 1956; Mullin and Park, 1992).

The usual assumptions for Method 4 analysis are (i) regular diploid behavior during meiosis; (ii) absence of cytoplasmic effects; (iii) linkage equilibrium, relatives are random members of a specified population; and (iv) because of the vegetative propagation of cassava, negligible C-effects (Libby and Jund, 1962). In the case of cassava, C-effects (resulting from differences in the physiological/sanitary status between F1 mother plants and/or among the six stakes used to clone each genotype) would be confounded with the environmental and/or genotype x environment interaction components of variation. Since the F1 plants from which the six stakes were taken had been grown in Palmira under excellent management practices, differences (if any) in the physiological/sanitary status of these vegetative cuttings are reasonably expected to be small and negligible.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Whitefly pressure was negligible at Palmira but severe at Jamundí. Because of the low whitefly pressure at Palmira, damage score from another pest (mites) could be taken there.

The coefficients of variability indicated that the experimental errors involved in this study were relatively low. Results are, therefore, reliable and the precision of the analysis acceptable.

The two locations used in the evaluation showed statistical differences for harvest index and root dry-matter content (Table 2). Statistical differences among crosses were found for all traits analyzed, except plant type. Because no genetic differences were found for plant type, it was not included any further in the analyses (Jaramillo et al., 2005). The crosses x environment interactions were also significant for the three traits analyzed in the two environments.


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  		Table 2. Combined analysis of variance for a nine-parent diallel cross evaluated across two locations (Jamundí and Palmira) in Valle del Cauca Department, Colombia.

 
Mean squares for GCA were significant for all traits except fresh-root yield and root dry-matter content. Specific combining ability mean squares were significant for all traits except whitefly score (Table 2). The relative proportion of the sum of squares for differences among F1 crosses accounted for by GCA and SCA is informative. For the scores relative to whiteflies and mites, SCA accounted for less than 15% of the F1 crosses' sum of squares. For harvest index and root dry-matter content, SCA accounted for about 35% of the F1 crosses' sum of squares. Fresh-root yield showed the highest dependency on SCA, explaining about 59% of the F1 crosses' sum of squares.

Since individual clone data have been included, the degrees of freedom involved are considerably larger (Table 2) than those reported for the between-family analysis (Jaramillo et al., 2005). In all cases, within-family genetic variation was statistically significant. The interaction between environment and the within-family genetic variation also was statistically significant for the three traits analyzed in the two locations. From the mean squares (Table 2), estimates for {sigma}2A, {sigma}2D, and the test for epistasis were obtained (Table 3) as described above.


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  		Table 3. Variances and test for epistasis from the evaluation of a diallel set combining data from two locations (Jamundí and Palmira) in Valle del Cauca Department, Colombia. Standard errors for each estimate are given in parenthesis.

 
Variance components were considered important if the standard errors were less than half of the component estimates (Isik et al., 2003). Negative estimates of variance were considered to be zero.

The reaction to whiteflies showed a very distinctive result. Most of the genetic variation was additive, and the negative estimates for dominance and epistasis suggested that these nonadditive effects were negligible. Similar results were observed for mites; additive effects were prominent, and the test for epistasis was negative. The estimate for dominance variance, however, in the case of mites, was positive and statistically significant, but still its magnitude was only about one-third of that for additive variance.

In contrast with the reaction to mites and whitefly, additive variance was negligible (compared with its standard error) for fresh-root yield (11.9 ± 24.7) and root dry-matter content (1.43 ± 1.33), but it played a more important role in harvest index (0.0029 ± 0.0015). Dominance variances were always significantly different from zero for the three traits analyzed across the two locations, with estimates about three times larger than their respective standard errors (Table 3). As noted above, the only case with nonsignificant dominance variance was for the reaction to whitefly.

The epistasis test suggested significant effects only for fresh-root yield (168.9 ± 40.2). For all the remaining traits the test for epistasis resulted in negative estimates or failed to reach statistical significance. Even when individual location data were used for estimating epistasis for harvest index and root dry-matter content, the test statistic failed to reach statistical significance (data not presented).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The consideration of random genetic effects in the analysis of this diallel study can be questioned. The number of parents (nine) and clones representing each F1 cross ({approx}30) may not be enough to properly represent the genetic variability in the reference population (cassava adapted to midaltitude valleys). However, the number of parents and clones within each F1 cross in this study required the analysis of more than 1000 genotypes in a total of six replications. Even small increases in the number of parents and/or clones within each F1 cross would result in an unmanageably large experiment. The number of F1 families and clones per cross is representative of those typically used in the clonal evaluation trials in the cassava-breeding project at CIAT (Ceballos et al., 2004, Chapter 9, p. 4–8). Any bias that may affect the conclusions in this study (including those from linkage disequilibrium), therefore, would be similar to that affecting the breeding efforts this study aims to improve. Selection of parents in this kind of study is somewhat unavoidable, as acknowledged in Costa e Silva et al. (2004), and yet the genetic effects still can be considered random.

Genetic variation has been partitioned into the additive and nonadditive genetic effects. Dominance is a measure of nonadditivity of allelic effects within loci and epistasis describes the nonadditivity of effects between loci. Simple statistical arguments suggest that epistatic interactions are likely to be important in the expression of many quantitative traits. However, current designs and analytical tools have limitations that frequently result in lack of power to demonstrate the statistical significance of epistasis (Hallauer and Miranda Fo, 1988, p. 45–114; Lynch and Walsh, 1998, p. 558–563, 813–816). In this study, a large proportion of the genetic variability was found to be within-family variation (Tables 2 and 3). These results agree with observations made during the selection in evaluation trials, where numerous crosses among elite parental lines are represented by several clones. It was surprising to find such a large variation for the within-family component for reaction to the two pests; this was mostly attributable to additive variation.

The magnitude and generalized significance of {sigma}2D highlights the importance of nonadditive genetic effects (heterosis) in this allogamous species. Only the reactions to pests showed significant estimates for {sigma}2A. In this study, fresh-root yield was the only trait showing significant conditioning by epistatic effects. This is in sharp contrast to the results from a similar study conducted in the subhumid environments (CIAT, 2003, p. 18–27) where epistasis was significant for all traits analyzed.

Few studies have found as significant epistatic effects in annual crops as grain yield for maize (Ceballos et al., 1998; Gamble, 1962; Lamkey et al., 1995; Moreno-González and Dudley, 1981; Narro et al., 2000) and other traits (McConnell and Gardner, 1979; Olatinwo et al., 1999), as well as in perennial crops (Foster and Shaw, 1988; Rönnberg-Wästljung et al., 1994). Results from this study further demonstrate the importance of epistasis in complex traits such as fresh-root yield and to expose the limitation of most quantitative genetic studies based on the assumption of negligible epistasis. These results would also help explain the difficulties in finding QTL that satisfactorily explain the phenotypic variation observed in complex traits such as yield (Kao and Zeng, 2002).

The phenotypic clonal selection used for cassava breeding takes advantage of the vegetative reproduction of the crop. In selecting outstanding clones, all genetic effects (additive, dominance and epistatic) are exploited (Ceballos et al., 2004; Mullin and Park, 1992). However, the current recurrent selection system lacks the capacity to direct genetic improvement in such a way that the frequency of favorable (within or between loci) genetic combinations is maximized. To achieve this, special efforts to design parental clones that produce better crosses are required.

According to Ceballos et al. (2004), CIAT has recently introduced modifications that allow for the estimation of GCA effects in early stages of the selection process. This, in turn, allows the implementation of the Backward GCA Selection described by Mullin and Park in 1992. Results from this study suggest that this approach would be ideal for traits such as the reaction to pests, given the importance of GCA effects and the low or negligible relevance of dominance and epistatic effects. For complex traits such as fresh-root yield, however, the prevalence of nonadditive effects suggested by this study would require a different approach. The development of clones specifically designed for their utilization as parents in breeding nurseries would be one alternative that offers interesting advantages. Introduction of inbreeding in these parental clones would facilitate the gradual and consistent assembly of favorable gene combinations, which in the current system occur just by chance. Inbreeding would also facilitate the reduction of the genetic load of this crop, which is expected to be relatively large at this point in time.

One major constraint for the introduction of inbreeding in cassava is the time required for it. The production of doubled haploids through anther or microspore culture is an interesting approach that would reduce the time required to obtain homozygous genotypes. This, in turn, will maximize the exploitation of dominance and epistatic genetic variation, which have been found to be significant in this study.


   ACKNOWLEDGMENTS
 
The technical assistance of Drs. B. Li and R. Macchiavelli for the statistical analysis is greatly appreciated.

Received for publication October 12, 2004.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 




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M. C. Rojas, J. C. Perez, H. Ceballos, D. Baena, N. Morante, and F. Calle
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