Heritability and correlation among potato tuber traits

The objectives were to estimate variance, co-variance and heritability components of potato tuber shape and fresh weight and the correlation among these traits in the early generations of selection. Seed and harvested tubers of nine progeny were evaluated for length, larger and smaller diameter and fresh weight. In average, the tubers were lengthy, because the relationship between lenght with larger diameter was 1.30 and with smaller diameter was 1.51. High heritability estimations were gotten for progeny selection, and low heritability for clone selection in the progeny. Heritability estimations got from correlation between generations were high and similar to progeny mean estimations. The tuber shape and fresh weight traits were highly correlated. The breeding gain can be maximized combining the selection among and within progeny to early discard undesirable clones.


INTRODUCTION
Potato (Solanum tuberosum L.) is the fourth crop in the world, after wheat, rice and maize, with a production of 315.1 million tons in 2006 (http://www.fao.org/).In Brazil, potato is the most important horticultural crop, with 142,300 ha, producing 3.38 million of tons.The average was 23.7 t ha -1 in 2007 (http://www.ibge.gov.br/home/).The main producing States are Minas Gerais, Paraná, São Paulo and Rio Grande do Sul, responsible for 87% of the nationwide production (http://www.ibge.gov.br/home/).
Potato is an asexually propagated crop by tubers, which are underground and modified stems.Tubers are also stock pile organs, mainly starch, and show dormancy right after harvesting.The dormancy level greatly varies among cultivars, growing and storage conditions and tuber physiological age at harvest (Beukema andVan Der Zaag 1990, Bisognin et al. 2008).Breaking dormancy is necessary in the first clone generations of selection, because of the limited number of small tubers, which have higher levels of dormancy (Beukema andVan Der Zaag 1990, Bisognin et al. 1998), to minimize clone discard, due to either no or late plantlet emergence.
In the potato breeding program, usually have a generation of tuber family production from botanic seeds, followed by generations of clone selection in the field.The first generation is usually in single-hill plots, followed by clone generations of plots with variable and increasing number of hills (Bisognin 2003) to phenotypic select clones.In the first generation of selection, a large number of clones can be discarded, which reduces costs and facilitate the identification of superior clones to introduce in the crossing block (Thill and Peloquin 1995).If the purpose is to combine characters by recurrent selection, an evaluation and selection strategy to identify desirable clones should be developed and applied as soon as possible in the breeding program (Bisognin and Douches 2002).
Evaluating clones in different generations of selection or growing conditions make possible to estimate genetic parameters, such as heritability and selection gain, to identify the best breeding strategy (Bisognin and Douches 2002).The breeding strategy can also be based upon the percentage of selected clones, the correlation between generations and the expected gain in different selection indexes.The ideal selection index to get a balance between the expected gain and the discard of valuable clones in any generation can be adjusted by simulations (Bisognin 2003).

NOTE
The genetic parameters can also be estimated by components of variance.The expected mean squares can be gotten for a given model by deducing them from the expressions of mean squares and applying mathematical properties and assumptions made about the parameters of the model, or by using the modified Hicks method (Barbin 1998).The mean value of square (or mean products) with their mathematical assumptions are the estimations of variance (or covariance) components.These estimations can be used to compute the correlation coefficients and the heritability of a given trait (Vencovsky and Barriga 1992).The correlation estimations between traits indicate the possibility of indirect selection, which is also important to define the best breeding strategy.
The objectives were to estimate variance, covariance and heritability components of potato tuber shape and fresh weight and the correlation among these traits in the early generations of selection.

MATERIAL AND METHODS
The experiment was carried out in the experimental field of the Plant Science Department of the Federal University of Santa Maria (UFSM), in Santa Maria, Rio Grande do Sul State, Brazil.Clones representing nine progenies of the Potato Breeding and Genetics Program were evaluated.The first generation was planted on March 14 th , 2006.One tuber of each harvested clone was planted on August 25 th , 2006, for the second generation.The experiment of both generations was a random design, with one replication of a single-hill plot.Six harvested tubers of each clone of the second generation were planted on March 15 th , 2007, for the third generation.The experiment was a random design, with two replications of three-hill plots.
All tuber seeds were sprayed with 30 mg L -1 of gibberellic acid (Benedetti et al. 2005), approximately 60 days prior planting, and stored at 25 ºC for dormancy breaking.One seed tuber was planted in each hill.The hills were 0.30 m apart in the row and 0.80 m between rows.At harvest, data was recorded separately for each hill.All seed and harvested tubers were evaluated for length (L), larger diameter (LD) and smaller diameters (SD) and fresh weight (FW).The following tuber relationships were estimated: LLD = L/ LD and LSD = L/SD.Data from third generation were used to estimate variances, covariances and its components.For data analysis, J = 2 replications, I = 9 progenies, K = 3 hills per plot, and n = number of harvested tubers per hill.The mathematical model was characterized by Y ijkl = m + t i + e ij + d k(ij) + e l(ijk) ; where Y ijkl = the observed value of the tuber l of the hill k of the progeny i of the replication j; m = the average; t i = the random effect of the progeny i; e ij = the random effect of the experimental error ij; d k(ij) = the random effect of the hill k in the plot ij; and e l(ijk) = the random effect of the tuber l in the hill ijk.For the analysis of variance (Table 1), the number of the tubers per hill (n) and the number of the hills per plot were as a harmonic mean, considering the two replications.
For each of the traits (L, LD, SD, FW, LLD, and LSD) we estimated the mean coefficient of heritability (h² m ) for average progeny selection.Also, we estimated the linear correlation coefficient between progeny averages of two consecutive generations (Bisognin and Douches 2002).Therefore, the average of the nine harvested progenies in the first generation was correlated with the same harvested progenies in the second generation (r 12 ), and between the second and the third generation (r 23 ).
The values of MP1, MP2, MP3 and MP4 corresponded to the mean products defined in Table 2.The estimations of variance and covariance components were used to estimate the linear correlation coefficients (Pearson) between all the pairs (x and y) of traits (r xy ) with the expressions r gxy = sĝ xy /( sˆg x * sˆg y ), for progenies; r exy = sˆe xy /( sˆe x * sˆe y ), for plots; r dxy = sˆd xy /( sˆd x * sˆd y ), for hills; and r xy = sˆx y /( sˆx * sˆy ), for tubers.All the statistical analyses were done with the NTIA (Embrapa 1997) and Excel softwares.

RESULTS AND DISCUSSION
In average, the tubers showed a slightly long shape, because of the ratio between length and larger diameter was 1.297 and with the smaller diameter was 1.512 (Table 3).Therefore, tubers were 29.7% longer than the larger diameter and 51.2% longer than the smaller diameter.These results are important for selection; because of tuber shape is an indication of cultivar purpose.Cultivars with long tubers are suitable for french fry processing and round tubers for chip processing.In this case, there was variation for tuber shape, being predominant the long-shape type.
The variance among progenies was significant at 5% level for all individual and ratios between tuber traits (Table 3), with the exception of the smaller diameter.Also, there were differences among hill variance estimations for individual and ratios of a given trait.The mean square errors among hills were higher than among plots for all evaluated traits.This resulted in negative estimation of variance components among plots.These negative estimations can be explained by the fact that potato is planted in hills and/or three-hill plot was not representative for this experiment.In this case, plot size of one hill would increase replication number and experimental precision (Barbin 1998).
Heritability estimates for selecting clones were low ( 2 i h 0.27 ≤ ) (Table 3).However, heritability estimates for selecting progeny were high ( 2 m h 0.50 ≥ ).In general, rations between traits had higher estimations of heritability than individual traits, which were expected, because of the lower experimental error.Some of the heritability values for selecting progeny ( 2 m h ) estimated by components of variance were a little bit higher than the ones estimated by correlation between generations.As expected, the estimations of heritability also varied when data from different generations were correlated (r 12 or r 23 ).
The heritability estimate for tuber fresh weight ( 2 m h 0.79 = ) to select progeny was the same found by Rodrigues and Pereira (2003).We could not compare the heritability estimations of the other evaluated traits.However, we found different heritability estimations for other tuber traits.For reducing sugar content, the heritabilities varied from 0.32 (Salamoni et al. 2000) to 0.51 in spring and 0.73 in autumn (Chalá et al. 2001).For dry matter content, the heritabilities varied from 0.38 (Salamoni et al. 2000) to 0.72 (Rodrigues and Pereira 2003).Heritability estimates of 0.49 and 0.87 were found respectively for chip color and tuber number (Rodrigues and Pereira 2003).Heritability of 0.64, for tuber size (Silva et al. 2008a), and between 0.49 and 0.69, for skin smoothness (Silva et al. 2008b), were also estimated.
The estimation of heritability by correlation between generations (r 12 and r 23 ) express the heritability ( 2 m h ) for selecting progenies (Venkovsky and Barriga 1992, Bisognin and Douches 2002, Andreu 2005).In this work, we found similar estimations between second and third generations with the method of variance components in the third clone generation, with two replications of three-hill plots.This similarity of estimations  The correlation coefficients between tuber shape and fresh weight were highly and directly associated (Table 4).Interesting is that high correlations between the traits were also found among hills, exactly the way we select clones in the first generation in the field.Therefore, we can establish an indirect selection program for these tuber traits.The smallest correlation (0.348) was between length and smaller diameter, which is also important.Therefore, we would get selection gain in this group of clones for both long shape, for french fry processing, and round shape, for chip processing, cultivars.
The results of this work indicated that fresh weight and tuber shape traits can be selected in the first genera-tion of the potato breeding program.This generation is usually conducted in single-hill plots, the same way we also conducted the second generation.As the heritability estimations based upon data set from second and third generations (r 23 ) were quite high ( 2 m h 0.32 ≥ ), the gain from selection would be also high in the single-hill plot generation.The correlation analysis between generations gave a good estimation of the heritability, similar to the variance components.Therefore, data set from field evaluations of a high number of clones can be used to estimate the heritability and the gain from selection to identify the best breeding strategy.Considering that heritability estimations for clone selection were smaller than progeny selection, we should select the best progeny and discard only the less desirable clones in each selected one.As tuber shape and fresh weight were highly and directly correlated, applying selection for any of these characters would result in genetic gain for the others, which facilitates the breeding process.The breeding gain can be maximized combining the selection for tuber shape and fresh weight among and within progeny to early discard undesirable clones.

CONCLUSIONS
Potato tuber shape and fresh weight have higher heritability estimations for progeny selection.These traits are also highly correlated and indicated for indirect selection.The breeding gain can be maximized combining the selection among and within progeny to early discard undesirable clones.

Table 1 .
Summary of the variance analysis *J = number of replications; I = number of progenies; K = number of hills/plot; n = harmonic average of the number of tubers/hill.

Table 3 .
Summary of the analysis of variance, estimates of the components of variance and heritability for length (L), larger (LD) and smaller diameter (SD), and fresh weight (FW) of potato tubers and estimates of linear correlation coefficients between first and second generations (r 12 ), and second and third generations (r 23 ) the two methods is very important, because we can get the necessary data set directly from the breeding program without any specific experiment, as necessary to estimate the components of variance. between

Table 4 .
Mean products of the covariance analysis, estimates of covariance and coeficients of correlation between length (L), larger diameter (LD) and smaller diameter (SD) of potato tubers