Introduction

A potato genetic improvement program (Solanum tuberosum L.) will target the yield potential, stability and resistance to Phytophthora infestans. The yield potential considered as a quantitative variable is an overly complex physiological process that is determined by genotype, environment and genotype x ambient interaction (^{Vásquez 1988}; ^{Pérez et al., 2010}). Stability refers to the plant's ability to express its yield potential in a wide range of environments (^{Vásquez 2013}; ^{Lying et al., 2019}) and the resistance will be directed to the horizontal type (^{Rubio et al., 2016}). A study about the interaction of genotype x environment (IGE) for potato yield showed that all genotypes had a differential response to environmental effects (^{Vásquez et al., 2019}, ^{Tirado et al., 2018}).

In the Cajamarca Region many genotypes (clones) are sown under different environmental conditions, very marked effects of the environment on the phenotypic expression of them were observed, so the genotypic variability that is observed is due to genetic variation plus the effect of the environment (IGE), therefore should lessen the effect of IGE; through the use of suitable experimental designs and with good agronomic management (^{Vásquez et al., 2019}).

The objectives of this research were to determine the existence or non-existence of genotype x environment interaction (IGE) and its effect on tuber weight yield and total number of tubers and detect stable genotypes using the model suggested by ^{Eberhart and Russell (1966)}.

Materials and methods

Of the six environments studied, three experiments were established in the province of Cajamarca, two in the province of Chota both belonging to the Cajamarca Region and an experiment in the province of Sánchez Carrión (La Libertad Region). All installed under dry conditions (campaign 2016-2017). The characteristics of the six sites are in Table 1.

Eight potato genotypes from Baños del Inca-Cajamarca Agricultural Experimental Station (INIA) were considered. Genotypes represent the most advanced of S. andigena x S. andigena combinations and recurrent selection for five cycles (B1C1 to C1B5) and the resulting population was improved looking for resistance to P. infestans, precocity, adaptation, appearance of tubers in more defined forms, superficial eyes and commercial tubers yields higher than their close relatives (^{Gastelo et al., 2010}). The genotypes evaluated are shown in Table 2.

For the evaluation of the eight genotypes, a random complete blocks design was used with three repetitions per environment. The experimental plot was two grooves of three meters in length separated to 30 cm between strokes and 1 m between grooves. A sprouted seed was placed per knock. The weight of total tubers and the number of total tubers were assessed at harvest.

Results and discussion

In individual variance analyses, highly significant differences were found between genotypes (p<0. 01) for total yield and number of total tubers in the six environments (Santa Clotilde, Santa Margarita, Chucmar, Marcobamba, La Púcara and Chugay). Bartlett’s test indicated that the variances were homogeneous and the assumptions of normality of the errors were fulfilled (^{Vasquez, 2014}). The coefficients of variation ranged from 5. 23% to 2. 93%, considered good to give precision to the tests (^{Vásquez, 2013}). There was statistical significance (p≤ 0.01) for localities, genotypes and genotype x environment interaction (IGA) (Table 3). Heterogeneity between environments was mainly related to differences in altitude, soil type, temperatures and precipitation during the study years (Table 1).

Differences for genotypes showed the existence of genetic variability in total weight yield and number of total tubers. These results are consistent with ^{Tirado et al. (2018)} who evaluated potatoes with pigmented pulp in four environments obtaining statistical significance for environments, genotypes and IGE. IGA demonstrates that potato genotypes have different behavior in the various environments tested. These results are consistent with ^{Vásquez et al. (2019)}, who evaluated adaptation and yield of six clones in eight environments and they found differences for genotypes and for genotype-environment interaction. ^{Solomon et al. (2015)}, tested thirteen potato progenies in two environments, they found statistical significance at a 1% chance for progenies and for IGA.

Heterogeneity between environments was mainly related to differences in altitude, soil type, temperatures and precipitation during the study years (Table 1). It was noted that, the relationship between the ratio of the mean squares of genotypes and the average squares of the IGA is 57. 22, indicating greater importance of genotypes on interaction (Table 3). This demonstrates the existence of genetic variability, which let to select superior genotypes (^{Vásquez, 1988}).

According to Table 3, the environment was 2. 38% of total yield variation, genotype 87. 65% and interaction G × E 5. 76%. Based on the relative contribution of sum of squares, genotypes have a greater contribution, followed by the GxE interaction and finally the contribution of environments. For the total number of tubers, the environment represents 46.78%, genotypes 10. 31 and 25. 99% of the variation represents the IGA. These results differ with ^{Tirado et al. (2018)} and ^{Solomon et al. (2015)} who found that the largest contribution of IGE was 60.82 and 70.13%, that of the genotype of 26.03% and 10.3%.

Table 4 shows that the best environment for genotype evaluation was Chugay, Santa Clotilde and Púcara with averages 38.66, 37.16 and 37.10 t ha^-1 respectively, statistically surpassing the remaining five locations, and also surpassing regional average 14 t ha^-1 (^{MINAGRI, 2017}). No statistical differences were found between the towns Marcobamba, Chucmar and Santa Margarita, whose yields ranged from 36.98 tha^-1 to 36.24 t ha^-1 respectively.

The stability parameter model identified the town Chugay, Santa Clotilde and Pucara as the best environments to yield because the values of their environmental indices (Ij) are positive, that is to say, higher than the general average (37.11 t ha^-1). Environments with bad behavior were Marcobamba, Chucmar and Santa Margarita for having negative environmental indices; that is, less than the general average. For the number of total tubers, the best environments were Santa Clotilde, Marcobamba and Santa Margarita for having their positive environmental indices. These results are higher than those obtained by ^{Gastelo et al. (2010)} who evaluating these genotypes in four locations in Puno, achieved average yields ranging from 18 to 28 t ha^-1.

Stability parameters

1% probability significance was found for genotypes and G x Amb (linear) for tuber weight and total number of tubers (Table 5). No significance was found for joint deviation for the two variables in the eight genotypes. Differences between genotypes can detect those with better genetic potential. The significance of genotype x environmental interaction (linear) reveals that there is a changing differential response of genotypes through environments for the response variables studied. This suggests that it is possible to select genotypes with better genetic potential and stability in a number of environments as ^{Eberhart and Russell (1966)} point out. It should be noted that, in the average yield of the 8 genotypes, variation in productive potential was observed. This result considers the importance of conducting experiments in time and space, to observe the response of varieties and genotypes under different environmental conditions (^{Becker and León, 1988}; ^{Vásquez, 1988}; ^{Fikere et al., 2008}).

Conclusions

The highly significant differences observed between genotypes, between localities and their interaction (IGA) suggest that there is sufficient genetic variability to select outstanding genotypes, that the environments of the Cajamarca region are heterogeneous and that significant IGA makes it difficult to identify stable genotypes.

The best environmental indices for tubers weight and number of total tubers were in Santa Clotilde, La Púcara, Marcobamba and Santa Margarita, located in Cajamarca and Chota. The Ebarhart and Russell model identified the genotypes: 399062.115 (4), 393377.159 (5) and 396012.266 (3) with 46.01 t ha^-1, 42.01 t ha^-1 and 38.66 t ha^-1 above average (37.11 t ha^-1) and with bi= 1, s²di= 0, considered as stable genotypes. Genotype 399062.115 (4) for total number of tubers had a regression coefficient of bi= 1 and a regression deviation s²di= 0 considered a stable genotype.