Introduction
The green or husk tomato (Physalis ixocarpa Brot. ex Horm.) is of great importance in Mexico, as 43 thousand hectares were planted in 2017, resulting in a production volume of 773 thousand tons, with an average yield of 18.1 t·ha^{1} and per capita consumption of 5.1 kg. The main producing states are Sinaloa (150,697 t), Zacatecas (89,464 t) and Jalisco (83,162 t). The total volume of national production for the same year provided an economic benefit of MXN 3.515 billion. This volume covers domestic demand, and the surpluses are exported, representing an economic benefit of USD 73.4 million. The main buyer is the US market with USD 73,346,490.00, although it is also exported to England, Holland and Spain (^{Sistema de Información Agroalimentaria y Pesquera [SIAP], 2018}).
The study of metric traits focuses on the study of variation. The basic idea is to distribute into its components the causes of the differences of several factors. The relative magnitude of these components determines the properties of a population (^{Falconer & Mackay, 2001}). Variance measures the variation in a population. Likewise, phenotypic variance (V _{ P } ) is the sum of the genetic variance (V _{ G } ), the environmental variance (V _{ E } ) and the variance of the genotypeenvironment interaction (V _{ GxE } ); that is, V _{ P } = V _{ G } + V _{ E } + V _{ GxE } . Similarly, V _{ G } is the sum of the additive variance (V _{ A } ), the dominance variance (V _{ D } ) and the interaction variance (V _{ I } ), which refers to the epistatic effect of the genes; that is, V _{ G } = V _{ A } + V _{ D } + V _{ I } .
One of the questions that often arises among geneticists working with multifactorial traits is how much of the observed variation in a population is due to genetic differences between individuals and how much is due to the environment. Therefore, heritability is quite useful, since it can be defined as the proportion of phenotypic variation that can be attributed to the genetic variation within a given population in a particular environment. Furthermore, heritability is useful for the development of animal breeds and plant varieties, as it indicates a population's potential response to artificial selection of a quantitative nature; that is, it indicates whether it is possible for a certain quantitative trait to be modified through selection (^{Klug, Cummings, Spencer, & Palladino, 2013}). In husk tomato, the most appropriate methods for its breeding are mass, halfsib family and combined halfsib selection (^{PeñaLomelí & MárquezSánchez, 1990}), which have been studied in relation to their expected response based on genetic parameters and that observed after making the selection (^{PeñaLomelí et al., 2002}).
Broadsense heritability (H) measures the contribution of V _{ G } to V _{ P }: H = V _{ G } /V _{ P } . The V _{ G } component used in the estimation of H includes all types of genetic variation in the population, not only the additive effects, and also considers that the genotypeenvironment interaction is negligible. Therefore, its estimation is not very useful for breeding programs. On the other hand, narrowsense heritability (ĥ ^{ 2 } ) is the proportion of V _{ P } due to V _{ A }: ĥ ^{ 2 } = V _{ A } /V _{ P } . Because it only considers additive effects, ĥ ^{ 2 } provides a more accurate prediction of the response to selection than H.
The coefficient of additive genetic variation (CV _{A}) is a measure that reports on the additive genetic dispersion with respect to the arithmetic mean of the trait; that is, it is a measure of the additive variance in relation to its mean within the population. The CV _{A} does not depend on units of measurement, so its values are comparable between traits of a different nature and allows comparison of the additive genetic variance of different traits in a population (^{MolinaGalán, 1992}). With this information, the expected response to the selection in different traits and populations can be compared (^{Falconer & Mackay, 2001}). The existence of genetic variation is essential for varietal improvement. The greater the genetic variance, the greater the opportunities for varietal improvement (^{Kiebre et al., 2017}), so having a measure of additive genetic variance is a valuable tool for defining the most appropriate breeding strategies.
The additive genetic correlation provides information about the nature of the relationship of two metric traits. Analyzing the correlation of variance components with yield and their level of contribution, direct or indirect, is of utmost importance (^{Talukder, Khan, Das, & Uddin, 2018}). Indirect selection refers to choosing one or more secondary traits to obtain a positive response in the primary trait or one of greatest interest. A greater genetic gain of the primary trait can be made in less time and with less effort with indirect selection when the heritability of the secondary trait is higher than that of the primary trait and there is a high correlation between the two traits (^{Hallauer, MirandaFilho, & Carena, 2010}). The efficacy of indirect selection has been demonstrated in husk tomato (^{PeñaLomelí, GuerreroRamos, RodríguezPérez, SahagúnCastellanos, & MagañaLira, 2013}).
The above indicators are normally recommended for species that have not yet been genetically improved, as it is key to know the genetic variance and heritability of the traits of interest in order to define an appropriate breeding strategy (^{Kencharahutđ, Mohanē, Shankar, & Balram, 2018}). However, empirical results have shown that genetic variance could be reduced in a population, even with only a few selection cycles (^{Hallauer et al., 2010}). Selection can be understood as the process by which parents are chosen to change the genetic properties of a population (^{Falconer & Mackay, 2001}).
There are previous studies on the estimation of variance components in husk tomato in the varieties M1Fitotecnia, product of the first selection cycle carried out in the Ixtlahualtengo variety (^{MorenoMaldonado, PeñaLomelí, SahagúnCastellanos, RodríguezPérez, & MoraAguilar, 2002}); Verde Puebla, obtained in the first in situ selection cycle in San Mateo Tecamachalco, Puebla (^{PeñaLomelí et al., 2004}), and CHF1Chapingo, which was obtained from the Rendidora variety through five mass selection cycles and one maternal halfsib family cycle (^{PeñaLomelí et al., 2008}).
The original Gema population is the result of selection towards very large fruit from F1 of the intervarietal crossing between Verde Puebla and CHF1Chapingo (^{SantiaguilloHernández, CervantesSantana, & PeñaLomelí, 2004}). After six selection cycles, the Gema variety was obtained, which is registered in the National Catalogue of Plant Varieties with registration TOM026061218 and plant breeder's title 2147 (^{Servicio Nacional de Inspección y Certificación de Semillas [SNICS], 2019}). However, more selection cycles are desired to generate other varieties, although genetic variance and heritability are likely to have decreased after the selection process. Therefore, the objective of this study was to determine if it is possible to continue with genetic improvement in the Gema population, this through ĥ ^{ 2 } , CV _{A} and additive genetic correlation.
Materials and methods
In the springsummer 2016 growing season and under irrigation conditions, the Gema population was established by transplant in the San Juan Experimental Field of Chapingo Autonomous University, located in Texcoco, State of Mexico (19° 29’ 15’’ NL and 98° 51’ 03” WL, at 2,350 masl). From this, 200 maternal halfsib families (MHSF) were derived.
The seedling nursery was located in greenhouse 25 of the Xaltepa Experimental Field of Chapingo Autonomous University (19° 29’ 32” NL and 98° 52’ 20” WL, at 2,260 masl). Sowing took place on February 18, 2017 in polystyrene trays with 200 cavities each. In black peat, two seeds per cavity were placed 0.5 cm deep and covered with the same substrate without overcompacting them. The seeds were watered and the trays were stowed and covered with plastic for four days to accelerate germination. After emergence, the trays were placed throughout the greenhouse and watering was carried out every morning.
Wet transplant was conducted in the San Martin Experimental Field of Chapingo Autonomous University (19° 29’ 52.7’’ NL and 98° 52’ 53.5’’ WL, at 2,260 masl) on March 25, 2017. Spacing was 0.3 m between plants and 1.2 m between rows, without tutoring. The 200 families were evaluated under a randomized complete block experimental design with three replications. The experimental unit was made up of a plot with 22 plants.
The variables evaluated were yield per plant (YPP, in g), weight of 10 fruits (W10F, in g), number of plants per plot (NPP), number of bags per plant (NBP) and number of fruits per plant (NFP). The number of bags per plot was calculated considering the ratio between NBP and NPP. The NFP was calculated with the YPP and W10F data: NFP = (YPPx10)/W10F. The data were taken at harvest, except for the number of bags per family, which was determined at the eighth week of transplant as the number of fruits set in that period, since a bag is a papyrus cover formed by the flower calyx that surrounds the fruit and indicates its presence. A bag or a set fruit was considered to be one with a bag size of 2 cm or more.
The genetic variance components were estimated with the model Y _{ ij } = μ + β _{ j } + f _{ i } + E _{ ij } , proposed by ^{MárquezSánchez and SahagúnCastellanos (1994)} for the analysis of variance of MHSF, where Y _{ ij } is the value of the variable in the ith family in the jth block, μ is the overall mean, β _{ j } is the effect of the jth block, f _{ i } is the effect of the ith family and E _{ ij } is the random error in the ith family of the jth block.
The format of the analysis of variance and covariance is presented in Table 1. Estimates were made assuming diploid inheritance, two alleles per locus, HardyWeinberg equilibrium, linkage equilibrium and absence of epistasis; for this, the formulas proposed by ^{PeñaLomelí et al. (2004)}, adapted to a single locality, were used.
SV^{1}  DF  MS  MCP  E (MS) 


Blocks  r1  C_{1} 

C_{1}/ M_{2}  
Families  f1  M_{1}  PCM1 

M_{1}/M_{2} 
Error  Difference  M_{2}  PCM2 


Total  rf1 
^{1}SV = sources of variation; DF = degrees of freedom; MS = mean squares; MCP = mean cross products; E (MS) = expectations of mean squares; FC = F calculation for the hypothesis that the variance of the source of variation (
Variance between families (
Additive variance (
Coefficient of additive genetic variation (CV_{A}). It was calculated with the estimated additive standard deviation (
Narrowsense heritability (ĥ
^{
2
}
). It was estimated from the mean squares of the families (M_{1}) and of the error (M_{2}) of the analysis of variance (Table 1):
1α confidence interval for ĥ
^{
2
}
(CIĥ
^{
2
}
). The lower (Ll) and upper (Ul) limits of the interval were calculated from the mean squares of the families (M_{1}) and of the error (M_{2}), the degrees of freedom of the families (df_{1}) and of the error (df_{2}) (Table 1), and the values
Confidence interval width for ĥ ^{ 2 } (CIW). It was calculated as the difference between Ul and Ll.
Heritability rate (RATE). It represents the magnitude of the CIW compared to the ĥ
^{
2
} point estimator:
Additive genetic correlation. From the mean cross products of families (MCP_{1}) and of the error (MCP_{2}) of the analysis of covariance (Table 1), the covariance was calculated for families and for each pair of traits (COV
_{
F
} ):
Using the result of the above formula, the additive covariance between two traits X and Y (COVA_{XY}) was calculated: COVA
_{
XY
}
= 4COV
_{
F
} . With the value obtained and the additive standard deviations of each pair of variables (
Phenotypic correlations. The Pearson correlation coefficient was calculated for each pair of variables with the SAS statistical package version 9.3 (^{SAS Institute Inc. [SAS], 2011}). Variance components were obtained by the VARCOMP procedure. To calculate mean cross products (MCP = SCP/DF), the sums of X  Y cross products (SCP) were obtained for families using the MANOVA option of the ANOVA procedure.
After obtaining the estimates, a comparative table was made of the results obtained from CV _{A}, ĥ ^{ 2 } , CIĥ ^{ 2 } , CIW and RATE, in contrast with previous studies carried out with husk tomato in the M1Fitotecnia, Verde Puebla and CHF1Chapingo populations (^{MorenoMaldonado et al., 2002}; ^{PeñaLomelí et al., 2004}; ^{PeñaLomelí et al., 2008}).
Results and discussion
Significant block and family effects (α = 0.05) were recorded for all traits except for W10F and NBP, which had no significant block and family effects (Table 2). Consequently, estimates of variance, coefficient of additive genetic variation, narrowsense heritability, and additive genetic correlations for NBP were not calculated. On the contrary, YPP, NFP and W10F traits were found to be highly significant for family effects (α = 0.01). This indicates that there is additive genetic variation between families for these traits (^{Shimelis, 2018}), which will be of interest to geneticists and plant breeders.
SV^{1}  DF  YPP  NBP  NFP  W10F 

Blocks  2  155,999.65**  26.80**  31.19*  254.10ns 
Families  199  22,861.99**  4.20ns  10.92**  22,889.14** 
Error  396  12,771.25  3.74  7.42  14,245.76 
Total  597  
CV  28.30  39.97  36.98  23.51 
^{1}SV = sources of variation; DF = degrees of freedom; YPP = yield per plant (g·plant^{1}); NBP = number of bags per plant; NFP = number of fruits per plant; W10F = weight of ten fruits (g); *, ** = significant with α of 0.05 and 0.01, respectively.
The CV _{A} ranged from 18.08 to 29.32 % in the three studied traits of the Gema population (Table 3). These values indicate that, for these traits, additive genetic variance can still be exploited to achieve significant gains by mass selection, since only a low response to mass selection with CV _{A} values less than 12 % has been detected in crosspollinated populations (^{Sahagún, Molina, Castillo, & Sahagún, 1991}). It is also possible to carry out genetic improvement by selection of halfsib or fullsib families, which would allow a better exploitation of the additive genetic variance, as suggested by ^{MárquezSánchez (1985)} for crosspollinated populations, and ^{PeñaLomelí and MárquezSánchez (1990)} for husk tomato.
The W10F trait had the smallest CV _{A} of the three traits (18.08 %). Given its origin, it is congruent to infer that in the Gema population it has a low CV _{A} for fruit size, since it presents little variation. According to ^{Falconer and Mackay (2001)}, recurrent selection tends to decrease genetic variance as well as the response to selection. The YPP and NFP traits did not suffer a reduction in their additive variance because these traits were not the reason for selection at the origin of the population, which was reflected in the fact that the CV _{A} of W10F was the one with the lowest value in the Gema population, while the rest of the traits had higher values.
Estimator  YPP^{1}  NFP  W10F 


3,363.58  1.17  2,881.13 

13,454.32  4.66  11,524.50 
CV _{A}  29.05  29.32  18.80 
ĥ ^{ 2 }  44.14  32.03  37.8 
CIĥ ^{ 2 }  (29.2, 56.3)  (13.9, 46.9)  (21.2, 51.3) 
CIW  27.10  33.00  30.20 
RATE  0.61  1.03  0.80 
^{1}YPP = yield per plant (g); NFP = number of fruits per plant; W10F = weight of ten fruits (g);
For YPP and NFP, in Gema a CV _{A} similar to that of M1Fitotecnia and Verde Puebla was estimated, and all three populations were well above CHF1Chapingo, which presented values of 10.4 and 14.9 %, respectively (Table 4). For the average weight per fruit (AWF), the CV _{A} observed in Gema is close to that of Verde Puebla (15.1), and is intermediate between that of M1Fitotecnia and CHF1Chapingo. Under this parameter, in the Gema population, as in Verde Puebla, a high response to selection would be expected for YPP and NFP, since according to ^{Kavithamani and Amalabalu (2017)} the presence of genetic diversity is important to improve any crop. On the other hand, a moderate response is observed for AWF in these two populations, which belong to the Puebla race and are very largefruited (^{PeñaLomelí et al., 2011}), so in selection only maintaining fruit size and selecting for YPP, where a higher gain is expected, is suggested. This is because breeding programs depend on wide genetic variability within the population (^{Suganthi, Rajamani, John, Suresh, & Renuka, 2018}).
Trait  Parameter  M1Fitotecnia (MorenoMaldonado et al., 2002)  Verde Puebla (PeñaLomelí et al., 2004)  CHF1Chapingo (PeñaLomelí et al., 2008) 

YPP^{1}  CV _{A}  26.7  28.6  10.4 
ĥ ^{ 2 }  50.9  57.2  37.5  
CIĥ ^{ 2 }  (39.6.4, 59.4)  (40.2, 66.9)  (20.9, 51.2)  
CIW  19.7  29.7  30.3  
RATE  0.38  0.52  0.81  
NFP  CV _{A}  32.7  28.7  14.9 
ĥ ^{ 2 }  46.2  53.6  46.6  
CIĥ ^{ 2 }  (33.8, 55.5)  (35.3, 67.4)  (32.3, 58.2)  
CIW  21.7  32.1  25.9  
RATE  0.46  0.60  0.56  
AWF  CV _{A}  26.9  15.1  11.6 
ĥ ^{ 2 }  65.7  53.8  52.8  
CIĥ ^{ 2 }  (57.8, 71.7)  (35.5, 67.5)  (40.2, 63.1)  
CIW  13.8  32.0  22.9  
RATE  0.21  0.59  0.43 
^{1}YPP = yield per plant (g); NFP = number of fruits per plant; AWF = average weight per fruit (g); CV _{A} = coefficient of additive genetic variation (%); ĥ ^{ 2 } = narrowsense heritability (%); CIĥ ^{ 2 } = 1α confidence interval for ĥ^{2} (α = 0.05); CIW = CIĥ ^{ 2 } width; RATE = CIW/ĥ ^{ 2 } .
The ĥ ^{ 2 } estimated in the three traits of the Gema population ranged from 32.03 to 44.14 % (Table 3). According to the ^{EspitiaCamacho, AraméndizTatis, and CardonaAyala (2018)} classification, the ĥ ^{ 2 } values of the traits show a moderate magnitude (20 % ≤ ĥ ^{ 2 } ≤ 50 %). From the point of view of this parameter, it is still possible to make genetic improvement by selection with technically and economically viable advances. However, the ĥ ^{ 2 } values obtained for Gema are lower than those of M1Fitotecnia and Verde Puebla in the three traits compared, and only exceed CHF1Chapingo in YPP (Table 4).
The CIĥ ^{ 2 } width in Gema of the three traits (Table 3) was similar to that obtained in Verde Puebla and CHF1Chapingo, although greater than that of M1Fitotecnia (Table 4). The lowest width was obtained in YPP, while the highest occurred in NFP, the same traits that presented the lowest and highest heritability RATE respectively, so the precision was good (^{Knapp, Ross, & Stroup, 1987}). That is, in the best case (YPP), where the ĥ ^{ 2 } point estimate was 44.14 %, the actual value of this parameter is between 29.2 and 56.3 % (α = 0.05), and for the worst case (NFP), where the ĥ ^{ 2 } point estimate was 32.03 %, the actual value is between 13.9 and 46.9 % (α = 0.05).
The results in the comparison between populations can be explained by their origin, since in the case of M1Fitotecnia and Verde Puebla, the estimation of variance components was made after the first selection cycle, while Gema and CHF1Chapingo are populations with six selection cycles. This implies that in the latter there was already a reduction in the additive variance for the selected traits (^{Falconer & Mackay, 2001}), unlike the first ones in which the selection process began.
On the other hand, the greater magnitude of CV _{A} in the Gema population traits, compared to those of CHF1Chapingo, is due to the differences in the target of their respective breeding programs. The Gema population started from the selection of plants with very large fruits in an intervarietal hybrid and has subsequently undergone six selection cycles, taking into account yield and fruit size. The CHF1Chapingo variety was obtained through five cycles of mass selection and one of maternal halfsib family selection from the Rendidora variety (^{PeñaLomelí et al., 2008}), directing the selection towards yield and earliness. This also explains why Gema has a higher ĥ ^{ 2 } value than CHF1Chapingo for yield, although because of its origin, Gema has a very low ĥ ^{ 2 } value for fruit size due to its low genetic variability.
Despite having a similar CV _{A} to those of CHF1Chapingo (^{PeñaLomelí et al., 2008}) and Verde Puebla (^{PeñaLomelí et al., 2004}), the Gema population had a lower ĥ ^{ 2 } for the studied traits, which can be explained by the environmental effect, since ĥ ^{ 2 } measures the magnitude of the additive genetic variance as a function of total V _{ P } , which is composed of the V _{ G } , V _{ E } and V _{ I } . Because it was only evaluated in one environment, there is no interaction variance, and the magnitude of the genetic variance is similar, so the differences in ĥ ^{ 2 } are attributed to the environment. This is consistent with what was stated by ^{Hallauer et al. (2010)}, who indicate that if the environmental effects are increased, the heritability will be of lesser magnitude, due to the masking that the latter cause on the variance of the populations.
The phenotypic correlation between YPP and NFP was high and significant (Table 5), while for the additive genetic correlations of the same trait (YPP) it was significant with NFP and W10F, although the correlation was only high with NFP. This shows that there is a correspondence between phenotypic and additive genetic correlations between YPP and NFP, as their correlations were high, positive and significant in both cases, suggesting that there is an association between these traits. In practical terms, this means that focusing on either of these two traits is enough to modify the mean of the other (^{Hallauer et al., 2010}). Because the heritability of YPP is greater than that of NFP, and the former variable is easier to assess, the Gema population breeding strategy can be directed at increasing YPP to make indirect improvement towards NFP, as noted by ^{PeñaLomelí et al. (2013)} for husk tomato.
Conclusions
Both the values of the coefficient of additive genetic variation and narrowsense heritability indicate that it is possible to obtain significant gains through selective breeding and to derive new varieties from the Gema population.
The greatest genetic advances in the improvement of the Gema population through selection are expected for yield per plant and number of fruits per plant, although fruit size must be kept very large.
Due to the additive genetic correlation between yield per plant and number of fruits per plant, and to the higher heritability of the first trait, the Gema population breeding strategy can be directly focused on yield per plant, with which a gain in both traits would be expected.