*2.4. Statistical Analyses*

The total fruit mass (TFM g/plant) was obtained for each harvest from August 2019 to February 2020. Each month was considered a collection period to perform adaptability and stability studies.

Statistical analyses were performed using a linear mixed model methodology, where the genetic parameters were estimated using the restricted maximum likelihood method (REML). The genetic values were predicted using the BLUP method [29].

Data were subjected to individual and joint analyses of variance. To analyze the individual variance, the statistical model was adopted as follows:

$$y = Xb + Z\_{\mathbb{S}}c + e$$

where:

*y* = data vector;

*b* = vector of the fixed effects of the blocks added to the general mean;

*g* = vector of random data effects for genotypes;

*e* = effect of random vector errors;

and *X* and *Z* represent the incidence matrices for vectors *b* and *g*, respectively.

Data were standardized using the correction factor obtained for cases where the coefficients of variation of heritability were verified in a broad sense according to the following expression described by Resende (2007) [25]:

$$\sqrt{\hbar^2} \, \_{i\bar{k}} \sqrt{\hbar^2} \, \_{t\nu}$$

where:

*h*2 *ik* = the broad sense of individual heritability for characteristic *i* in the evaluation of *k*;

and *h*<sup>2</sup> *<sup>t</sup>* = the broad sense of individual mean heritability to evaluate *k* for characteristic *i*. After standardizing the data, a joint analysis of variance was performed to consider the genotypes and harvesting according to the following statistical model:

$$y = Xb + Za + Wc + e$$

where:

*b* = vector of the block effects (assumed as fixed) added to the general mean;

*a* = vector of individual genotypic effects (random);

*c* = vector of plot effects (randomized);

*e* = error vector (aleatory);

and *X*, *Z*, and *W* represent the incidence matrices for the said effects (*b*, *a*, and *c*, respectively).

Analysis of deviance (ANADEV) was performed to test the significance of the variance components according to the random effects of the model. The likelihood ratio test (LRT) was used to implement the variance components, in which the significance of the model was evaluated using the chi-square test with one degree of freedom [25].

The classification of genotypes simultaneously considering productivity and stability was performed using the harmonic mean of the genetic values (*HMGV*), which was obtained as follows:

$$HMG\,V\_{\vec{i}} = n\prime \Sigma^{\prime \prime}\_{\ \vec{j}} = 1 \,\,\mathrm{1}\%\,V\_{\vec{i}\vec{j}}\,\,$$

where:

*n* = the number of months/harvests (*n* = 7) for which genotype *i* was evaluated;

and *GVij* = the genetic value of genotype *i* in month/harvest *j* expressed by the ratio of the mean in the month/harvest.

The genotypes, considering productivity and adaptability, were selected simultaneously by the performance of their genotypic values (*RPGV*) during the months/harvest obtained by the formula:

$$RPGV\_i = 1/n \left(\frac{\sum\_{j=1}^{n} GV\_{ij}}{M\_j}\right)$$

where:

*Mj* = fruit productivity means during the month/harvest *j*.

Strawberry genotypes were simultaneously classified in terms of productivity, stability, and adaptability through the harmonic mean of the relative performance of genotypic values (*HMRPGV*), obtained according to the following expression:

$$HMRPGV\_i = \frac{n}{\sum\_{j=1}^{n} \frac{1}{RPGV\_{ij}}}$$

The values of *RPGVμ* and *HMRPGVμ* were obtained by multiplying *RPGV* and *HMRPGV* by the general mean of each characteristic and then considering all months/harvests. Thus, the mean values of the genotype were provided, penalized for instability, and capitalized by adaptability. Selective precision and selection gains were obtained according to Resende [29]. Statistical model 20 was adopted for individual analyses, which refers to the evaluation of unrelated genotypes obtained from randomized blocks containing five plants per plot. In addition, model 55 was used in the conjoint analysis for genotypes in an RBD, with stability and temporal adaptability for one place and seven months/harvests using the Selegen REML/BLUP program [29]. From the *HMRPGVμ* values, a box plot was generated using the R software with the ggplot2 package.

#### **3. Results**

A desirable strawberry cultivar should have good productivity, post-harvest characteristics, disease and pest tolerance, adaptability, and temporal stability, distributing production uniformly throughout the cultivation period. Adapted and stable genotypes are typically identified during the final selection cycles, and only those that demonstrate superiority are tested.

The climate conditions for the experiment cultivation period are shown in Figure 1. The minimum temperature (daily average) varied from 8.26 ◦C in July to 17.8 ◦C in March 2019. The maximum temperatures varied on a daily average from 20.11 ◦C in July 2019 to 28.4 ◦C in March 2020. The lowest rainfall value was observed in July (0.63 mm as the mean per day), and the highest was in December (5.04 mm per day). The monthly mean temperatures gradually increased during the cultivation period, ranging from 14.17 ◦C at the time of

transplantation (July 2019) to 21 ◦C in February 2020 at the end of the harvest period (Figure 1).

**Figure 1.** Rainfall and temperature data of the strawberry experimental location from March 2019 to February 2020.

For the analyses of adaptability and stability of the genotypes, the total mass of fruit was used for the analysis of the mixed models.

Significant differences were observed for total fruit mass in the sources of variation, genotypes, genotype interactions by harvest time, and permanent effects using deviance analysis based on the likelihood ratio test (Table 2). The interaction between genotype (G) and environment (E) showed variations in performance among different harvest periods (months).

**Table 2.** Deviance analysis (ANADEV) for total fruit mass in strawberry genotypes evaluated for seven months.


\*\* significant at 1% of probability by deviance analysis based on the LRT test (X2) with 1 degree of freedom (ttable = 6.63).

From the estimates of the variance components obtained using REML/BLUP, for the total mass of fruit of the genotypes, heritability in the broad sense was 33%. The mean heritability of the genotypes (79%) was superior to broad-sense heritability. The data presented an accuracy of 0.89, which was considered high, and the repeatability was 36% (Table 3).

Among the 44 genotypes evaluated, 17 showed positive genetic effects, and their predicted genotypic values ranged from 128.16 (RVDA11M-25) up to 278.02 (RVFS07M-34) (Table 4). Through the analyses based on mixed models, the genotypic values were considered to evaluate the strawberry genotypes for the general performance in all seven harvests analyzed and for the individual performance for each harvest. The 11 best genotypes selected for each harvest period are presented in Table 5. As for overall performance, the mean genotypic values ranged from 158.18 g/plant (RVDA11M-13) up to 311.86 g/plant (RVFS07M-34). In general, considering every harvest, genotypes RVFS07M-34 and RVFS07M-24 were among those selected with the highest values of total fruit mass. Among the evaluated controls, Monterey, RVCA44, and RVFS07 were selected only in some specific harvests. Monterey was a unique commercial cultivar (control) ranked among the

11 most productive genotypes but only in the last harvest (February), whereas, RVCA44 was selected in harvest 1 (August) and harvest 2 (September), and RVFS07 was selected in harvest 5 (December).

**Table 3.** Estimation of variance components for total fruit mass in strawberry genotypes evaluated for seven months of cultivation.


**Table 4.** Predicted genotypic values for total fruit mass obtained from 44 strawberry genotypes.



**Table 4.** *Cont.*

<sup>1</sup> Predicted genotypic value; <sup>2</sup> confidence interval.

**Table 5.** Genotype selection in all harvests and in each harvest based on predicted genotypic values for the total fruit mass obtained from 44 strawberry genotypes.


<sup>1</sup> Harvest 1 = August; harvest 2 = September; harvest 3 = October; harvest 4 = November; harvest 5 = December; harvest 6 = January; harvest 7 = February; <sup>2</sup> mean genotypic value in 7 harvests that capitalizes the mean interaction with all evaluated harvests; <sup>3</sup> predicted genotypic value in each harvest, i.e., the genotypic values capitalizing the interaction with the harvests.

Mean genotypic values penalized by instability and capitalized by adaptability were obtained. Data dispersion showed the 11 genotypes that stood out from the others (Figure 2). They had the highest yields and were the most stable and adaptable: RVFS07M-34, RVFS07M-24, RCDA11M-04, RVFS07M-154, RVFS07M-36, RVFS07M-33, RVFS07M-80, RVFS07M-10, RVDA11M-21, RVDA11M-13, and RVFS06AL-132. This demonstrated the potential of theses genotypes as commercial cultivars.

When considering the means of each harvest separately, the RVFS07M-34 (Figure 3) genotype stood out as always being among the seven best in all harvests. It had the highest predicted genotypic value (278.02 g/plant) and the highest mean genotypic value (311.86 g/plant) (Table 4 and Table 5, respectively). The RVFS07M-24 hybrid also showed high performance in almost all harvests, except in harvest 3 (October) (Table 5). In addition, RVFS07M-24 had the highest production stability in several harvesting periods, such as harvests 4 (November, 373.76 g/plant), 5 (December, 416.42 g/plant), 6 (January, 340.98 g/plant), and 7 (February, 400.41 g/plant).

**Figure 2.** Box plot of adaptability and stability of the 44 evaluated genotypes of strawberry.

**Figure 3.** Morphoagronomic aspects of genotype RVFS07M-34 developed with high yield, stability, and temporal adaptability. (**A**) Production; (**B**) plant size, architecture, and flowering; (**C**) pseudo-fruit shape; (**D**) pseudo-fruit internal and external colors.
