**1. Introduction**

Strawberry production in the southern hemisphere is totally dependent on cultivars developed by breeding programs in the United States and Spain [1]. In addition to low adaptability and stability in tropical regions, these cultivars increase production costs, since commercial nursery plants are multiplied and imported in dollars [2]. Another recurring problem concerns the physiological and phytosanitary quality, where several crops were affected by pathogens that did not exist in the producing regions, and they were probably introduced by imported nursery plants.

Climate change has promoted an increase in the temperature and in the concentration of carbon dioxide (CO2) in the atmosphere [3,4]. High temperatures limit the culture, as strawberry plants require cold hours for floral induction. Thus, it can negatively affect the yield of cultivated plants, interfering with the balance of morphophysiological and hormonal processes [5,6].

**Citation:** Nascimento, D.A.; Gomes, G.C.; de Oliveira, L.V.B.; de Paula Gomes, G.F.; Ivamoto-Suzuki, S.T.; Ziest, A.R.; Mariguele, K.H.; Roberto, S.R.; de Resende, J.T.V. Adaptability and Stability Analyses of Improved Strawberry Genotypes for Tropical Climate. *Horticulturae* **2023**, *9*, 643. https://doi.org/10.3390/ horticulturae9060643

Academic Editor: Yuepeng Han

Received: 19 April 2023 Revised: 23 May 2023 Accepted: 25 May 2023 Published: 30 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

5

The development of adaptable and stable tropical cultivars can be a solution to overcome this issue. Therefore, it is important that genetic breeding programs are stimulated to develop productive cultivars and adapted to a wide range of latitudes, allowing cultivation area expansion [7]. Several studies in tropical regions have demonstrated the potential of new genotypes with low chilling requirements and higher yields, compared to well-established cultivars in the market [2,8–10].

The environment interferes with agronomic characteristics [11] and the quality of the fruit post-harvest [12]. Considering the wide latitude of strawberry cultivation worldwide, studies of adaptability and stability should be carried out both in relation to the location and throughout the harvest period [1].

Studying the genotype × environment interaction aims to identify the behavioral variation that genotypes undergo when exposed to varied environmental conditions [13]. One way to measure these interaction effects is through correlation studies between the characteristics of interest [14]. Correlations estimated among variables provide strategic information for studies to improve adaptability and stability in strawberries [15]. In addition, these studies allow genotype identification with predictable behavior, as well as those responsive to environmental variations, under specific conditions [16,17].

The variability of the genus Fragaria is wide, and it is classified according to the ploidy level, in which the basic number of chromosomes is equal to seven (x = 7) [18]. Among the twenty-five known species, thirteen are diploid (2n = 2x = 14), five are tetraploid (2n = 4x = 28), one is petaploid (2n = 5x = 35), one is hexaploid (2n = 6x = 42), three are octaploid (2n = 8x = 56), and two are decaploids [18]. The cultivated species (*Fragaria* × *ananassa*), classified as octaploid, is derived from immediate ancestors (*F. chiloensis* and *F. virginiana*), considered allopolyploids [19], which, in turn, are derived from two or more different diploid ancestors [20]. The octaploid commercial strawberry genome comprises 813.4 megabases (Mb) that are distributed across 28 pseudochromosomes, with 108,087 protein-coding genes and 30,703 RNA-coding genes [21]. Therefore, this wide variability generates expectations of obtaining genotypes adapted to a low chilling requirement.

Most polyploids obtained by chromosome duplication have characteristics of vigorous plants and larger fruits [22]. Eukaryotic polyploids also show strong resistance to biotic and abiotic factors [23].

Mixed linear models consider genotype effects as modifications to estimate adaptability and stability, allowing a genetic effects analysis to be made using best linear unbiased predictors (BLUPs) [24]. However, mixed linear models are routinely prone to experimental inconstancy and the heterogeneity of environmental variations [25]. Therefore, in this method, the genotypic values (e.g., productivity), adaptability, and genotypic stability are analyzed simultaneously [26]. This methodology is based on the harmonic mean of the relative performance of genotypic values (HMRPGV) method, which considers the genotype mean and its variation in different environments.

The relationship between genotype and phenotype in different regions helps to anticipate more precise responses to the selection of individuals with heterogeneous habitats, whether spatial or temporal. If the genotype has phenotypic expression for a particular trait, depending on the environment, heritability measures can be altered according to variations in environmental conditions [27].

Thus, the objective of this work was to estimate the adaptability and the temporal stability, as well to select strawberry genotypes easy to propagate with lower cold requirements using a mixed linear model.

#### **2. Materials and Methods**

#### *2.1. Location*

The experiment was conducted at the University of Centro-Oeste, Guarapuava, Brazil (25◦23 01 S, 51◦29 50 W, elevation of 1025 m a.s.l.) from August 2019 to February of 2020. The soil was classified as typical dystroferric Latosol Bruno [28]. The climate was humid subtropical Cfb (temperate oceanic climate, warm summer, and without a dry season), which includes hot summers and frosty winters. The average annual temperature was 17 ◦C, with maximum and minimum temperatures of 23.5 ◦C and 12.7 ◦C, respectively. The average annual rainfall was 1946 mm [28].
