Trial establishment and biological material

In the fall of 2014, a progeny trial with 90 open-pollinated families of P. greggii var. australis was established on land in the community of San Miguel Achiutla, Oaxaca. The site has a semi-warm temperate sub-humid (A)C(w₁) climate, precipitation and mean annual temperature of 700 mm and 18.1 °C, without frost (^{Instituto Nacional de Estadística y Geografía [INEGI], 2005}). The trial consisted of two sites 1 km apart (site 1: 17.29° N and 97.47° W, 1 924 m elevation, western exposure; site 2: 17.29° N and 97.48° W, 1 915 m elevation, eastern exposure), both with slight erosion and shallow soil with pH of 8.4. Site 2 soil had higher levels of nitrogen (0.6 vs. 0.3 mg∙kg^-1), iron (2.7 vs. 2.2 mg∙kg^-1), copper (0.5 vs. 0.2 mg∙kg^-1), zinc (0.3 vs. 0.2 mg∙kg^-1), less sodium (15.8 vs. 20.7 mg∙kg^-1), equal amount of phosphorus (1.1 vs. 1.1 mg∙kg^-1) and higher percentage of clay than site 1. N concentrations were determined by the micro-Kjeldahl method and those of P, K, Fe, Cu and Zn by inductively coupled plasma optical emission spectrometry (ICP-OES model 725, Agilent; Mulgrave, Australia) (^{Alcántar & Sandoval, 1999}). A randomized complete block experimental design was used at each site, 20 replicates for each family, in one-tree plots at 3 x 3 m spacing (1 800 trees per site). A row of trees of the same species was established around the perimeter of both plantations to ensure complete competition between plants.

Variables evaluated

Survival, total height with a graduated level staff, diameter at 1 m above the ground using a digital vernier, number of whorls with two or more branches, and tree conformation on a scale of 1 to 5 (1 = greater straightness and branches with flat angles., 5 = sinuous trunk and branches with acute angles) were evaluated after five years (winter 2019). Tree conformation was determined by two independent observers to avoid bias in appreciation (^{Reyes de la Barra, Ponce-Donoso, Vallejo-Barra, Daniluk-Mosquera, & Coelho-Duarte, 2018}) and average was determined. In the whorl closest to the height of 1 m, the angle was obtained with a graduated protractor, regarding the average of the thickest branch and its opposite (^{Bustillos-Aguirre, Vargas-Hernández, López-Upton, & Ramírez-Valverde, 2018}; ^{Escobar-Sandoval, Vargas-Hernández, López-Upton, Espinosa-Zaragoza, & Borja de la Rosa, 2018}). Diameter was measured in the same branches where the angle was evaluated, obtaining an average. The stem straightness was evaluated with two criteria: straightness 1, that of the entire stem with a scale from 1 (straight stem) to 5 (with pronounced twists) (^{Gutiérrez-Vázquez, Cornejo-Oviedo, Zermeño-González, Valencia-Manzo, & Mendoza-Villarreal, 2010}); and straightness 2, the average value of straightness of three equal sections of the stem, each graded on a scale of 1 = straight, 2 = with a single curve and 3 = with two curvatures (^{Sierra de Grado, Diez-Barra, & Alia-Miranda, 1999}). The volume of the trunk (dm³) was calculated as V = 0.0003 * diameter² * height (^{Dvorak, Kietzka, Donahue, Hodge, & Stanger, 2000}).

Statistical analysis and estimation of genetic parameters

The pooled analysis of the two evaluation sites showed significant differences between all variables; therefore, analysis by each evaluation trial was selected. The analysis of variance for each site was performed with the MIXED procedure of SAS (^{Littell, Milliken, Stroup, Wolfinger, & Schabenberger, 2006}) and variance components were obtained by the restricted maximum likelihood method. The model of the completely randomized blocks design was:

where,

Y_jk = measured value of the individual of the k-th family, within the j-th block (repetition)

µ = population mean

B_j = block fixed effect

F_k = random effect of the k-th family ∼ NID (0, σ² _f)

e_jk = error associated with these effects ∼ NID (0, σ ² _e )

j = 1, 2..., 20 blocks

k = 1, 2..., 90 families.

The additive genetic variation coefficient was estimated with the relation: CVGA = (σ² _A)^1/2/ *100.

Strict sense heritability at the individual level (h² _i) and of family means (h² _f), for all variables per site, was calculated with variance components using the following equations (^{Falconer, 2017}):

where,

σ² _f = variance of families

σ² _e = error variance

b = harmonic mean of the number of plants per family for each site.

A coefficient of genetic determination of 3 was used to avoid overestimating the additive variance (σ² _A = 3σ² _f) and heritability.

The standard error of individual heritability [EE(h²i)] was estimated with the ^{Falconer (2017}) equation:

where,

nf = number of families

na = number of trees per family.

Phenotypic correlations between pairs of variables were evaluated based on Pearson's correlation coefficient, while genetic correlations (r_{g (XY)}) per site were obtained with the equation described by ^{Falconer (2017}):

where,

COV_f(X,Y) = covariance of families between X and Y

σ² _f(X) and σ² _f(Y) = variances of families for the same traits.

COV_{f (X,Y)} was estimated from the sum of X and Y (^{Rice, 1988}): COVf(X,Y)= [σf(X + Y)2-σfX2* σfY2] / 2, where σ² _{f (X+Y)} is the variance of families of variable X + Y.

The standard error of genetic correlations [EE(rg)] was calculated according to the procedure described by ^{Falconer (2017}):

Genetic control of traits evaluated

Table 2 shows that individual heritabilities (h² _i) at both sites were classified as low (^{Cornelius, 1994}); family heritabilities (h² _f) at site 2 were slightly higher. Height, volume, number of whorls and straightness 1 had the highest individual and family mean heritabilities in both evaluation sites; site 1 also had it for branch angle and site 2 for stem conformation, perhaps due to environmental differences in soil fertility and texture. In trials carried out on Pinus patula Schiede ex Schltd. et Cham. heritability differences between sites have been determined with values that double the numbers from one trial to another (^{Salaya-Domínguez, López-Upton, & Vargas-Hernández, 2012}; ^{Morales González, López-Upton, Vargas-Hernández, Ramírez-Herrera, & Gil-Muñoz, 2013}).

Heritabilities of traits of interest such as stem straightness, height, diameter at breast height and volume per tree are in the range of 0.1 to 0.3 for forest species (^{Bustillos-Aguirre et al., 2018}; ^{Escobar-Sandoval et al., 2018}; ^{Mora & Zamudio, 2006}; ^{Morales-González et al., 2013}; ^{Sánchez-Vargas, Cambrón-Sandoval, Sáenz-Romero, & Vargas-Hernández, 2014}). Therefore, the values found in this trial are also within the range of realistic values and are conservatives for these variables.

h² _i and h² _f values in diameter are lower than that in height and volume; this trend has been observed in other studies with values in diameter of 0.10 < h² _i < 0.30 compared to height and volume (0.10 < h² _i < 0.35) in P. pinaster Ait. (^{Zas-Arregui, Merlo, & Fernández-López, 2004}) and in P. patula (^{Bustillos-Aguirre et al., 2018}; ^{Escobar-Sandoval et al., 2018}; ^{Salaya-Domínguez et al., 2012}). Values of h² _i = 0.28 for diameter and h² _i = 0.25 for height have been reported for P. greggii, but lower than volume (h² _i = 0.32) (^{Azamar-Oviedo, López-Upton, Vargas-Hernández, & Plancarte-Barrera, 2000}). Height and diameter are sensitive to microenvironmental effects and competition between trees (Vargas-Hernández, Adams, & Joyce, 2003).

Conformation and straightness 1 had slightly higher heritability than the more precisely measured traits (diameter and angle of branches and straightness 2) as reported by ^{Haapanen, Velling, and Annala (1997}), except for branch angle at site 1. Reports on heritabilities for stem straightness show great variability and differences in both ages and material used, environments and evaluation methods may be influencing such discrepancies (^{Sierra de Grado et al., 1999}; ^{Zas-Arregui et al., 2004}).

^{Bustillos-Aguirre et al. (2018}) reported low to moderate genetic control values of 0.00 < h² _i < 0.23 and 0.00 < h² _f < 0.42 for branching traits of P. patula. In the present study, branch angle and diameter showed less genetic control than number of whorls. Low heritabilities in branch diameter agree with the results obtained by Bustillos-Aguirre et al. (2018) for P. patula, and ^{Jansons, Baumanis, and Haapanen (2009}) for P. sylvestris L., who indicate that branch size is weakly heritable (reduced additive variance) and is influenced by environmental factors. Branch traits have an important effect on wood quality (^{Lowell et al., 2014}) and evaluation should be incorporated as a long-term selection criterion. For practicality, two branches were evaluated in the whorl closest to the height of the point where stem diameter was measured; however, under open field conditions, high variability was observed within and between whorls, so obtaining data in a single whorl may not be the best indicator of branch quality. In this regard, for the selection it was better to consider the number of whorls, because it has a higher heritability and it is more practical to measure it in the open-field, as recommended by ^{Zas-Arregui et al. (2004}).

The number of whorls, which is related to the annual growth pattern of the terminal bud and height growth rate, had a moderate to high genetic control. ^{Jansons et al. (2009}) indicate that longer shoot length result in more knot-free wood.

Additive genetic variability (CV_GA) was considerable in most variables. In the case of Pinus, CV_GA values close to 10 % indicate substantial gains per selection, with values between 5 and 15 % being common for growth variables (^{Cornelius, 1994}). Volume had the highest CV_GA values (46 and 27.6 % for sites 1 and 2, respectively). These results were lower than those reported in P. patula by ^{Salaya-Domínguez et al. (2012}), where diameter, height and volume reached ranges of 24 to 39 %, 19 to 30 % and 55 to 80 %, respectively.

Phenotypic and genetic correlations between variables

Genetic correlations were high and positive among growth traits ((r_g ≥ 0.776, Tables 3 and 4). Based on correlations, it will be appropriate to use diameter as a classification criterion, due to simplicity and precision of its measurement, contrary to what occurs with the height of trees greater than 7 m if branches make it difficult to observe the crown of the tree. High r_g values are attributed to the presence of common genes that influence traits and to the effect of linkage between close genes (^{Falconer, 2017}).

Genetic correlations between branch diameter and growth traits were high (r_g ≥ 0.85) for site 1. When selecting tall trees with larger stem diameter and volume, their progeny will have branches with larger diameters, but only at this site, because at site 2 there is almost no genetic correlation between these variables. For both sites, genetic correlations were positive between conformation and straightness 2 (average of three stem sections); trees with optimal conformation values will also have the best straightness values. Correlations of branch diameter with conformation and straightness of the total stem were positive at a medium level (0.38 < r_g < 0.70), so selecting trees with smaller diameters would moderately improve conformation and straightness of the stem (given the scale of measurement).

For site 1, branch angle showed positive, but moderate correlation (0.27 < r_g < 0.46), with total stem growth and straightness traits. This means that genotypes with more horizontal branches will be those with higher productivity (^{Escobar-Sandoval et al., 2018}), but will be prone to generate sinuous stems (higher values in straightness scale). On the other hand, the number of whorls was negatively correlated with conformation and straightness of the three stem sections (-0.67 < r_g < -0.54), indicating there will be better conformation and straight stems when the number of whorls is higher. Site 2 shows negative genetic correlations among conformation, growth variables and number of whorls (-0.67< r_g < -0.29), so that trees with better conformation will generate progenies with higher growth and a greater number of whorls (^{Bustillos-Aguirre et al., 2018}).

Some genetic correlations differed contrastingly between sites 1 and 2; for example, the pairs of traits where r_g were positive (high and moderate) for site 1, but negative (moderate) for site 2, were diameter vs. conformation, and angle vs. branch diameter. Correlations between branch diameter vs. stem diameter and height showed positive values for both sites, but with different magnitudes, being high for site 1. On the contrary, branch angle vs. conformation had negative genetic correlation (high) for site 1, while site 2 had positive correlation (moderate or null). Differences between sites may be because the environment influences correlations through different physiological mechanisms (^{Falconer, 2017}), in this case, differences in fertility and soil texture. Genetic correlations depend on gene frequencies, so they also vary by different half-siblings of the same family among sites (^{Valencia-Manzo & Vargas-Hernández, 2001}).

In terms of phenotypic correlation coefficients, high and positive values were found for both sites between growth traits (r_p > 0.85), as well as between branch diameter and growth traits (r_p > 0.61). In this regard, ^{Vargas-Hernández et al. (2003}) indicate that trees with higher productivity are those that regularly have fewer branches with reduced size and long internodes, and higher quality wood.

When selecting genotypes, genetic correlations should be considered, otherwise severe deterioration of growth and stem quality may result as well as subsequent loss of economic gain (^{Haapanen et al., 1997}). Reports on genetic correlations between growth and stem traits show great variability (^{Zas-Arregui et al., 2004}). The results of the present study suggest that, while improving growth will not be detrimental to stem quality, neither will it result in a simultaneous improvement of both.

The families with larger stem volume, which represent 20 %, have an overall average of 1.55 dm³; 1.14 dm³ for site 1 and 1.95 dm³ for site 2. The overall trial average was 1.13 dm³ with an average of 0.80 dm³ for site 1 and 1.46 dm³ for site 2. This is a five-year selection differential in volume of 0.42 dm³ in a general average and 0.34 dm³ and 0.49 dm³ for site 1 and 2, respectively. Although the selection of the best individuals within families has yet to be considered, it is possible to understand the progress that can be achieved in a first breeding cycle, and based on genetic correlations observed, to make gains for most of the variables evaluated. Usually, selection in fast-growing pines has been carried out up to the age of eight years (^{Dvorak et al., 2000}). At this age it is possible to find the best parents by selecting the best families and the best individuals of these, and to take advantage of the precocity of the species for seed collection to have more productive trees for the area.