## 2 Materials and Methods
### Statistical Analysis  
The comparisons of cross-pollinated (CP) with self-cross-pollinated (SP) were made in the Statistica 10.0 [38] and R software [39]. Factorial ANOVA was used for analyzing the influence of environment, genetic components, and the interactions between them, while [PERSON] and [PERSON]'s HSD post hoc tests were used to separate the families into homogeneous groups and analyze the significance of the differences among them. For Paltinis 10 \(\times\) 10 diallel mating design, [PERSON]'s [32] method 3 was used, where one set of FIs and reciprocals but not the consanguineous were included, while for full-sib of Rodna, [PERSON]'s [32] method 1 was used. The mathematical model for diallel analysis was taken from [PERSON] [40], and is a combination of [PERSON] [41] and [PERSON]'s [32] models, as follows:  
\[\mathrm{x_{kij}=u+g_{i}+g_{j}+s_{ji}+m_{i}+n_{ij}+e_{kij}}\]  
where \(\mathrm{x_{kij}}\) = the value of the kth progeny from the cross between \(\mathrm{i^{th}}\) female and \(\mathrm{j^{th}}\) male; \(\mathrm{u}\) = the general mean; \(\mathrm{g_{i}}\) and \(\mathrm{g_{j}}\) = the general combining ability effects for the \(\mathrm{i^{th}}\) and \(\mathrm{j^{th}}\) parents, respectively; \(\mathrm{m_{i}}\) = the maternal effect of the \(\mathrm{i^{th}}\) parent; \(\mathrm{s_{ij}}\) = the specific combining ability effect for the cross between the \(\mathrm{i^{th}}\) and \(\mathrm{j^{th}}\) parents; \(\mathrm{n_{ij}}\) = the interaction effect between the \(\mathrm{i^{th}}\) and \(\mathrm{j^{th}}\) parents, such that \(\mathrm{r_{ij}}\) = \(-\mathrm{r_{ji}}\) (reciprocal effect not accounted for by maternal or paternal effects); and \(\mathrm{e_{kij}}\) = random error [29]. The additive variance was used to estimate the variance of GCA among all of the parents and was estimated as \(1/4\sigma^{2}\mathrm{A}\), assuming that all the epistatic genetic variances were irrelevantly small. Also, the estimated variance of SCA was an estimator of \(1/4\sigma^{2}\mathrm{D}\)[29; 42; 43]. In both trials, for breeding strategy, two types of heritabilities were calculated, and, consequently, two genetic gains were determined, as follows:  
* Broad-sense family mean heritability (\(\mathrm{h^{2}}_{1}\)): \[\mathrm{h^{2}}_{1}=(2\sigma^{2}_{\mathrm{GCA}}+\sigma^{2}_{\mathrm{SCA}})/ \sigma^{2}_{\mathrm{Ph}}=(2\sigma^{2}_{\mathrm{GCA}}+\sigma^{2}_{\mathrm{SCA}}) /(2\sigma^{2}_{\mathrm{GCA}}+\sigma^{2}_{\mathrm{SCA}}+\sigma^{2}_{\mathrm{ Mat}}+\sigma^{2}_{\mathrm{Mat-Int}}+\sigma^{2}_{\mathrm{e}}/\mathrm{k})\] where \(\sigma^{2}_{\mathrm{GCA}}\), \(\sigma^{2}_{\mathrm{SCA}}\), \(\sigma^{2}_{\mathrm{Mat}}\), \(\sigma^{2}_{\mathrm{Mat-Int}}\), \(\sigma^{2}_{\mathrm{e}}\), and \(\sigma^{2}_{\mathrm{Ph}}\) = general, specific, maternal, maternal interaction, error, and phenotypic variances, respectively, and \(\mathrm{k}\) = number of blocks = 4. According to [PERSON] [44], the genetic gain (G\({}_{1}\)) was estimated as follows:  
\[\Delta\mathrm{G_{1}=i_{1}\times h^{2}}_{1}\times\sigma_{\mathrm{Ph}}\]  
where \(\mathrm{i_{1}}\) is the selection intensity proposed by [PERSON] [43] and \(\sigma_{\mathrm{Ph}}\) is the family mean phenotypic standard deviation. * Narrow-sense family mean heritability (\(\mathrm{h^{2}}_{2}\)): \[\mathrm{h^{2}}_{2}=2\sigma^{2}_{\mathrm{GCA}}/\sigma^{2}_{\mathrm{Ph}}=(2\sigma ^{2}_{\mathrm{GCA}})/(2\sigma^{2}_{\mathrm{GCA}}+\sigma^{2}_{\mathrm{SCA}}+ \sigma^{2}_{\mathrm{Mat}}+\sigma^{2}_{\mathrm{Mat-Int}}+\sigma^{2}_{\mathrm{e}}/ \mathrm{k})\]  
For _diameter at breast height_ (Dbh), the CP families registered in the Paltinis trial had an average value of 16.2 cm, superior by 15% to the Rodna CP mean value. For the common five families, the superiority is even higher, at 17%. Also, for SP, a 10.7% superiority was registered in Paltinis. The CP tree combinations registered 37% and 42% higher mean values than SP in the Rodna and Paltinis trials.