Survival of side grafts with scions from pure species Pinus engelmannii Carr. and the P. engelmannii × P. arizonica Engelm. var. arizonica hybrid

Place of origin and preparation method of rootstocks

The seed to produce the rootstocks was collected in a natural stand of P. engelmannii trees located in Empalme Purísima, municipality of Durango, Dgo., México, at coordinates 23°55′48.1″N and 105°05′43.0″W, at 2,480 m elevation. In this stand, no morphological evidence of natural hybridization was observed, for which reason the rootstocks produced were considered pure trees of said specie. For 11 months the rootstocks grew in 77-cavity, expanded polystyrene seedling trays with 170 mL per cavity. Afterwards, the plant grew for 19 months in black polyethylene 5 L bags (20 cm in width and 30 cm in length). At the time of grafting, the rootstocks were 2.5 years old. During this period, the plants reached an average neck diameter of 18.4 mm and an average height of 17.4 cm.

Selection of donor trees and collection of scions

The scions were collected in a free access natural stand located in the area known as El Río, in the Ejido La Casita, municipality of Durango, Dgo., México, at coordinates 23°43′26.8″N and 104°47′27.1″W, at an elevation of 2,335 m. A permit for the collection of samples in the field was not required, since the species studied are not under any conservation status. The scions were collected on March 15, 2018, from a seed producer stand consisting of both tree types, pure species P. engelmannii and P. engelmannii × P. arizonica hybrids, detected by AFLP and morphological traits (analyzed by Ávila-Flores et al., 2016a).

Scions’ donor trees were divided in the two categories of hybrids and trees of the pure species, based on the membership probabilities (MP) of each individual to pure P. engelmannii (pure trees corresponded to an MP larger than 0.945, while the hybrids’ MP was smaller than 0.610). Three trees were chosen from each category; the growth and vigor of each was similar between these two categories within the stand (Ávila-Flores et al., 2016a).

The average age of the three trees of the pure species was 37 years, with a height of 13 m and diameter of 30 cm on average. The average age of the hybrid trees also was 37 years, with a height of 14.5 m and a diameter of 36 cm on average. During the collection of the donor trees scions, selected from the pure species of P. engelmannii and P. engelmannii × P. arizonica hybrids, the following morphological differences were detected between the studied groups of trees: Conical crown in the trees of the pure species and irregular shaped crown in the hybrids trees, slightly hanging branches in the lower part of the hybrid tree crowns, while more erect branches in the whole crown of the trees of the pure species (Figs. 1A and 1B). The cone size of the P. engelmannii × P. arizonica hybrids was smaller than the cones of the pure species P. engelmannii (Figs. 1C and 1D). Erect fascicles in the trees of the pure species and fallen fascicles in hybrids (Figs. 1E and 1F).

From the crown of each donor tree, 20 scions were collected from the upper third and 20 from the middle third. Each scion had an approximate length of 20 cm. In order to safely transport the scions to the grafting site, they were packed in rectangular 72 L plastic boxes containing sawdust moistened with a solution of Captán^® fungicide at a dose of 3 gL⁻¹, to prevent the drying of the scions and their contamination by fungi. Of the 20 scions collected from each tree, only 10 were selected to be grafted. The selection of these scions was made according to their possibility of diameter size tie with the rootstocks.

Grafting

The grafting was done in the nursery at the Instituto de Silvicultura e Industria de la Madera de la Universidad Juárez del Estado de Durango (ISIMA-UJED). The grafts were placed in a greenhouse of 6 × 8 × 3 m of width, length and height, respectively, with a white plastic cover. To reduce the temperature inside the greenhouse, two shade meshes were placed above the roof, with an average spacing of 30 cm between them. The upper mesh had 70% light retention and the lower mesh had 50% light retention.

A total of 120 grafts were made using P. engelmannii rootstocks; 60 of these grafts were done with scions from P. engelmannii × P. arizonica hybrid donor trees, and the other 60 with scions from pure species of P. engelmannii trees. The grafting was done on March 16, 2018, 1 day after the scions were picked. The side-veneer grafting technique described by Muñoz Flores et al. (2013) and Pérez-Luna et al. (2019) was used.

The graft substrate was watered every 3 days and as a complement in each irrigation, triple 19 water-soluble fertilizer (N-P-K) was applied at a dose of 3 gL⁻¹. Fertigation was carried out during the 5 months of evaluation, using a 7 L manual watering can. In addition, from the 2nd month after grafting (May 2019) Promyl^® fungicide was applied to plants’ substrates through irrigation at a dose of 2 gL⁻¹ to prevent fungal damage. This activity was carried out every 8 days for a month.

Treatments, variables evaluated and statistical analysis

Four treatments were evaluated: Two types of donor trees (P. engelmannii × P. arizonica hybrids and pure species P. engelmannii) and two positions of the scions in the donor tree crown (middle and upper third). Each graft represented an experimental unit, and there were 30 repetitions for each treatment, distributed under a randomized block arrangement.

Before grafting, the following graft variables corresponding to the scions and rootstocks were recorded: Scion length (SL), scion diameter (SD), rootstock height (RH), rootstock diameter at the root crown (RD), graft height (GH) and RD at graft height (GD). The sections of scions and rootstocks measured for obtaining the grafts variables are described in Fig. 2.

An analysis of variance (one-way ANOVA) was performed in the R program (R Core Team, 2013), finding significant differences between the pure species and hybrid donor trees in regard to the values of each analyzed graft variable (Table 1).

After grafting, graft survival was evaluated as a response variable each month for 5 months. As independent variables, the type of scion donor tree (hybrid or tree of the pure species) (TDT), the position of the scion in the donor tree crown (SPC) and the graft variables obtained from the scions and rootstocks were considered. The normality of the graft variables was evaluated with the Kolmogorov–Smirnov test. To evaluate the effect of the treatments on survival, an analysis of variance and a comparison test of means, with a proposed initial value of α = 0.05, were performed with the data obtained in each month.

Before carrying out this test and in order to reduce the probability of committing a type I error, the Bonferroni correction was applied to adjust the level of significance (Weisstein, 2004), resulting in the corrected α value = 0.0083, which was obtained by dividing the initial value of alpha by the number of parallel comparisons (0.05/6 = 0.0083). The same adjustment and corrected alpha value (0.0083) was used in the analysis of all the survival models described below.

Also, a Pearson’s correlation test was performed to detect the possible multicollinearity between the analyzed graft variables, and thus be able to discriminate the redundant variables in the adjustment of the evaluated survival models. In addition, two models were adjusted to determine the probability of graft survival based on the treatments evaluated. These models were the Logit function and the Weibull accelerated failure time model. All the statistical tests described were performed on the free software platform R (R Core Team, 2013).

Adjustment in the logit model

To assess the effect of treatments and graft variables on the probability of occurrence of successful events (graft survival) at the end of the evaluation period, the non-parametric Logit model (Hastie & Tibshirani, 1987; Kleinbaum & Klein, 2002), was adjusted with the “aod” package of the R platform (R Core Team, 2013). The Logit model is defined by the following equation: (1) $$p\left(x_i\right)={\displaystyle \frac{1}{1+e^{-(\mathrm{\alpha }+\sum {\mathrm{\beta }}_i{x}_i)}}}$$Where: p(x_i) is the probability of occurrence of an event to be evaluated (in this case the survival of grafts) of the response variable, which is inversely proportional to an exponential function elevated to the sum of the intercept α and n predictors x. The Logit model works with dichotomous (dummy) and discrete variables. Likewise, the adjustment of the Logit model generates estimators of the β coefficients for the predictors; if the value of the estimator is positive, the probability of occurrence of the successful event (p(x_i)) increases when the value of the respective independent variable (x_i) increases by one unit, and if the estimator is negative, the probability of the successful event decreases by increasing the value of the independent variable by one unit (Kleinbaum & Klein, 2002).

Furthermore, the Logit model generates the odds ratio that allows determining the probability of occurrence of the event to be evaluated (survival rate) (Bland & Altman, 2000; Kleinbaum & Klein, 2002; Aedo, Pavlov & Clavero, 2010). The equation to calculate the odds ratio is: (2) $$\mathrm{O}\mathrm{d}\mathrm{d}\mathrm{s}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}={\displaystyle \frac{p\left(x_1\right)\left(1-p\left(x_0\right)\right)}{p\left(x_0\right)\left(1-p\left(x_1\right)\right)}}$$Where p(x₁) is the probability of the occurrence of the graft survival event with hybrid donor tree scions and p(x₀) is the probability of graft survival with pure species donor tree scions. The interpretation of the odds ratio is always relative, since its value is dimensionless and is obtained by dividing the product of multiplying the probability of graft survival with hybrid tree scions (p(x₁)) by the probability of graft mortality with scions from trees of the pure species (1 − p(x₀)), divided by the product of multiplying the probability of graft survival with scions from trees of the pure species (p(x₀)) by the probability of graft mortality with hybrid tree scions (1 − p(x₁)) (Bland & Altman, 2000; Kleinbaum & Klein, 2002; Aedo, Pavlov & Clavero, 2010).

To calculate the odds ratio, the most successful treatment of the event to be evaluated is used as a reference; that is, if the odds ratio of survival is desired to be obtained, the first factor of the numerator (Eq. 2), will be the p(x_i) of the treatment with the highest proportion of living specimens, which in this study was the graft of hybrid tree scions (x₁ = 1), that is to say p(x₁) and therefore the first denominator factor will be p(x₀), which is the proportion of live grafts coming from the other treatment (scions from trees of the pure species).

However, the odds ratio can also be calculated in another way, through an operation that involves the relative frequencies of the living and dead specimens of each treatment under study (Eq. 3) (Kleinbaum & Klein, 2002).

Where: a is the relative frequency of hybrid tree scion grafts (x₁ = 1) that are alive at the end of the evaluation period and c is the relative frequency of grafts with scions from trees of the pure species (x₀ = 0) that are found alive at the end of that period, while b and d are the relative frequencies of dead grafts of hybrid tree scions (x₁ = 1) and scions from trees of the pure species (x₀ = 0), respectively.

In the study, graft survival was considered as the event to be evaluated. To evaluate it, dead grafts were coded with zero (0), while live grafts were coded as one (1), in order to obtain the odds ratio of the most successful treatment (survival) and contrast it with the treatment of least survival. In the case of the variables referring to the type of scion donor tree and the scion position in the donor tree crown, the following dichotomous coding was used: grafts with pure species tree scions (0) and grafts with hybrid tree scions (1); grafts with scions from the upper third of the crown (0) and grafts with scions from the middle third of the crown (1).

Adjustment of the Weibull accelerated failure time model and the Weibull risk function

Graft survival was analyzed with a Weibull accelerated failure time model (AFT) under a two-parameter Weibull distribution to obtain the graft mortality risk ratio (hazard ratio) based on the evaluated treatments and variables. The AFT model was adjusted with the R “survival” library (R Core Team, 2013). For this, the variables TDT (type of donor tree), SPC (scion position in the crown) and the graft variables were used as predictor variables. The AFT model is a logarithmic-linear variant of the Weibull distribution model (Van Houwelingen, 2000), and allows estimating the effect of a variable or set of variables on the duration of survival, which helps to estimate the average time (T) in which there is at least one failure (illness or death) (Carroll, 2003; Zhang, 2016). This model is defined as: (4) $$In\left(T\right)=\mathrm{\alpha }+\mathrm{\delta }x+\mathrm{\sigma }\mathrm{\epsilon }$$Where: In(T) is the natural logarithm of the average time (T) in which it is estimated that there will be at least one mortality (failure) event among the evaluated variables (live grafts), α is the scale parameter, δ it is the coefficient of the explanatory variable, which in the AFT model is known as the “acceleration factor,” σ is the shape parameter of the model and ε is the error of the distribution function (George, Seals & Aban, 2014). All these parameters were estimated with the “survival” library of the R program (R Core Team, 2013). In the AFT model, if δ < 0 the survival time decreases due to the effect of the variable x, if δ = 0 the effect of x is constant, so the survival time does not increase or decrease due to the effect of any change in the value of the variable x, and if δ > 0 the survival time increases due to the effect of the variable x. To interpret the value of δ linearly, it is necessary to apply this coefficient as an exponent, that is, e^(δ) (Qi, 2009). It is important to mention that if δ < 0 the value of α increases, and if δ > 0 the value of α decreases, keeping the value of σ constant in both cases. Therefore, the effect of the predictor variable x is multiplicative (logarithmic) on the time scale, so it is said that this model accelerates (increases or decreases) the estimated average survival time of the specimens studied up to time T, which depends on the effectiveness or ineffectiveness of the treatments evaluated. Said time T is always longer than the duration of the evaluation (Carroll, 2003; Ghorbani et al., 2016; Zhang, 2016). On the other hand, it is also necessary to apply the exponent “time” T(e^(T)) to obtain a linear result of the estimated survival time after the graft evaluation period.

In addition, this study allowed adjusting the Weibull risk function to estimate the probability of occurrence of negative events (graft mortality). To make this adjustment, the “SurvRegCensCov” library was used, which allows transforming the AFT model into the Weibull risk function, which is defined as: (5) $$h\left(t\right)=\mathrm{\lambda }\mathrm{\gamma }{\left(t{e}^{-\mathrm{\beta }x}\right)}^{\mathrm{\lambda }-1}{e}^{-\mathrm{\beta }x}$$Where: h(t) is the risk function, λ is the model form parameter (λ > 0), γ is the scale parameter (γ > 0), β is the explanatory variable coefficient, which can take values between positive and negative infinity (Carroll, 2003). Finally, t is the average elapsed survival time in which graft mortality events occurred at some moment within the evaluation period (note that t < T), when the start of the first monthly evaluation is considered as the study origin. The values for the parameters λ, γ and β are estimated with the following equations, that imply the use of the parameters calculated for the above AFT model (Eq. 4): (6) $$\mathrm{\lambda }=e^{-\mathrm{\alpha }/\mathrm{\sigma }}$$ (7) $$\mathrm{\gamma }={\displaystyle \frac{1}{\mathrm{\sigma }}}$$ (8) $$\mathrm{\beta }={\displaystyle \frac{-\mathrm{\delta }}{\mathrm{\sigma }}}$$

In turn, the Weibull risk function allows obtaining the risk coefficient or ratio (hazard ratio, HR) of an explanatory variable (x), which measures a specimen’s probability of death based on said variable, over a time (t) previously defined by the researcher. If λ > 1 the value of HR increases, while HR decreases if λ < 1 (Carroll, 2003; Zhang, 2016). If the value of the hazard ratio is 1.0, means that the risk of death is equal between treatments; if the value of the hazard ratio is less than one, it means a reduction in the risk of death in one of the treatments, while if the hazard ratio is greater than one, the risk of death increases in one of the treatments (Carroll, 2003; Ghorbani et al., 2016) The HR is determined by the following equation (Igl, 2018): (9) $$HR={\left(e^{-\mathrm{\beta }}\right)}^{\mathrm{\lambda }-1}$$

The parameters β and λ of the HR equation (Eq. 9), are the same parameters calculated for the Weibull risk function (Eq. 5).

The Weibull risk function model uses dummy variables to predict the HR. To perform survival analysis on the R platform, the “censored” data is used to indicate living specimens, which are coded with a zero (0) (Pohar & Stare, 2006). The censored data are those specimens which are alive at the end of the evaluation, and are named that way because it is not possible to know precisely at what time they will experience the death event. Therefore, dead grafts at the end of the evaluation period were coded with a one (1). The donor-tree type (TDT) and scion position in the donor’s tree crown (SPC) were coded as follows: Grafts made with scions from trees of the pure species (0) and grafts made with hybrid tree scions (1); grafts with scions from the upper third of the crown (0) and grafts with scions from the middle third of the crown (1).

Survival rate

Figure 3 shows the results of grafts survival during the first 4 months of evaluation. In the 1st month after grafting, the survival condition of the scion grafts from the middle third of the crown of hybrid trees was total, while the treatment with lower survival was that of scion grafts from the upper third of the crown of trees of the pure species with 86.6%.

On the other hand, scion graft treatments from the middle third of the pure species tree crown and scion grafts from the upper third of the hybrid tree crown had 90.0% and 93.3% survival, respectively. In the first monthly evaluation no significant differences were found between treatments (p = 0.390).

In the 2nd month of evaluation, scion treatments from the upper third of the pure-species tree crown and scions from the middle third of the pure-species tree crown, showed a survival of less than 80%. In contrast, scion grafts from the middle third of the crown of hybrid trees survived in their entirety, while the survival in the treatment of scion grafts from the upper third of the crown of hybrid trees was 93.3%; even so, no significant differences were found (p = 0.126).

In the 3rd month of evaluation, survival decreased to 66.6% for both scion treatments of pure species-donor trees; the treatment with the highest survival was that of grafts made with scions from the upper third of the crown of hybrid trees with 93.3%. The survival of the scion grafts from the middle third of the crown of hybrid trees decreased from 100% to 86.6% in the third month of evaluation; however, the four treatments were statistically equal (p = 0.128).

Survival decreased in the four treatments in the fourth month of evaluation, when the best treatment was that of scion grafts from the upper third of the crown of hybrid trees, with survival at 86.6%, however, the treatments continued without showing significant differences (p = 0.132).

Five months after grafting, survival varied from 86.6% to 13.3% among the treatments evaluated, with significant differences after the Bonferroni correction (p < 0.0083) between treatments. The grafts with better results occurred in the materials with hybrid tree scions (Fig. 4). In the two treatments where the effect of the position of the scion in the crown of the hybrid donor trees was separately evaluated, the results were statistically the same. On the other hand, the successful sprouting of the graft achieved with hybrid scions taken from both positions of the crown, was statistically superior to the grafting performed in the two treatments in which pure species donor tree scions were used. Significant differences were not found (p ≥ 0.0083) when the comparison was made just between grafts made with scions taken from the two crown positions of pure species donor trees (Fig. 4).

Pearson’s correlation test and stepwise regression to adjust the logit and Weibull models

A Pearson’s correlation test indicated that there is highly significant collinearity only between the height of the rootstock and height of the graft, so it was decided to exclude the RH variable in the adjustment of the Logit and Weibull models and include graft height, since the literature on Pinus grafts indicates that this last variable influences survival (González Jiménez et al., 2017). However, the stepwise regression applied to select variables to adjust the Logit and Weibull models, indicated that none of the graft variables was useful to describe the probability of survival significantly and not affected the probability of graft mortality (Table 2), since the only predictor variable that showed significant effect was the type of scion’s donor tree.

Odds ratio for graft survival according to the logit model

It was found in the Logit model that the intercept and the coefficient of the variable “type of scion donor tree” were highly significant (p < 0.0001) after the Bonferroni correction, in terms of the mortality of P. engelmannii grafts (Table 3). The probability p(x_i) of graft survival rates for each type of scion donor tree, during the evaluation period, is illustrated in Fig. 5.

The probability dispersion diagram (Fig. 5) indicates a different decreasing rate of the probability of graft survival, between the analyzed hybrid trees and trees of the pure species trough time. In the probability diagram, it is possible to verify that due to the positive value of the β₁ coefficient of the “type of scion donor tree” predictor variable (Table 3), the probability of survival increases by increasing the predictor variable x_i by one unit, that is to say when increasing from x₀ = 0 (trees of the pure species) to x₁ = 1 (hybrid trees). The probability of graft survival with pure-species tree scions (p(x₀)) was 25%, while the probability of graft survival with hybrid tree scions (p(x₁)) was 83.3% at the end of the 5 month evaluation period.

At the end of the evaluation, the number of live specimens were 50 grafts with scions from hybrid-donor trees and 15 grafts with scions from trees of the pure species; meanwhile, there were 10 and 45 dead grafts with scions from hybrids and trees of the pure species, respectively. The estimated odds ratio (Eq. 3) for the variable “type of scion donor tree” was 15.0, which was obtained with the following operation, which uses the relative frequencies of live and dead grafts by treatment: $$\mathrm{O}\mathrm{d}\mathrm{d}\mathrm{s}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}={\displaystyle \frac{a\times d}{b\times c}={\displaystyle \frac{\left(50/120\right)\times \left(45/120\right)}{\left(10/120\right)\times \left(15/120\right)}=15.0}}$$

Note that because the numerator variable a represents the relative frequency of living grafts with scions from hybrid-donor trees, the result of the equation means that the odds ratio (proportion) of successful grafts made with scions from hybrid-donor trees, in the long run after the evaluation period, will be 15 to one with respect to grafts made with pure species-donor tree scions.

Survival probability of P. engelmannii grafts according to the AFT model and Weibull risk function

The AFT model was highly significant for predicting the average survival time elapsed until the occurrence of the death event of one or more of the grafts that reached alive up until the end of the evaluation period. In addition, all parameters of the AFT model were highly significant even after the Bonferroni correction (Table 4).

According to the coefficient value δ of the “type of scion donor tree” variable, and when applying the exponent (e^(1.06) = 2.88), it is interpreted that when the x variable takes the value of 1 (hybrid-donor trees), the survival time T increases at a rate of 2.88 compared to what happens when x = 0 (pure species-donor trees). When developing the AFT model (Eq. 4), with the estimated parameters (Table 4) it was obtained that the estimated survival time for grafts with scions from pure species-donor trees is 156 days on average, while the graft survival time with scions from hybrid-donor trees is 450 days on average. In other words, it is estimated that the death of at least one graft would occur at 156 days in the case of scions from trees of the pure species and up to 450 days among the grafts of hybrid tree scions.

Depending on the T results mentioned above, the difference in survival between treatments will increase as time T also increases. The high statistical significance (p < 0.0001) of the two parameters (α and σ) and the coefficient δ shown in Table 4, allows accepting that the AFT model is significant and therefore, its parameters can be used to estimate the risk function (Eq. 5) and to estimate the hazard ratio (Eq. 9) of graft mortality, as a function of the type of scion donor tree. The parameters obtained for the Weibull risk function (h(t)) are shown in Table 5.

When applying Eq. (9), the hazard ratio at a time t = 150 days for the “type of scion donor tree” variable was 0.14 when referring to hybrid trees, while the hazard ratio in relation to scions donated by trees of the pure species is much higher (1.22). Whereby, the risk of graft death when using hybrid-donor tree scions is reduced by 86% ((1.0 minus hazard ratio) (100) = (1 − 0.14) (100) = 86). This risk of death, depending on the “type of scion donor tree” variable, is represented in the diagnostic diagram of the Weibull model (Fig. 6).

The cumulative risk of death of grafts with pure species-donor tree scions is greater during the entire evaluation period compared to graft survival when using hybrid tree scions. The cumulative risk of death of grafts with hybrid tree scions was only 0.14 at 5 months of evaluation. The differences are notorious in the risk of death between treatments, since the accumulated hazard ratio curves are not intercepted at any point in the diagram.