Heloisa Guimarães Santos · Flávia Maria Avelar Gonçalves · José Luis Lima ·Aurélio Mendes Aguiar · Gabriel Dehon Sampaio Peçanha Rezende ·Bruno Marco de Lima · Magno Antonio Patto Ramalho

Abstract To verify if the response by Eucalyptus clones in a single-tree plot is inf luenced by neighboring plants and to determine the ef fect of missing and/or dominated plants,seven eucalyptus trials in four Brazilian states were analyzed in a randomized complete block design with one plant/plot and 30 replications. Mean annual increment (MAI, m 3 ha −1 per year) was determined for three-year-old clones. The inf luence of neighboring clones was estimated by a linear regression coef ficient between the MAI of each clone/plot and the average of a clonal MAI and its eight neighbors.To determine the ef fect of missing and/or dominated trees,a correction between the MAI and the area available/plant was applied. Subsequent analysis considered unadjusted and adjusted data for missing and dominated trees. Estimate of accuracy and index of coincidence were used to compare the adjustments. In single-tree plots, clone performances were not inf luenced by neighboring plants. Experimental accuracy was not increased by any of the adjustments employed and the clone ranking was not altered, and therefore did not justify their use.

Keywords Single-tree plot · Missing plant adjustment ·Eucalyptus breeding

Introduction

One of the greatest challenges inEucalyptusbreeding is to continue to obtain gains in selected attributes. To achieve this, it is essential to use phenotyping strategies to detect genotypic dif ferences that are progressively smaller. It is also necessary to evaluate trials with a large number of progenies or clones. In addition, in plots with perennial species with wide spacing between individuals, the area is large, making trials dif ficult to conduct and decreases their accuracy.

An alternative is to use single-tree plots (STPs) that allow the use of a greater number of repetitions regardless of the number of progenies/clones assessed. This design has been carried out for several years and has been shown to be ef fective (Gezan et al. 2006; Stanger et al. 2012; Zhang et al.2015). In Brazil, especially inEucalyptustrials, STPs have been widely used (Santos et al. 2016; Nunes et al. 2018;Rezende et al. 2019).

Some critics of STPs argue that plants neighboring a particular plant may positively or negatively inf luence their performance. The main counter-argument is the high probability that each plant will have all other treatments in close proximity due to the large number of repetitions. For example, if 60 clones with 30 STP repeats were evaluated, each clone would have 240 (8 × 30) possibilities of having any of the other clones as neighbors and not just eight. It would be important, nonetheless, to use other strategies to show if the treatments are inf luenced or not by neighboring plants.

Another common aspect in STP trials is the occurrence of failed plants. If a particular treatment occurs near a missing plant, this treatment could, in theory, benef it from it,accordingly changing the ranking. Studies on the occurrence of missing plants, and particularly how to mitigate this, are common for annual crops. Some methodologies are well explained, such as the method of Zuber ( 1942) cited by Vencovsky and Cruz ( 1991), Cargnelutti Filho and Storck( 2004) and Silva et al. ( 2014), the use of covariance (Cargnelutti Filho and Storck 2004; Schmildt et al. 2006; Pavan et al. 2012), the adjust by means of other plants in the plot(Cargnelutti Filho and Storck 2004) or compensation (Vencovsky and Cruz 1991). With regards to forestry, there are only a few studies that consider missing plants for adjustment purposes (Andrade et al. 2006; Ferreira et al. 2020).

WithEucalyptus, Andrade et al. ( 2006) simulated the ef fect of failed plants on plots containing more than one plant and attempted to mitigate the damage by replanting.They found that this was only successful if replanting was carried out immediately, which is not always feasible in practice. Ferreira et al. ( 2020) evaluated the ef fect of missing plants using various clone and progeny trials and found that, in trials with less than 20% plant loss, no adjustment for missing plants was warranted.

In addition to missing plants, another common situation inEucalyptustrials is the occurrence of dominated plants,i.e., individuals with growth performance below average. In this situation, the plant neighboring a dominated plant could benef it and, especially in a STP, the ef fect of this advantage could alter the ranking and consequently the selection result. This aspect has also been poorly explored in analysis ofEucalyptusculture.

As previously noted, the ef fect of missing plants has been addressed using dif ferent approaches and mostly for annuals (Fernandes et al. 1989; Schmildt et al. 2001; Silva et al. 2014; Souza et al. 2014). With perennials, an empirical correction factor is often applied. Ferreira et al. ( 2020)proposed a linear regression coef ficient between the area explored by each plant—the independent variable (X), and the plant’s performance, in volume or any other trait—the dependent variable (Y). However, the use of this adjustment methodology, particularly in STPs, is still rare.

Given this context, the present study investigated the occurrence of neighbor inf luence on the performance ofEucalyptusclones and the ef fect of missing and/or dominated plants, in single-tree plots.

Materials and methods

The data used are from the evaluation ofEucalyptusclones by the company Suzano Incorporated. The trials were carried out in four Brazilian states in 2015. Two sites were located in Espírito Santo, two in São Paulo, two in Mato Grosso do Sul and one in Bahia. The environmental parameters of each site are shown in Table 1.

In this study, a dif ferent number of 3-year-old clones ofEucalyptus urophyllaS.T. Blake,E. grandisW. Hill and their hybrids were evaluated. The clones had dif ferent origins of selection and most were present in all trials. The spacing varied among the sites according to the company’s operational farms (Table 2). A randomized complete block design with one plant per plot (single-tree plot) and 30 repetitions was used.

Table 1 Characterization of Eucalyptus clonal test sites in each region

Table 2 Spacing, age and number of clones in each Eucalyptus clonal test

The stem cubic volume (V) was estimated from measurements of diameter at breast height (DBH, cm) and height (h,m) and a cylindrical form factor (f), determined by the company, corresponded tof= 0.43.

Mean annual increment (MAI, m 3 ha −1 per year) was determined by multiplying individual volume by the number of trees/ hectare and dividing by the age.

The possible inf luence of neighboring plant on the performance of a given clone was obtained by estimating the linear regression coef ficient (b) between the MAI of each clone by plot, the dependent variable Y, and the mean of its neighbors’ MAI of the 30 repetitions, independent variable X. Thus, an estimate of b was obtained for each clone on each site. The number of null hypotheses to be tested, i.e.,the lack of inf luence of neighboring plants for each clone,was very large, totaling 490 estimates. However, admitting the non-zero b estimate test to the same probability level increased the chance of type I error occurring, i.e., rejecting a true null hypothesis. The Bonferroni ( 1936 ) correction has been proposed to avoid this error, and consists in determining the value of the individual signif icance level (αT) as a function of the joint signif icance level (αE) and the number of tests performed (M), given by:

The evaluation of clones consisted of 490 tests (total number of clones including all seven trials), withα E= 0.05,and the individual signif icance level chosen to discuss the results of clone ef fects was 1.01 × 10 −4 .

A methodology similar to Ferreira et al. ( 2020) was used to verify the ef fect of missing plants in dif ferent trials. In this case, the absence of a neighboring plant was corrected by estimating a linear equation between the dependent variable Y (MAI) and the independent variable X (available area for the reference plant).

To calculate the area occupied by the plant, it was considered that the area of a missing plant was redistributed to a number of surrounding neighbors. For example, in a 3.0 m × 2.0 m spacing, if there were eight individuals around the missing plant, each individual would have 0.75 m 2 of area increased; if there were only seven individuals, each area would have increased by 0.86 m 2 and so on (Table 3 ).

The corrected MAI estimate was obtained by the following:

whereYcis the adjusted MAI per plot;Yis the observed MAI for each plot (clone);bis the angular coef ficient of the linearregression in m 3 ha −1 per year;Xis the area occupied by the plant;X0is the area that was supposed to be occupied by the plant if there were no missing plants (Table 3).

Table 3 Available area (m 2 ) according to the number of missing plants and spacing in Eucalyptus clonal tests

In the same way, another adjustment was made for absent and dominated trees. All plants with MAI 1.5 standard deviations below the mean were considered.

Subsequently, three analyses utilizing a linear mixed model for each trial were performed. The first analysis was done with unadjusted data (UA), the second used data adjusted only for the missing plants (MA), and the third used data adjusted for both missing and dominated plants (MDA).The model applied was:

whereyis the data vector Nx1 of clones in N blocks;is the vector for the f ixed ef fect from the clones;bis vector of random ef fects from the blocks;eis the vector of random ef fects from the errors;QandZare the incidence matrixes that relate observations to the ef fect of clones and blocks,respectively.

Estimates of the accuracy and index of coincidence were used to compare the ef fects of the proposed adjustments.

whereAis the number of matching clones in the two adjustments,Bis the number of clones selected in one adjustment, andCis the random number of clones selected in both adjustments. It is assumed that, among the selected clones,a proportion referring to the selection intensity coincides randomly. Thus, from 100 clones if 10% was selected, then one will coincide randomly.

Results

As expected, the linear regression estimate between the mean performance of the eight neighboring plants, independent variable (X), and the performance of the reference plant, dependent variable (Y), varied among the clones. As noted, b can assume negative and positive values. It was negative when clone performance was negatively af fected by neighbors and positive otherwise. However, it was found that the estimates were all small, ranging from − 2.6 for clone 19 in the MUC trial to 1.2 for clone 28 in the SMT trial, meaning that when the clone was most af fected by its neighbors,its performance decrease was only − 2.6 m 3 ha −1 per year.The largest benef it was 1.2 m 3 ha −1 per year. Nevertheless,it is important to note that in none of the 490 estimates of b did the value dif fer from zero using the signif icance level correction proposed by Bonferroni ( 1936) (Table 4).

The percentage of missing plants also varied among the trials. It was smaller in ARA at only 3.1% and higher in TLA2, with *32.1%. No association was found between the site mean per trial and the percentage of missing plants. The highest average was on the CBO site, 64.6 m 3 ha −1 per year and the percentage of lost plants was 4.7%. On the SMT site,

Table 4 Larger and smaller estimates of the linear regression coef ficient (b)between the dependent variable clone and the independent variable mean MAI of neighbors and standard errors(Se) in Eucalyptus clonal tests

where the mean was 25.0 m 3 ha −1 per year, the percentage of missing plants was the same 4.7% (Table 5).

The percentage of plants considered to be dominated,i.e., with performances 1.5 standard deviations below the average, ranged from 9.0% on the CBO site to 2.2% in the TLA1. The average percentage of dominated plants was 5.8%. Again, no association was found between the percentage of dominated plants and the overall trial mean (Table 5).

MAI frequency distributions (m 3 ha −1 per year) of each trial are shown in Fig. 1. The estimates of the mean in Table 5 and the maximum MAI limits 1.5 standard deviations below the mean (MDA adjustment) are shown (Fig. 1).The lowest mean estimate, as noted, occurred in SMT (25.0)and the largest in CBO (64.6). The maximum MAI limits with the MDA adjustment ranged from 17.1 for CBO and 2.5 for TLA1. This means that all plants in the CBO trial with a MAI lower than 17.1 m 3 ha −1 per year were not considered in the analyses; in the case of TLA1 this value was much lower at 2.5 m 3 ha −1 per year.

The estimates of b in the adjustments as a function of the available area ranged from 0.5 to 4.7 m 3 ha −1 per year and dif fered from zero to 5% (α < 0.05) for all clonal tests under both MAI adjustments except for MDA in SMT and MA in TLA1 (Table 6). The highest value was 4.7 in CBO for the MA adjustment, which means that under this condition,for each additional square meter available for the plant, it increased MAI by 4.7 m 3 ha −1 per year. Similarly, the estimate of b = 0.5 in the MDA trial conducted in SMT indicates that the increase per square meter due to missing plants was only 0.5 m 3 ha −1 per year. It is noteworthy that b estimates were always lower when considering missing and dominated plants (MDA), except for TLA1 and TLA2.

All estimates of accuracy were of high magnitude, indicating good experimental accuracy (Table 7). The values were higher than 90% in the dif ferent MAI adjustments except for the TLA2 clonal test which was accurate below 75%. TLA2 is the one with the highest numbers of missing plants (Table 5). Initially, this factor was responsible for the lower accuracy estimates. It was also found that when thepercentage of missing plant is below 30%, there are practically no signif icant dif ferences in the estimates of accuracy at dif ferent adjustment levels. It should be noted that changes in estimate accuracy are usually not signif icant when adjustments are implemented.

Table 5 Estimates of mean and percentages of missing plants, dominated trees (plants with 1.5 standard deviations below the mean) and total (missing plants + trees with 1.5 standard deviations below the mean) in Eucalyptus clonal tests without any type of adjustment

Fig. 1 Frequency distribution of mean annual increment (MAI, m 3 ha −1 per year) in six single-tree plot (STP) design trials evaluating Eucalyptus sp. The trials were conducted in seven environments

Table 6 Estimates of the linear regression coef ficient (b) between the dependent variable MAI and the independent variable available area and standard errors (Se) in Eucalyptus clonal tests considering the adjustments for missing plants (MA) and the adjustment for missing and dominated trees (MDA)

Table 7 Experimental accuracy obtained in Eucalyptus clonal tests for the variable MAI without any adjustment (UA) and with missing plant adjustment (MA) and adjustment for missing and dominated trees (MDA)

The indexes of coincidence, considering dif ferent percentages of plants that should be selected in the clonal tests,were higher than 70 in all selection intensities, apart from CBO with a selection intensity of 10% (Table 8). No changes were observed in clone ranking when only the MA adjustment was considered.

Discussion

A signif icant challenge for conducting clone evaluation trials is to obtain the highest possible estimates of selective accuracy (rgg′). Some factors nonetheless contribute to a reduced estimate of rgg′. One of these, inherent to the clones,is the genetic variation between treatments. Other factors are related to the experimental design and to the execution of the experiment (Ramalho et al. 2012).

One factor that most af fects the estimate of accuracy is the number of repetitions. In obtaining the phenotypic variance estimates (VF) between clonal means, which are the denominators of the selective accuracy estimates, the mean square of the source of clonal variation is divided by the number of repetitions. Consequently, the higher the number of repetitions, the lower the VFand the higher the experimental accuracy. However, increasing the number of repetitions in perennial plant trials on multi-plant plots is practically prohibitive due to the magnitude of the trials,especially regarding the evaluation stage. As noted, the use of a STP was recommended to solve this issue.

Plant breeders have adopted STPs in many breeding programs for perennial species due to the advantages (Zhang et al. 2015; Nunes et al. 2018). Some studies have compared the ef ficiencies of STPs against plots with several plants,especially for classifying progenies and clones and overall,it was found that the classif ication of treatments is similar(Scarpinati et al. 2009; Stanger et al. 2012).

Table 8 Percentage of coincidences between clones selected by the MAI ranking without any adjustments (UA), with missing plant adjustment(MA) and adjustment for missing and trees with 1.5 standard deviations below the mean (MDA)

As expected, estimates of b varied between clones and between trials. Although no estimate was signif icantly different from zero, the performance of each clone did not vary among the dif ferent possible neighbors. However, a literature search did not f ind studies that used this procedure to justify the use of STP. Considering that this present study analyzed seven trials over a wide range of sites and assessed a signif icant number of clones, the estimates obtained of b build a strong argument in favor of the use of STP, always including a large number of repetitions.

To further conf irm this, the highest estimate of b was for clone 19 in MUC, i.e., b = − 2.6 m 3 ha −1 per year as a function of its neighbors in dif ferent repetitions. Nevertheless,in this location the overall MAI was 54.0 m 3 ha −1 per year(Tables 4, 5). This estimate was not higher than 5% of the mean. Thus, given that there was no relationship between the performance of a particular clone and its neighbors, the use of single-tree plots should be encouraged, as they contribute to better estimates of genetic values due to the large number of repetitions, and consequently higher accuracy, as noted by Resende and Duarte ( 2007).

The situation of missing plants is another major concern when it comes to plant breeding trials and may lead to misinterpretation of results. This is particularly signif icant when it comes to perennial species and when the missing plants occur in early stages of the trials (Schmildt et al. 2001; Ferreira et al. 2020). In this study, the extent of missing plants ranged from 3% for ARA to 32% for TLA2, which corresponds to 67 and 693 individuals per experiment, respectively (Table 5). Reports of trials of missing plants ranging from 8 to 49% are common in the literature (Osorio et al.2003; Torres-Dini et al. 2016; Silva et al. 2019).

Apparently, it may be impossible to carry out trials of most cultivated species without failed plants. Thus, strategies are needed to mitigate the ef fects of missing plants. This is very common in annual species (Fernandes et al. 1989;Schmildt et al. 2001; Silva et al. 2014; Souza et al. 2014). In plots with perennial species, all plants are measured and it is possible to obtain the ef fect of the missing plant for each neighboring plant. The greatest challenge is to infer what benef it a failed plant might provide to its neighbor. Some results show that it is not viable to replant lost plants unless this is done early in the establishment stage (Andrade et al.2006).

One question that arises in trials with missing plants is whether plant survival varies with the treatments, clones or progenies being tested. In this case, the ef fect of missing plants must not be diminished. Steel et al. ( 1997) suggested performing a stand analysis before carrying out any procedure to mitigate the ef fect of missing plants. However, when dealing with STP, it is not possible to perform an analysis of variance using the number of missing plants per plot since it will be always zero or 100%. To verify whether it is feasible to apply any method to adjust the treatment means for missing plants, it was considered if there was any tendency for missing plants to happen in specif ic clones. However, it was impossible to infer if plant survivability was associated to a specif ic clone since, although variation between clones was detected, it was very small and varied from one environment to another. In this scenario, the adjustments for missing plants are viable.

Andrade et al. ( 2006) simulated f ive missing plant levels inEucalyptus urophyllaclones, ranging from 10 to 50%at two sites. They randomly selected a number of threemonth- old plants and eliminated them from the plot. Then,a covariance analysis for linear and quadratic ef fects were performed. Since the stands × clones interaction was signif icant, the stand ef fect within each clone was decomposed and the linear regression coef ficient for each was estimated to adjust the data. They verif ied that the linear regression stand correction using the number of missing plants as an independent variable was ef ficient and that there was a different compensation capacity in relation to the locations and clones.

As mentioned, studies analyzing both missing and dominated plants for methodological adjustments are rare and there is no consensus on which plants should be considered.However, it is believed that dominated trees individuals have a benef icial ef fect on growth and development of neighboring trees by allowing greater availability of light and nutrients and less competition (Leornardecz-Neto et al. 2003).Thus, the ef fect of a dominated plant may be similar to the absence of a plant (Ferreira et al. 2020).

More recently, Ferreira et al. ( 2020) proposed an adjustment based on the available area for each plant. Tree performance was adjusted for the missing plant by a linear regression with available area and MAI of each tree. However,most of the trials were for progeny evaluation and had more than one plant per plot.

Considering that in STPs the adjustment for missing plants is more decisive since the performance of each clone in a given plot refers to a single plant, the possible benef it of not having a neighboring plant may have greater repercussions in singletree plots than in trials with more plants per plot. Thus, we sought to verify the ef fect of missing plants in the STP experiment carried out under seven environmental conditions with wide variation in various factors. Not only missing plants, but plants with performances below average, particularly in singletree plots, are also likely to alter the performance of a neighboring plant due to less competition. This study considered a dominated plant as one with 1.5 standard deviations below the overall mean of the experiment. It was found that this varied among the plots (Fig. 1). However, as predicted, the mean of trees considered dominated was 5.8%, which was close to the expected (6.7%), with 1.5 standard deviations below the mean in a perfect normal distribution (Steel et al. 1997).

The alternative adopted to evaluate the ef fect of missing or dominated plants was to estimate the linear regression considering the available area for each plant, a method similar to the one by Ferreira et al. ( 2020). In the present study,the estimates of b varied among the trials, although all values were positive as expected, ranging from 1 to 4.6. It was also found, in most cases, that b estimates were higher when considering only missing plants (Table 6). This is because when dominated plants are eliminated, the variation in the MAI of evaluated clones decreases. Consequently, this contributes to the decreases in the estimates of the linear regression coef ficients. This was also found by Ferreira et al.( 2020) in trials with several plants per plot.

It appears that the advantage of a plant near a missing plant was relatively small. Considering for example, the highest estimate of B obtained, 4.7 m 3 ha −1 per year, the increase due to missing plants was only 7.2% of the overall environment mean. Unfortunately, this methodology has not been adopted by other researchers apart from Ferreira et al ( 2020), especially for trials with more than one plant per plot. As these data refer to three-year-old clones, it may be inferred that the spacing used by companies reduces competition between trees and consequently the ef fect of the absence of any plant ref lects little on the behavior of its neighbors. This information is obviously favorable for the use of STP.

Although the estimate of b may be considered small, it was checked to see if the adjustment could improve experimental accuracy or af fect the clone ranking. Virtually all estimate accuracies can be considered high (Resende and Duarte 2007), regardless of the adjustment applied (Table 7).In both types of adjustments (MA or MDA), changes in the magnitude of the accuracy were insignif icant, and in some cases the estimate of rgg′ was even lower. According to the analysis carried out, the use of the adjustment for improving the accuracy in STP trials is not justif ied since it normally presents high rgg′ estimates due to the large number of repetitions.

Another question is whether adjusting for stands or dominated plants alters the coincidence of clones that would be selected within dif ferent selection intensities. Although the coincidence estimates varied, they were small in magnitude to what would be obtained without the adjustment. Again, it is possible to infer that the use of adjustments for missing or dominated trees is not justif ied in single-tree plots.

Conclusions

Considering the more than 60 clones evaluated in this single-tree plot experiment, no signif icant variation was observed due to neighboring plants. Although there was an increase in the MAI of a tree neighboring a missing plant,the advantage was insignif icant. The use of adjustments for failures or dominated trees does not signif icantly change the experimental accuracy or ranking of the clones.

AcknowledgementsThe authors thank the Universidade Federal de Lavras and Suzano Papel e Celulose Incorporated, for providing the data.