Best Stand Correction Methods for Attenuating the Effects of Plant Loss in Experimental Plots of Coffea arabica Progenies

1. Introduction

The productivity performance of coffee crops in Brazil is linked mostly to the evolution of cultivation techniques and the use of improved cultivars [4]. Productivity gains have become significant over time and were achieved directly through the selection of cultivars with better production components and indirectly via the development of lineages resistant and/or tolerant to abiotic and biotic stresses.

In breeding programmes, progeny evaluation is the most costly and time-consuming stage. Experiments must be conducted with the greatest rigour and precision possible so that they have less errors and phenotypic differences represent the genotypic ones. The magnitude of experimental errors is directly related to the success of agricultural experimentation and plant breeding. Experimental accuracy is affected by several factors, such as the soil heterogeneity, presence of pests and diseases, plot size, design used, number of replications, and number of plants per plot [5].

There are many questions about the methods used in the evaluation of coffee progenies, and some of them have not yet been thoroughly researched. An example is plant loss in the plots, which reduces experimental precision and hinders identification of the best progenies [6]. Thus, measuring the effect of experimental plot failures and using methods that can attenuate such effect are necessary for improving the accuracy of estimates of genetic parameters.

Several stand correction approaches are found in the literature. A remarkably simple method is the rule of three (RT), which assumes proportionality between productivity and the number of plants in the experimental plot. However, such proportionality does not always occur, often resulting in a biased productivity value for the genotypes evaluated [2]. Zuber [1] proposed a second method (hereinafter referred to as ‘Zb’) to correct the RT error. However, this adjustment method also has limitations, as it does not consider the disposition of faults in the field, and its coefficient of compensation for lack of competition defaults to 0.3. Other methods which have proven to be efficient in many cases apply analysis of covariance, where the final stand of the plot is assumed as a covariate. The methods proposed by Cruz [3] and Vencovsky and Cruz [2] (hereinafter ‘Cr’ and ‘VC’, respectively) have also been used efficiently.

The compensatory effect of the crop under plot failure is another issue to be considered, since the plants adjacent to the failures generally have higher productivity owing to less competition for water, nutrients, and light. Although the compensatory effect is known to vary among different crops [6,7] there are no published reports about its occurrence in Coffea plants and how it affects the accuracy of experiments with coffee crops.

Therefore, the objectives of this present study were to determine the magnitude of the compensatory effect in Coffea crops, to verify the need for correction of the number of failures in experiments, and to identify the best stand correction methods to use. The knowledge gained from this study will guide breeders on the appropriate data analysis procedures to use for plant selection in the event of stand reduction due to management and/or climatic events.

2. Materials and Methods

The analyses were performed using production data (in kilograms per plot) from six harvests obtained from 11 Coffea arabica progenies testing experiments conducted by the Agricultural Research Company of Minas Gerais (Empresa de Pesquisa Agropecuária de Minas Gerais - EPAMIG). The experiments, which were carried out in four cities in the state of Minas Gerais (Table 1), were performed using a randomised block design, with four replications and six plants per plot.

F4 progenies from Icatu × Catimor and Mundo Novo × Catuaí crosses and lineages from the Mundo Novo, Catuaí, and Icatu groups were analysed (Table 1). Harvesting of the individual plots was conducted annually, with the coffee (coffee fruits of mixed maturity) volume obtained in each plot converted into 60 kg bags of processed coffee per hectare (bags.ha^-1).

The compensatory effect was determined by estimating the compensation coefficient (a) using the estimator a=c/(Y ̅ ), where c is the linear regression coefficient proposed by Cruz [1] and Y ̅ is the mean production yield per plant obtained in the experiment. An a-value equal to or greater than 1 indicates a positive compensatory effect on the crop.

Following the recommendation by Steel et al. [9], correction was not applied whenever significant differences in the final number of plants per plot (stand) between treatments were detected with the F test. In the absence of grain production data adjustments (AA), plant loss in the plot was disregarded (in this case, Zij = Yij). Otherwise, the productivity data were adjusted as a function of the variable stand, using the following six procedures: (i) the RT method, using the expression Zij = Yij(H/Xij), where H represents the ideal stand (in this case, six plants); (ii) the Zb method, using Zij = Yij([(H – a)(H – Xij)])/Xij, where a represents the compensation coefficient for the absence of competition (in this case, a = 0.3); (iii) the VC method, using Zij = Yij([(H – a)(H – Xij)])/Xj, where a represents the compensation coefficient estimated from experimental data; (iv) analysis of covariance with the ideal stand as the covariate (hereinafter ‘ACI’ method), using Zij = Yij – b(Xij – H), where b represents the linear regression coefficient as a function of Yij, estimated according to the procedure described by Steel et al [1]; (v) analysis of covariance with the average stand as the covariate (hereinafter ‘ACA’ method), using Zij = Yij – b(Xij – A), where b represents the Yij residual regression coefficient, estimated according to the procedure described by Steel et al [9] and A represents the average stand of the experiment; and (vi) the Cr method, using Zij = Yij(H/Xij) – c(H – Xij), where c represents the residual regression coefficient of the variable Yij (corrected using the RT method) as a function of the number of failures in the plot. In all the adjustment expressions above, Zij represents the corrected yield and Yij the observed production in real plots/stands (Xij).

Analyses of the six harvests were carried out using Zij data in a split-plot design over time [9] by applying the following statistical model: , where represents the observation of the ijq-th plot in block j of harvest q which received progeny i; m represents the constant associated with all observations; b_j is the fixed effect of the j-th block; p_i is the random effect of the i-th progeny, where p_i ~ NMV (0, ); c_q is the fixed effect of the q-th harvest; 〖pb〗_ij is the random effect of the ij-th progeny–block interaction, where ~ NMV (0, σ_pb^2), 〖bc〗_jq is the fixed effect of the jq-th block–harvest interaction; 〖pc〗_iq is the random effect of the iq-th progeny–crop interaction, where ~ NMV (0, ); and e_ijq is the random effect of the experimental error associated with the observation of the ijq-th plot, where 〖 e〗_ijq~ NMV (0, ). The empirical best linear unbiased prediction (E-BLUP) value was estimated by considering each adjustment method and the uncorrected data [10]. Estimates of the experimental accuracy were obtained algebraically using the square root of the heritability at the mean progeny level.

The magnitudes of the parameter estimates were used to verify which method would be the most efficient, including the mean (Y ̅_…), standard deviation of the mean (s), p-value, and selective accuracy (r ̂_(g ̂g)). The most effective methods for stand correction are those that result in less interference in the mean, smaller s-values, smaller p-values, and greater r ̂_(g ̂g) estimates.

The E-BLUP estimates obtained with each correction method were used to estimate the index of coincidence (IC) for a selection intensity of 20%; that is, the proportion of superior progenies and/or lineages with the same behaviour for each method compared with the unadjusted data. The IC was estimated using the method proposed by Hamblin and Zimmermann [11], which considers the effect of chance: IC= (A-C)/(M-C) x 100, where C represents the number of progenies and/or superior lineages selected as a result of chance (i.e. the number of selected progenies and/or superior lines in proportion to the selection intensity is assumed to coincide by chance); A is the number of superior progenies selected, common to the different methods; and M is the number of superior progenies and/or lineages selected with the AA method.

3. Results

Analysis of variance testing of the number of failures in each plot revealed whether they had occurred by chance (Table 2). The percentage of failures per experiment ranged from 4.33% to 46.25%, with the greatest loss being observed in the lineage of the Catuaí group. In two cases (Icatu × Catimor progenies in São Sebastião do Paraíso and Catuaí lineages in Capelinha), significant differences between progenies with regard to plot stands were detected, indicating that the progeny effect influenced plant loss in the plots.

Estimates of the mean linear regression coefficient (b), which reflects the coffee production response in the plot as a function of the change in the number of plants (stand), were generally expressive of the six harvests (Table 1). The experiment with Mundo Novo × Catuaí de Campos Altos progenies presented a negative b estimate, indicating that each failure resulted in a decrease of 1.07 kg in the plot. For the other cases, the b estimates ranged from 0.88 to 1.99, indicating an increase of 3.64–14.08% relative to the mean production in the plot.

Considering the existence of b, the compensation coefficient for lack of competition (a) was estimated for each experiment and year of harvest (Table 2). There was variation between groups of progenies, between locations, and (mainly) between harvesting years. The greatest variation occurred in the Mundo Novo lineage experiment in Três Pontas, where estimates ranged from –0.001 (H 02) to 6.60 (H 05). In general, compensation within the same experiment increased over time until a level of equilibrium was reached. Comparisons of the coefficients between experiments showed that the failures in the Mundo Novo × Catuaí experiment (conducted in Três Pontas) were the ones that changed the productive response pattern of the plants the most (Y ̅_…= 1.63), since this experiment showed greater compensation for the lack of competition.

Having determined that failures did indeed change the productive response pattern of the coffee plants, it was necessary to apply methods that result in adequate selection. With this objective in mind, six methods for correcting the production data of the Coffea arabica progenies were tested. Comparisons of the adjusted data with the original data (AA) showed that the six correction methods used generally overestimated the means to different degrees (Table 3). The RT method provided the highest mean estimate, overestimating it by 18.72% in relation to the original data (AA). Likewise, the Zb method overestimated the mean of all trials by 15.56%. By contrast, the best mean estimates were obtained with the VC and ACA methods, which overestimated the unadjusted mean by only 4.34% and 4.72%, respectively (Table 3).

The standard deviation, which indicates the degree of data dispersion in relation to the mean, had the the highest value estimated in the RT method (6.81). This inferred that in addition to overestimating the data and not considering compensation, this method is inappropriate for increasing dispersion around the mean (Table 4).

For each set of adjusted data, the p-value, selective accuracy, and genetic correlation between progeny ordering and IC value of the five best progenies selected were estimated to evaluate the influence of plant loss on the selection carried out by coffee breeders in their routine work. The p-value was interpreted as a gradation of probabilities of accepting or rejecting H0, rather than being a fixed value above which no significant difference is considered. Therefore, regardless of the fixed level of significance, we analysed the possibility of a change in the variation probability due to the analysed factor.

Analysis of the F4 progenies generated by the Icatu × Catimor cross in Campos Altos showed that the lowest p-values were obtained with the Cr (0.08) and AA (0.09) methods, albeit they were not significant at the 5% level according to the standard procedure. These two methods were more accurate (0.63 and 0.61) and generated a 100% IC in the ACI and ACA methods (Table 4). Based on the IC values, the RT method resulted in the most discrepant transformation in the selections made (0.14). For this population, the best parameters were obtained using the Cr method, which resulted in greater selective accuracy and genetic correlation and an IC equal to the AA data, yielding a probability of differences due to genotype of 6.32%.

The progenies of Mundo Novo × Catuaí in Campos Altos obtained the best fit with the ACI, ACA, and Cr methods, which yielded the highest selective accuracy. About the correlation and coincidence in selection, the ACI, ACA, and Cr methods again provided the same ordering and selection as the AA method. In Capelinha, the genetic variance was not significant, indicating the difficulties in selecting superior genotypes in that location. The VC method performed well, since it promoted the best genetic discrimination of progenies, as verified by the p-value. Thus, the correlation and IC values of the VC method were equal to those of the correction methods with the best fit (i.e. ACI and ACA), leading to the conclusion it may be the best data adjustment approach in this situation. Likewise, in Três Pontas, the VC method achieved greater discriminatory power and selected the same progenies as the methods with best fit (ACI and ACA) did (Table 4).

For the Icatu progenies, whether in Campos Altos or in Capelinha, the best parameter estimates were obtained with the ACI, ACA, and AA methods. There was no genetic variation in the progenies in Campos Altos, whereas genetic effects were highly significant in those in Capelinha and the selective accuracy was high. The genetic correlation of the ACI- and ACA-corrected data with the AA data was high, generating a selection IC of 100% in Campos Altos and 76% in Capelinha.

About the Mundo Novo progenies, the ACI and ACA methods stood out in fitting the data to the model in the three experimental locations. In Campos Altos, the AA method presented the highest selective accuracy value. An identical pattern was observed for the progenies in Capelinha. By contrast, the AA, ACI, and ACA methods were not able to identify genetic differences in the progenies in Três Pontas and selected only 70% of coinciding progenies.

4. Discussion

For perennial crops such as coffee, the breeder must pay attention to the use of appropriate experimental techniques that minimise experimental errors. Losses caused by the inadequacy of techniques will only be verified after several years and may reduce selection efficiency and delay the obtention of progenies and/or new cultivars. Regardless of whether they are controllable or not, all factors that affect the error must be observed by breeders in order to increase the efficiency of the selection process.

The loss of plants in the plot causes major problems in data analysis and experimental result interpretation, since it results in uneven stands and compromises experimental precision, with the consequences being greater for perennial crops as they perpetuate errors throughout the duration of the experiment [12]. Currently, information on how to deal with plant losses in plots of coffee experiments in the field remains scarce. Therefore, in this study, an extensive EPAMIG database was analysed to understand the influence of the compensatory effect of Coffea arabica progeny production on productivity data and identify alternatives for overcoming this problem.

In this study, the linear regression coefficient of productivity with the number of plants in the plot and the compensatory effect of the production of adjacent plants against an absent plant were estimated. This balance between production loss and compensation is genetically determined and depends on the planting spacing and arrangement failures in the plot [2]. Of the 54 harvests studied, 32 had a compensation coefficient value of greater than 1, indicating a positive mean capacity for production compensation as a function of each failure present in the plot of 1.15 (Table 3). Considering that this set of data is quite representative of actual scenarios, coffee trees possibly have a significant capacity to compensate for the absence of plants in the plot or a decrease in the stand in the case of wider spacing. These results appear to make biological sense, since compensation follows the natural productive increase in coffee trees, which reaches a peak between the sixth and eighth harvest, stabilising their biennial production until ageing of the plants [13]

The results obtained corroborate those of other researchers, who reported that plant production compensation in the same crop varies between experiments, demonstrating the influence of genotypes and soil and climate conditions on this parameter. These effects were verified in maize [15] and beans [16,17]. In the present study, the observed differences in compensation for lack of competition (Table 3) can be attributed to the fact that coffee progenies vary in their ability to respond to spacing via root growth differentials [17] and respond to light through different plagiotropic branches, angles, and plant heights [18].

After verifying the fit of the model and analysing whether the variation is heritable and the phenotype faithfully represents the genotype, we observed the impact of data transformations in terms of plant loss in the plot on progeny selection. First, the analysis was carried out in a split-plot design over time, which is a common procedure for production data in coffee breeding as it identifies precocious progenies in relation to production and allows estimation of genetic variances free of progeny–crop and progeny–block interaction variances [19].

For progeny and cultivar competition tests, it is necessary to work on the data in order to verify their need for correction due to plant loss in the plots. Genetic correlation and IC analyses were then performed to determine the magnitude of progeny ordering change and the proportion of similarity between the selections carried out by the different methods in association with a probability chosen by the breeder. In this study, the most adequate methods for correcting the productive data of the progeny tests were chosen on the basis of the p-value and selective accuracy and verified for each population (Table 4). The results revealed that generalisations are not appropriate, making it impossible to establish fixed rules, since the interaction of the evaluated plant with the cultivation environment results in a relatively plastic response.

The estimated compensation coefficients obtained from the various experiments varied greatly when the fixed factor of 0.3 used in the Zb method was applied, revealing this method to be ineffective. Only 13% of the studied estimates were similar to the 0.3 value recommended by Zuber [1], indicating the need to reconsider this correction method for coffee crops.

Likewise, stand correction using the RT method was not effective, as it did not provide greater estimates of selective accuracy in any of the experimental situations studied and instead presented the highest production means, which overestimated the mean production value. According to Vencovsky and Cruz [2], this method has been efficient in situations where the degree of failure compensation in the plot was low but has proven to be inefficient in cases where the compensation was high (close to 1). Although the RT method is not useful for data correction, it is necessary for calculating the compensation coefficient due to irregularities in the experimental stand.

In general, the covariance correction methods for average and ideal stands were efficient, as they promoted greater decrease in the residual variance through a reduced p-value and increased the experimental precision, corroborating the findings by other researchers who analysed maize [14] and grain sorghum [17].

In the search to establish a relationship between selection decisions based on data corrections and those based on the original data (unadjusted), it was found that six of the nine selection decisions by the breeders were completely coincident with what was conducted in the populations of Icatu × Catimor [21,22], Mundo Novo × Catuaí [23,24], and lineages from the Mundo Novo [25], Catuaí [26], and Icatu groups [27]. Therefore, assuming that the adjustments are biologically correct, the breeders were correct 66.67% of the time. As breeding requires intensive use of resources, a 33.33% probability of error in selection is considerably high and demonstrates, once again, the importance of considering the effect of plant loss in the plot.

If we ignore the importance of properly applying a correction method in experiments with plot failures, the possible effects of competition between plots may result in the selection of genotypes that have limited value for the trait and target environments. Furthermore, many of the actual genetic effects are small in magnitude for a polygenic trait, potentially contributing to statistical bias and error [28].

Despite not being the focus of this study, data correction needs to be understood in the context of genotype–environment interaction. In this study, the data were analysed according to experimentation locations within populations. However, after identifying the most suitable methods for correcting failures, these data can be used in joint analyses of the environments under study, increasing the chance of correct decisions being made.

Another aspect identified through the interpretation of the results of this study is the criterion for choosing the correction methods to be applied. This decision should consider several parameters together and first analyse the existence of genetic variance, selective accuracy, correlation between phenotype and genotype, and ordering of the progenies, lineages, or cultivars under evaluation. The comparison of progenies under equal conditions is essential for ensuring the genetic progress of cultivars and the efficiency of breeding programmes. Therefore, it is important to carry out experiments that allow plants to express their genetic potential. Although many unforeseen events may occur, the experiments need to be carefully conducted, especially in the crop formation phase.