Classifying coefficients of genetic variation and heritability for <i>Eucalyptus</i> spp.

Ziegler, Ana Cristina da Fonseca; Tambarussi, Evandro Vagner

doi:10.1590/1984-70332022v22n2a12

Abstract

The objective of this study was to establish classification ranges for genetic and additive genetic coefficients of variation, as well as for broad and narrow sense heritability, as a function of growth and wood quality traits for Eucalyptus spp. We conducted statistical analyses to determine differences in this classification the types of coefficients used. The selected studies that met the inclusion criteria, 58 presented genetic variation coefficients (448 data points) and 53 presented heritability coefficients (423 data points). To descriptive statistics and the Shapiro-Wilk test, we confirmed that it was necessary to separate coefficients and traits into groups. Inconsistencies for growth traits were observed, confirming the influence of experimental error, indirect estimation methods, and environmental effects on coefficient estimates. We recommend the use of the classification tables included in this literature review to interpret results in studies so as to standardize the classification of coefficients of genetic variation and heritability.

Keywords:
Eucalyptus; genetic parameters; coefficient of genetic variation; coefficient of heritability

INTRODUCTION

According to a report published by the Brazilian Tree Industry (IBÁ 2021IBÁ - Indústria Brasileira de Árvores2021 Relatório anual. Available at: < Available at: https://iba.org/datafiles/publicacoes/relatorios/iba-relatorioanual2020.pdf >. Accessed on June 03, 2021.
https://iba.org/datafiles/publicacoes/re... ) in 2020, Eucalyptus is the most commonly planted genus and crop in commercial forestry in Brazil, occurring on 77% of the total area of planted forests, for a total of 6.97 million hectares. Brazil is a prominent player worldwide in terms of genetic improvement programs. Therefore, potential studies related to the genetic improvement of Eucalypt species are important in the global context.

Currently, research on Eucalyptus spp. is aimed at the selection of individuals based on both quantitative genetic parameters and the combination of quantitative and molecular genetics. Therefore, well-conducted experiments are extremely important. In agricultural and forestry studies, experimental coefficients of variation (CV _e) are frequently estimated to obtain the degree of precision and infer errors in data analysis. Pimentel-Gomes (1985Pimentel-GomesF1985 Curso de estatística experimental. Nobel, Piracicaba, 466p) established classification ranges for the experimental coefficient of variation for agricultural species, and four years later, Garcia (1989GarciaCH1989 Tabelas para classificação do coeficiente de variação. IPEF, Piracicaba. (Circular Técnica, 171).) proposed a methodology to classify these coefficients with data from Eucalyptus spp. Later, Mora and Arriagada (2016MoraFArriagadaO2016 A classification proposal for coefficients of variation in Eucalyptus experiments involving survival, growth and wood quality variables. Bragantia 75:263-267) further complemented these studies with the classification of wood quality and growth variables, also based on the experimental coefficient of variation for Eucalyptus spp.

Another frequently estimated parameter is the coefficient of heritability that indicate the success of breeding with selection. Resende (2002ResendeMDV2002 Genética biométrica e estatística no melhoramento de plantas perenes. Embrapa Informação Tecnológica, Brasília, 975p) established a general classification range for this parameter, categorizing genetic heritability within the range of 0.1 to 15% as low, 15 to 50% as moderate, and greater than 50% as high.

However, to understand the genetic variation existing in experiments using progenies or clones, two coefficients are generally used: coefficients of genetic variation (CV _g, CV _gi), based on the method described by Burton (1952BurtonGW1952 Qualitative inheritance in grasses. In Proceedings of the 6th international grassland congress. Pennsylvania State College, Pennsylvania, p. 277-283); and coefficients of heritability ( $h_{g}^{2}$ , $h_{a}^{2}$ ) defined between 1918 and 1940 by FisherFisherRA1918 The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh 52:399-433, Wright, and Lush LushJL1940 Intrusive collection of regression of offspring on dams as a method of estimating heritability of characters. Proceedings of the American Society of Animal Nutrition 33:293-301(Visscher et al. 2008VisscherPMHillWGWrayNR2008 Heritability in the genomics era - concepts and misconceptions. Nature Reviews Genetics 9:255-266).

To ensure success in the selection of genetic materials with desirable traits, coefficients of genetic variation help to identify, quantify, and compare the genetic variability of traits that can be maintained, thus making inferences about the possible outcomes of selection (Resende 1991ResendeMDV1991 Correções nas expressões do progresso genético com seleção em função da amostragem finita dentro de famílias de populações e implicações no melhoramento florestal. Boletim Pesquisa Florestal 22/23: 61-77. , Houle 1992HouleD1992 Comparing evolvability and variability of quantitative traits. Genetics 130:195-204, Santos et al. 2018SantosWDAguiarASouzaDCDiniDGSouzaFDalastraCMachadoJASousaVAMoraesMDFreitasMSebbennA2018 Genetic variation and effective population size in Dipteryx alata progenies in Pederneiras. Revista Árvore 42:1-8). Along with heritability coefficients, which offer estimates of the genetic contribution for each trait or quantify the genetic origins of phenotypic variation, it is possible to infer and analyze the proportion of traits that are inherited, the genetic control over traits, and the impact of non-heritable factors, such as environmental effects.

These parameters have been used in several studies and applied to several species. However, more specific classification ranges are needed for Eucalyptus. In particular, statistical analyses are required to determine whether there are differences in classification between the coefficients of genetic variation and additive genetic variation, and between broad and narrow sense genetic heritability, as a function of Eucalyptus spp. growth and wood quality traits. Both of these issues are objectives of the present study.

MATERIAL AND METHODS

The values of the coefficients of genetic variation (CV_g and CV_gi) and genetic heritability ( $h_{g}^{2}$ and $h_{a}^{2}$ ) were obtained from selected studies through a systematic review of Brazilian and international research on species of the genus Eucalyptus published between 1990 and 2021. The inclusion criteria included only scientific articles that present one or both coefficients of genetic variation (CV _g, CV _gi) or coefficients of genetic heritability ( $h_{g}^{2}$ , $h_{a}^{2}$ ) in the field of genetics and forest improvement. Coefficients are calculated based on genetic variance, whether additive or non-additive, and obtained through estimation for each trait. As for nomenclature, the genetic parameters differ depending on the analyzed genetic material: a) CV _g and $h_{g}^{2}$ are used for data obtained from clonal tests; b) CV _gi and $h_{a}^{2}$ for data obtained from progenies.

From a total of 64 identified studies, 58 on Eucalyptus spp. met the inclusion criteria for coefficients of genetic variation, while 53 presented heritability coefficients for the most common traits of interest for wood quality and growth. Data presented for coefficients of genetic variation and heritability were collected for the following traits: tree height (H, m), diameter at breast height (DBH,cm), volume (VOL,m³), mean annual increment (MAI,m³), basic wood density (BWD,kg m^-3), stem straightness (STR) and survival (SURV.,%). The coefficients of genetic variation and heritability of all traits were expressed as a percentage (%).

We used the Shapiro-Wilk test to assess normality in three scenarios: a) normality test for all traits without separating the two coefficients of variation (CV) or the two heritability estimates (h²); b) normality test for each trait independent of the coefficients of genetic variation or heritability; c) normality test for each trait for each group (coefficient of genetic variation or heritability considered separately or together) established in the previous steps. These analyses were performed to filter the data and identify common and divergent groups between the traits and the two coefficients of variation. According to the second scenario (b), CV or CVs and h² are defined as common groups, that is, the traits that follow the normality of the data do not require the separation of the coefficients according to the type of genetic material.

After this separation, we estimated the number of observations for each situation and trait (n), the minimum value (min), the maximum value (max), the average ( $\bar{x}$ ) and the standard deviation (SD), to describe the shape of distribution. Statistical analyses were performed in the R statistical environment (R Core Team 2017R Core Team2017 A language and environment for statistical computing. Available at < Available at https://www.R-project.org/ >. Accessed on June 05, 2021.
https://www.R-project.org/... ), using the “fBasics” package through the “basicStats” function.

The classification of coefficients of variation and heritability were established according to the methodology proposed by Costa et al. (2002CostaNHADSeraphinJCZimmermannFJP2002 Novo método de classificação de coeficientes de variação para a cultura do arroz de terras altas. Pesquisa Agropecuária Brasileira 37:243-249), in which an independent interpretation of the normality of the data is proposed. Intervals of coefficients of variation were developed as a function of the median (MD) and pseudo-sigma (PS). According to the methodology presented by Costa et al. (2002CostaNHADSeraphinJCZimmermannFJP2002 Novo método de classificação de coeficientes de variação para a cultura do arroz de terras altas. Pesquisa Agropecuária Brasileira 37:243-249), the pseudo-sigma is a standard deviation based on the interquartile range that can be used independently of a normal distribution (W) hen there is no normal data distribution, the use of pseudo-sigma is more robust than the standard deviation.

The median (MD) was estimated using the formula: $M D = \frac{(Q 1 + Q 3)}{2}$ , where Q1 is the first quartile and Q3 is the third quartile. The pseudo-sigma (PS) was calculated with the formula:

$P S = \frac{(Q 3 - Q 1)}{1.35}$ . The classification ranges of the coefficients of variation were determined as follows:

a) low $(C V_{g}, C V_{g i} or C V_{S} \leq M D - P S)$ ;

b) moderate $(M D - P S < C V_{g}, C V_{g i} or C V_{S} \leq M D + P S)$ ;

c) high $(M D + P S < C V_{g}, C V_{g i} or C V_{S} \leq M D + 2 P S)$ ;

d) very high $(C V_{g}, C V_{g i} or C V_{S} > M D + 2 P S)$ .

The classification ranges for coefficients of heritability:

a) low $(h_{g}^{2}, h_{a}^{2} or h^{2} \leq M D - P S)$

b) moderate $(M D - P S < h_{g}^{2}, h_{a}^{2} or h^{2} \leq M D + P S)$ ;

c) high $(M D + P S < h_{g}^{2}, h_{a}^{2} or h^{2} \leq M D + 2 P S)$ ;

d) very high $(h_{g}^{2}, h_{a}^{2} or h^{2} > M D + 2 P S)$ .

In this classification, negative values and values above 100% were not considered, as heritability coefficients do not fall below zero or above 100%.

RESULTS AND DISCUSSION

Genetic coefficients of variation

Of the 58 identified studies on different Eucalyptus species, 448 data points for coefficients of genetic variation were obtained. From 53 studies we found 423 data points for heritability. For both parameters, data for the traits diameter (DBH) and height (H) were the most frequent.

According to the Shapiro-Wilk test, the normality of the data without separating the coefficients of variation (CV _g and CV _gi) and regardless of the traits, provided a p value < 2.2×10^-16, indicating that there is no normal distribution of data between the two coefficients of variation. Thus, it is possible to treat them separately.

The results obtained for the normality of the data without separating either the coefficients of genetic variation or the coefficients of heritability, we identified a significant difference between the data due to variations found in the published research, such as the types of genetic materials used (seminal or clonal), small sample sizes used in studies on clones, and environmental effects. Pimentel-Gomes (1985Pimentel-GomesF1985 Curso de estatística experimental. Nobel, Piracicaba, 466p) suggests that the data should be stratified when it does not follow a normal distribution, enabling separation into variables and covariates according to the normality of the data. As such, herein we used the median and pseudo-sigma proposed by Costa et al. (2002CostaNHADSeraphinJCZimmermannFJP2002 Novo método de classificação de coeficientes de variação para a cultura do arroz de terras altas. Pesquisa Agropecuária Brasileira 37:243-249).

Regarding the differences between the minimum and maximum values of the coefficients, for wood quality (BWD) low values were obtained (min = 2.75%;max = 7.32%). For traits related to growth, volume (VOL) showed a wider range of variability between the minimum and maximum values ( CV _gi min = 6.0%;max = 40.38%). For (VOL) when considering the coefficient of genetic variation (CV _g ) min = 7.60%; max = 87.10%).

When we separated the traits as independent of the type of coefficient of genetic variation (CV _g and CV _gi ), we observed a normal distribution of data for the following traits: a) mean annual increment (MAI - p value =0.2246); b) survival (SURV, - p value =0.05211) and c) stem straightness (STR - p value=0.5266), suggest that these traits do not depend on the coefficients of genetic variation (CV _g or CV _gi ),being treated separately, thus it is possible to establish a common range for the interpretation and classification of these traits. For height (H - p value=1.696×10^-05); diameter (DBH - p value=9.231×10^-09); volume (VOL - p value=2.068×10^-06) and basic wood density it was (BWD- p value=1.703×10^-07) we observed that the data do not follow a normal distribution at a significance level of 5%, suggesting the need to separate traits as a function of each coefficient of genetic variation (CV _g or CV _gi ) (Table 1). Based on the analysis of normality, we tabulated the results for the traits separating the two coefficients of genetic variation (CV _g ) (Table 1A); CV _gi (Table 1B) and created a common group (CV_S = CV _g and CV _gi , Table 1C) for traits that can be interpreted independently of the differentiation of these two coefficients.

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Table 1
Shapiro-Wilk test, descriptive statistics, and classification range for coefficients of variation: A - genetic (CVg), B - additive genetic (CV _gi ) and C - common range group(CV = CV _g and CV _gi )for Eucalyptus spp

Although the coefficients and traits were stratified, we did detect a normal distribution in the data for the coefficient of additive genetic variation (CV _gi ) with the traits volume (VOL) and basic wood density (BWD). In these cases, there were no significant differences between their means or as a function of sample size, i.e., with small sample sizes there is insufficient data to detect the effects.

For height, diameter, volume, and BWD, the classification ranges for the coefficients of genetic variation (CV _g ) and additive genetic variation (CV _gi ) must be unique and interpreted individually. For MAI, survival, and stem straightness, they can be classified with a common range, regardless of the nomenclature used for the coefficients of genetic variation.

As for the interval ranges for the coefficients of genetic variation (CV _g ), we found an overall average classification of values below 5.66% as low, from 5.66 to 18.34% as moderate, 18.34 to 24.68% high, and above 28.68% very high. The traits height, diameter, and BWD presented classifications similar to the overall average, while volume showed a classification of values below 12.31% as low, from 12.31 to 35.44% as moderate, from 35.44 to 47% as high, and above 47% as very high.

The results presented indicate high levels of significance between the data for the coefficients of genetic variation (CV _g ) even after stratification. This is likely due to the differentiation found in the data from studies with clones of Eucalyptus spp., which can be attributed to the sample size of the tested genetic material. According to Gonçalves et al. (2001GonçalvesFRezendeGDSPBertolucciFLGRamalhoMAP2001 Progresso genético por meio da seleção de clones de eucalipto em plantios comerciais. Revista Árvore 25:295-301) a large number of clones should be tested to increase the chance of selecting individuals and obtaining better clones than the existing ones. Thus, we suggest that for these studies a greater number of clonal materials should be included so that they are representative and effective for future selection.

For coefficients of additive genetic variation (CV_gi), the general classification showed values below 5.50% as low, from 5.50 to 17.96% moderate, from 17.96 to 24.19% high, and greater than 24.19% very high. The traits height and diameter were similar to the average classification intervals, while volume and BWD presented different ranges. For volume, we established values below 8.52% as low, from 8.52 to 35.12% as moderate, from 35.12 to 48.43% high, and above 48.43% very high. For BWD, values below 4.75% were interpreted as low, from 4.75 to 6.89% as moderate, from 6.89 to 7.95% as high, and above 7.95 % rated very high.

The additive genetic variation coefficient (CV _gi ) the basic wood density (BWD) is noteworthy due to the limited variation between minimum and maximum values, suggesting that this wood quality trait tends to be more stable or may be less severely affected by environmental factors (O'Brien et al. 2007O’Brien EK, Mazanec RA and Krauss SL2007 Provenance variation of ecologically important traits of forest trees: implications for restoration. Journal of Applied Ecology 44:583-593, Fritsche Neto et al. 2012Fritsche NetoRVieiraRAScapimCAMirandaGVRezendeLM2012 Updating the ranking of the coefficients of variation from maize experiments. Acta Scientiarum. Agronomy 34:99-101). The same was not observed for volume (VOL), considering either the coefficient of genetic variation (CV _g ) or the additive genetic variation (CV _gi ). This result indicates that this growth trait is unstable and influenced by experimental errors, indirect estimates, as well as environmental factors.

For the common range group (CV_S), there was an overall average classification of values below 9.22% as low, from 9.22 to 25.10% as moderate, from 25.10 to 33.04% as high, and greater than 33.04% very high. The traits survival and stem straightness showed intervals similar to the observed overall average. MAI presented intervals that differed from the average, with values below 16.73% classified as low, from 16.73 to 38.64% as moderate, from 38.64 to 49.59% as high, and above 49.59% as very high.

Heritability coefficients

According to the Shapiro-Wilk test, when checking the normality of the data without separating the heritability coefficients ( $h_{g}^{2}$ and $h_{a}^{2}$ ) regardless of the traits, we found a p-value of < 2.2×10^-16, indicating no normal distribution of the data.

When we consider traits independent of the type of heritability coefficient ( $h_{g}^{2}$ and $h_{a}^{2}$ ), we observed a normal distribution of data for the following traits: a) BWD ( p value=0.395 ) and b) stem straightness (STR - p value=0.1273 ). This suggests that these traits do not depend on the separation of the heritability coefficients ( $h_{g}^{2}$ and $h_{a}^{2}$ ) and it is therefore possible to establish a common range of coefficients for the interpretation and classification of these traits. For height (H - p value =3.842×10^-05); diameter (BWD - p value=1.175×10^-10); volume (VOL - p value=1.675×10^-05); mean annual increment (MAI - p value =0.01055) and survival (SURV, - p value =0,008447) the data does not follow a normal distribution at a significance level of 5%, suggesting the need to separate traits according to each heritability coefficient ( $h_{g}^{2}$ or $h_{a}^{2}$ ) (Table 2).

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Table 2
Shapiro-Wilk test, descriptive statistics, and range for genetic heritability: A - in the broad sense (

h_{g}^{2}

), B - in the narrow sense (

h_{a}^{2}

) and C - both combined for Eucalyptus spp

Based on the analysis of normality, the separation of traits for the heritability coefficients was performed ( $h_{g}^{2}$ ) (Table 2A) or $h_{a}^{2}$ $h_{g}^{2}$ (Table 2B). The common range group ( $h^{2} = h_{g}^{2} and h_{a}^{2}$ , Table 2C) included the traits that can be interpreted independently of the nomenclature used or whether these coefficients are treated separately.

According to the descriptive statistics of broad sense heritability, we observed relatively high and similar median and pseudo-sigma values for diameter (DBH), height (H) and volume (VOL). Similar results were found for mean annual increment (MAI) with narrow sense heritability. Meanwhile, basic wood density BWD for the common heritability group had high median values and moderate pseudo-sigma.

The classification range of heritability coefficients ( $h_{g}^{2}$ or $h_{a}^{2}$ ) for height, diameter, volume, mean annual increment, and survival must be treated separately and interpreted individually. Basic wood density and stem straightness were classified according to a common range, regardless of the difference in nomenclature used for the coefficients.

For broad sense heritability ( $h_{g}^{2}$ ) a mean average classification range was established in which values below 4.5% were classified as low, from 4.5 to 63.5% as moderate, from 63.5 to 80.6% as high, and above 80.6% very high. All traits showed wide variation, with survival presenting the smallest variation with the most similar values to the mean classification interval in relation to the others. Thus, for survival, values below 1.23% were classified as low, from 1.23 to 10.60% as moderate, from 10.60 to 15.28% as high, and greater than 15.28% very high.

According to the results obtained for broad sense heritability, the median and pseudo-sigma values related to the growth traits were high and relatively similar, showing a wide variation in the data. Estimates of genetic parameters obtained in clonal tests of Eucalyptus spp. showed that variations in broad sense genetic heritability depend on growth traits, which is consistent to what was observed in this article; however, the general averages of these values were similar among them and close to 0.5 for diameter, height and volume (Furlan et al. 2020FurlanRATambarussiEVMoraesCB2020 Genetic parameters of Eucalyptus spp. clones in northeastern Brazil. Floresta 50:1267-1278).

In relation to the coefficient of narrow sense heritability ( $h_{a}^{2}$ ), the average overall classification considers values below 7.3% as low, from 7.3 to 40.0% as moderate, 40.0 to 56.3% high, and above 56.3% as very high. The traits height, diameter, volume, and survival presented classifications similar to the general average, while MAI was classified with values below 17.46% as low, from 17.46 to 51.54% as moderate, from 51.54 to 68.57% high, and greater than 68.57% as very high.

Again, this indicates that growth traits are unstable, with diameter and height measurement errors associated with the use of equations that directly influence the accuracy of the estimate, i.e., volume. Furthermore, these results can be influenced by environmental effects, making genetic control difficult, an issue that is not observed for narrow sense heritability. According to Vencovsky (1987VencovskyR1987 Tamanho efetivo populacional na coleta e preservação de germoplasmas de espécies alógamas. Revista IPEF 35:79-84) the lower the genetic control over the traits the greater the influence of environmental factors and vice versa. Another possibility is that there is a reduction in preexisting genetic variability due to the number of clonal materials tested in the studies (similar to what occurs for coefficients of genetic variation) and the fact that clonal materials have a non-additive genetic variance and are not used of crosses to obtain selected clones. Again, the greater the number of clones tested, the greater the genetic variability and, consequently, the greater the potential to select superior clones (Gonçalves et al. 2001GonçalvesFRezendeGDSPBertolucciFLGRamalhoMAP2001 Progresso genético por meio da seleção de clones de eucalipto em plantios comerciais. Revista Árvore 25:295-301).

In terms of the common range for heritability coefficients (h²), the average classification showed values below 21.1% as low, from 21.1 to 48.3% as moderate, from 48.3 to 61.9% as high, and above 61.9% as very high. The two traits included in this group presented classifications similar to the general average, but with variation. For example, BWD values below 34.63% were interpreted as low, from 34.63 to 64.58% as moderate, from 64.58 to 79.55% as high, and above 79.55% as very high, while stem straightness (STR) showed less variation, with values below 7.57% classified as low, from 7.57 to 32.01% as moderate, from 32.01 to 44.23% as high, and above 44.23% as very high.

The for the narrow sense heritability and BWD for the common heritability group showed similar median values (MD) but differed due to high and moderate pseudo-sigma, respectively. This suggests that there is better data distribution than that obtained for the broad sense heritability data. Materials obtained from progenies (CV _gi and $h_{a}^{2}$ , which have a high magnitude of genetic control (Resende et al. 1995ResendeMDVVencovskyRFernandesJSC1995 Selection and genetic gains in populations of Eucalyptus with a mixed mating system. In Proceedings of CRC-THF - IUFRO conference Hobart, Australia “Eucalypt plantations: improving fibre yield and quality”. Cooperative Research Centre for Temperate Hardwood Forestry, Hobart, p. 191-193) due to a lower degree of relatedness and selection, will consequently have greater genetic variability and greater additive genetic variance (Tambarussi et al. 2018TambarussiEVPereiraFBSilvaPHMLeeDBushD2018 Are tree breeders properly predicting genetic gain? A case study involving Corymbia species. Euphytica 214:150-161).

When analyzing the estimated average for the traits, we found that the average values fall within the moderate classification range, regardless of the separation of the coefficients of genetic variation or heritability. This supports the work of Burdon (2008BurdonRD2008 Short note: coefficients of variation in variables with bounded scales. Silvae Genetica 57:179-180) who states that the mean must be close to the moderate range so that the correction and interpretation of the scales of variation of the traits are effective. In general, the average heritability of BWD was greater than the other traits; however, BWD has a low average coefficient of genetic variation, which is a limiting factor for the selection of potential genetic materials (Houle 1992HouleD1992 Comparing evolvability and variability of quantitative traits. Genetics 130:195-204), as was observed by Hamilton and Potts (2008HamiltonMPottsB2008 Eucalyptus nitens genetic parameters. New Zealand Journal of Forestry Science 38:102-119).

In conservation, forest improvement programs and genetics studies, many authors have considered values of coefficients of genetic variation above 7% as high, referring to a study carried out by Sebbenn et al. (1998SebbennAMSiqueiraACMFKageyamaPYMachadoJAR1998 Parâmetros genéticos na conservação da cabreúva - Myroxylon peruiferum L.F. Allemão. Scientia Forestalis 53:31-38) with the forest species Cabreúva (Myroxylon peruiferum LF Allemão), or have compared their work to this previous study to interpret the results. Through statistical analyses, the present study provides a basis to specifically interpret each parameter and trait.

As observed herein, there is distinct nomenclature for the coefficients of genetic variation and heritability, which is due to the type of genetic variance used to calculate these parameters and is a function of the genetic material in question. For progenies, the coefficient of additive genetic variation (CV _gi ) is calculated, from which narrow sense heritability ( $h_{a}^{2}$ ) is estimated. Similarly, for clones, the coefficient of genetic variation (CV _g ) is calculated and broad sense heritability ( $h_{g}^{2}$ ) is based on the total genetic variance (additive, dominance, and epistatic).

When analyzing data from previous research, it is possible that different types of progenies were used in each study, and the lack of information about the type of progenies, whether half- or full-sibs, can directly influence the estimates of coefficients of heritability and genetic variation. However, the more pronounced influence on the classification ranges for heritability is attributed to their estimation and uncertainty around inbreeding coefficients in open pollinated progeny tests in the forest and not the classification proposed in this article.

Generally, in breeding programs, a selection intensity of 10% is established in the short term and 50% in the long term; thus, the higher the coefficient of genetic variation, the greater the possibility of genetic gains. Cornelius (1994CorneliusJ1994 Heritabilities and additive genetic coefficients of variation in forest trees. Canadian Journal of Forest Research 24:372-379) states that genetic selection must be based mainly on the coefficient of genetic variation in addition to heritability and from that the selection intensity can be defined. When selection intensity is defined solely based on heritability, we may wrongly assume the level of genetic variation, thus creating problems in the future. When estimating a parameter considering inappropriate genetic variances for that genetic material or stating that the coefficient of genetic variation is high or low without proper classification, that mistakes can be made in the selection of individuals which in turn will affect the desired outcome for genetic variability. According to a study of genetic variability in Eucalyptus progenies, estimates of the genetic variation coefficients can characterize the existence of genetic variability among progenies and indicate the genetic nature of the material; therefore, the classification proposed in this article may inform the genetic variability through the classification intervals for each trait, complementing and explaining the information obtained in the estimates (Moraes et al. 2015MoraesCCarvalhoEZimbackZimbackLLLuzOPieroniGMoriELealT2015 Variabilidade genética em progênies de meios-irmãos de eucaliptos para tolerância ao frio. Revista Árvore 39:1047-1054).

CONCLUSIONS

Through the present literature review, we obtained data from studies published in journals on species of the genus Eucalyptus and found the need for a universal classification for coefficients of genetic variation and heritability for studies on forest improvement and genetics. The present study provides a basis for classifying and interpreting genetic variation and heritability coefficients for diameter, height, volume, BWD, MAI, survival, and stem straightness in analyses on the Eucalyptus genus. The use of the classification interval tables (Tables 1 and 2) presented herein is recommended for the interpretation of results in future studies, which can help to standardize and simplify the classification of coefficients of genetic variation and heritability.

ACKNOWLEDGEMENTS

Ana C. F. Ziegler received a scholarship from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Prof. Dr. Evandro V. Tambarussi is supported by a research productivity fellowship granted by CNPq (grant number 304899/2019-4).

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HamiltonMPottsB2008 Eucalyptus nitens genetic parameters. New Zealand Journal of Forestry Science 38:102-119
HouleD1992 Comparing evolvability and variability of quantitative traits. Genetics 130:195-204
IBÁ - Indústria Brasileira de Árvores2021 Relatório anual. Available at: < Available at: https://iba.org/datafiles/publicacoes/relatorios/iba-relatorioanual2020.pdf >. Accessed on June 03, 2021.
» https://iba.org/datafiles/publicacoes/relatorios/iba-relatorioanual2020.pdf
LushJL1940 Intrusive collection of regression of offspring on dams as a method of estimating heritability of characters. Proceedings of the American Society of Animal Nutrition 33:293-301
MoraFArriagadaO2016 A classification proposal for coefficients of variation in Eucalyptus experiments involving survival, growth and wood quality variables. Bragantia 75:263-267
MoraesCCarvalhoEZimbackZimbackLLLuzOPieroniGMoriELealT2015 Variabilidade genética em progênies de meios-irmãos de eucaliptos para tolerância ao frio. Revista Árvore 39:1047-1054
O’Brien EK, Mazanec RA and Krauss SL2007 Provenance variation of ecologically important traits of forest trees: implications for restoration. Journal of Applied Ecology 44:583-593
Pimentel-GomesF1985 Curso de estatística experimental. Nobel, Piracicaba, 466p
R Core Team2017 A language and environment for statistical computing. Available at < Available at https://www.R-project.org/ >. Accessed on June 05, 2021.
» https://www.R-project.org/
ResendeMDV1991 Correções nas expressões do progresso genético com seleção em função da amostragem finita dentro de famílias de populações e implicações no melhoramento florestal. Boletim Pesquisa Florestal 22/23: 61-77.
ResendeMDV2002 Genética biométrica e estatística no melhoramento de plantas perenes. Embrapa Informação Tecnológica, Brasília, 975p
ResendeMDVVencovskyRFernandesJSC1995 Selection and genetic gains in populations of Eucalyptus with a mixed mating system. In Proceedings of CRC-THF - IUFRO conference Hobart, Australia “Eucalypt plantations: improving fibre yield and quality”. Cooperative Research Centre for Temperate Hardwood Forestry, Hobart, p. 191-193
SantosWDAguiarASouzaDCDiniDGSouzaFDalastraCMachadoJASousaVAMoraesMDFreitasMSebbennA2018 Genetic variation and effective population size in Dipteryx alata progenies in Pederneiras. Revista Árvore 42:1-8
SebbennAMSiqueiraACMFKageyamaPYMachadoJAR1998 Parâmetros genéticos na conservação da cabreúva - Myroxylon peruiferum L.F. Allemão. Scientia Forestalis 53:31-38
TambarussiEVPereiraFBSilvaPHMLeeDBushD2018 Are tree breeders properly predicting genetic gain? A case study involving Corymbia species. Euphytica 214:150-161
VencovskyR1987 Tamanho efetivo populacional na coleta e preservação de germoplasmas de espécies alógamas. Revista IPEF 35:79-84
VisscherPMHillWGWrayNR2008 Heritability in the genomics era - concepts and misconceptions. Nature Reviews Genetics 9:255-266

Publication Dates

Publication in this collection
01 July 2022
Date of issue
2022

History

Received
14 Nov 2021
Accepted
03 Apr 2022
Published
15 Apr 2022

This is an open-access article distributed under the terms of the Creative Commons Attribution License

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[9] GonçalvesFRezendeGDSPBertolucciFLGRamalhoMAP2001 Progresso genético por meio da seleção de clones de eucalipto em plantios comerciais. Revista Árvore 25:295-301

[10] HaldaneJBS1932 A mathematical theory of natural and artificial selection. Part IX. Rapid selection. Proceedings - Cambridge Philosophical Society 28:244-248

[11] HamiltonMPottsB2008 Eucalyptus nitens genetic parameters. New Zealand Journal of Forestry Science 38:102-119

[12] HouleD1992 Comparing evolvability and variability of quantitative traits. Genetics 130:195-204

[13] IBÁ - Indústria Brasileira de Árvores2021 Relatório anual. Available at: < Available at: https://iba.org/datafiles/publicacoes/relatorios/iba-relatorioanual2020.pdf >. Accessed on June 03, 2021.
» https://iba.org/datafiles/publicacoes/relatorios/iba-relatorioanual2020.pdf

[14] LushJL1940 Intrusive collection of regression of offspring on dams as a method of estimating heritability of characters. Proceedings of the American Society of Animal Nutrition 33:293-301

[15] MoraFArriagadaO2016 A classification proposal for coefficients of variation in Eucalyptus experiments involving survival, growth and wood quality variables. Bragantia 75:263-267

[16] MoraesCCarvalhoEZimbackZimbackLLLuzOPieroniGMoriELealT2015 Variabilidade genética em progênies de meios-irmãos de eucaliptos para tolerância ao frio. Revista Árvore 39:1047-1054

[17] O’Brien EK, Mazanec RA and Krauss SL2007 Provenance variation of ecologically important traits of forest trees: implications for restoration. Journal of Applied Ecology 44:583-593

[18] Pimentel-GomesF1985 Curso de estatística experimental. Nobel, Piracicaba, 466p

[19] R Core Team2017 A language and environment for statistical computing. Available at < Available at https://www.R-project.org/ >. Accessed on June 05, 2021.
» https://www.R-project.org/

[20] ResendeMDV1991 Correções nas expressões do progresso genético com seleção em função da amostragem finita dentro de famílias de populações e implicações no melhoramento florestal. Boletim Pesquisa Florestal 22/23: 61-77.

[21] ResendeMDV2002 Genética biométrica e estatística no melhoramento de plantas perenes. Embrapa Informação Tecnológica, Brasília, 975p

[22] ResendeMDVVencovskyRFernandesJSC1995 Selection and genetic gains in populations of Eucalyptus with a mixed mating system. In Proceedings of CRC-THF - IUFRO conference Hobart, Australia “Eucalypt plantations: improving fibre yield and quality”. Cooperative Research Centre for Temperate Hardwood Forestry, Hobart, p. 191-193

[23] SantosWDAguiarASouzaDCDiniDGSouzaFDalastraCMachadoJASousaVAMoraesMDFreitasMSebbennA2018 Genetic variation and effective population size in Dipteryx alata progenies in Pederneiras. Revista Árvore 42:1-8

[24] SebbennAMSiqueiraACMFKageyamaPYMachadoJAR1998 Parâmetros genéticos na conservação da cabreúva - Myroxylon peruiferum L.F. Allemão. Scientia Forestalis 53:31-38

[25] TambarussiEVPereiraFBSilvaPHMLeeDBushD2018 Are tree breeders properly predicting genetic gain? A case study involving Corymbia species. Euphytica 214:150-161

[26] VencovskyR1987 Tamanho efetivo populacional na coleta e preservação de germoplasmas de espécies alógamas. Revista IPEF 35:79-84

[27] VisscherPMHillWGWrayNR2008 Heritability in the genomics era - concepts and misconceptions. Nature Reviews Genetics 9:255-266

Trait	n	P(W)	min	máx	X ̄	SD	MD	PS	Interval (%)
									Low	Moderate	High	Very high
A - CV_g (%)
H	77	0.001	1.8	20.0	8.1	3.9	7.9	3.1	CV_g ≤ 4.80	4.80 < CV _g ≤ 10.97	10.97 < CV _g ≤ 14.06	CV_g > 14.06
DBH	76	0.0004	2.3	23.7	10.0	4.9	9.3	4.6	CV_g ≤ 4.69	4.69 < CV _g ≤ 13.93	13.93 < CV _g ≤ 18.54	CV_g > 18.54
VOL	33	0.0001	7.6	87.1	25.7	16.7	23.9	11.6	CV_g ≤ 12.31	12.31 < CV _g ≤ 35.44	35.44 < CV _g ≤ 47.00	CV_g > 47.00
BWD	8	0.0064	2.4	27.9	8.4	8.7	6.9	6.1	CV_g ≤ 0.85	0.85 < CV _g ≤ 13.03	13.03 < CV _g ≤ 19.12	CV_g > 19.12
Mean	49	0.0019	3.5	39.7	13.1	8.6	12.0	6.4	CV_g ≤ 5.66	5.66 < CV _g ≤ 18.34	18.34 < CV _g ≤ 24.68	CV_g > 24.68
B - CV_gi (%)
H	62	0.0101	1.7	23.3	9.0	4.8	8.1	4.5	CV_gi ≤ 3.57	3.57 < CV_gi ≤ 12.63	12.63 < CV_gi ≤ 17.17	CV_gi > 17.17
DBH	84	0.0121	3.0	32.4	12.4	6.9	11.2	6.0	CV_gi ≤ 5.16	5.16 < CV_gi ≤ 17.21	17.21 < CV_gi ≤ 23.23	CV_gi > 23.23
VOL	28	0.050*	6.0	40.4	20.9	10.0	21.8	13.3	CV_gi ≤ 8.52	8.52 < CV_gi ≤ 35.12	35.12 < CV_gi ≤ 48.43	CV_gi > 48.43
BWD	19	0.388*	2.8	7.3	5.6	1.2	5.8	1.1	CV_gi ≤ 4.75	4.75 < CV_gi ≤ 6.89	6.89 < CV_gi ≤ 7.95	CV_gi > 7.95
Mean	48	0.1150*	3.4	25.9	12.0	5.7	11.7	6.2	CV_gi ≤5.50	5.50< CV_gi ≤ 17.96	17.96 < CV_gi ≤ 24.19	CV_gi >24.19
C - CV= CV_g (%) and CV_gi (%)
MAI	24	0.225*	6.6	52.1	28.2	12.5	27.7	11.0	CV_S≤ 16.73	16.73 < CV_S ≤ 38.64	38.64 < CV_S ≤ 49.59	CV_S > 49.59
SURV.	12	0.050*	1.0	39.6	14.2	11.5	12.3	7.7	CV_S ≤ 4.61	4.61 < CV_S ≤ 19.97	19.97 < CV_S ≤ 27.64	CV_S > 27.64
STR	25	0.527*	0.6	20.0	11.0	5.5	11.5	5.2	CV_S ≤ 6.31	6.31 < CV_S ≤ 16.69	16.69 < CV_S ≤ 21.87	CV_S > 21.87
Mean	20	0.2673*	2.7	37.2	17.8	9.8	17.2	8.0	CV_S ≤ 9.22	9.22 < CV_S ≤25.10	25.10 < CV_S ≤33.04	CV_S > 19.12
Overall	448

Trait n P(W) min máx X ̄ SD MD PS Interval (%) Low Moderate High Very high
A - h² _g (%)
H	48	0.0010	1.0	95.0	38.7	30.4	38.0	39.6	$h_{g}^{2}$ = 0	0 < $h_{g}^{2}$ ≤ 77.63	77.63< $h_{g}^{2}$ ≤ 100	$h_{g}^{2}$ = 100
DBH	47	0.0011	1.0	93.0	40.1	30.3	39.3	33.7	$h_{g}^{2}$ ≤ 5.53	5.53< $h_{g}^{2}$ ≤ 72.95	72.95< $h_{g}^{2}$ ≤ 100	$h_{g}^{2}$ = 100
VOL	33	0.0061	4.0	93.0	50.8	29.3	53.0	43.0	$h_{g}^{2}$ ≤ 10.04	10.04< $h_{g}^{2}$ ≤ 95.96	95.96< $h_{g}^{2}$ ≤ 100	$h_{g}^{2}$ = 100
MAI	11	0.0166	6.0	92.2	36.3	31.2	33.0	27.5	$h_{g}^{2}$ ≤ 5.47	5.47< $h_{g}^{2}$ ≤ 60.43	60.43< $h_{g}^{2}$ ≤ 87.91	$h_{g}^{2}$ > 87.91
SURV	8	0.3479*	1.0	11.2	6.3	4.0	5.9	4.7	$h_{g}^{2}$ ≤ 1.23	1.23< $h_{g}^{2}$ ≤10.60	10.60< $h_{g}^{2}$ ≤15.28	$h_{g}^{2}$ > 15.28
Mean	29	0.0062	2.6	76.9	34.4	25.0	33.8	29.7	$h_{g}^{2}$ ≤ 4.5	4.5< $h_{g}^{2}$ ≤63.5	63.5< $h_{g}^{2}$ ≤80.6	$h_{g}^{2}$ > 80.6
B - $h_{a}^{2} (%)$
H	75	0.0000	3.0	92.0	21.9	17.3	18.8	15.5	$h_{a}^{2}$ ≤ 3.29	3.29< $h_{a}^{2}$ ≤ 34.25	34.25< $h_{a}^{2}$ ≤ 49.73	$h_{a}^{2}$ > 49.73
DBH	97	0.0000	2.0	99.8	23.3	18.4	21.5	15.6	$h_{a}^{2}$ ≤ 5.94	5.94< $h_{a}^{2}$ ≤ 37.06	37.06< $h_{a}^{2}$ ≤ 52.61	$h_{a}^{2}$ > 52.61
VOL	33	0.0017	3.0	60.0	20.0	15.8	19.6	16.8	$h_{a}^{2}$ ≤ 2.79	2.79< $h_{a}^{2}$ ≤ 36.47	36.47< $h_{a}^{2}$ ≤ 53.32	$h_{a}^{2}$ > 53.32
MAI	9	0.6149*	14.0	64.4	33.6	16.7	34.5	17.0	$h_{a}^{2}$ ≤ 17.46	17.46< $h_{a}^{2}$ ≤ 51.54	51.54< $h_{a}^{2}$ ≤ 68.57	$h_{a}^{2}$ > 68.57
SURV	5	0.3351*	0.5	35.0	21.8	15.1	23.7	16.8	$h_{a}^{2}$ ≤ 6.88	6.88< $h_{a}^{2}$ ≤40.46	40.46< $h_{a}^{2}$ ≤57.24	$h_{a}^{2}$ > 57.24
Mean	44	0.1903*	4.5	70.2	24.1	16.7	23.6	16.3	$h_{a}^{2}$ ≤ 7.3	7.3< $h_{a}^{2}$ ≤40.0	40.0< $h_{a}^{2}$ ≤56.3	$h_{a}^{2}$ > 56.3
C - $h^{2} = h_{g}^{2} (%) and h_{a}^{2} (%)$
BWD	27	0.3950*	11.0	96.0	51.1	21.4	49.6	15.0	h²≤ 34.63	34.63< h²≤ 64.58	64.58< h²≤ 79.55	h² > 79.55
STR	30	0.1273*	2.0	47.0	20.5	12.6	19.8	12.2	h²≤ 7.57	7.57< h² ≤ 32.01	32.01< h² ≤ 44.23	h²> 44.23
Mean	29	0.2611*	6.5	71.5	35.8	17.0	34.7	13.6	h²≤ 21.1	21.1< h² ≤48.3	48.3< h² ≤61.9	h²> 61.9
Overall	423

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