ORIGINAL PAPER

Genetic parameters in a rubber tree population: heritabilities,genotype-by-environment interactions and multi-traitcorrelations

Guilherme Augusto Peres Silva & Salvador Alejandro Gezan &

Melissa Pisaroglo de Carvalho & Lígia Regina Lima Gouvêa & Cecília Khusala Verardi &André Luis Bombonato de Oliveira & Paulo de Souza Gonçalves

Received: 12 December 2013 /Revised: 31 May 2014 /Accepted: 18 June 2014# Springer-Verlag Berlin Heidelberg 2014

Abstract Rubber tree breeding programs are mainly drivenby selection of individuals with high yield and quality ofrubber. Data from 51 open-pollinated progenies tested on sixsites in Brazil were analyzed over several traits to estimate thefollowing: genetic parameters such as narrow-sense heritabil-ity and additive genetic variance in single- and multi-siteanalyses, type B correlations to determine the relevance ofgenotype-by-environment interactions and its effects on alter-native selection strategies, additive genetic repeatability cor-relation for rubber yield based on three consecutive yearlymeasurements, and typeA correlations to evaluate trait-to-traitgenetic associations for all measured traits. Average rubberyield (RYm) showed an estimated narrow-sense heritability of0.31, with an estimated type B correlation of 0.84, indicatinglow levels of genotype-by-environment interaction. The traitsurvival and number of latex vessel rings (RG) showed largergenotype-by-environment interaction and the lowestheritabilites. High to moderate type B correlation was foundfor most traits, with a value of 0.85 between diameter (or girth)and RYm; therefore, it is possible to achieve interesting rubberyield genetic gains (over 3 years of measurements) fromindirect selection based on diameter at age 2.

Keywords Hevea brasiliensis . Yield . Genetic parameters .

Narrow-sense heritability . Genetic correlations . Geneticgain . Genotype-by-environment interaction

Introduction

Rubber tree [Hevea brasiliensis (Willd. ex Adr. Than Juss.)Muell-Arg.], a member of the family Euphorbiaceae genusHevea, is native to the Amazon region (Priyadarshan andGonçalves 2003). According to the International RubberStudyGroup (IRSG 2013), in 2012, the worldwide productionof natural rubber was 11.33 million tons. From this, Brazilcontributes with only a small amount of the production total-ing 0.17 million tons; also, 0.18 million tons of rubber wereimported to the country in 2012. The national yield of rubbergrew 23% between 2010 and 2011 (IBGE 2011). This growthis due to a booming demand from the tire industry whichtracks the automobile industry and which have both achievedhigh growth rates in recent years. The limited cultivation ofrubber tree in South America is essentially due to the presenceof a disease known as South American leaf blight (SALB),which is caused by the Ascomycete fungus Microcylus ulei(Le Guen et al. 2011). Currently in Brazil, the rubber tree isplanted in areas without the SALB such as São Paulo, EspíritoSanto, Mato Grosso, Mato Grosso do Sul, Goiás, Bahia, andParaná States (Gonçalves and Marques 2008).

In Brazil, breeding programs for this species are mainlydriven by selection of individuals with high rubber yieldpotential. The Instituto Agronomico (IAC) from Campinas,São Paulo, conducts a breeding program that aims to selectsuperior genotypes for vigor and rubber quality. Selection ismainly based on secondary traits, such as the following: vigor,stem growth during bleeding, virgin bark thickness, bark

Communicated by R. Burdon

Electronic supplementary material The online version of this article(doi:10.1007/s11295-014-0766-5) contains supplementary material,which is available to authorized users.

G. A. P. Silva : L. R. L. Gouvêa :C. K. Verardi :A. L. B. de Oliveira : P. d. S. GonçalvesInstituto Agronômico de Campinas, Programa Seringueira,Campinas, SP, Brazil

S. A. Gezan (*) :M. P. de CarvalhoSchool of Forest Resources and Conservation, University of Florida,P.O. Box 110410, Gainesville, FL 32611, USAe-mail: sgezan@ufl.edu

Tree Genetics & GenomesDOI 10.1007/s11295-014-0766-5

healing, resistance to diseases, resistance to wind damage, andtolerance of drought. Most breeding is done with parents thatshow outstanding performance in field trials; however, theinformation about the genetic worth of many of these parentsis limited (Gonçalves and Marques 2008). The average timerequired to release tested genotypes is between 20 and30 years; due to this long period, breeders are currently aimingto reduce the selection cycle through early production assess-ments and to make better use of secondary traits that showhigh correlations with latex production.

The establishment of effective breeding strategies dependson a detailed knowledge of the genetic architecture underlyingthe inheritance of the traits of interest, such as the following:magnitude of heritability, levels of genotype-by-environmentinteraction (GEI) or type B correlations (Burdon 1977), andgenetic correlations between traits (or type A correlations), allelements that influence the level of response to selection.Knowledge of the genetic control of a trait through the esti-mation of the heritability is critical to identify relevant traitsand to evaluate the scope for genetic gains. The identificationof genotypes with good performance and wide adaptability toseveral environments is an important aspect for breedingprograms that span a large geographical area and/or withcontrasting environments. In addition, knowledge of pheno-typic and genetic correlations between primary and secondarytraits is key to predicting the effects of direct and indirectselection.

Few reports of heritabilities, and particularly genetic cor-relations, from countries such as Malasia (Tan et al. 1975),Nigeria (Alika 1985), Sri Lanka (Jayasekera et al. 1994), andBrazil (Costa et al. 2000; Furlani et al. 2005; Gonçalveset al. 2005, 2006; Verardi et al. 2012; Gouvêa et al. 2013; Silvaet al. 2013) are available for rubber tree. However, none ofthese studies has been exhaustive enough to explore all thecritical elements of the genetic architecture on a givenpopulation.

In this study, data originated from six sites established onthe State of São Paulo, Brazil, where several growth andcommercial yield related traits, are analyzed in detail to esti-mate the following: (1) genetic parameters such as narrow-sense heritability and additive genetic variance in single- andmulti-site analyses, (2) type B genetic correlations to deter-mine the relevance of GEIs and its effect on alternativeselection strategies, (3) additive genetic correlationrepresenting year-to-year repeatability for rubber yield basedon three consecutive yearly measurements, and (4) type Agenetic correlations to evaluate trait-to-trait genetic associa-tions for all measured traits. Despite rubber quality been animportant aspect, we concentrate in the traits related to vigorand rubber yield. Other publications (Costa et al. 2000)have reported analyses with a subset of this data, but weexpand this to additional traits and sites, with a more completemodel specification.

Material and methods

Genetic material and data

The genetic material comprises open-pollinated progenies of51 parents, where 24 of these parents came from original, wildpopulation selections and 27 correspond to second- or third-generation breeding parents. To evaluate these progenies,seeds were collected at Campinas Experimental Center(CEC), grown in polyethylene bags, and planted when theyhad at least two open leaves. A set of three field trials (Jaú,Pindorama, and Votuporanga) was established using 22 fam-ilies, and a second set (Colina, Ilha Solteria, and Votuporanga)contained 30 families. Only one of the families (RRIM 600)was common to all six trials; however, their parents corre-spond to individuals that are related to each other throughmultiple relatives. The farms where the trials wereestablished belong to the Agência Paulista de Agronegócios(APTA) and represent a range of rubber cropping regionsin the state of São Paulo, Brazil. Further details about thesesites are shown in Table 1, and their locations are shown inFig. 1.

The experimental design for each trial was a randomizedcomplete block layout with six replicates, with row plots often plants spaced at 1.5×1.5 m. The response variables mea-sured for each tree correspond to stem diameter, bark thick-ness, survival, rubber yield, and number of latex vessel rings.Individual-tree diameter (D50, cm) at age 2 was measured50 cm above the ground level. Bark thickness (BT, mm)measured at age 3 was calculated by taking the average ofthree virgin bark samples obtained by an extractor placed20 cm above the extraction panel. Individual survival (Surv)at age 3 was recorded as 1 for alive trees and 0 for dead trees.Rubber yield (RY, g/cut) was assessed at ages 2, 3, and 4 foreach tree, obtained by using a modified Hamaker Morris-Mann test (Tan and Subramaniam 1976). Briefly, this assayinvolved opening a panel with 10 cuts 15 cm above soil levelusing the S/2 (half spiral cut) and d/3 (interval between tap-pings, one each 3 days) system. The first five tapping sampleswere discarded as they represent the adaptation time of thepanel. Number of latex vessel rings (RG) at age 3 was obtain-ed by placing bark samples in histological paraffin andperforming radial longitudinal cuts. Samples were sectionedin a microton at a thickness of 125 μm, dehydrated in 90 %ethyl alcohol, stained with Sudan III, and number of latexvessel rings was counted in an optical microscope (10×).

Statistical analyses

In order to study the genetic architecture of rubber tree, severalanalyses were performed using the response variables previ-ously described. Single-site, multi-site, and repeatability anal-yses were performed to estimate narrow-sense heritabilities,

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type B, and repeatability correlations. Also, bivariate analyseswere performed in order to obtain types A and B correlationsbetween pairs of traits across all sites. Linear mixed modelsfitted to these data were done using the statistical softwareASReml v. 3 (Gilmour et al. 2009) including a pedigree filewith a total of 87 related entities. The incorporation of thispedigree is critical as it considers dependencies (i.e., geneticrelationships) that occur in this reduced population and pres-ence of inbreeding, hence improving the estimation of geneticparameters. Diagnostic plots were used to verify for normal

distribution of residuals and presence of outliers. For RYmeasured at any year, a log transformation was used basedon the expression ln(RY + 10) to achieve normality ofresiduals.

For single-site analyses, data from each trial and eachvariable (D50, BT, Surv, RY2, RY3, RY4, average RY, andRG) were fitted individually to the following linear mixedmodel equation:

y ¼ μ1þ Xbþ Zg þWpþ e

Table 1 Site details of the rubber tree tests established in the state of São Paulo, Brazil

Site Jaúb Pindoramab Votuporanga1b Colina Ilha Solteira Votuporanga2b

Trial set 1 1 1 2 2 2

Year of establishment 1989 1989 1989 2007 2007 2007

Latitude (S) 22° 17′ 21° 13′ 20° 25′ 20° 43′ 20° 20′ 20° 25′

Longitude (W) 48° 34′ 48° 56′ 49° 50′ 48° 32′ 51° 24′ 49° 50′

Elevation (m) 580 560 480 568 370 482

Mean annual temperature (°C) 21.6 21.0 22.3 22.6 24.5 22.3

Annual rainfall (mm) 1,344 1,390 1,480 1,255 1,232 1,480

Soila Rhodic hapludox Kandiudox Kandiudox Kandiudox Kandiudox Kandiudox

aOliveira (1999)bMinor corrections from values reported by Costa et al. (2000)

Fig. 1 Map of the trial locations (set 1 circles; set 2 triangles) on the state of São Paulo, Brazil. For Jaú, Pindorama, and Votuporanga, minor correctionsare included from those details reported by Costa et al. (2000)

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where y is the vector of phenotypes; μ is the overall meaneffect; b is the fixed vector of block effects; g is the randomvector of parental effects or general combining ability,with g~MVN(0, σg

2 A); p is the random vector of ploteffects, with p~MVN(0, σp

2 I); and e is the randomvector of errors, with e~MVN(0, σe

2 I). The letters X,Z, and W represent the incidence matrices for the respectiveeffects. The matrix A is the numerator relationship matrixobtained from pedigree, and I is an identity matrix of itsproper size.

Multi-site analyses were done to estimate GEIs by fittingthe following model to each variable (D50, BT, Surv, RY2,RY3, RY4, average RY, and RG):

y ¼ μ1þ X1sþ X2bsþ ZgsþWpsþ e

where y is the data vector; μ is the overall mean effect; sis the fixed vector of site effects; bs is the fixed vector ofblocks within site effects; gs is the random vector ofparental half additive effects within site, with gs~MVN(0, A⊗G); ps is the random effects vector of plotswithin site, with ps~MVN(0, Dps); and e is the randomvector of errors, with e~MVN(0, De). The letters X1, X2,Z, and W represent incidence matrices, and 1 is a vectorof ones. The matrix A is the numerator relationship matrixfor individuals, G is a 6×6 matrix of variance-covariancebetween genotypes across sites, modeled by considering asingle genetic correlation term, rB, and a unique ith varianceterm, σ2

gsi, for each site (i.e., CORUH), Dps and De arediagonal matrices where each site has a different and indepen-dent ith plot and error term component, σ2psi and σ

2ei, respec-

tively, and⊗is the Kronecker or direct product.For both of the univariate models, single- and multi-sites,

the genetic parameters were estimated using the followingpopulation relationships:

Narrow-sense heritability (biased single-site)

h2b ¼3σ2g

σ2gþσ2pþσ2e

Additive genetic by site variance σ2axs ¼ 3σ2

gs

Additive genetic variance σa2=σa× s

2 ×(1−rB)/rBTotal variance σ2

T ¼ σ2axs þ σ2

ps þ σ2e

Narrow-sense heritability (multi-sites) h2 ¼ σ2aσ2T

where the bars over the components represent average valuesacross all sites, and all other components were previouslydefined. For heritability estimations, a coefficient of relation-ship of 3 instead of 4 was used in order to allow for presenceof selfing and some full-sib relationships within the open-pollinated families.

A repeatability model was fitted in order to evaluate thestability of genetic effects over time based on the repeated

measurements of RYs obtained at ages 2, 3, and 4 using a logtransformation (RY2, RY3, RY4). This was done for each siteindividually by fitting the model

y ¼ μ1þ X1t þ X2bt þ Z1g þ Z2gt þWpt þ e

where y is the data vector; μ is the overall mean effect; t is thefixed vector of time (i.e., age); bt is the fixed vector of blockeffects within time; g is the random vector of parent effects,with g~MVN(0, σg

2A); gt is the random vector of parental andtime interactions, with gt~MVN(0, σgt

2 A⊗I3); pt is the ran-dom effects vector of plots within time, with pt~MVN(0, D);and e is the random vector of errors, with e~MVN(0, R⊗In).The matrix D corresponds to a diagonal matrix where each ith

measurement has a different and independent plot componentσpi2 , and R is a 3×3 matrix of variance-covariance components

between residuals of the same plot defined as anautoregressive heterogeneous order 1 error structure with acorrelation between residuals of ρe (estimated as re) and adifferent residual variance for each ith measurement time,σei2 . All other matrices were previously defined.Estimates of variance components were used to estimate

the genetic parameters and correlations based on the followingpopulation expressions:

Narrow-sense heritability h2b ¼3σ2g

σ2gþσ2gtþσ2pþσ2e

Repeatability additive genetic correlation rt ¼ σ2gσ2gþσ2gt

where all terms were previously defined.In order to estimate all phenotypic and genetic correlations

across traits and sites, multivariate analyses were performedby fitting two traits simultaneously into the following singlemodel that combined all six sites and both traits. The traitsconsidered were diameter, bark thickness, average yield, andnumber of latex vessel rings. The bivariate fitted modelcorresponded to the following:

y ¼ X1uþ X2buþ ZguþWpuþ e

where y is the data vector; u is the fixed vector of groupeffects, where each of the 12 groups (6 sites×2 traits)were defined as the combination of site-by-trait obser-vations; bu is the fixed vector of block effects withingroup; gu is the random vector of parental effects withingroup, with gu~MVN(0, A⊗Gu); pu is the random effectsvector of plots within group, with pu~MVN(0, Dps); and e isthe random vector of errors, with e~MVN(0, ⊕ i=1

6 Ri⊗Ini).The matrix Gu is a 12×12 matrix of variances and covari-ance between the combinations site-by-trait defined by fourgenetic correlations: (1) rA, the average correlations betweenpairs of traits within the same site; (2) rB1 and rB2, theaverage correlation across all sites for traits 1 and 2,

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respectively; and (3) rC, average correlations between traitsacross two different sites. Also, the matrix Ri is an unstruc-tured 2×2 matrix of variance-covariance components be-tween residuals of the same ith group, and ⨁ denotes thedirect sum of matrices. All the other terms were previouslydefined.

Genetic gains

In order to evaluate the response of parental selection fordifferent intensities, the predicted mean values for each geno-type, based on the multi-site analyses models, were used tocalculate genetic gains in relative terms by averaging thepredictions of the approximate top 10 and 20 % of the indi-viduals and dividing them by the average phenotypic value.This was done by using the ranking of each site and an overallranking across all sites. In addition, to quantify the potentialgenetic gain loss within a given site by selecting individualsbased on their overall performance, a ratio of potential geneticgain was calculated for each site based on a selection of theapproximately 10 and 20 % top of the individuals.

Results

The biased narrow-sense heritability estimates for the single-site analyses varied considerably between traits and sites(Table 2) which could reflect a range of situations as well asrandom estimation errors. The highest values were found forthe traits D50 and BT on all sites with the exception ofVotuporanga2 that presented moderate or low heritabilitiesfor most traits. In addition, often-higher heritabilities werefound on trial set 1. For annual RY (RY2, RY3, RY4), differ-ent heritabilities were found across years within a given site.

However, average RY (RYm) presented a moderate to highvalue that ranged from 0.275 (Colina) to 0.460 (Ilha Solteira).For survival, low to moderate levels of heritability were de-tected for most sites with an average estimate of 0.144.

Multi-site analyses showed narrow-sense heritabilites esti-mates that ranged from 0.032 to 0.341, with the lowest valuefor survival and the largest for BT (Table 3). As with thesingle-site analyses, a higher heritability was observed forRYm (0.305) than the ones obtained from annual RY mea-surements. Type B correlations ranged from 0.300 to 0.872 forall traits. These values indicate low levels of GEI, with theexception of survival and RG with values of 0.300 and 0.623,respectively. Interestingly, these traits also showed the lowestheritabilites.

The estimated repeatability additive genetic correlation, rt,for RY obtained at ages 2, 3, and 4 was high in all sites(>0.786, Table 4) with slightly lower values for trial set 1 thantrail set 2. Note that the high values of rt are found on thosesites with the lowest heritabilities. These results indicate thatranking of genotypes are stable across the 3 years of evalua-tion. Also, high values of temporal correlations were obtainedfor most sites (>0.695), with the exception of site Ilha Solteira.

Average correlation estimates between pairs of traits withinthe same site and across two different sites are shown inTable 5. The estimated additive genetic correlations betweenpairs of traits within the same site (rA) from the bivariateanalyses were all larger than 0.605. The highest correlationwas observed between RYm and RG (0.920), and all additivegenetic correlation estimates of RY with any trait were largerthan 0.617, and particularly, the correlation of RYm and D50(0.722) is of practical importance for indirect selection. Incomparison, as expected, average additive genetic correlationbetween pairs of traits across two sites (rC, Table 5) is lower,ranging from 0.394 (between RYm and BT) to 0.747 (betweenD50 and BT). Type B genetic correlations are not shown here

Table 2 Estimates of biased narrow-sense heritabilities (hb2) from sin-

gle-site analyses. The variables considered correspond to individual-treediameter at age 2 (D50, cm), bark thickness at age 3 (BT, mm),survival at age 3 (Surv), log-transformed rubber yield at age 2 (RY2,

g/cut), age 3 (RY3, g/cut), and age 4 (RY4, g/cut), log-transformedaverage yield (RYm, g/cut), and number of latex vessel rings at age3 (RG). Values in parentheses are approximate standard errors

Site Jaú Pindorama Votuporanga1 Colina Ilha Solteira Votuporanga2

Trial set 1 1 1 2 2 2

D50 0.647 (0.188) 0.513 (0.176) 0.413 (0.134) 0.131 (0.091) 0.251 (0.097) 0.056 (0.074)

BT 0.527 (0.163) 0.764 (0.195) 0.543 (0.155) 0.194 (0.104) 0.275 (0.116) 0.000 (−)a

Surv 0.090 (0.044) 0.242 (0.083) 0.049 (0.030) 0.461 (0.167) 0.021 (0.029) 0.000 (−)RY2 0.216 (0.083) 0.451 (0.142) 0.287 (0.095) 0.134 (0.110) 0.131 (0.076) 0.120 (0.086)

RY3 0.308 (0.104) 0.487 (0.149) 0.301 (0.098) 0.270 (0.107) 0.029 (0.050) 0.270 (0.095)

RY4 0.362 (0.120) 0.373 (0.122) 0.301 (0.095) 0.212 (0.110) 0.048 (0.064) 0.434 (0.137)

RYm 0.373 (0.122) 0.454 (0.142) 0.321 (0.103) 0.275 (0.114) 0.460 (0.167) 0.413 (0.130)

RG 0.145 (0.059) 0.163 (0.067) 0.114 (0.052) 0.183 (0.083) 0.279 (0.097) 0.000 (−)

a Standard errors are not reported as parameters were bounded to 0

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as these are similar to the ones shown in Table 3. These resultsillustrate the small effect of GEI on between-trait geneticcorrelation estimates for this study.

Interesting genetic gains from parental selection at differentintensities were found for most traits and sites (Table 6).Selecting the top 20 % of the parents for RY, based on a log-transformed variable, produced a relative genetic gain of28.2 % based on the overall ranking, with genetic gains rangingfrom 22.8 (Ilha Solteira) to 47.8 % (Jau). For the other traits,lower relative genetic gains were found, ranging between 3.30(Surv) and 8.80 % (RG) for the top 20 % parents. The lowergains for survival are expected as it presents the lowest narrow-sense heritability. Site Votuporanga2 presented the lowest rela-tive genetic gains for all traits, with the exception of RYm. Theestimated genetic gain loss in a given site from selecting the topparents, based on an overall ranking, resulted in an efficiency of97.8 % or greater for any site and trait (details not shown). Thishigh value is expected due to low levels of GEI.

Discussion

The results from this study explore several aspects of thegenetic architecture of rubber tree that are relevant to define

breeding strategies. As in many other programs, a wide rangeof single-site narrow-sense heritabilites were observed,reflecting the span of environmental, experimental, and man-agement conditions present in this population as well asrandom sampling errors. A promising unbiased narrow-sense heritability estimate was found for average RY(0.305), the most important commercial trait. The implicationof this result is that large potential genetic gains are possible;for example, a selection of the top 10 % parents will producean approximate 37 % gain across all six sites. Note that thesevalues were obtained from the use of a log-transformed aver-age RY, and this transformation can yield to underestimationsof the predicted parental means. The heritability estimatesobtained in this study are higher than reported elsewhere.For example, a study done in Nigeria found narrow-senseheritability values for RY of 0.045, 0.133, and 0.125 corre-sponding to 5-, 6-, and 7-year-old evaluations, respectively(Alika 1985). Also, Tan et al. (1975) reported family-meanheritability values for 2-, 3-, and 4-year-old average yields of0.13, 0.14, and 0.14, respectively, and for BT values of 0.11and 0.29 for ages 2 and 3, respectively. However, Gonçalveset al. (2009) found higher single-site values for RY for 3-year-old trees in different sites (0.635, 0.314, and 0.224).

The levels of GEI found in this study are low for all traits,with the exception of survival. Particularly for RYm, the typeB genetic correlation estimate was 0.843, a high value thatindicates a good consistency of the parental rankings across allsites evaluated. Gonçalves et al. (2009), for a related

Table 3 Estimates of narrow-sense heritabilities for multi-site analyses(h2) and type B correlations (rB). The variables considered correspond toindividual-tree diameter at age 2 (D50, cm), bark thickness at age 3(BT, mm), survival at age 3 (Surv), log-transformed rubber yield atage 2 (RY2, g/cut), age 3 (RY3, g/cut), and age 4 (RY4, g/cut), log-transformed average yield (RYm, g/cut), and number of latex vesselrings at age 3 (RG)

Variable h2 rB

D50 0.217 0.819

BT 0.341 0.739

Surv 0.032 0.300

RY2 0.120 0.774

RY3 0.121 0.853

RY4 0.165 0.872

RYm 0.305 0.843

RG 0.102 0.623

Table 4 Estimates of narrow-sense heritabilities (hb2), repeatability addi-

tive genetic correlations (rt), and temporal error correlations (re) forsingle-site analyses based on repeated measures of log-transformed

rubber yield at ages 2, 3, and 4 (RY, g/cut). Values in parenthesis areapproximate standard errors

Site Jaú Pindorama Votuporanga1 Colina Ilha Solteria Votuporanga2

Trial set 1 1 1 2 2 2

hb2 0.149 (0.056) 0.346 (0.107) 0.180 (0.065) 0.015 (0.012) 0.107 (0.034) 0.019 (0.015)

rt 0.786 (0.086) 0.958 (0.020) 0.885 (0.054) 0.999 (-) 0.999 (-) 0.999 (-)

re 0.695 (0.012) 0.858 (0.006) 0.788 (0.009) 0.712 (0.016) -0.391 (0.025) 0.751 (0.013)

Table 5 Estimates of average correlations between pairs of traits withinthe same site (rA, above the diagonal), and average correlations betweentraits across two different sites (rC, below the diagonal). The variablesconsidered correspond to individual-tree diameter at age 2 (D50, cm),bark thickness at age 1 (BT, mm), log-transformed average yield (RYm,g/cut), and number of latex vessel rings at age 1 (RG). Values in paren-thesis are approximate standard errors

Variable D50 BT RYm RG

D50 – 0.845 (0.063) 0.722 (0.123) 0.765 (0.111)

BT 0.747 (0.083) – 0.617 (0.149) 0.605 (0.133)

RYm 0.574 (0.141) 0.394 (0.170) – 0.920 (0.067)

RG 0.562 (0.136) 0.494 (0.111) 0.629 (0.099) –

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population, in a study that evaluated stem girth at 1, 2, and3 years, RYat 3 years, and BT at 3 years of age, found type Bcorrelations at progeny level close to one.

The high values of the repeatability correlation estimatesobserved for the three RY measurements are potentially anindication of breeding value consistency across measure-ments. For this reason, using any individual measurementshould provide relatively stable ranking of parents acrossyears. However, these individual measurements appear tohave a wide range of genetic control (as noted by the herita-bility values). Hence, the use of an average yield value isrecommended as it will provide a good summary across years,without loss of relevant information, and in addition, withgreater genetic control, reflected by a higher heritability esti-mates (0.305, instead of 0.120, 0.121, and 0.165).

For the traits studied here, all estimates of type A geneticcorrelations (rA) were high. Indirect selection will work wellfor this population (as all rA are >0.6), and of special interest isthe estimated correlation between D50 and RYm with a valueof 0.845. Therefore, for this population, it is possible toachieve interesting average RY genetic gains by selectingparents based on their diameter (or girth) at age 2, a trait thatis easier and cheaper to measure. A similar result was reportedby Gonçalves et al. (2009) for type A correlation (>0.6)between girth and RY within all sites presented in their study.

As indicated before, rC (correlation across sites, Table 5)estimates were high; therefore, the GEI is small, and it ispossible to make selection across multiple traits for one siteto another site without much genetic gain loss. Other studiesreported similar correlation values across sites (Gonçalveset al. 2009).

In conclusion, in our study, we found that interesting RYgenetic gains can be obtained from selection of the best

parents. The low levels of genotype-by-environment foundfor this trait (based on six trials) justify the use of an overallranking that should give genetic gain efficiencies greater than98.1 %. Rubber breeders typically require from 10 to 15 yearsto complete one breeding cycle (Furlani et al. 2005); however,the results from this study justify the use of early selection ongirth (or diameter) to accelerate this cycle and to increase RYgains.

Acknowledgments This work was supported by the Fundação deAmparo à Pesquisa do Estado de São Paulo (FAPESP), ConselhoNacional de Desenvolvimento Científico e Tecnológico (CNPq),Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(CAPES), and Secretaria de Agricultura e Abastecimento do Estado deSão Paulo, Brazil. We want to thank several researchers responsible forthe trials: Mario Luiz Teixeira de Moraes (Single Island), Elaine CristinePiffer Gonçalves (Colina), and Erivaldo José Scaloppi Jr. (Votuporanga).And, we also thank Dr. Rowland Burdon for his dedicated comments onthis manuscript.

Data Archiving Statement We followed standard Tree Genetics andGenomes policy. Data used in the study came from Instituto Agronômico.In addition, supplementary information of original genotype numbers/names and data are included in the Supplemental Files.

References

Alika JE (1985) Heritability and genotypic gain from selection in rubber(Hevea brasiliensis). Silvae Genet 34:1–4

Burdon RD (1977) Genetic correlation as a concept for studyinggenotype-environment interaction in forest tree breeding. SilvaeGenet 25:168–175

Costa RB da, Resende MDV, Araujo AJ, Gonçalves PS, Higa AR (2000)Selection and genetic gain in rubber tree (Hevea) populations usinga mixed mating system. Genet Mol Biol 23:671–679

Table 6 Expected genetic gains(%) from selecting overall top 10and 20 % of parental genotypeswithin each site. The variables con-sidered correspond to tree diameterat age 2 (D50, cm), bark thicknessat age 3 (BT, mm), survival at age 3(Surv), log-transformed averageyield (RYm, g/cut), and number oflatex vessel rings at age 3 (RG).Number in parenthesis correspondto the number of genotypes select-ed. Note that the total number ofparents correspond to all those in-cluded in the pedigree file that willhave a predicted genetic effect

Overall Jaú Pindorama Votuporanga1 Colina Ilha Solteira Votuporanga2

D50

10 % (9) 7.7 13.4 13.5 11.8 5.3 7.2 2.7

20 % (17) 6.3 10.8 11.2 9.2 4.5 5.9 2.2

BT

10 % (9) 8.6 12.0 15.3 12.2 6.5 6.4 2.8

20 % (17) 6.9 9.5 12.4 9.7 5.2 5.2 2.2

Surv

10 % (9) 4.0 5.6 5.1 2.4 9.2 4.6 0.0

20 % (17) 3.3 4.3 4.0 1.8 8.2 3.6 0.0

RYm

10 % (9) 36.7 61.7 56.2 43.1 40.1 29.3 51.5

20 % (17) 28.2 47.8 42.5 33.4 31.1 22.8 39.9

RG

10 % (9) 11.5 13.5 12.8 9.7 19.8 16.4 0.8

20 % (17) 8.8 10.4 10.0 7.4 15.9 13.3 0.6

Tree Genetics & Genomes

Furlani RCM, Moraes MLT, Resende MDV, Furlani Junior E,Gonçalves PS, Valerio Filho WV, de Paiva JR (2005) Estimationof variance components and prediction of breeding values inrubber tree breeding using the REML/BLUP procedure. GenetMol Biol 28:271–276

Gilmour AR, Gogel BJ, Cullis BR, Thompson R (2009) ASReml userguide v. 3.0. VSN International Ltd, Hemel Hempstead.

Gonçalves PS, Marques JRB (2008) Melhoramento genético daseringueira: passado, presente e futuro. In: Alvarenga AP, CarmoCAFS (eds) Seringueira. Epamig, Viçosa, pp 399–534

Gonçalves PS, Cardinal ABB, Costa RB, Bortoletto N, GouvêaLRL (2005) Genetic variability and selection for laticiferoussystem characters in Hevea brasiliensis. Genet Mol Biol 28:414–422

Gonçalves PS, Silva MA, Gouvêa LRL, Scaloppi Junior EJ (2006)Genetic variability for girth growth and rubber yield characters inHevea brasiliensis. Sci Agric 63:246–254

Gonçalves PS, Aguiar ATE, Costa RBC, Gonçalves ECP,Scaloppi-Júnior EJ, Branco RF (2009) Genetic variation andrealized genetic gain from rubber tree improvement. SciAgric 66:44–51

Gouvêa LRL, Silva GAP, Verardi CK, Oliveira ALB, Gonçalves ECP,Scaloppi-Junior EJ, Moraes MLT, Gonçalves PS (2013) Rubber treeearly selection for yield stability in time and among locations.Euphytica 191:365–373

IBGE (2011) Instituto Brasileiro de geográfica e estatística. Produçãoagrícola Municipal-Culturas temporárias e permanentes. Rio deJaneiro. 38:1-97. ISSN 0101-3963. http://biblioteca.ibge.gov.br/d_detalhes.php?id=766. Accessed 10 Nov 2013

IRSG (2013) International Rubber Study Group. Rubber statistical bul-letin vol. 66. Wembley, United Kingdom

Jayasekera NEM, Karunasekera KB, Kearsey MJ (1994) Genetics ofproduction traits in Hevea brasiliensis (rubber). I. Changes in ge-netical control with age. Heredity 73:650–656

Le Guen V, Garcia D, Doaré F, Mattos CRR, Condina V, Couturier C,Chambon A, Weber C, Espéout S, Segui M (2011) A rubber tree’sdurable resistance to Microcyclus ulei is conferred by a qualitativegene and a major quantitative resistance factor. Tree Genet Genome7:877–889

Oliveira JB (1999) Solos do estado de Sao Paulo: descricao das classesregistradas no mapa pedologico. Boletim Cientifico. InstitutoAgronomico, Campinas

Priyadarshan PM, Gonçalves PS (2003) Hevea gene pool for breeding.Genet Resour Crop Evol 50:101–104

Silva GAP, Gouvêa LRL, Verardi CK, Resende MDV, Scaloppi-Junior EJ, Gonçalves PS (2013) Genetic parameters andcorrelation in early measurement cycles in rubber trees. Euphytica189:343–350

Tan H, Subramaniam SA (1976) A five-parent diallel cross analysis forcertain characters of young Hevea seedlings. In: Proceedings ofInternational Rubber Conference, 1975, Kuala Lumpur: ResearchInstitute of Malaysia. pp. 13–26.

Tan H, Mukherjee TK, Subramaiam SA (1975) Estimates of geneticparameters of certain characters in Hevea brasiliensis. Theor ApplGenet 46:181–190

Verardi CK, Resende MDV, Costa RB, Gonçalves PS (2012) Estimationof genetic parameters in rubber progenies. Crop Breed ApplBiotechnol 12:185–190

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