# Genetic Structure of a Loblolly Pine Breeding Population at Brazil

Authors: Juliane Rezende Mercer; Milena de Luna Alves Lima; Antonio Rioyei Higa; Chirlei Glienke; Marina Isabel Mateus de Almeida
Journal: ISRN Forestry
 (2013)

---

## Abstract

The genetic structure of a Brazilian loblolly pine (Pinus taeda L.) breeding population, represented by 120 open-pollinated families, was determined using Bayesian inference and genotypes of 15 microsatellite (simple sequence repeat (SSR)) loci in 1,130 seedling progeny. The 120 maternal parents had been phenotypically selected about 15 years ago for wood volume in five different forestry plantations (FPs) in the south of Brazil. Additional selection for wood volume, based on a previous progeny test, was applied to the first best (i) and second best (ii) tree per block within each family. We adopted a procedure of “learning samples” to find the most likely number of inferred genetic clusters (K) or ancestral populations. The first hypothesis that was rejected was that the most probable value of K=5 was coincident with the five FPs, since the FPs were, a priori, assumed to be from 5 different backgrounds or origins. It was used the familiar structure of the population to infer the genotypes of maternal ancestors. It was concluded that the maternal generation is the most likely to have been planted by the mixture of three different seed sources or origins, that there are five genetic groups (K=5) in the population of progeny, and that they have been formed from the occurrence of assortative mating and also from a strong pressure in the selection within families. The trees with the best genetic value (i) maintained a higher genetic variability when compared to the trees of second best performance (ii), with higher values of heterozygosity and of numbers of maternal alleles that were kept the same. The migration model that best explains the results is the contact zone model. The population differentiation (FST) was 2-3 times higher in offspring than in relation to the maternal generation. The relevancy of the results and the way they were explored may be of value both for studies of population genetics, as for plant breeding programs, since they help monitoring the population's genetic variability during generations of selection.


---

## Body

## 1. Introduction

Loblolly pine (Pinus taedaL.) is a monoecious conifer, diploid tree with a predominant cross-fertilization. Its native range is in southeastern United States, and it was first introduced in Brazil in the 1940s. Its wood is used for industry panels and sawn timber. It is a fast-growing tree and is well adapted to temperate climate that makes it a good candidate for planting forests in southern Brazil. Among 5.74 million hectares (ha) of all existing forest plantations in Brazil in 2006, P. taeda occupies 1.52 million hectares in the southern states [1]. Most of these plantations were established from genetically improved seeds produced in clonal seed orchards that were established by breeding programs using phenotypically selected trees.The main objective of this research was to study the genetic structure of a breeding population that consists of open-pollinated progenies of multipleP. taeda families using microsatellite or simple sequence repeats (SSR) markers and a Bayesian clustering approach implemented in the STRUCTURE software (Pritchard et al. [2]) to infer groups or subpopulations in this population.The software calculates log likelihoods for user-defined number (K) of subpopulations. Individuals in the sample are probabilistically assigned to a subpopulation “cluster” or partitioned between two or more subpopulations “clusters”, if their genotypes indicate that they are hybrids or admixtures [3]. The model choice criterion implemented in structure to detect the true K is an estimate of the posterior probability of the data for a given K, called the Pr(X∣K) [3] and called lnP(D) in Evanno et al. [4].It allows to infer the most likely number ofK based on maximum likelihood estimates lnP(D). However, this analysis greatly depends on the modeling assumptions, such as Hardy-Weinberg equilibrium and others. It was observed as in Evanno et al. [4] simulations that, in most cases, once the real K is reached, lnP(D) stabilizes at larger Ks plateaus or continues increasing slightly. This phenomenon is also reported in the structure’s manual (Pritchard et al. [3]), in which the variance between runs increases. Evanno et al. [4] proposed an ad hoc statistic (ΔK) based on the rate of change of maximum likelihood estimates computed by the STRUCTURE software. The rational for this ΔK is to make salient the break in slope for the distribution of lnP(D) at the true K.However, selfing can lead to spurious clustering of structured population using the standard STRUCTURE algorithm that can bias admixture estimates. Therefore, Gao et al. [5] extended the Bayesian clustering approach of STRUCTURE [3] to simultaneous inference of inbreeding or selfing rates and classification of the source population using multilocus genetic data. The Hardy-Weinberg equilibrium is no longer assumed within groups, and the expected genotype frequencies are estimated based on rates of inbreeding or selfing.Unaccounted population structure can lead to false-positive spurious associations between traits and polymorphic alleles in association mapping studies. That is why it is very important to analyze population structure and take it into account in association mapping studies. As a next goal in this research aims to conduct an association mapping to detect genetic variation between strong candidate genes and some wood quality traits, the present approach assumes great relevance.


## 2. Material and Methods

Breeding population used in this study consisted of 12-year-old seedlings representing open-pollinated progenies from 120 families planted in a complete block design with five repetitions. The total numbers of trees studied were 1.130. Seeds for these seedlings were collected about 15 years ago in one of five forestry plantations (FPs) in Santa Catarina, a Brazilian southern state. Geographic origins of these FPs are unknown. The seeds were collected from 120 maternal trees that had been phenotypically selected for wood volume at the five FPs—the seeds represent the first round of selection within families.The needles were collected from 1130 individual seedlings, stored at −20°C and then used to isolate DNA using the CTAB method [6]. Microsatellite loci were genotyped using MegaBace 1000 (GE Healthcare), and the multiplex system protocol was established during this research. The following microsatellites loci (and their respective Genbank accession numbers) were genotyped in the study: PtTX3026 (AF143971), PtTX3002 (AF277846), PtTX3088 (AF277843), PtTX3091 (AF277848), PtTX3098 (AF277847), PtTX3118 (AF277845), PtTX2037 (AF143959), PtTX3025 (AF143970), RPtest5 (BV728798), 2n11e (AA556153), PRtest8 (BV728799), PRtest11 (BV728796), 8934 M (AA739818), 9317 M (AA740072), and PRtest1 (BV728795).


### 2.1. Statistical Analyses

The segregation of microsatellite loci was tested by inferring the maternal genotype for each open-pollinated family. Linkage and Hardy-Weinberg disequilibrium analyses were done using GDA 1.1http://hydrodictyon.eeb.uconn.edu/people/plewis/software.php) [7]. The population structure was studied using Bayesian cluster inference based on 15 microsatellite loci (SSRs) genotyped in 1130 seedlings, under two scenarios, assuming Hardy-Weinberg equilibrium (software STRUCTURE 2.3; http://pritch.bsd.uchicago.edu/structure.html) and assuming inbreeding (software INSTRUCT; http://cbsuapps.tc.cornell.edu/InStruct.aspx). The permutation analysis for testing assignment of individual trees to clusters was done using CLUMPP 1.1.2, a Cluster Matching and Permutation Program [8]. An ad hoc statistic suggested by Evanno et al. [4] was used to analyze the STRUCTURE results.A preliminary analysis with 20 independent runs was done to determine the number of burn-in and the number of repetitions for the STRUCTURE software using the admixture model and correlated allele frequencies assumptions. It was observed that the posterior distributions, respectively, converge with burn-in and MCMC of 10,000 and 50,000 cycles, respectively. Thead hoc statistic of Evanno et al. [4] was also computed for these 20 runs for K=1 to 21.Before implementing the EVANNOad hoc statistic, an exploratory study was conducted to determine the set of values for the logarithms of likelihood represented by the posterior probabilities [Pr(X∣K)]. It was concluded that the arithmetic mean was not a good estimator for the observed data dispersion, and it was concluded that the median values provided a better fit (data will be soon published). Thus, a change in the authors’ equations [4] was implemented, which basically consisted in using the median values instead of the arithmetic mean of [Pr(X∣K)]. Therefore, instead of using the ΔK introduced by the authors, it was referred here as ΔKm.The equations used by the STRUCTURE software to measure population substructureFST, expected heterozygosity (He), coancestry coefficients (q), and genetic distance using the allelic frequencies are fully described in [3, 9]. The equations and the inference of genetic parameters used by the INSTRUCT software are fully described in Gao et al. [5].The CLUMPP 1.1.2 software with 10,000 permutations for the 30 Q matrices generated in 30 runs of the STRUCTURE 2.2 software was used to perform permutations that test assignment of each seedling to a particular cluster and also to determine admixtures.Based on the initial analysis, the mode 5 of the INSTRUCT software proved to have the best performance for this population. This mode has estimated rates of selfing or inbreeding using back reflection. A hundred runs of the INSTRUCT were performed to estimate the parameters of inbreeding and clustering that provide the best probabilities of likelihood for the posteriorK. The numbers of burn-in and MCMC iterations were 10,000 and 50,000, respectively, and 10 for the thinning period.A series of hypothesis for the subsequent analysis was constructed, similar to a methodology of learning samples. These exploratory data analyses were an approach to increase the analyzing data sets, to observe their main characteristics in an easy-to-understand form, in order to formulate hypotheses that could be tested on new data sets.


## 2.1. Statistical Analyses

The segregation of microsatellite loci was tested by inferring the maternal genotype for each open-pollinated family. Linkage and Hardy-Weinberg disequilibrium analyses were done using GDA 1.1http://hydrodictyon.eeb.uconn.edu/people/plewis/software.php) [7]. The population structure was studied using Bayesian cluster inference based on 15 microsatellite loci (SSRs) genotyped in 1130 seedlings, under two scenarios, assuming Hardy-Weinberg equilibrium (software STRUCTURE 2.3; http://pritch.bsd.uchicago.edu/structure.html) and assuming inbreeding (software INSTRUCT; http://cbsuapps.tc.cornell.edu/InStruct.aspx). The permutation analysis for testing assignment of individual trees to clusters was done using CLUMPP 1.1.2, a Cluster Matching and Permutation Program [8]. An ad hoc statistic suggested by Evanno et al. [4] was used to analyze the STRUCTURE results.A preliminary analysis with 20 independent runs was done to determine the number of burn-in and the number of repetitions for the STRUCTURE software using the admixture model and correlated allele frequencies assumptions. It was observed that the posterior distributions, respectively, converge with burn-in and MCMC of 10,000 and 50,000 cycles, respectively. Thead hoc statistic of Evanno et al. [4] was also computed for these 20 runs for K=1 to 21.Before implementing the EVANNOad hoc statistic, an exploratory study was conducted to determine the set of values for the logarithms of likelihood represented by the posterior probabilities [Pr(X∣K)]. It was concluded that the arithmetic mean was not a good estimator for the observed data dispersion, and it was concluded that the median values provided a better fit (data will be soon published). Thus, a change in the authors’ equations [4] was implemented, which basically consisted in using the median values instead of the arithmetic mean of [Pr(X∣K)]. Therefore, instead of using the ΔK introduced by the authors, it was referred here as ΔKm.The equations used by the STRUCTURE software to measure population substructureFST, expected heterozygosity (He), coancestry coefficients (q), and genetic distance using the allelic frequencies are fully described in [3, 9]. The equations and the inference of genetic parameters used by the INSTRUCT software are fully described in Gao et al. [5].The CLUMPP 1.1.2 software with 10,000 permutations for the 30 Q matrices generated in 30 runs of the STRUCTURE 2.2 software was used to perform permutations that test assignment of each seedling to a particular cluster and also to determine admixtures.Based on the initial analysis, the mode 5 of the INSTRUCT software proved to have the best performance for this population. This mode has estimated rates of selfing or inbreeding using back reflection. A hundred runs of the INSTRUCT were performed to estimate the parameters of inbreeding and clustering that provide the best probabilities of likelihood for the posteriorK. The numbers of burn-in and MCMC iterations were 10,000 and 50,000, respectively, and 10 for the thinning period.A series of hypothesis for the subsequent analysis was constructed, similar to a methodology of learning samples. These exploratory data analyses were an approach to increase the analyzing data sets, to observe their main characteristics in an easy-to-understand form, in order to formulate hypotheses that could be tested on new data sets.


## 3. Results and Discussion

The STRUCTURE analysis was run first using the admixture model with correlated allele frequencies, withK=5, and no a priori information about the population. The objective was to test the hypothesis that FPs are distinct genetic groups. The results did not indicate the homogeneity of FPs. Each FP consisted of five groups or clusters. The analyses that were performed by informing software about the FP origin confirmed the previous results (Figure 1).Figure 1
Distribution of the five genetic clusters (K) in each of the five forestry plantations (FPs). Upper graph: individual seedlings arranged in five FPs; lower graph: distribution of coancestry (Q) for five clusters in 1.130 seedlings.These results indicate that each FP consists of five genetic clusters in different proportions. There is almost no difference in genetic diversity between the FPs, numbers of polymorphic alleles, and expected and observed heterozygosities were similar between FPs (Table1).Table 1
Descriptive statistics for the five forestry plantations (FPs).
Population
N
n
n
,
%
P
A
H
e
H
o
f
FP1
266
163.46
61.5
1.00
4.62
0.49
0.33
0.32
FP2
167
108.69
65.1
1.00
4.92
0.51
0.38
0.26
FP3
264
173.54
65.7
1.00
4.54
0.51
0.35
0.31
FP4
46
29.38
63.9
1.00
3.92
0.51
0.34
0.34
FP5
387
245.62
63.5
1.00
4.77
0.48
0.31
0.35
Mean
226
144.14
63.8
1.00
4.55
0.50
0.34
0.32
Total
1130
720.69
N: number of individuals in each FP; n: number of admixture individuals or individuals that had less than 95% of coancestry to a determined cluster; P: the proportion of polymorphic loci; A: the mean number of alleles per locus; He: the expected heterozygosity; Ho: the observed heterozygosity; f: estimate of the fixation index using the method of moments in GDA.To verify the gene flow between the FPs, the analyses considered the FP origin information, but it was settle as not informed for the individuals classified as being admixture in the first analysis. The results estimated the confidence interval of the admixture individuals’ coancestry to each of the five genetic clusters and also the probabilities for the number of past generations in which the hybridization event have happened (parents, grandparents, and great grandparents). The results indicated that 60% of admixtures were generated in the parental generation during the maternal ancestral pollination in the forestry plantations.To study the admixtures effects, all the nonadmixture individuals resulted from previous analysis, and also the smallest forestry plantation population (FP4) were excluded from the analysis. The best posterior probability for this dataset resulted in K=3 (Figure 2). The most distinct forestry populations were FP2 and FP3; the majority of FP5 are hybrid between FP2 and FP3. Although half of the individuals in FP1 are the same hybrids, this population have a distinct genetic group, which also appears in the other four forestry plantations and almost did not hybridize among the other genetic groups. However, deeper analyses in order to test this hypothesis of gene flow could not be stated since no information was provided about the geographical origin of the forestry plantations.Figure 2
Analyses for the admixtures detected in previous analysis forK=5. The nonadmixtureseedlings and data from FP4 were excluded. For the present analysis, the best posterior probability was K=3.The results of the STRUCTURE are presented in Table2. The best [Pr(X∣K)] was detected for K=19 (−12, 238.4), but the most appropriate value, according to the literature, although arbitrary, would be the smallest number of cluster that captured most of the genetic structure; after that, it occurs an increasing pattern for the next K’s [Pr(X∣K)] until a plateau is reached. Nonetheless, K=4 and K=5 had similar results; here, K=5 (−13337.3) was considered. The adjustments of alpha and FST values during the burn-in MCMC, resulted in the best posterior distribution analysis for K1, K5, and K19. Note that for K=5, they showed the best adjustments.Table 2
The posterior probability [Pr(X∣K)] on average for 10 consecutive analyses of each K  a priori. (K=1 to 20).  Wright's FST and inferred values of alpha.
K
ln
Pr
(
X
∣
K
)
Alpha
F
ST1
F
ST
2
F
ST
3
F
ST
4
F
ST
5
F
ST
6
1
-
16672.1
—
0.1080
2
−15056.9
*
0.0666
0.1620
0.1878
3
-
14416.8
0.0473
0.192
0.169
0.295
4
−13541.4
0.0427
0.3256
0.2054
0.3522
0.2757
5
−13337.3
0.0415
0.3186
0.3885
0.3017
0.3778
0.1964
6
-
13084.8
0.0418
0.3037
0.1942
0.3892
0.3861
0.3701
0.3786
7
-
12814.6
0.0402
0.4003
0.4197
0.3179
0.4532
0.3536
0.3944
8
−12700.5
0.0395
0.2619
0.2847
0.4235
0.5584
0.4340
0.4157
9
-
12553.3
0.0380
0.5705
0.3574
0.4223
0.4284
0.3811
0.5048
10
-
12937.5
0.0384
0.4098
0.3624
0.5221
0.4361
0.4866
0.4091
11
-
12469.0
0.0374
0.4400
0.3308
0.4720
0.4553
0.5905
0.4737
15
-
12319.5
0.0367
0.5479
0.4228
0.4794
0.5518
0.5449
0.3863
19
−12238.4
0.0372
0.3775
0.5804
0.5108
0.4279
0.4106
0.5439
20
-
12693.2
0.0374
0.4783
0.5684
0.5109
0.4521
0.4646
0.5389
*
Bold numbers are the best posterior values.Evanno et al. [4] proposed a statistic to determine the most probable number of K that could be graphically interpreted. In Figure 3, the graph depicts the results for ΔKm, which demonstrates that the highest peak is for K=2. In Figure 4, there is the same graphic with K2 not included, in order to have a better visualization of the second highest peaks detected for K4, K19, and K8.Figure 3
The graph with the results forΔKm and the highest peak detected for K2.Figure 4
Δ
K
m using medians values. Not including K2 (the strongest signal) but including the second higher peaks at K4, K19, and K8, in analyses of ΔKm.The greatest magnitude ofΔKm was at K2 with smaller peaks at K4 and K19. Figure 5 summarizes the results. These results came from the analysis that leads to a stepping stone model, expressing the distance in allele frequency divergence among all the 19 substructures detected. This graphic was created by plotting the distances among all the 19 substructures that comprise the five major genetic groups. On the x-axis, were plotted the genetic distances among the three most similar genetic groups, and on the y-axis, the distances of the two most divergent genetic groups in relation to those three similar groups. This same procedure was performed within each of the five main groups. This artifice generated a better interpretation of the genetic distances results, making it more visually comprehensible.Figure 5
Migration model proposed based on the distribution of the five genetic groups (K=5) and how is it distributed within 19 subpopulations.Though the results from the twoad hoc statistics seem different, after performing an analysis within groups and subgroups, the conclusion is that both of them lead to the same results. Hence, it was assumed that five may be the most real number of genetic groups to represent the breeding population.


### 3.1. Genetic Structure of the Maternal Generation

TheFST coefficient for the five clusters of the breeding population ranged from 0.19 to 0.42 (Table 3) indicating a very differentiated population. For the genetic structure detected in the maternal generation it was found that the most real number of genetic groups is K=3, and FST coefficient ranged from 0.01 to 0.15 (Table 3).Table 3
F
ST values and expected heterozygosity (He) between the three maternal clusters and the five genetic clusters of the breeding population.
F
ST
1
H
e
1
F
ST
2
H
e
2
F
ST
3
H
e
3
F
ST
4
H
e
4
F
ST
5
H
e
5
1
20
mothers
(
K
=
3
)
[
ln
P
(
D
)
=
-
3184.9
;
Var
[
ln
P
(
D
)
]
=
242.7
;
α
=
0.188
]
0.01
0.5
0.13
0.53
0.16
0.45
1130
OP
indv.
(
K
=
5
)
[
ln
P
(
D
)
=
-
13263.4
;
Var
[
ln
P
(
D
)
]
=
1120.2
;
α
=
0.046
3
]
0.19
0.5
0.42
0.38
0.32
0.38
0.24
0.44
0.30
0.41


### 3.2. Bayesian Analysis Assuming Inbreeding

The best posterior probability in the analyses of INSTRUCT software and assuming inbreeding was, again, obtained forK=5, with the lower value for the log likelihood in mean and in variance (mean and variance were −6855.3 and 13710.5, resp.).The result of the Bayesian analysis under inbreeding that had the best convergence for the Markov chain is being considered. This is determined by the value of the Gelman-Rubin (GR) statistic. This statistic measures the convergence of the log likelihood. The value for this chain was 1.022.The distribution of the five resulting clusters using INSTRUCT was similar to the STRUCTURE, indicating again that forestry plantations are a mosaic of all five groups and that were coincident in analysis assuming Hardy-Weinberg (STRUCTURE) and assuming inbreeding (INSTRUCT).STRUCTURE generates clusters based on both transient Hardy-Weinberg disequilibrium (HWD) and linkage disequilibrium (LD) caused by admixture between populations. The program works by clustering individuals in groups in which both linkage and HWD are minimized, and, as a result, the presence of LD in the data improves clustering results [9]. On the other hand, strong LD or departure from Hardy-Weinberg equilibrium could lead to an overestimation of the number of detected clusters [9]. Since almost all microsatellite loci in this study departure from Hardy-Weinberg equilibrium, it was expected that those K=5 were overestimated and, if so, INSTRUCT would detect a lower number of genetic clusters. However, it did not occur. In fact, the results indicated the same most probable K in both methods.In the STRUCTURE analysis theFST varied from 0.19 to 0.42 for 1.130 individuals and 15 microsatellite loci. In the INSTRUCT analysis that assumes this inbreeding, the FST values ranged from 0.022 to 0.227; however, these results were analyzed with only 738 individuals (that have the lower number of missing data for the genotyped alleles) from the existing 1.130, and with a reduction of 15 to 10 in the number of microsatellite loci (by excluding the loci: 01, 06, 08, 17, and 21). This has occurred because the stability of the convergence for the log of likelihood of the posterior distributions of K occurred for this dataset configurations in the INSTRUCT analysis. Table 4 summarizes this result. The FST values assuming inbreeding were lower than assuming Hardy-Weinberg.Table 4
ComparingFST values of the inferred maternal genotypes and the open-pollinated progenies assuming Hardy-Weinberg equilibrium (STRUCTURE, 1st and 2nd lines, resp.) and assuming inbreeding (INSTRUCT, 3rd line).
Independent structure analyses
K
ln
P
(
D
)
Var
[
ln
P
(
D
)
]
F
ST1
F
ST2
F
ST3
F
ST4
F
ST5
120 maternal trees
3
-
3184
242.7
0.099
0.126
0.156
1130 seedlings
5
-
13353
1108.0
0.375
0.326
0.384
0.194
0.290
738 seedlings
5
−6905,2
13810.4
0.170
0.227
0.212
0.022
0.045Thus, this result confirms that the population consists of five groups or clusters under both assumptions, Hardy-Weinberg equilibrium and inbreeding. These results may indicate that the reduction in expected heterozygosity is probably caused by the occurrence of higher rates of selfing and assortative mating.In a publication [10], as well as in other references [11], FST values from 0.01 to 0.05 would be expected for open-pollinating populations of conifer of open cross-pollinating under natural conditions and from 0.05 to 0.30 for divergent populations [11]. The values obtained in this study indicate the high degree of differentiation in this population of breeding.Pinus taeda has historically large, interconnected populations which extend along the US Atlantic coast, from Maryland to Florida and from westward to central Texas. The loblolly pine area was divided also into five regions with a high level of gene flow within each region obtained in earlier studies [12]. The origin of the maternal trees is unknown, and the five Ks detected in the present study cannot be directly linked to the five regions detected in [12]. However, such coincidence is unlikely to occur by chance alone and needs further investigation.


## 3.1. Genetic Structure of the Maternal Generation

TheFST coefficient for the five clusters of the breeding population ranged from 0.19 to 0.42 (Table 3) indicating a very differentiated population. For the genetic structure detected in the maternal generation it was found that the most real number of genetic groups is K=3, and FST coefficient ranged from 0.01 to 0.15 (Table 3).Table 3
F
ST values and expected heterozygosity (He) between the three maternal clusters and the five genetic clusters of the breeding population.
F
ST
1
H
e
1
F
ST
2
H
e
2
F
ST
3
H
e
3
F
ST
4
H
e
4
F
ST
5
H
e
5
1
20
mothers
(
K
=
3
)
[
ln
P
(
D
)
=
-
3184.9
;
Var
[
ln
P
(
D
)
]
=
242.7
;
α
=
0.188
]
0.01
0.5
0.13
0.53
0.16
0.45
1130
OP
indv.
(
K
=
5
)
[
ln
P
(
D
)
=
-
13263.4
;
Var
[
ln
P
(
D
)
]
=
1120.2
;
α
=
0.046
3
]
0.19
0.5
0.42
0.38
0.32
0.38
0.24
0.44
0.30
0.41


## 3.2. Bayesian Analysis Assuming Inbreeding

The best posterior probability in the analyses of INSTRUCT software and assuming inbreeding was, again, obtained forK=5, with the lower value for the log likelihood in mean and in variance (mean and variance were −6855.3 and 13710.5, resp.).The result of the Bayesian analysis under inbreeding that had the best convergence for the Markov chain is being considered. This is determined by the value of the Gelman-Rubin (GR) statistic. This statistic measures the convergence of the log likelihood. The value for this chain was 1.022.The distribution of the five resulting clusters using INSTRUCT was similar to the STRUCTURE, indicating again that forestry plantations are a mosaic of all five groups and that were coincident in analysis assuming Hardy-Weinberg (STRUCTURE) and assuming inbreeding (INSTRUCT).STRUCTURE generates clusters based on both transient Hardy-Weinberg disequilibrium (HWD) and linkage disequilibrium (LD) caused by admixture between populations. The program works by clustering individuals in groups in which both linkage and HWD are minimized, and, as a result, the presence of LD in the data improves clustering results [9]. On the other hand, strong LD or departure from Hardy-Weinberg equilibrium could lead to an overestimation of the number of detected clusters [9]. Since almost all microsatellite loci in this study departure from Hardy-Weinberg equilibrium, it was expected that those K=5 were overestimated and, if so, INSTRUCT would detect a lower number of genetic clusters. However, it did not occur. In fact, the results indicated the same most probable K in both methods.In the STRUCTURE analysis theFST varied from 0.19 to 0.42 for 1.130 individuals and 15 microsatellite loci. In the INSTRUCT analysis that assumes this inbreeding, the FST values ranged from 0.022 to 0.227; however, these results were analyzed with only 738 individuals (that have the lower number of missing data for the genotyped alleles) from the existing 1.130, and with a reduction of 15 to 10 in the number of microsatellite loci (by excluding the loci: 01, 06, 08, 17, and 21). This has occurred because the stability of the convergence for the log of likelihood of the posterior distributions of K occurred for this dataset configurations in the INSTRUCT analysis. Table 4 summarizes this result. The FST values assuming inbreeding were lower than assuming Hardy-Weinberg.Table 4
ComparingFST values of the inferred maternal genotypes and the open-pollinated progenies assuming Hardy-Weinberg equilibrium (STRUCTURE, 1st and 2nd lines, resp.) and assuming inbreeding (INSTRUCT, 3rd line).
Independent structure analyses
K
ln
P
(
D
)
Var
[
ln
P
(
D
)
]
F
ST1
F
ST2
F
ST3
F
ST4
F
ST5
120 maternal trees
3
-
3184
242.7
0.099
0.126
0.156
1130 seedlings
5
-
13353
1108.0
0.375
0.326
0.384
0.194
0.290
738 seedlings
5
−6905,2
13810.4
0.170
0.227
0.212
0.022
0.045Thus, this result confirms that the population consists of five groups or clusters under both assumptions, Hardy-Weinberg equilibrium and inbreeding. These results may indicate that the reduction in expected heterozygosity is probably caused by the occurrence of higher rates of selfing and assortative mating.In a publication [10], as well as in other references [11], FST values from 0.01 to 0.05 would be expected for open-pollinating populations of conifer of open cross-pollinating under natural conditions and from 0.05 to 0.30 for divergent populations [11]. The values obtained in this study indicate the high degree of differentiation in this population of breeding.Pinus taeda has historically large, interconnected populations which extend along the US Atlantic coast, from Maryland to Florida and from westward to central Texas. The loblolly pine area was divided also into five regions with a high level of gene flow within each region obtained in earlier studies [12]. The origin of the maternal trees is unknown, and the five Ks detected in the present study cannot be directly linked to the five regions detected in [12]. However, such coincidence is unlikely to occur by chance alone and needs further investigation.


## 4. Conclusions

The Bayesian method of clustering analysis based on the 15 microsatelliteloci helped to study the genetic structure of the breeding population. Based on the observed results, it is possible to conclude that the five forestry plantations, used as the seed sources to establish a breeding population in this study, were a mosaic of 3 genetic groups (the maternal generation), and after one generation of open-pollination at the FPs, the genetic differentiation became even higher, leading to the five genetic groups determined at the breeding population.Both Bayesian analyses that assumed Hardy-Weinberg equilibrium and inbreeding resulted in five consensus genetic groups that most likely represent the breeding population.TheFST values that assumed inbreeding were lower than the ones that assumed Hardy-Weinberg equilibrium. Hence, the definition for the genetic parameters of FST and He will be considered from the Hardy-Weinberg equilibrium analyses, which is FST=0.194–0.384 and He=0.38–0.50.It is possible that the highly fragmented breeding population detected in the Bayesian analyses has first occurred not only due to the selection pressure within open-pollinated progeny when the program selected the first and second best trees for wood volume but also due to the occurrence of assortative mating phenomenon.If the higher inbreeding levels detected are real, this phenomenon should be observed with caution, as they are not expected in outcrossing plants, and narrowing the genetic base of the population may represent a risk in advancing generations of selection, particularly in the long-term genetic breeding.What draws attention in this study was the relevance of the applied methodology on the data analyses, which means that, by implementing both the Bayesian algorithms in a learning sample approach, it has allowed a richness in the data interpretation that might be undetected, if routine analysis was applied instead, as commonly observed in similar studies.



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*Source: 747591-2013-06-04.xml*