# Comparison among Methods and Statistical Software Packages to Analyze Germplasm Genetic Diversity by Means of Codominant Markers

## Abstract

**:**

## 1. Introduction

#### 1.1. Hardy–Weinberg Principle

^{2}= p

^{2}+ q

^{2}+ 2pq = 1”, where p

^{2}is the frequency of the AA genotype, q

^{2}indicates the aa genotype frequency, 2pq the Aa genotype frequency, p the A allele frequency, and q the a allele frequency. This equation is true only for a population in the Hardy–Weinberg equilibrium where it is possible to compute allele frequencies from knowing the genotype frequencies and vice versa. The above is if only two alleles, A and a, are possible for that locus. If, instead, three alleles may occur at a locus, the formula would be a trinomial square development ((p + q + r)

^{2}= p

^{2}+ q

^{2}+ r

^{2}+ 2pq + 2pr + 2qr = 1) and so on for higher numbers of alleles. It should be noted that the square terms (i.e., p

^{2}+ q

^{2}+ r

^{2}, etc.) are homozygote frequencies while the others (i.e., 2pq + 2pr + 2qr, etc.) are heterozygotes. Considering several alleles, I, with a frequency, p

_{i}, the homozygote frequency is Ʃp

_{i}

^{2}and heterozygote frequency can be calculated as the complementary difference from the homozygote frequency (i.e., 2pq = 1 − (p

^{2}+ q

^{2}) or 1 − Ʃp

_{i}

^{2}).

#### 1.2. Genetic Diversity

_{i}

^{2}, which is the heterozygosity expected if the population is in Hardy–Weinberg equilibrium. In analogy, the genetic identity (J) is Ʃp

_{i}

^{2}(homozygotes). However, since He could be computed for all populations, including non-random mating systems (e.g., autogamus, which, by definition, will not in Hardy–Weinberg equilibrium being a pure line with homozygosity for all loci), the terminology for He is thus gene diversity, rather than expected heterozygosity.

_{T}for total observed diversity; H

_{S}for within-population diversity; and D

_{ST}for the between-population diversity, with H

_{T}= H

_{S}+ D

_{ST}.

_{IS}, F

_{ST}, and F

_{IT}[7], are often used, also the F-statistics are based on the expected level of heterozygosity. The measures describe the different levels of population structures, such as variance of allele frequencies within populations (F

_{IS}), variance of allele frequencies between populations (F

_{ST}), and an inbreeding coefficient of an individual relative to the total population (F

_{IT}), all of which are related to heterozygosity at various levels of population structure. The terms mentioned above are represented by the formula, 1 − F

_{IT}= 1 − F

_{IS}+ 1 − F

_{ST}, where I is the individual, S the subpopulation, and T the total population. F

_{IT}thus refers to the individual in comparison with the total, F

_{IS}is the individual in comparison with the subpopulation, and F

_{ST}is the subpopulation in comparison with the total. As shown in Figure 1, total F, indicated by F

_{IT}, can be partitioned into F

_{IS}(or f) and F

_{ST}(or θ).

_{ST}can be calculated using the formula: F

_{ST}= (H

_{T}− H

_{S})/H

_{T}, where H

_{T}is the proportion of the heterozygotes in the total population and H

_{S}the average proportion of heterozygotes in subpopulations.

_{i}

^{2}), different figures can be obtained. In particular:

- For each locus and each population, He = (1 − Ʃp
_{i}_{(lg)}^{2}), where p_{i}_{(lg)}is the ith allele frequency of the lth locus in the gth population. - The average of the above He over populations gives the genetic diversity within a population for each locus, while the average of all the loci within a population diversity gives H
_{S}. The formula can thus be written as: H_{S}= (Ʃ_{l}(Ʃ_{g}(1 − Ʃ_{pi}_{(lg)}^{2})/_{g})/_{l}), where (1 − Ʃp_{i}_{(lg)}^{2}) indicates the expected heterozygosity for each locus in each population, g indicates the number of populations, and l the loci number. - The total genetic diversity, H
_{T}, is calculated using the allele frequency, p_{i}_{(l)}, for each locus over all populations and calculating the mean over loci: H_{T}= Ʃ(1 − Ʃ_{pi}_{(l)}^{2})/_{l}). - The between population component of diversity is calculated using the formula: D
_{ST}= H_{T}− H_{S}. - The between population component may also be expressed in relation to the total genetic diversity (for each locus and overall loci) as G
_{ST}= H_{T}/D_{ST}[4].

_{T}for each locus corresponds to the polymorphic information content (PIC) of that locus, which in other words, consists in the capacity of that locus (or better a marker) to assess polymorphism and diversity. Botstein et al. [9] proposed an adjustment of this value as:

_{i}and p

_{j}are the population frequency of the ith and jth alleles. The PIC proposed by Botstein and colleagues [9] subtracts from the He value an additional probability (ƩƩ2p

_{i}

^{2}p

_{j}

^{2}) due to the fact that linked individuals do not add information to the overall variation.

#### 1.3. Genetic Distance

_{x}= Ʃp

_{xi}

^{2}is the probability of identity in population x with p

_{xi}the frequency of the i-th allele and J

_{y}= Ʃp

_{yi}

^{2}is the probability of identity in population y, the probability of identity in both populations is J

_{xy}= Ʃp

_{xi}p

_{yi}as described by Nei [10,11]. The probability of identity in population x for all normalized loci is I = J

_{xy}/√(J

_{x}J

_{y}) and, in turn, the genetic distance is D = −LnI = −Ln (J

_{xy}/√(J

_{x}J

_{y})). In a small sample set with many loci, any biases can be corrected using Ď = −Ln G

_{xy}/√(G

_{x}G

_{y}), where G

_{x}and G

_{y}are (2n

_{x}J

_{x}− 1)/(2n

_{x}− 1) and (2n

_{y}J

_{y}− 1)/(2n

_{y}− 1) over the l loci studied, respectively, and G

_{xy}= J

_{xy}[12]. In this case, Ď could be negative, due to sampling errors, and hence considered as zero.

- Popogene [15], https://sites.ualberta.ca/~fyeh/popgene.html
- Power Market [16], http://statgen.ncsu.edu/powermarker/index.html
- Cervus [17], www.fieldgenetics.com
- Arlequin [18], http://cmpg.unibe.ch/software/arlequin3/
- Structure v 2.3 [19], http://web.stanford.edu/group/pritchardlab/structure.html

## 2. Data Input

**is not**missing data) could be named as zero, but zero is considered missing for some software, such as GenAlEx, when co-dominance is the option selected. In these cases, it is important to rename the null allele, for example, by substituting zero with 1.

## 3. Data Analysis

#### 3.1. GenAlEx

_{ST}) together with some graphic options (Figure 3).

- N: (number of genotypes);
- Na: (No. of Different Alleles);
- Ne: (No. of Effective Alleles = 1/(Σp
_{i}^{2})); - I: (Shannon’s Information Index = −1 × Σ(p
_{i}× Ln(p_{i}))); - Ho: (Observed Heterozygosity = No. of Hets/N);
- He: (Expected Heterozygosity = 1 − Σp
_{i}^{2}); - uHe: (Unbiased Expected Heterozygosity = (2N/(2N − 1)) × He);
- F: (Fixation Index = (He − Ho)/He = 1 − (Ho/He));
- Fis: (Mean He − Mean Ho)/Mean He);
- Fit: (H
_{T}− Mean Ho)/H_{T}), F_{ST}(H_{T}− Mean He)/H_{T}); - Nm: ([(1/Fst) − 1]/4);
- H
_{T}: Total Expected Heterozygosity = 1 − Σtp_{i}^{2}.

_{i}is the frequency of the ith allele for the total and Σtp

_{i}

^{2}is the sum of the squared total allele frequencies.

_{IS}, F

_{IT}, F

_{ST}) are computed per locus and not per population as in other programs, such as Arlequin (see below).

_{ST}, are reported in Table 4.

#### 3.2. GDA

#### 3.3. Popgene

_{IT}, F

_{ST}, F

_{IS}), gene flow, and genetic distance (following Nei 1972 [10] and Nei 1978 [6]). It also produces a dendrogram using UPGMA of the Nei’s distance, neutrality test, and the linkage disequilibrium (LD) between two loci. In the cases of several alleles per locus, the required input is not straightforward, based on the Mendelian convention (Figure 5), i.e., providing a letter for each allele, but it is possible to export the Popgene format from GenAlEx. However, a significant disadvantage is that it assigns the same letter to alleles from different loci, as if they were the same allele. This creates confusions and errors especially when reading the tables of “Allele Frequency”.

#### 3.4. Power Marker

#### 3.5. Cervus

#### 3.6. Arlequin

_{ij}− p

_{i}p

_{j}, is a potentially useful additional feature of Arlequin. However, although the instruction manual asserts the computation of the linkage disequilibrium coefficient (D) is possible, this seems not to be true. On the contrary, significance is reported as the P values of χ

^{2}with 1000 permutations. Moreover, the number of loci linked to each locus for each population analyzed is provided. Unfortunately, even when the locus name is inserted, it is not reflected in the output, where the loci are simply numbered starting at zero. Similarly, the populations are numbered as pop1#, pop2#, pop3#, etc. rather than using the given name. This could easily lead to mistakes and confusion. In addition, there are sometimes discrepancies between the data saved in the browser output file and that saved as an xls file.

#### 3.7. Structure

## 4. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Diagram of the relationships between the gene diversity components. I = individual, S = subpopulation, T = total population.

**Figure 2.**Structure of the data inserted by GenAlEx, the Excel macro for genetic analyses. (

**a**) Template; (

**b**) data in D sheet.

**Figure 9.**Structure output of the bar plot clusters either by populations (

**a**) or sorted by the Q value (

**b**) are reported with different colors.

**Table 1.**Allelic situation and computation of the genetic parameters in three populations analyzed using two markers where each one has three possible alleles; adapted from Turpeinen et al. [8].

Locus\Pop | Pop1 | Pop2 | Pop3 | Mean | |||
---|---|---|---|---|---|---|---|

Locus 1 | 10 | 10 | |||||

167 | 0.00 | 0 | 0 | 0.00 | |||

168 | 0.50 | 0 | 0.9 | 0.47 | |||

172 | 0.50 | 1 | 0.1 | 0.53 | |||

He | 0.50 | 0.00 | 0.18 | H_{S} | 0.23 | H_{T} | 0.50 |

Locus 2 | |||||||

218 | 0.50 | 0.00 | 0.10 | 0.20 | |||

221 | 0.10 | 1.00 | 0.10 | 0.40 | |||

224 | 0.40 | 0.00 | 0.80 | 0.40 | |||

He | 0.58 | 0.00 | 0.34 | H_{S} | 0.31 | H_{T} | 0.64 |

H_{T} | H_{S} | D_{ST} | G_{ST} | ||||

Locus 1 | 0.50 | 0.23 | 0.27 | 0.54 | |||

Locus 2 | 0.64 | 0.31 | 0.33 | 0.52 | |||

Mean | 0.57 | 0.27 | 0.30 | 0.53 |

**Table 2.**GenAlEx output of the data in Figure 2 per locus. Sheet HFL.

WMC24 | BARC213 | BARC8 | wms124 | WMC177 | WMC170 | CFA2278 | Mean | SE | ||
---|---|---|---|---|---|---|---|---|---|---|

N | Mean | 9.333 | 8.667 | 9.889 | 9.556 | 10.000 | 9.667 | 9.889 | ||

SE | 0.333 | 0.236 | 0.111 | 0.242 | 0.000 | 0.167 | 0.111 | |||

Na | Mean | 3.222 | 4.444 | 3.222 | 1.667 | 3.444 | 4.000 | 1.444 | ||

SE | 0.547 | 0.475 | 0.401 | 0.289 | 0.475 | 0.408 | 0.176 | |||

Ne | Mean | 2.167 | 3.374 | 1.949 | 1.424 | 2.106 | 2.742 | 1.176 | ||

SE | 0.287 | 0.411 | 0.322 | 0.212 | 0.308 | 0.292 | 0.100 | |||

I | Mean | 0.825 | 1.266 | 0.747 | 0.321 | 0.829 | 1.099 | 0.183 | ||

SE | 0.154 | 0.131 | 0.145 | 0.140 | 0.158 | 0.132 | 0.081 | |||

Ho | Mean | 0.289 | 0.143 | 0.035 | 0.000 | 0.122 | 0.117 | 0.000 | ||

SE | 0.084 | 0.032 | 0.017 | 0.000 | 0.057 | 0.029 | 0.000 | |||

He | Mean | 0.466 | 0.657 | 0.395 | 0.198 | 0.436 | 0.585 | 0.113 | ||

SE | 0.074 | 0.051 | 0.075 | 0.087 | 0.079 | 0.065 | 0.054 | |||

uHe | Mean | 0.493 | 0.698 | 0.416 | 0.209 | 0.459 | 0.617 | 0.119 | ||

SE | 0.078 | 0.054 | 0.079 | 0.092 | 0.084 | 0.068 | 0.057 | |||

F | Mean | 0.426 | 0.803 | 0.887 | 1.000 | 0.693 | 0.726 | 1.000 | ||

SE | 0.119 | 0.045 | 0.054 | 0.000 | 0.130 | 0.106 | 0.000 | |||

Pops | F_{IS} | 0.381 | 0.783 | 0.913 | 1.000 | 0.720 | 0.799 | 1.000 | ||

F_{IT} | 0.566 | 0.838 | 0.954 | 1.000 | 0.767 | 0.853 | 1.000 | 0.854 | 0.058 | |

F_{ST} | 0.300 | 0.253 | 0.471 | 0.308 | 0.167 | 0.269 | 0.210 | 0.282 | 0.037 | |

Nm | 0.584 | 0.739 | 0.281 | 0.562 | 1.246 | 0.680 | 0.941 | 0.719 | 0.116 |

**Table 3.**GenAlEx output of the data in Figure 2 per population. Sheet HFP.

Mean and SE over Loci for Each Pop | |||||||||

Population | N | Na | Ne | I | Ho | He | uHe | F | |

Pop1 | Mean | 9.000 | 3.286 | 2.400 | 0.921 | 0.068 | 0.520 | 0.551 | 0.857 |

SE | 0.436 | 0.421 | 0.348 | 0.147 | 0.025 | 0.077 | 0.081 | 0.059 | |

Pop2 | Mean | 9.714 | 3.286 | 2.268 | 0.853 | 0.073 | 0.475 | 0.501 | 0.750 |

SE | 0.184 | 0.565 | 0.412 | 0.174 | 0.029 | 0.083 | 0.088 | 0.142 | |

Pop3 | Mean | 9.857 | 2.286 | 1.535 | 0.450 | 0.057 | 0.249 | 0.262 | 0.832 |

SE | 0.143 | 0.522 | 0.254 | 0.186 | 0.043 | 0.103 | 0.108 | 0.090 | |

Pop4 | Mean | 9.571 | 2.714 | 1.697 | 0.622 | 0.089 | 0.347 | 0.367 | 0.783 |

SE | 0.297 | 0.360 | 0.246 | 0.138 | 0.041 | 0.074 | 0.079 | 0.106 | |

Pop5 | Mean | 9.714 | 4.286 | 2.934 | 1.088 | 0.221 | 0.541 | 0.571 | 0.635 |

SE | 0.184 | 0.778 | 0.509 | 0.245 | 0.097 | 0.119 | 0.125 | 0.143 | |

Pop6 | Mean | 9.714 | 3.571 | 2.461 | 0.900 | 0.164 | 0.477 | 0.504 | 0.694 |

SE | 0.286 | 0.719 | 0.550 | 0.217 | 0.096 | 0.101 | 0.107 | 0.161 | |

Pop7 | Mean | 9.286 | 2.429 | 1.733 | 0.539 | 0.122 | 0.303 | 0.320 | 0.547 |

SE | 0.286 | 0.528 | 0.358 | 0.195 | 0.068 | 0.105 | 0.111 | 0.171 | |

Pop8 | Mean | 9.429 | 2.857 | 1.932 | 0.687 | 0.066 | 0.370 | 0.392 | 0.840 |

SE | 0.297 | 0.595 | 0.359 | 0.209 | 0.036 | 0.108 | 0.114 | 0.064 | |

Pop9 | Mean | 9.857 | 2.857 | 2.245 | 0.716 | 0.046 | 0.383 | 0.404 | 0.886 |

SE | 0.143 | 0.705 | 0.481 | 0.262 | 0.033 | 0.138 | 0.145 | 0.056 | |

Grand Mean and SE over Loci and Pops | |||||||||

N | Na | Ne | I | Ho | He | uHe | F | ||

Total | Mean | 9.571 | 3.063 | 2.134 | 0.753 | 0.101 | 0.407 | 0.430 | 0.755 |

SE | 0.090 | 0.198 | 0.136 | 0.067 | 0.019 | 0.034 | 0.036 | 0.039 | |

Population | %P | ||||||||

Pop1 | 100.00% | ||||||||

Pop2 | 100.00% | ||||||||

Pop3 | 57.14% | ||||||||

Pop4 | 100.00% | ||||||||

Pop5 | 85.71% | ||||||||

Pop6 | 85.71% | ||||||||

Pop7 | 71.43% | ||||||||

Pop8 | 71.43% | ||||||||

Pop9 | 57.14% | ||||||||

Mean | 80.95% | ||||||||

SE | 5.83% |

**Table 4.**Computation of different parameters of distance between populations. Sheets NeiP, uNeiP, and F

_{ST}P. (A) Nei’s genetic distance [10]; (B) Pairwise Population Matrix of Nei’s Unbiased Genetic Distance; (C) Pairwise Population F

_{ST}Values.

(A) | |||||||||

Population | Pop1 | Pop2 | Pop3 | Pop4 | Pop5 | Pop6 | Pop7 | Pop8 | Pop9 |

Pop2 | 0.406 | 0.000 | |||||||

Pop3 | 0.569 | 0.234 | 0.000 | ||||||

Pop4 | 0.602 | 0.224 | 0.032 | 0.000 | |||||

Pop5 | 0.615 | 0.401 | 0.236 | 0.222 | 0.000 | ||||

Pop6 | 0.513 | 0.250 | 0.120 | 0.127 | 0.249 | 0.000 | |||

Pop7 | 0.947 | 0.619 | 0.598 | 0.577 | 0.445 | 0.495 | 0.000 | ||

Pop8 | 0.624 | 0.540 | 0.398 | 0.376 | 0.163 | 0.416 | 0.579 | 0.000 | |

Pop9 | 0.392 | 0.386 | 0.336 | 0.290 | 0.237 | 0.374 | 0.619 | 0.251 | 0.000 |

(B) | |||||||||

Population | Pop1 | Pop2 | Pop3 | Pop4 | Pop5 | Pop6 | Pop7 | Pop8 | Pop9 |

Pop2 | 0.347 | 0.000 | |||||||

Pop3 | 0.527 | 0.200 | 0.000 | ||||||

Pop4 | 0.553 | 0.183 | 0.008 | 0.000 | |||||

Pop5 | 0.548 | 0.342 | 0.194 | 0.173 | 0.000 | ||||

Pop6 | 0.453 | 0.199 | 0.085 | 0.085 | 0.189 | 0.000 | |||

Pop7 | 0.901 | 0.582 | 0.577 | 0.549 | 0.399 | 0.456 | 0.000 | ||

Pop8 | 0.573 | 0.497 | 0.372 | 0.343 | 0.112 | 0.373 | 0.550 | 0.000 | |

Pop9 | 0.341 | 0.344 | 0.310 | 0.258 | 0.186 | 0.330 | 0.589 | 0.217 | 0.000 |

(C) | |||||||||

Population | Pop1 | Pop2 | Pop3 | Pop4 | Pop5 | Pop6 | Pop7 | Pop8 | Pop9 |

Pop2 | 0.142 | 0.000 | |||||||

Pop3 | 0.248 | 0.140 | 0.000 | ||||||

Pop4 | 0.214 | 0.105 | 0.044 | 0.000 | |||||

Pop5 | 0.162 | 0.139 | 0.141 | 0.096 | 0.000 | ||||

Pop6 | 0.157 | 0.108 | 0.105 | 0.076 | 0.104 | 0.000 | |||

Pop7 | 0.279 | 0.246 | 0.364 | 0.241 | 0.181 | 0.234 | 0.000 | ||

Pop8 | 0.215 | 0.211 | 0.257 | 0.163 | 0.080 | 0.187 | 0.290 | 0.000 | |

Pop9 | 0.179 | 0.197 | 0.234 | 0.143 | 0.110 | 0.190 | 0.308 | 0.152 | 0.000 |

Source | df | SS | MS | Est. Var. | % |
---|---|---|---|---|---|

Among Regions | 2 | 27.828 | 13.914 | 0.033 | 2% |

Among Pops | 6 | 71.567 | 11.928 | 0.515 | 24% |

Within Pops | 171 | 277.550 | 1.623 | 1.623 | 75% |

Total | 179 | 376.944 | 2.171 | 100% |

**Table 6.**Descriptive statistics output of GDA per population (A) and per locus (B). Where n is the number of observations, P the polymorphism, A the alleles number, Ap the polymorphic alleles number, He the expected heterozygosity, and Ho the observed heterozygosity.

(A) output per population | ||||||

Population | n | P | A | Ap | He | Ho |

Pop1 | 9.00 | 1.00 | 3.29 | 3.29 | 0.55 | 0.07 |

Pop2 | 9.71 | 1.00 | 3.29 | 3.29 | 0.50 | 0.07 |

Pop3 | 9.86 | 0.57 | 2.29 | 3.25 | 0.26 | 0.06 |

Pop4 | 9.57 | 1.00 | 2.71 | 2.71 | 0.37 | 0.09 |

Pop5 | 9.71 | 0.86 | 4.29 | 4.83 | 0.57 | 0.22 |

Pop6 | 9.71 | 0.86 | 3.57 | 4.00 | 0.50 | 0.16 |

Pop7 | 9.29 | 0.71 | 2.43 | 3.00 | 0.32 | 0.12 |

Pop8 | 9.43 | 0.71 | 2.86 | 3.60 | 0.39 | 0.07 |

Pop9 | 9.86 | 0.57 | 2.86 | 4.25 | 0.40 | 0.05 |

Mean | 9.57 | 0.81 | 3.06 | 3.58 | 0.43 | 0.10 |

(B) output per locus | ||||||

Locus | n | P | A | Ap | He | Ho |

WMC24 | 84.00 | 1.00 | 8.00 | 8.00 | 0.66 | 0.30 |

BARC213 | 78.00 | 1.00 | 12.00 | 12.00 | 0.89 | 0.14 |

BARC8 | 89.00 | 1.00 | 12.00 | 12.00 | 0.75 | 0.03 |

wms124 | 86.00 | 1.00 | 3.00 | 3.00 | 0.29 | 0.00 |

WMC177 | 90.00 | 1.00 | 10.00 | 10.00 | 0.53 | 0.12 |

WMC170 | 87.00 | 1.00 | 11.00 | 11.00 | 0.80 | 0.11 |

CFA2278 | 89.00 | 1.00 | 2.00 | 2.00 | 0.15 | 0.00 |

All | 86.14 | 1.00 | 8.29 | 8.29 | 0.58 | 0.10 |

Locus | Allele | Frequency | Found in |
---|---|---|---|

WMC24 | 171 | 0.050 | Pop5 |

WMC24 | 153 | 0.050 | Pop5 |

WMC24 | 169 | 0.150 | Pop5 |

BARC213 | 204 | 0.200 | Pop6 |

BARC213 | 224 | 0.050 | Pop4 |

BARC8 | 248 | 0.100 | Pop8 |

BARC8 | 242 | 0.100 | Pop7 |

BARC8 | 272 | 0.050 | Pop2 |

BARC8 | 274 | 0.050 | Pop1 |

WMC177 | 246 | 0.300 | Pop9 |

WMC177 | 212 | 0.100 | Pop8 |

WMC177 | 204 | 0.100 | Pop7 |

WMC177 | 220 | 0.150 | Pop5 |

WMC177 | 222 | 0.050 | Pop5 |

WMC170 | 214 | 0.100 | Pop8 |

WMC170 | 220 | 0.100 | Pop8 |

WMC170 | 248 | 0.050 | Pop6 |

WMC170 | 230 | 0.050 | Pop4 |

Pop1 | Pop2 | Pop3 | Pop4 | Pop5 | Pop6 | Pop7 | Pop8 | Pop9 | |

Pop1 | 0.35 | 0.53 | 0.55 | 0.55 | 0.45 | 0.90 | 0.57 | 0.34 | |

Pop2 | 0.41 | 0.20 | 0.18 | 0.34 | 0.20 | 0.58 | 0.50 | 0.34 | |

Pop3 | 0.57 | 0.23 | 0.01 | 0.19 | 0.09 | 0.58 | 0.37 | 0.31 | |

Pop4 | 0.60 | 0.22 | 0.03 | 0.17 | 0.09 | 0.55 | 0.34 | 0.26 | |

Pop5 | 0.62 | 0.40 | 0.24 | 0.22 | 0.19 | 0.40 | 0.11 | 0.19 | |

Pop6 | 0.51 | 0.25 | 0.12 | 0.13 | 0.25 | 0.46 | 0.37 | 0.33 | |

Pop7 | 0.95 | 0.62 | 0.60 | 0.58 | 0.45 | 0.49 | 0.55 | 0.59 | |

Pop8 | 0.62 | 0.54 | 0.40 | 0.38 | 0.16 | 0.42 | 0.58 | 0.22 | |

Pop9 | 0.39 | 0.39 | 0.34 | 0.29 | 0.24 | 0.37 | 0.62 | 0.25 |

**Table 9.**Cervus output reporting the number of alleles per locus (k), number of individuals (N), observed (Hobs) and expected (Hexp) heterozygosity, PIC, combined non-exclusion probability for first parent (NE-1P), second parent (NE-2P), parent pair (NE-PP), identity (NE-I) and sib identity (NE-SI), the Hardy–Weinberg equilibrium significance (HW), and the F test (F).

Locus | k | N | HObs | HExp | PIC | NE-1P | NE-2P | NE-PP | NE-I | NE-SI | HW | F(Null) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

WMC24 | 8 | 84 | 0.298 | 0.663 | 0.615 | 0.748 | 0.575 | 0.387 | 0.160 | 0.460 | *** | +0.3786 |

BARC213 | 12 | 78 | 0.141 | 0.886 | 0.868 | 0.391 | 0.242 | 0.090 | 0.026 | 0.317 | ND | +0.7244 |

BARC8 | 12 | 89 | 0.034 | 0.754 | 0.727 | 0.620 | 0.435 | 0.230 | 0.086 | 0.397 | *** | +0.9145 |

wms124 | 3 | 86 | 0.000 | 0.285 | 0.261 | 0.960 | 0.858 | 0.754 | 0.536 | 0.742 | ND | +0.9766 |

WMC177 | 10 | 90 | 0.122 | 0.527 | 0.508 | 0.835 | 0.655 | 0.448 | 0.243 | 0.549 | *** | +0.6174 |

WMC170 | 11 | 87 | 0.115 | 0.804 | 0.772 | 0.565 | 0.388 | 0.204 | 0.067 | 0.367 | *** | +0.7509 |

CFA2278 | 2 | 89 | 0.000 | 0.146 | 0.134 | 0.989 | 0.933 | 0.879 | 0.742 | 0.863 | ND | +0.8551 |

Mean | 8.29 | 0.580 | 0.555 | 0.081 | 0.012 | 0.000 | 0.000 | 0.007 |

Source of Variation | d.f. | Sum of Squares | Variance Components | Percentage of Variation | Expected Mean Square |
---|---|---|---|---|---|

Among Region | 2 (R − 1) | 27.828 | 0.03310 V_{a} | 1.52 | Nσ^{2}_{a} + 2σ^{2}_{b}+ σ^{2}_{c} |

Among Populations within Region | 6 (P − R) | 71.567 | 0.51523 V_{b} | 23.73 | 2σ^{2}_{b} + σ^{2}_{c} |

Within Populations | 171 (2N − P) | 277.550 | 1.62310 V_{c} | 74.75 | σ^{2}_{c} |

Total | 179 (2N − 1) | 376.944 | 2.17144 | σ^{2}_{T} |

^{2}

_{a}= F

_{ct}σ

^{2}

_{T}, σ

^{2}

_{b}= (F

_{ST}− F

_{CT}) σ

^{2}

_{T}, σ

^{2}

_{c}= (1 − F

_{st}) σ

^{2}

_{T}, F

_{ST}= (σ

^{2}

_{a}+ σ

^{2}

_{b})/σ

^{2}

_{T}, F

_{SC}= σ

^{2}

_{b}/(σ

^{2}

_{b}+ σ

^{2}

_{c}), F

_{CT}= σ

^{2}

_{a}/σ

^{2}

_{T}, F

_{ST}= 0.252 = F

_{IT}, F

_{SC}= 0.240 = F

_{IS}, and F

_{CT}= 0.015 = F

_{ST}.

Software | GenAlEx | GDA | Popgene | Power Marker | Cervus | Arlequin | Structure |
---|---|---|---|---|---|---|---|

Insert Data | Excel | Text | Text | Excel | Text | Text | Text |

Descriptive Statistics | |||||||

Genetic Diversity | X | X | X | X | |||

Degree of Polymorphism | X | X | X | ||||

Heterozygosity | X | X | X | X | X | X | |

Expected Heterozygosity | X | X | X | X | X | X | |

Number of Alleles | X | X | X | X | X | X | |

Private Alleles | X | ||||||

Effective Allele Number | X | X | |||||

PIC | X | X | |||||

Gene Flow | X | ||||||

Homogeneity Test | X | ||||||

Genetic Distance | X | X | X | X | X | X | |

Graphic Options | X | X | X | X | |||

Fisher Parameters (Fis, Fit, Fst) | X | X | X | X | |||

MANOVA | X | X | |||||

LD | X | X | X |

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## Share and Cite

**MDPI and ACS Style**

Pagnotta, M.A.
Comparison among Methods and Statistical Software Packages to Analyze Germplasm Genetic Diversity by Means of Codominant Markers. *J* **2018**, *1*, 197-215.
https://doi.org/10.3390/j1010018

**AMA Style**

Pagnotta MA.
Comparison among Methods and Statistical Software Packages to Analyze Germplasm Genetic Diversity by Means of Codominant Markers. *J*. 2018; 1(1):197-215.
https://doi.org/10.3390/j1010018

**Chicago/Turabian Style**

Pagnotta, Mario A.
2018. "Comparison among Methods and Statistical Software Packages to Analyze Germplasm Genetic Diversity by Means of Codominant Markers" *J* 1, no. 1: 197-215.
https://doi.org/10.3390/j1010018