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Which heterozygosity should I use?

Source: vignettes/articles/PopGenHelpR_heterozygosity.Rmd
PopGenHelpR_heterozygosity.Rmd

Purpose

To help you understand the different measures of heterozygosity in PopGenHelpR and determine which measure is appropriate for your question/objective.

What is heterozygosity and why is it important?

Heterozygosity refers to the presence of two alleles at a locus. We often use heterozygosity to measure genetic diversity, which is essential for a species’ ability to adapt and persist.

What measures of heterozygosity can PopGenHelpR estimate?

PopGenHelpR can estimate seven measures of heterozygosity with the function Heterozygosity. We list each measure below before providing brief descriptions of each one.

  • Population Measures
    • Observed heterozygosity (Ho)
    • Expected heterozygosity (He)
  • Individual Measures
    • Proportion of heterozygous loci (PHt)
    • Proportion of heterozygous loci standardized by the average expected heterozygosity (Hsexp)
    • Proportion of heterozygous loci standardized by the average observed heterozygosity (Hsobs)
    • Internal relatedness (IR)
    • Homozygosity by locus (HL)

PopGenHelpR can calculate all of these measures using the Heterozygosity function. See the code below.

# Load package and toy data for all of the statistics
library(PopGenHelpR)
data("HornedLizard_Pop")
data("HornedLizard_VCF")

All_Het <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "all")

Population measures of heterozygosity

PopGenHelpR users can estimate the expected and observed heterozygosity (He and Ho, respectively) of each population in their data set.

Expected heterozygosity (He)

PopGenHelpR estimates He per locus and population following the equations provided by the Hardy-Weinberg equation. Briefly, the equation estimates He as one minus the squared frequency of each allele (\(p^2\) and \(q^2\), respectively), thus giving us the expected frequency of heterozygous genotypes (2pq) at a locus. The overall measure of He is calculated as the average of the per locus estimates.

The equation per locus is below, where p is the reference allele and q is the alternate allele:

\[ H_e = 1-p^2-q^2 \]

Thus, the equation to calculate the overall He is below, where K is the number of SNPs.

\[ H_e = \frac{\sum_{k=1}^K(1-p^2-q^2)}{K} \]

How do we use He

We use He as a null model to test against and determine if Hardy-Weinberg equilibrium is being violated. Violations could indicate mutation, non-random mating, gene flow, non-infinite population size, natural selection, or any combination.

How do we calculate He in PopGenHelpR?

You can calculate He in PopGenHelpR using the command below.

He <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "He")

Observed heterozygosity (Ho)

PopGenHelpR estimates Ho per locus and population following the equations of Nei (1987). Briefly, the equations estimate Ho as one minus the proportion of homozygotes in the population at each locus, thus giving us the proportion of heterozygotes at a locus. The overall measure of Ho is calculated as the average of the per locus estimates.

The equation per locus is below:

\[ H_o = 1- \frac{Number\; of\; homoyzgotes}{Number\; of\; samples} \]

Thus the overall measure of Ho is below, where K is the number of SNPs:

\[ H_o = \frac{\sum_{k = 1}^K{1- \frac{Number\; of\; homoyzgotes}{Number\; of\; samples}}}{K} \]

The formal equation of Ho from Nei (1987) is below: Pkii is the proportion of homozygote (i) in a sample (k), and np is the number of samples:

\[ H_o = 1-\sum_{k}\sum_{i}\frac{Pkii}{np} \]

How do we use Ho

We use Ho as a measure of genetic diversity and also to compare to He to determine if our data is exhibiting different patterns, such as inbreeding (Ho < He) or heterozygote advantage (Ho > He).

How do we calculate Ho in PopGenHelpR?

You can calculate Ho in PopGenHelpR using the command below.

Ho <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "Ho")

Individual measures of heterozygosity

PopGenHelpR users can estimate the proportion of heterozygous loci (PHt), the proportion of heterozygous loci standardized by the average expected heterozygosity (Hsexp), the proportion of heterozygous loci standardized by the average observed heterozygosity (Hsobs), the internal relatedness (IR), and the homozygosity by locus (HL) of individuals in their data set.

Proportion of heterozygous loci (PHt)

The proportion of heterozygous loci (PHt) is calculated as the number of heterozygous SNPs divided by the number of genotyped SNPs in each individual.

\[ PHt = \frac{Number\; of\; heterozygous\; SNPs}{Number\; of\; genotyped\; SNPs} \]

How do we use PHt

PHt is helpful for evaluating the diversity within each individual and comparing it to other samples. Individual heterozygosity is also commonly used to investigate inbreeding (Miller et al., 2014). Individual heterozygosity is used in heterozygosity-fitness correlations (HFC), assuming that heterozygosity positively correlates with fitness. Thus, increased heterozygosity (decreased inbreeding) indicates higher fitness.

How do we calculate PHt in PopGenHelpR?

You can calculate PHt in PopGenHelpR using the command below.

PHt <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "PHt")

Proportion of heterozygous loci standardized by the average expected heterozygosity (Hsexp)

The proportion of heterozygous loci standardized by the average expected heterozygosity (Hsexp) is calculated as PHt divided by the mean expected heterozygosity (He) for each individual. Please see the equation below.

\[ Hs_{exp} = \frac{PHt}{H_e} \]

How do we use Hsexp

Hsexp was introduced by Coltman et al. (1999) to evaluate individual heterozygosity across individuals who were genotyped with different markers; this allows us to compare individual heterozygosity on the same scale and to assess inbreeding. Like PHt, higher Hsexp indicates less inbreeding.

How do we calculate Hsexp in PopGenHelpR?

You can calculate Hsexp in PopGenHelpR using the command below.

Hs_exp <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "Hs_exp")

Proportion of heterozygous loci standardized by the average observed heterozygosity (Hsobs)

The proportion of heterozygous loci standardized by the average observed heterozygosity (Hsobs) is calculated as PHt divided by the mean observed heterozygosity (Ho) for each individual. Please see the equation below.

\[ Hs_{obs} = \frac{PHt}{H_o} \]

How do we use Hsobs

Hsobs was introduced by Coltman et al. (1999) to evaluate individual heterozygosity across individuals who were genotyped with different markers; this allows us to compare individual heterozygosity on the same scale and to assess inbreeding. Like PHt, higher Hsobs indicates less inbreeding.

How do we calculate Hsobs in PopGenHelpR?

You can calculate Hsobs in PopGenHelpR using the command below.

Hs_obs <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "Hs_obs")

Internal relatedness (IR)

The equation for Internal relatedness (IR) is more complex and qutie the mouthful(or sentence full?). Please see the equation below. IR is calculated as two times the number of homozygous loci minus the sum of the frequency of the ith allele divided by two times the number of loci minus the sum of the frequency of the ith allele (see equation 2.1 in Amos et al., 2001).

\[ IR = \frac{(2H-\sum{f_i})}{(2N-\sum{f_i})} \]

How do we use IR?

IR was developed by Amos et al. (2001) to measure the diversity within individuals (Amos et al., 2001). Negative IR values suggest that individuals are outbred (tend to be more heterozygous), while positive values indicate that individuals are inbred (tend to be more homozygous).

How do we calculate IR in PopGenHelpR?

You can calculate IR in PopGenHelpR using the command below.

IR <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "IR")

Homozygosity by locus (HL)

Homozygosity by locus (HL) is calculated as the expected heterozygosity of loci in homozygosis (\(E_h\)) divided by the sum of the expected heterozygosity of loci in homozygosis (\(E_h\)) and the expected heterozygosity of loci in heterozygosis (\(E_j\); see Aparicio et al., 2006). Please see the equation below.

\[ HL = \frac{\sum{E_h}}{\sum{E_h} + \sum{E_j}} \]

How do we use HL?

HL was proposed by Aparicio et al. (2006) to improve on IR by weighing the contribution of each locus to the index depending on their allelic variability (Aparicio et al., 2006). HL, like IR, is useful for evaluating the diversity within an individual. HL ranges from 0 when all loci are heterozygous and 1 when all loci are homozygous (Aparicio et al., 2006).

How do we calculate HL in PopGenHelpR?

You can calculate HL in PopGenHelpR using the command below.

HL <- Heterozygosity(data = HornedLizard_VCF, pops = HornedLizard_Pop, statistic = "HL")

Please reach out to Keaka Farleigh () if you have questions or need any help.

References

Amos W., Worthington Wilmer J., Fullard K., Burg T. M., Croxall J. P., Bloch D., Coulson T. 2001. The influence of parental relatedness on reproductive success. Proceedings of the Royal Society B: Biological Sciences. 268: 2021-2027.

Aparicio J. M., Ortego J., Cordero P. J. 2006. What should we weigh to estimate heterozygosity, alleles or loci? Molecular Ecology. 15: 4659-4665

Coltman D. W., Pilkington J. G., Smith J. A., Pemberton J. M. 1999. Parasite-mediated selection against inbred Soay sheep in a free-living, island population. Evolution. 53: 1259-1267.

Miller, J. M., Malenfant, R. M., David, P., Davis, C. S., Poissant, J., Hogg, J. T., … & Coltman, D. (2014). Estimating genome-wide heterozygosity: effects of demographic history and marker type. Heredity, 112(3), 240-247.

Nei, M. (1987). Molecular evolutionary genetics. Columbia university press.