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Abstract > Effect of Inbreeding Factor

Effect of Inbreeding Factor



What can be learned about the allele frequencies in human population                 from the allele in the blood meal, departure from the Hardy-Weinberg distribution, measured by an inbreeding coefficient?
In previous sections, we assumed Hardy Weinberg equilibrium. However, in the reality, there are many factors that might interfere the balance of genomic frequency. Inbreeding is breeding between close relatives and is one of the potential reasons that interfere the equilibrium. In terms of genetic epidemiology, Inbreeding factor (F) can be considered to be the probability to have a pair of alleles that are identical by decent from a common ancestor. Under high inbreeding factor, the genetic diversity decreases from one generation to the next and genome composition tends to be homozygous in the human population. In this experiment, while the simulated human genome is created from the last generation with the known genomes, inbreeding factor was identified to be the probability that converts the heterozygous alleles to the homozygous alleles.
The inbreeding factor equation can be expanded further:

F=[Exp(f(heterozygote))-Obs(f(heterozygote))]/ Exp(f(heterozygote))

F* Exp(f(heterozygote)) = Exp(f(heterozygote))-Obs(f(heterozygote))

Obs(f(heterozygote)) = (1-F) Exp(f(heterozygote))

Obs(f(homozygote | heterozygote)) = F *Exp(f(heterozygote))

Last equation states inbreeding factor (F) can be used to be the probability that converts the heterozygous alleles to the homozygous alleles.

In simulation, with inbreeding factor, not only the genome tends to be homozygous but also one blood meal probability is overestimated and multiple blood-meal probability is underestimated. In an extreme case, with inbreeding factor equal to one, each next generation individual only carries homozygous microsatellite alleles for each locus; even every mosquito interacts with two people, in every blood meal, only two types of alleles can be observed at most. In the lower bound method, those mosquitoes are only considered to feed from a single. 
If we say high inbreeding factor blurs the situation, as stated before, increasing analyzed locus number provides better view to the reality.


Graph 3: Trend of multiple blood meal probabilities by microsatellite locus number. Inbreeding factor: 0, 0.2, and 0.5.



Table 3-1: Cross analysis of inbreeding factor and locus number (number of blood meal = 1), given the simulating multiple blood meal distribution parameters: 80% one blood meal, 18% 2 blood meal, and 2% 3 blood meal. Human Population = 1000. Mosquito population = 324.

Inbreeding Factor 0 0.05 0.1 0.2 0.5
Number of Locus:1 Number of Blood Meal=1 87.91% ± 1.80 % 86.22% ± 1.99% 89.01% ± 1.66% 89.77% ± 1.77% 91.26% ± 1.51%
Number of Locus:2 Number of Blood Meal=1 82.04% ± 2.30 % 82.22% ± 1.92% 82.58%± 2.08% 84.07% ± 2.13% 86.92% ± 1.95%
Number of Locus:3 Number of Blood Meal=1 80.69% ± 1.89 % 80.62% ± 2.33% 81.00% ± 2.08% 81.77% ± 2.18% 84.91% ± 1.91%
Number of Locus:4 Number of Blood Meal=1 80.15% ± 2.25 % 80.07% ± 2.48% 80.50% ± 2.03% 80.39% ± 2.34% 82.91% ± 1.97%
Number of Locus:5 Number of Blood Meal=1 79.93% ± 2.18 % 80.23% ± 1.88% 80.60% ± 2.26% 80.42% ± 2.18% 81.53% ± 2.21%

Table 3-2: Cross analysis of inbreeding factor and locus number (number of blood meal = 2), given the simulating multiple blood meal distribution parameters: 80% one blood meal, 18% 2 blood meals, and 2% 3 blood meals. Human Population = 1000. Mosquito population = 324.

Inbreeding Factor 0 0.05 0.1 0.2 0.5
Number of Locus:1 Number of Blood Meal=2 12.04% ± 1.80 % 13.58% ± 1.97% 10.97% ± 1.66% 10.19% ± 1.75% 8.62% ± 1.50%
Number of Locus:2 Number of Blood Meal=2 17.53% ± 2.31 % 17.25% ± 1.98% 16.99% ± 1.99% 15.67% ± 2.11% 12.94% ± 1.93%
Number of Locus:3 Number of Blood Meal=2 18.72% ± 1.92 % 18.88% ± 2.32% 18.55% ± 2.09% 17.89% ± 2.13% 14.89% ± 1.90%
Number of Locus:4 Number of Blood Meal=2 18.97% ± 2.17 % 19.17% ± 2.39% 18.85% ± 2.08% 18.97% ± 2.29% 16.83% ± 1.98%
Number of Locus:5 Number of Blood Meal=2 19.14% ± 2.21 % 18.81% ± 1.98% 18.58% ± 2.19% 19.13% ± 2.18% 18.22% ± 2.18%

As Graph 3, Table 3-1, and Table 3-2 show, when locus number is small and inbreeding factor is as high as 0.5, the resulting multiple blood meal probabilities are farther from the theoretical number. However, the probabilities are getting improved as locus number increases and inbreeding factor decreases.