Can anyone explain to me why in population genetics the expected heterozygosity is equivalent to gene diversity? It's probably a stupid question but I am stuck.
What about a population composed of a lot of individuals that are homozygous for different allele expressions? (e.g. AA, BB, CC, DD...). Why does a high amount of heterozygotes makes a popualtion diverse? (e.g. AB, AB, AB, AB...).
Thank you for your help!
Hello J.M.,
Remember that gene diversity is composed of two elements; 1) the number of alleles and 2) the abundance (or evenness) of the alleles. Both of these would increase the expected heterozygosity. If a population consists of an excess of homozygotes for different alleles this leads to a low observed heterozygosity but does not affect the expected heterozygosity calculated from HWE.
So for your above example the observed heterozygosity for population 1 (e.g. AA, BB, CC, DD) would be zero and for population 2 (e.g. AB, AB, AB, AB) would be one, leading to the wrong conclusion that pop 2 is more diverse than pop1. However the expected heterozygosity for pop 1 under HWE would be 0.75 and for pop 2 would be 0.5, leading to the correct conclusion that pop 1 has more allele diversity.
The reason we do not use simply the number of alleles is that it does not account for the evenness of the alleles, which can be important for the robustness of the population to bottleneck events. Thus, using expected heterozygosity is preferred since it accounts for but richness and evenness.
Hope this helps
Hi JM
Short answer: by definition. Nei called gene diversity to the expected heterozygosity.
Otherwise, Max has given you some good hints to think about.
Dear J. M.
I am also agree with Dr. Max R. Bangs. A beautiful explanation about your query. Nothing to speak.
Good Luck !
Gene diversity (GD) is equal to the probability of drawing two different alleles at random from a population: GD = 1 - Sum(pi)^2. So if you have four equally frequent alleles (A=0.25, B=0.25, C=0.25, D=0.25) then your GD = 1 - (4*0.25^2)= 0.75. This means that you have a 75% chance of drawing two different alleles from a population. If allele frequencies of the same alleles were different in another population (for example A=0.7, B=0.1, C=0.1, D=0.1) then your GD = 1-(0.25^2+3*0.1^2)=0.48, quite a bit lower than in the first population as A is a lot more frequent than the other alleles (so you are less likely to draw two different alleles from the second population). In a nutshell, the higher GD the more alleles are in your population, i. e. the more diverse it is.
GD is mathematically the same as the calculation of the percentage of heterozygotes you would expect to find in your population if it was in HWE, i. e. your expected heterozygosity He. So if your GD=0.75 then you would also expect 75% of your samples to be heterozygous if, and only if, your population was in HWE. If that is also what you actually observe (observed heterozygosity Ho=0.75) then you conclude that your population is in HWE. If Ho=0.5 for example then your population is not in HWE (and therfore not mating randomly).
Heterozigosity is an index created by Nei in the 70's as a rough estimate of the proportion of a population that is heterozygote for at least one of the studied loci. Applying heterozygosity on one single gene is easier to understand. The larger the proportion of heterozygote people for that one gene, the more diverse the genotype of that population of one gene it is. If you, now, consider more genes and their alleles, there will be a larger number of combinations, increasing the genetic diversity.
The expected heterozygosity is calculated for each gene through the number of alleles assuming the Harvey-Weinberg equilibrium. For example, if you have two alleles (p+q)^2 = p^2 +2pq+q^2 = 1 and then isolating mathematically the homozigote 2pq = 1-p^2-q^2. This says that the proportion of the heterozygote population for a gene with two alleles, 2pq, can be calculated through the frequencies of each allele p and q, separately, p^2 and q^2.
The only explanation I have for the equation of the mean heterozygosity for many loci instead of a calculation of the actual proportion of heterozygote population, taking in account the combinations of alleles from different loci, is for simplicity of calculation and because there was practically no data available at the time.
I'm not sure if, with today's and future amount of variation data and growing computational capacity, it will make sense to keep only rough estimates of heterozygosity. We will have the sequences and the numbers for large samples. It will be possible to actually map the population variation, per individual, per allele of each gene.
Sonalika,
For haploids you would simply calculate Gene Diversity as Markus explained: GD = 1 - Sum(pi)^2. This number would be equal to expected heterozygosity in a diploid organism, but you would report it as gene diversity instead of expected heterozygosity in haploids since there is no heterozygosity.
You can also calculate a reciprocal index of gene diversity by doing 1/Sum(pi)^2, which is equal to the effective number of alleles in a population (some people find this easier to interpret then a faction similar to the Simpson's Reciprocal Index used for species diversity). In both cases these calculations of gene diversity are more informative since it factors in both the number of alleles and evenness of alleles in the population which are important in determining robustness of a population to a bottleneck.
Hope this helps.
what if my population is not under HWE? does it still make sense to use He to represent genetic diversity?
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size