# What percentage of the (additive or not) genetic variance is explained by the 'n'- most important loci?

Standard models in population genetics look up at the evolution of few loci which impact fitness. The variance in fitness is determined by the genetic variance and the environmental variance (and the co-variance between environment and genetics). In this question I am interested only about genetic variance and about what percentage of the total genetic variance in fitness do 'n' loci explain.

The question is:

In general, in natural populations, what percentage of the total genetic variance is explained by the 'n'- most important loci? Here, by "most important loci" I mean loci which variance explain much of the total genetic variance.

In other words, the subquestions are of the kind:

• how much of the fitness variance does the most important locus explain?
• How much of the fitness variance do the 3 most important loci explain?
• How much of the fitness variance do the 100 most important loci explain? … or if you prefer…

It is obvious that the answer depends on the population under consideration. Factors that might influence the answers are for example

• species
• population size
• environment stability

Beside this question, I also welcome some insights concerning how different factors are likely to influence the answer.

Update

After @SYK's answer, I want to make sure that you understand what definition "genetic variance" I am implicitly using...

Implicitly, I meant the following definition: VG = H . VP, that is the genetic variance is equal to the heritability times the phenotype variance. For, example one could consider one continuous phenotypic trait and measure its variance in a given population (VP). One can then calculate the heritability (in the narrow sense) by calculating for example a regression of the mean (in case of sexual reproduction) parents phenotypes on the offspring phenotypes, where the slope of the regression is the heritability in the narrow sense (HN). From these VP and HN, one can calculate the (additive) genetic variance.

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Do you have at least one example of an empirical study of the type you are looking for ? It may be a helpful starting point for us in finding other ones. – Barbara Feb 10 '14 at 13:16
No, unfortunately I don't know any empirical study that investigates my question. – Remi.b Feb 10 '14 at 14:25
And do you have any study, which measures percentual increase in fitness, regardless of the cause ? – Barbara Feb 10 '14 at 14:33
Could you phrase this in terms of just one question? – Atticus29 Sep 21 '14 at 3:00
I think its exceptionally rare for the most important loci to collectively explain more than a small percentage of the total genetic variance, it's a fundamental problem with QTL - looking for something of large effect when by definition we expect most or all effects to be tiny. I'm looking forward to seeing an answer to this one! It's going on my favorites – rg255 Nov 20 '14 at 16:27

From the statistical point of view, this question is rather vague. One would need a mathematical definition for the term "genetic variance".

In one extreme, if the "genetic variance" merely means the categorial variations of nucleotides (i.e. ACTG) in the pooled genomes of interest, then the distribution of total "genetic variance" vs. loci variation is uniform and only depends on the size of the locus.

In another extreme (among many dimensions of extremes), if the "genetic variance" is only manifest by the organism's immediate "fitness" and only has two values: life and death (on birth), then all the "essential genes" are "the most important" loci. If you're interested in the n most important loci where n > the number of essential genes, then you would first look at the binary genetic interactions in the database such as BioGrid where two non-essential genes would "interact" and change the organism's fitness (in life and death).

Of course none of the two extremes is very interesting in population genetics or evolution, but a statistical question is best phrased by statistical terms. I would try to find the mathematical definition for "fitness variance", too.

---EDIT---

For a semi-empirical/informatics study, I think you could start with the simplest organism whose genome is well studied.

• Choose an organism (e.g. yeast)
• Assume uniform inheritability
• Choose a specific measurable phenotype/environment (e.g. the ability to grow on a specific sugar x)
• Scan each gene in the yeast genome and see its quantitative impact on growth (They're documented in various database)
• Ignore genetic interaction
• (Or scan each gene pair/triplet/.../n-cluster to see its impact on growth on x)
• Try to model your empirical distribution. It's only valid for that specific phenotype/environment
• Define your "TOTAL genetic variance in fitness" meaningfully and rigorously. "Additivity" would be a very drastic assumption.

My guess as a non-geneticist is that, as GriffinEvo suggested, for each phenotype as a function of the environment, the distribution would follow a power law. They would not have the properties that would allow you to use central limit theorem to "add them up". But for a specific phenotype, your empirical cumulative distribution function (cdf) would answer your question.

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Thanks for your answer. Please have a look to my update in my question and let me know if this makes more sense to you now. – Remi.b Nov 20 '14 at 15:02