Data and definitions

Populations genetics foundations

Per Unneberg

DNA variation

Goal of section: look at the data that forms the foundation for population genomic analyses

From (Nei & Kumar, 2000, p. 231):

The main subject of population genetics is to study the generation and maintenance of genetic polymorphism and to understand the mechanisms of evolution at the population level

(Casillas & Barbadilla, 2017, p. 1026):

Big data samples of complete genome sequences of many individuals from natural populations of many species have transformed population genetics inferences on samples of loci to population genomics: the analysis of genome-wide patterns of DNA variation within and between species.

(Gillespie, 2004, p. 1)

Population geneticists spend most of their time doing one of two things: describing the genetic structure of populations or theorizing on the evolutionary forces acting on populations. On a good day, these two activities mesh and true insights emerge.

DNA variation - monomorphic sites

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
T	T	A	C	A	A	T	C	C	G	A	T	C	G	T
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
T	C	A	C	A	A	T	G	C	G	A	T	G	G	A
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
*		*	*		*	*		*	*		*		*	T

The alignment has 4 DNA sequences where each sequence has length L=15. A site where all nucleotides (alleles) are identical is called a monomorphic site (indicated with asterisks above). There are 9 monomorphic sites.

DNA variation - segregating sites

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
T	T	A	C	A	A	T	C	C	G	A	T	C	G	T
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
T	C	A	C	A	A	T	G	C	G	A	T	G	G	A
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
	*			*			*			*		*		*

A site where there are different nucleotides (alleles) is called a segregating site (indicated with asterisks above), often denoted S. There are S=6 segregating sites.

Alternative names for segregating site are:

• polymorphism
• mutation
• single nucleotide polymorphism (SNP)

mutation here and onwards refers to the process that generates new variation and the new variants generated by this process

In contrast to mutation which corresponds to within-species variation, a substitution refers to DNA differences between species.

DNA variation - major and minor alleles

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
T	T	A	C	A	A	T	C	C	G	A	T	C	G	T
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
T	C	A	C	A	A	T	G	C	G	A	T	G	G	A
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
	*			*			*			*		*		*

Much of the nucleotide variation we study consists of bi-allelic SNPs. The most common variant is called the major allele, and the least common the minor allele.

The set of alleles found on a single sequence is called haplotype.

Describing DNA variation - heterozygosity

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
T	T	A	C	A	A	T	C	C	G	A	T	C	G	T
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
T	C	A	C	A	A	T	G	C	G	A	T	G	G	A
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
	*			*			*			*		*		*

Once we have a sample of sequences we want to describe the observed variation. At any position the ith allele has sample frequency p_i, where the sum of all allele frequencies is 1. For instance, at site 1, p_T=1 (and by extension p_A=p_C=p_G=0), and at site 2 p_C=1/4 and p_T=3/4.

Heterozygosity

The heterozygosity at a site j is given by

h_j = \frac{n}{n-1}\left(1 - \sum_i p_i^2\right)

where the summation is over all alleles and p_i is the frequency of the i-th allele

Exercise: calculate the heterozygosity at sites 1, 2 and 5

\begin{align*} h_1 & = \frac{4}{3} \left(1 - p_T^2 \right) = 0 \\[10pt] h_2 & = \frac{4}{3} \left(1 - \left(p_C^2 + p_T^2\right) \right) = \frac{4}{3} \left( 1 - \left(\frac{1}{16} + \frac{9}{16}\right)\right) = \frac{1}{2}\\[10pt] h_5 & = \frac{4}{3} \left(1 - \left(p_A^2 + p_G^2\right) \right) = \frac{4}{3} \left( 1 - \left(\frac{1}{4} + \frac{1}{4}\right)\right) = \frac{2}{3} \end{align*}

In a randomly mating population, the heterozygosity is equal to the frequency of heterozygotes. Note however that the definition of heterozygosity only relies on allele frequencies, which means it can be applied to populations that are not in Hardy-Weinberg equilibrium, or to more general variation, such as protein isoforms. It can also be applied to haploid organisms, like bacteria.

Describing DNA variation - nucleotide diversity

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
T	T	A	C	A	A	T	C	C	G	A	T	C	G	T
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
T	C	A	C	A	A	T	G	C	G	A	T	G	G	A
T	T	A	C	G	A	T	G	C	G	C	T	C	G	T
	*			*			*			*		*		*

Nucleotide diversity \pi

The nucleotide diversity is the sum of site heterozygosities:

\pi = \sum_{j=1}^S h_j

where S is the number of segregating sites

Calculate the nucleotide diversity

Observation: h_i either 1/2 or 2/3 (for sites with p_{major}=p_{minor}).

\pi = \frac{1}{2} + \frac{2}{3} + \frac{1}{2} + \frac{2}{3} + \frac{1}{2} + \frac{1}{2} = 3\frac{1}{3}

Often we report \pi per site:

\pi = 3.33/15 = 0.222

Hahn (2019) implicitly assumes we are looking at DNA polymorphism. The expression actually holds for any genetic variation at a locus, and is sometimes called the gene diversity (Nei & Kumar, 2000, p. 245).

Under the infinite sites model, E(\pi)=\theta=4N_e\mu, for which reason \pi sometimes is called \theta_\pi. The measure gives the average number of pairwise nucleotide differences between two sequences, so an alternative expression is

\pi = \frac{\sum_{i<j}k_{ij}}{n(n-1)/2}

The latter expression is called the nucleotide diversity (Nei & Kumar, 2000, p. 251).

The real data

@SRR9309790.10003134
TAAATCGATTCGTTTTTGCTATCTTCGTCT
+
AAFFFJJJJJJJFJJJJJJJJJJJJJJJJJ
@SRR9309790.10003222
TAAATCGATTCGTTTTTGCTATCTTCGTCT
+
AAFFFJJJJJJJJJJJJJJJJJJJJJJJJJ

LG4:30430

 30431     30441     30451     30461           
CATTGGCAATGGCATCAGTTGAGCATCTTAGTACGAACTAAAAGCTG
...............M...............................
...............A...                            
...............A.................              
.............................................. 
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...............A...............................
...............A...............................
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Before getting to variants and genotypes a lot of processing has to be done, from FASTQ input, to mapped data, to variant and genotype calls.

Before getting to variants and genotypes a lot of processing has to be done, from FASTQ input, to mapped data, to variant and genotype calls.

The process

Bibliography

Casillas, S., & Barbadilla, A. (2017). Molecular Population Genetics. Genetics, 205(3), 1003–1035. https://doi.org/10.1534/genetics.116.196493

Gillespie, J. H. (2004). Population Genetics: A Concise Guide (2nd edition). Johns Hopkins University Press.

Hahn, M. (2019). Molecular Population Genetics (First). Oxford University Press.

Kreitman, M. (1983). Nucleotide polymorphism at the alcohol dehydrogenase locus of Drosophila melanogaster. Nature, 304(5925), 412. https://doi.org/10.1038/304412a0

Nei, M., & Kumar, S. (2000). Molecular Evolution and Phylogenetics. Oxford University Press.