Hello Mustapha,

For a population under a bottleneck you would expect low nucleotide diversity, low haplotype diversity, positive Tajima's D, and positive Fu's F.

Fore a recent population expansion you should also expect low nucleotide diversity, but high haplotype  diversity, negative Tajima's D, and negative Fu's F.

Fu's F is also more sensitive to recent population expansion than Tajima's D, thus some prefer using Fu's F for looking for population expansion, however if Tajima's D is significant I would expect Fu's F to also be significant. You can also try Fay and Wu's H and Zeng et al.'s E. Below is a nice short summary of each of these metrics. I would suggest running at least a few of these different metrics and just making a summary table of all values. 

http://darwin.eeb.uconn.edu/eeb348/lecturenotes/molevol-tajima.pdf

Hope this helps.

Hello,

You should also take into account the (possible) effect of gene flow between populations, since it can impact nucleotide diversity and values of Tajima's D. For example, the observed low nucleotide diversity could be caused by lower gene flow with the other populations. Looking at the population structure could help you explain the values of your indices of diversity and neutrality (anyway, these indices are often not so straightforward to interpret).

Max: I am not sure that you would expect a low nucleotide diversity after a expansion, I think it would increase.

Hope this helps,

Best regards.

Hello Yann,

In an expanding population mutations are not lost, thus all new mutations are incorporated into the population. This increases haplotype diversity and results in what many call a starburst phylogeny, where a population has many low frequency haplotypes with low divergence between them.

Nucleotide diversity is calculated by summing multiplications of the frequency of two haplotypes by the number of segregating sites between these haplotyps divided by the total sequence length. Thus, in an expanding phylogeny you expect low nucleotide diversity since there should be a lot low frequency haplotypes and low average number of segregating sites between haplotypes.

So, in an expanding population haplotype diversity and number of polymorphic sites quickly increase while nucleotide diversity lags behind. Over time when the population stops expanding and starts to stabilize nucleotide diversity will increase as newly created low frequency haplotypes either increase in the population or are lost, which overtime increases the average number of segregating sites  between haplotypes.

Hopefully this makes sense, the attached document in my previous post does a better job explaining the rational and math behind these metrics.

Best regards.

I agree that in an expanding population, nucleotide diversity (theta pi estimator) will increase slower than the Watterson estimator (which uses the number of segregating sites). What I meant was that, all other things being equal, an expanding population will show a higher nucleotide diversity that a population with a constant effective size.

Best regards.

 Hello Yann,

I disagree that an expanding population will show higher nucleotide diversity (pi) than that of a constant effective size, instead I think it should be the opposite. Mathematically nucleotide diversity (pi) is calculated by multiplying the frequency of two alleles by the fraction of pair-wise differences between the alleles and summing for all combinations of alleles. In an expanding population there are many low frequency alleles and low average pair-wise distance leading to a starburst phylogeny. Thus, if allele frequency and pair-wise distance between alleles are low and nucleotide diversity is the product of these metrics then nucleotide diversity should be low. 

I hope my explanation is clear. I am curious on why you think the opposite should occur?

Best regards.

Well, my first reflex was to think: effective population size increases = diversity increases. To be honest, I never thought about the behavior of the different terms of the pi equation (I am ashamed to say that I am a population geneticist that hates maths). But after doing some back of the envelope calculations, I am not sure you are right. The frequencies of the haplotypes that were present in the ancestral population do not change much, so they contribute for the most part to nucleotide diversity. Then you add to that the new haplotypes, which certainly have a low pairwise distance with their ancestral haplotype (and the haplotypes derived from it), but a high pairwise distance with the other haplotypes from the ancestral population. I could be wrong, but it also seems to me that nucleotide diversity increases when allelic frequencies become similar.

I am not sure my explanation is clear and I do not entirely trust my reasoning on this one, so I ran some coalescent simulations with fastsimcoal (initial 4Nµ=8e-5, expansion x10 at t=5000, sample=15 diploid individuals, 20 independent genes of 10kb without recombination), and you can see in the attached file that nucleotide diversity increases after an expansion (each black line is a gene, the red line is the mean over all genes - 20 genes is not much, but we can see a trend). You can also check Table 1 in Tajima 1989 (see link), it describes the evolution of nucleotide diversity after an expansion (second column, S2(t) being the nucleotide diversity if I am not mistaken – I am never sure with the notation in old papers).

Tell me what you think!

Best regards.

Article The Effect of Change in Population Size on DNA Polymorphism

Hello Yann,

This is an interesting discussion, I always enjoy talking population genetics with someone else in the field.

The Tajima's paper attached is a great paper it has been a while since I have last read it, so the refresher is quite nice. Your simulations are interesting, as expected nucleotide diversity does increase as the population increases, and I am not arguing that. However, nucleotide diversity in an expanding population is more heavily affected by the previous bottleneck than that of haplotype diversity and number of segregating sites, which recover quicker and are more affected by the size of the current population than that of a historical population. This is the same conclusion of Tajima in the paper where he states that:

“…the average number of nucleotide differences is affected by the bottleneck of population size more strongly than is the number of segregating sites. ... Results obtained indicate that the number segregating sites is influenced by the size of current population more strongly than is the average number of nucleotide differences, while the average number of nucleotide differences is affected by the size of original population more severely than is the number of segregating sites.” 

The basic principle behind Tajima's D when it comes to increases/decreases in population size is that the number of segregating sites is more affected by current population size and nucleotide diversity is more affected by past population size. Thus, in a population that is going through a bottleneck the number of segregating sites will fall more rapidly than that of a nucleotide diversity leading to a positive D. In a population that is increasing from a bottleneck the number of segregating sites will increase more rapidly than that of nucleotide diversity leading to a negative D.

Hope this makes sense and tell me what you think.

Also, sorry for hijacking your question Mustapha, although this discussion is probably useful for you. If there is anything else you had questions on feel free to add it to the discussion.

Best regards.

Hello,

I agree with all you said about the rate of change of nucleotide diversity values and number of segregating sites during effective population size variations. I was just arguing that nucleotide diversity was higher in a population that recently expanded, compared to a population with a constant size (the starting effective sizes being equal).

By the way, in the past I saw some papers linking low nucleotide diversity and recent expansion, that' is why I wanted to discuss this issue. I guess the authors of these papers meant a bottleneck followed by a recent expansion/recovery, but it always bugged me.

Indeed, it is always interesting to discuss these concepts with others!

Best regards.

I have also read some papers linking low nucleotide diversity and recent expansion. I think these authors are referring to lower nucleotide diversity than would be expect given the current population size or haplotype diversity.

Best regards.

Thank very much for the wonderful contrebutions to my study. I really learned a lot from your discussions. But please can you look into the attached file. it cotained the mismatch analysis of that same population

Hello Mustapha,

Before I say anything about your mismatch analysis, I have a couple of questions.

1. What locus are you using or more importantly is it haploid (e.g. mitochondrial) or diploid (e.g. nuclear)?

2. Do you have any gaps in your alignment? If so, how did you treat these gaps (e.g. as missing data or as individual mutations)?

3. What is your haplotype diversity and frequency of haplotypes (e.g do you have one or two very common haplotypes and a few less common haplotypes that are one mutation away)?

1. I'm using control region (D-loop) of mitochondrial DNA.

2. I did not observed any gap during the alignment.

3. The population has 3 commomn haplotypes (75% of the total of the samples).

     and 2 unique haplotypes (25% of the total samples)

Hello Mustapha,

If I understand your data correctly, it sounds like you have low haplotype diversity (5 haplotypes) and low nucleotide diversity, along with a significant negative D. For an expanding population you would expect the later two results but would not expect the low haplotype diversity. Instead you should expect a few common haplotypes and a lot of rare haplotypes that are one or two mutations different from the common haplotypes (often called a star phylogeny or starburst phylogeny). This is due to expanding populations maintaining all or most new mutations since everyone is reproducing, thus drift and selection fail to remove haplotypes. 

Based on your mismatch analysis it seems that your three common haplotypes are all fairly similar (one to two base pair differences between them) and your two rare haplotypes are six and eleven base pairs apart from the common haplotypes. I have seen similar results in other projects and this is usually due to unidentified variation, often do to misidentifications of samples, unknown population structure (either current or historic), or cryptic variation. 

If my above assumptions about your data are correct, the first thing I would suggest is to make sure your identifications are accurate. In a recent project I was helping out with we found that some haplotypes were very different from the rest (~6%) and seem to pop up is various sample sites. This seemed odd so we ran a second gene that had a lot of sequences on GenBank for this genus and it turns at that the odd haplotypes belonged to a different species that is morphologically very similar and co-occurs in the same streams.

If your identifications are indeed correct, I would suggest running nuclear markers (e.g. microsatellites or intron sequencing) to figure out what is going on. You could have cryptic variation (e.g. cryptic species) or you could be picking up historic population structure (e.g. reconnection of different refugia populations during a recent expansion).

Hope this helps.

Thank you very much all.

I really appreciated your efforts, thank you for your time and energy.

Dear All friends

I red your quite interesting messages. I am working on green sea turtles genetic in Iran,the persian Gulf, I am confused with Tajima and Fu's test results an dont know how to interpret them

(Number of polymorphic (segregating) sites, S: 30

Total number of mutations, Eta: 30

Average number of nucleotide differences, k: 10.05797

Nucleotide diversity, Pi: 0.01451

Theta (per sequence) from Eta: 6.22594

Theta (per site) from Eta: 0.00898

Tajima's D: 1.95572 Statistical significance: Not significant, 0.10 > P > 0.05)

and

(Average number of pairwise nucleotide differences, k: 10.058

Nucleotide diversity, Pi: 0.01451

Theta estimated from k: 10.058

Theta estimated from Eta(s): 5.914

Theta estimated from Eta: 6.226

Fu and Li's D* test statistic: 0.09466

Statistical significance: Not significant, P > 0.10

Fu and Li's F* test statistic: 0.94215

Statistical significance: Not significant, P > 0.10)

I would be grateful for your advises and if you have some papers published usung these tests ls let me to have.

Regards

Asghar Mobaraki

Dear Asgha ,

The non significant values for the tests shows that the polymorphism occurring is random and is not under pressure.

Max R. Bangs Is there any threshold for the nucleotide diversity values, I mean you mentioned in a previous answer "lower nucleotide diversity". Is there any criteria to map the same, I mean if the value is X, then it is low nucleotide diversity, or if it is Y then it is high nucleotide diversity?

Daly Noll Is there any limit for lower and higher haplotype diversity?