The article was published in Nature communications in August 2014.

The Ashkenazi group is large and has a very high degree of endogamy. This, in combination with a relatively large population growth, makes it possible to study the growth of the Ashkenazi population and the size of the original group.

The article is very interesting and uses high quality auDNA data of 128 Ashkenazim and 26 Flemish persons. The researches concluded that 57 of the 128 were acceptable as 100 percent Ashkenazi; the rest had partial non-Ashkenazi SNVs.

The data is compared with the simulations of a modal. This model (paragraph 4.3.1 of the supplements) has a few assumptions and four parameters. One important assumption is that the population bottleneck took place at one moment for the complete group. As demonstrated on this website this is a simplification of the history of the Ashkenazim. The assumed average generation length is 25 years. The model has four parameters: at moment T in history (expressed in number of generations ago) the population was reduced from N0 to Nb. The fourth parameter is the population growth rate. In this case it is expressed as population growth per generation. Figure 11 below is reproduced from the original article.

The data and analysis of Carmi et al. are completely unrelated to the data and analysis of this website. However, the conclusions are on the same subjects:

- when did the Ashkenazi have their population bottleneck?
- Carmi et al: 25-32 generations (625-800 years)
*To compare it with the results of this website we first have to translate the years. 625-800 years before present means (in terms of this website) a birthperiod of 1150 (1950-800) resp. 1325 (1950-625), so 1150-1325 CE. The period that was found for the haplotypes gives, using bootstrap, 1135 +- 28 CE. This means that the two resuls are consistent with each other. Notice that 28 is a 1-sigma error. Since we know that the presently largest groups arrived earlier, it is better to use the arrival time of the individuals. If we do this, we determined a bootstrapped mean of 990 +- 5 CE. It is likely that this statistical error is smaller than the systematic error. The differences between the two methods is small, but significant.*

- How many Ashkenazim are the ancestrals of the Ashkenazi population?
- Carmi et al: effective size: 250-420 persons
*The amount of persons in the Carmi et al. article is the amount people that is infered from the present auDNA variability. In this case it is easier to see what the effective size is that is expected from the value of 400 male line ancestors of this website. The starting value of 400 male line ancestors should be added by 400 female line ancestors. In the model of this website we have a population growth of 1.25 per generation. This means that each couple will have 2.5 children that will reach the age to have children. Using the model that is discussed in the simulations section, we have 28.5% of the first generation that has no childrend. Additional we will have 20.4% that has only one child. This means that 16.3% is single child. Changes that they marry to a single child (and both do not give their auDNA to their children) is only 2.6%. The next groups are negligible. This means that we would have an effective size of 800*(1-0.285-0.026)=551.*

The difference between the effective size 550 in this model and the value of Carmi et al. is significant. This difference can be the result of the simplification of the Carmi et al. model that all Ashkenazi ancestors are equal in their contribution to the auDNA of the Ashkenazi. This is not the case, and reduces the measured value of effective size in Carmi et al..

- What is the population growth?
- Carmi et al: 15-53% per generation (25 years)
*If we translate this to a population growth per generation (30 years), we have 18-65%. In this website we find a population growth of 25% per generation (30 years). The two values are consistent with each other.*

- The effective size of the originating Ashkenazi is 300-500 persons.
- For the majority of Ashkenazim, the population bottleneck took place for people that were born between 1000-1300 CE.
- The population growth was between 20-40% per generation (30 years)