What are you trying to find out?

simply put have more people left UK than arrived based on above data if you include the living offspring of all those who have emigrated?

I'm sorry but I still don't see how this question makes any sense. If the offspring emigrated with their parents they would be included in the net emigration figure. If they didn't leave, then they don't impact the statistics, unless you're counting birth as entering the country.

Doesn't the uK offer census data.

Wait do you want to know how many people the UK would have if people who emigrated didn't and had their kids in the UK instead of wherever they went to?

It's too late anyway. The country went to hell after we let the Saxons in. And the least said about the Jutes the better.

I guess abgemacht hit the nail. there exist some models to estimate this. I personal would like to know what kind of argument you'd like to make. Because this deeply affects the way you would estimate (there is no "true" nor "good" estimator for population with only the data you're using here).

I think you are looking for something like this:
Start with your initial population (p), net population growth rate (g), time periods (t1, t2, t3, etc.) number of generations remaining until end of period for each time period in your evaluation period (n1, n2, n3, etc.).
So if you are breaking things out by decade (say 1901-1910 is time period t1, 1911-1920 is time period t2, … 2001-2010 is time period t11), say p is 10,000,000 (10 million), net growth rate g is 1.2 (2 adult members of population produce an avg of 2.4 children that will survive to adulthood and can in turn reproduce) and you say each generation is 20 years (so n1 is 5 or 100 yrs/20yrs per generation) then your initial population p would grow as follows over 100 years - p*(g^(n1)) = 10,000,000*(1.2^5)= 24,883,200. Now if you want to find out the total impact over the next 100 years of 50,000 people (e for emigration) leaving the country in that first decade t1, then you use e+e*(g^(n1))=50,000+50,000*(1.2^5)=174,416 (50K that left plus the 124K future offspring they would have generated).

Now when you are looking at emigration in later time periods such as t4 (1931-1940) there will be 70 years remaining so your n4 is just 3.5 (70 yrs/20yrs per generation), so 50k people emigrating in t4 would have impact 50,000+50,000*(1.2^3.5)=144,646.

If you want to get even more complex you could add in different growth rates for emigrees vs. immigrants, in which case you would calculate the impact of emigration and immigration individually first and then perform your subtraction to determine net overall impact.

@octavious yes exactly - i want to count the unborn offspring of each emigree that would still be alive today.

This is what I would do to start. For a 1st generation emigrant use average birthrate in UK to estimate how many kids they had.

For 2nd and later generations, you should use the destination country birthrate.

Not terribly accurate, but should be very quick to calculate.

Yeah, or just do what Yal said.

Yes you could also have the birth rates vary over time if you want to add even more complexity. In that case rather than using 1.2^5 from my example you would use something like 1.2*1.25*1.17*1.29*1.24 (you could research historical rates these are entirely made up by me).

Yaleunc - does your figures factor in the death of the original migrees?

I don't think I should use other country's growth rate as I'm trying to ascertain how many offspring they would have had if they had stayed.

My figures are made up for illustrative purposes. If you use growth rate rather than birth rate (as some offspring die off before being able to reproduce) then it should already have that factored in. Not sure how easy those figures are to obtain. If you can only get birth rates then you probably also need to add lifespan impact to your calculations as well.

Kick out all the chavs.

You spelled math wrong.

#obligitotyAmericanTroll