How do I figure the population growth rate if couples have two babies and adults live 75 years?

If a couple has 2 children, then that is only a replacement level birth rate, and that is assuming that these offspring both survive long enough to create spawn themselves, and that they actually do it. Otherwise, population will start to decline once the initial progenitors start dying, instead of just stagnating.

If couples literally only have 2 kids than that population will decline over time. Some of those offspring will not be able to have kids, others will die before reproducing, etc.

If some have more than 2 and others just one or none, such that the mean birth rate is 2.0 kids per couple, then the growth rate would be 0%.

This has an explanation I believe you can use to prove the numbers you were given.

In my head, just thinking it out logically, if people live 2–3 times older than baby making age, it seems like the population grows even with just two children per couple.

If there are 100 people in 2023 and 30 couples have 2 children over 20 years time, that’s an additional 60 people. Take away 20 people dying, we have 140 people in 2043.

There will be more than 20 people dying. What counts is not the age to which people live, but the time time it takes to reproduce. If each couple has 2 children, each successive generation will be as large as the previous one, so the population size remains constant.

So, to get a 5% growth, how many babies does a couple (or women in the population) need to have?

I was looking at stats that at 5% the population doubles every 35 years. It was about the Jewish population if there had been no Holocaust. I guessed it would be 50 million now, but my sister saw on TV someone say 250 million. I can’t imagine it would be anywhere close to that large. Before the Holocaust it was approximately 18 million.

Is that 5% per year? That seems a bit high. At that rate, the population would ha
More realistic would be .5%. It has been about 80 years ve grown by a factor of over 5 since the holocaust, so the population growth would have been by a facctor of (1.005)**80 = 1.49.

If we take a generation to be 35 years, that works out to (1.005)**35 = 1.19. 1.19 per woman is 2.38 children per couple.

I just read it is 2% to double every 35 years. Ugh. Some conflicting info.

I also found this worksheet. https://pcapes.weebly.com/uploads/8/8/3/0/8830216/population_calculation_worksheet_answers.pdf

We weren’t trying to figure out the population since the Holocaust, but rather if the Holocaust did not happen. The Jewish population went down to less than 12 million after the Holocaust, and now is at around 17 million 80 years later. Obviously, with exponential type of growth the number you start with is extremely important. At some point, all of sudden. the population will grow quickly to much larger numbers if there are more babies being born than deaths happening.

The birth rate wouldn’t really have been a constant in that time frame, because 80 years ago people tended to have more children, especially in Eastern Bloc countries. The mass exodus to the US probably would not have happened. everything would have been different.

@JLeslie Also, keep in mind the demographics within the Jewish population have shifted over time. The most radical Jewish extremists tend to have very large families, vs. secular and reformed Jews (and other more moderates) tend to have 2 or less kids, so the population overalll is shifting to the extreme right (pretty quickly). We have the same thing with extremist Christians in the US.

@gorillapaws Yes, but I an just trying to figure it if the Holocaust didn’t happen. Probably 3 or 4 children per woman is a more realistic average for the exercise.

@JLeslie , If you know the number of Jews before the holocaust, just multiply that by 1.49 to get how many Jews there would be now. That 1.49 factor seems to be pretty good. 12 million to 17 million is a factor of about 1.4.

If you want to increase the birth rate to 3 or 4, let’s suppose it would have been 3.5. That would give a rate of 3.5/2=1.75 per generation. There are about 2 generations since the Holocaust, so we could estimate a factor of about 1.75**2 = 3.06.

If that were my goal, I’d look at the demographic makeup of the Jewish population pre-holocaust (perhaps by continent or region) and forecast out those population growth rates into the future. It’s kind of an exercise fraught with error and requires many assumptions.

Was there still a WW2 with lots of death around the globe and a postwar baby boom? Would the Jewish people have experienced the same rates of death due to war as other groups (absent the holocaust of course)? Or would WW2 have never happened at all, in which case it’s really hard to forecast what the population ANYWHERE would have been.

The proportion of deaths in World War 2 is about 3%. As horrific as that figure is, the effect on overall population growth is not that great.

@LostInParadise But was that equally distributed? It seems to me the proportion of death was concentrated in Europe and East Asia vs. a global rate. Also it’s probably relevant for population growth to note that most of the deaths were young men. Given that young women are much more necessary for a population growth, I guess it would be less of a factor.

For what it’s worth, this is what ChatGPT had to say about it:

”
Estimating the current population of Jewish people in the world if the Holocaust had never happened is a complex and speculative task. The Holocaust had a profound and tragic impact on the Jewish population, making it difficult to determine what the population would be like today in an alternate history. However, if you want to make an educated estimate, you can consider the following approach:

Historical population data: Begin by examining historical records of the Jewish population before World War II and the Holocaust. Look at population data from the late 1930s, which was the last period before the Holocaust significantly reduced the Jewish population.

Natural population growth: Assuming that the Holocaust had not occurred, you could estimate the natural population growth of Jewish communities over the years. This would involve considering birth rates, death rates, and immigration/emigration patterns.

Geographic distribution: The Jewish population is not evenly distributed around the world. Different regions have different growth rates and factors affecting the Jewish population. You would need to consider the specific demographics of Jewish communities in various countries and regions.

Historical events and geopolitical changes: Take into account other historical events and geopolitical changes that could have influenced Jewish population growth, such as the establishment of the State of Israel in 1948, which had a significant impact on Jewish migration and demographics.

Assumptions and uncertainties: It’s important to recognize that any estimate is speculative, and there are many unknown factors and variables at play. The accuracy of your estimate would depend on the quality of the data and the assumptions you make.

Consult experts and demographic studies: You may want to consult with demographers and historians who specialize in Jewish population studies to gain more insights and access to relevant data sources.

Keep in mind that any estimate you make would be highly speculative, as it’s impossible to predict with certainty what the world would look like if the Holocaust had never happened. Additionally, it’s important to approach this topic with sensitivity and respect for the historical significance of the Holocaust and its impact on Jewish communities worldwide.

”

The Rule of 72 states that at a 2% growth rate, any quantity doubles in 36 years. At a 5% growth rate, and quantity doubles in 14.4 years.

A percentage growth rate, is an end result of what’s really going on. It only applies to a specific start and end date, and it pretty much never describes the situation adequately.

A percentage figure might be useful for something like bacteria in stable conditions. But outside a lab, conditions are almost never stable in the long-term (even bacteria alters its conditions by living), and with animal populations, there is a lot more going on.

Life expectancy, and number of children per woman, also doesn’t paint a complete picture.

Real populations have age distributions, which may vary per gender (but you mainly need to consider the women) and also different death rates by age, and different age distributions by when people tend to have children.

Even if you have all of that, it all changes over time, and many people live quite a few decades, over which time, conditions definitely will change.

Not to mention that demographic data tends to be incomplete and inaccurate.

It all works out in terms of averages. A generation ig is the average number of years between the time a person is born and the time that the person gives birth to their own child. If the population increases by a proportion p per year then, like bank interest, the average population growth factor from one generation to the next is (1+p)**g, which gives the number of new people in the next generation per person in the current generation. To find the average number of births per couple, you multiply that last number by 2, because a couple accounts for two people.

Here again is the example I gave. Population growth is about .5% per year in industrial nations and a generation is roughly 35 years. The growth factor from one generation to the next is (1.005)**35. Multiply this by 2 and you get roughly 2.4 children per couple. Going in the reverse direction, you get yearly population growth from the children per couple.

⅓ of Jews were killed during WWII! Over 30%! Other groups were targeted too, like gypsies and disabled people, but let’s stick with the Jews for now.

So, what’s the answer if we start at 18 million and go out 80 years at the rate of 3.5?

18 million people growing at an annual rate of 3.5% over 80 years results in a population of 282,160,000 people.

@gorillapaws 282 million?! I guess that’s where Donny Deutsch got that 250 million number from that my sister cited to me. Thank you for helping with the math.

I have a hard time wrapping my head around that big of a number. Even half that is shocking to me. Very depressing for me. As usual it makes me feel like I wish I had ten children.

@zenvelo 5% doubles at 14.4 years is compound interest. Is it the same for population growth?

12 million went to 17 million, so it seems reasonable to suppose that 18 million would have made it to around 30 or 40 million.

If the Holocaust had never happened the German Jews probably would have had relatively low children per family maybe 2–3, because the Jews there were educated and I guess middle class to the extent that middle class existed. By contrast, many Eastern European Jews were poor, and likely more religious and more babies. Although we should keep in mind, Jews did leave Eastern Europe for America well before WWII, because of poverty and antisemitism.

@LostInParadise That’s what I originally thought, although what would be different is some of the Jewish people who came to the US and who went to Israel might have stayed in Europe where they might have been more likely to have more babies.

Hard to know what the number would have been, but Hitler made a huge dent.

@JLeslie “If the Holocaust had never happened the German Jews probably would have had relatively low children per family maybe 2–3, because the Jews there were educated and I guess middle class to the extent that middle class existed.”

Maybe… WW2 caused a lot of “rethinking” in the world. If someone went back in time and stuffed out Hitler, Himmler and the rest of the monsters in their respective cribs such that the Nazi party never formed, I feel like there still would have been a major world war (perhaps with different alliances). This idea that you could conquer territory and expand your sphere of influence via military victory was still considered a viable option. The nightmares of the Holocaust and the atomic bombs, the devastation of Europe and parts of Asia really caused the world to sit down and say: “Ok, we can NEVER do this again. How do we change things to prevent WW3?”

So what I’m saying is that without the Nazis and the atomic bomb, we might have had a WW3, a WW4 and a WW5 etc.

@gorillapaws That might be true, but the other war or wars might not have targeted Jewish people in the same way. The Holocaust killed a tremendous amount of Jewish adults who were still fertile. I remember once reading 1.5 million Jewish children were killed. If that’s correct, that also was a huge impact on possible future births.

Japan lost 2.5 million of their 79 million population (I’m rounding from memory).

Germany I don’t know. I never figured out if the losses include Jewish Germans. iAs a percentage those are nothing compared to Jewish people in Europe or the world. Remember the 18 million before the war is the world population.

All people count of course, and in an ideal world we wouldn’t look at religion, borders, race, but the haters box us in by targeting specific groups.

@JLeslie Don’t get me wrong, I’m sure the Holocaust did way more to decimate the Jewish population than a hypothetical WW3, WW4, etc. would have. My point was that assuming birth rates in a world with multiple world wars is kinda tricky to the point of being impossible. I think things would have fluxed a lot. Maybe Russia would have successfully invaded Western Europe and driven most of the people to South Africa and South America? It’s just hard to forecast how many kids people would be having under alternative histories like that. It’s an interesting thought experiment though.

@gorillapaws I have no argument with hard to forecast.

Assume that, under normal conditions, the Earth’s population will grow by 90 million per year.

Another thing that makes it even more wrong to think of percentage growth rates as something that exists before you measure the result of what happened in the past, is this:

With something like the world population of people of Jewish ancestry – THAT’S NOT HOW HUMANS REPRODUCE – we don’t only have children within our own ethnic backgrounds. So it’s particularly silly to expect the number of people with some ethnic background to have some constant growth rate over 80 years.

@Zaku That’s true that there is some mixing. The Jews only recently started to intermarry in large numbers. In fact Jewish DNA is used for studies in genetics because we were so “clannish.” When I was a fertility patient one of the genetic panels I was tested for was the Jewish panel of genetic diseases. Those recessive genes survived because the Jewish people were a tight knit group. There are other groups like that. The Icelandic people, and some towns in Europe where the same families have lived for hundreds of years are some examples.

There were several reasons Jewish people didn’t intermarry much. Antisemitism is one obvious reason, and also Jewish people themselves worried about Judaism fading into nothing so some Jewish parents want their children to marry someone who is Jewish and put pressure to do so. Not only to continue Judaism, but also because they feel there is less likely conflict within the marriage, because of similar backgrounds.

I personally would count converts, but we don’t have many converts, so that’s a mini small number. I also count people who are only part Jewish, meaning one parent. Should we count Olivia Newton John? Just to use a celebrity that everyone knows. I would say probably not, but if her grandfather had been killed in the Holocaust she would not have existed.