The greatest threat to humanity is a thermonuclear war. This could kill hundreds of millions of people--possibly, in the worst case, all of humanity.
Less dramatic, but very serious, are the effects of our generation of vast quantities of carbon dioxide, methane and other greenhouse gases. This is trapping enough heat in our atmosphere to cause major effects on our weather, that are having increasingly serious consequences all over the world . A related problem is that of overpopulation, which, among other things would be a major contributor to the greenhouse gas problem.
When I was born (in 1931), world population was 2.1 billion. It is now over 3.5 times that size: about 7.7 billion! The population of the US over that period grew from 125 million to 331 million--as a result of immigration (legal and illegal). There are forecasts for world population growing to the neighborhood of 10 billion over the next century . Population growth in developed countries is generally due to immigration (often illegal.), whereas, in underdeveloped countries, it is generally the result of a high birth rate. A dramatic example is that of North Korea. After losing over 1.3 million people in the Korean War (out of a population of about 10 million), roughly a million North Koreans died as a result of famine in the mid 1990s. But its current population is about 25 million! (During that same period the population of South Korea rose at a similar rate: from about 19 to 51 million.) Detailed estimates of national populations give us a good overall picture of a bad situation. .
In general, the populations of poor countries tend to grow rapidly. One cause of this is that low-income farmers tend to have large families, as they utilize their children to help raise their crops. The measure used to specify the average number of children that women give birth to is the total fertility rate. If all children born survived to adulthood, then a fertility rate of 2.0 (2 children per woman) would result in a stable population. A more realistic total fertility rate that accounts for some children dying prior to adulthood, is 2.1, generally accepted as the rate for stability .
The total fertility rates in poor countries are high. This is the case for most African countries, where typical numbers range from 4 to 6. So their populations are rising rapidly. (Because of high death rates, this growth rate is a bit less than might be expected from the high birth rates.)
On the other hand, the total fertility rates in most prosperous countries are quite low. The US, and most Western European countries, have numbers such as 1.8, well under the rate for stability. For Japan, the number is 1.4. Without immigration, populations of these countries would be decreasing at substantial rates.
It is clearly in the interest of the great majority of people of poor countries to have fewer children. This is achieved in virtually all the low birth-rate countries via the widespread use of birth control measures. An obvious step to bringing this about in the poor countries is via an educational process that starts in schools. But that alone would not suffice, since, in many poor countries, most young people do not receive much in the way of formal education. Probably the most practical approach would be via an expanded Peace Corps operation aimed at educating both adults and teenagers about the problem and the solutions. The assumption here is that the governments of the countries involved would support such an effort.
An important factor that accounts to a large extent for the low birth rates in developed countries is that substantial numbers of women in these countries have jobs outside the home. Ensuring that women are properly educated, and have good opportunities for satisfying work, at the same pay rates men receive, would, by itself, reduce the birth rate substantially in Africa and elsewhere.
Open borders facilitating immigration obviously lead to increasing populations in advanced countries. But it does not stop population growth in underdeveloped countries, since those who leave such countries are largely the most educated and well to do. If they did not emigrate, many of them would support reforms that would eventually reduce the high birth rates associated with poverty.
The demise of American labor unions in the private sector (fewer than 7% of workers in industry are in unions) has had a strong effect on lowering American wages, both directly, and indirectly. It has facilitated both the replacement of American workers with immigrants, legal and illegal, and the exporting of jobs to low-wage countries. As mentioned above, reduction of worker income generally leads to an increased birth rate.
 Environmental Protection Agency, "Overview of Greenhouse Gases"
 , "World population estimates From Wikipedia,", 2019
 Wikipedia, "List of countries by past and future population "
 Wikipedia, "List of sovereign states and dependencies by total fertility rate"
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