Archive for the 'One Way Migration' Category

Population Genetics Island Model One Way Migration

June 30, 2007

One way immigration causes the complete genetic extinction of the target population. This is a theorem already established in population genetics. It can be traced back to a 1931 paper by S. Wright.

University of Chicago. Chicago. Illinois
Received January 20. 1930

More on this paper below.  But first let’s review the actual decline in fertility since 1800 during immigration periods, but the rise in fertility during immigration restriction from 1940 to 1957.

The graph of declining fertility in the US from 1800 to 1990 is”

Fertility falls except during immigration restriction. This is a combined economics population genetics interaction. Wages are part of this economics genetics combined situation. However, wages in an economic model have counterparts in seemingly non-economic ecologies.  In a pure animal or plant population other variables play the same role of an indicator of survival that wages do in a modern human economy.  So there is a wages dimension even in the wild. Food is the wage for work in the wild. Or survival from a fight or from the natural elements.

Men’s median wages are flat since 1973 in the US.  This is a marker that men can’t provide as well in the human ecology. The result is lower fertility since women can’t find a substitute for men.

In population genetics, the case of one way migration is often treated in what is called the “Island Model”.

Genetics. 1979 January; 91(1): 163–176.

The Island Model with Stochastic Migration

Thomas Nagylaki

Department of Biophysics and Theoretical Biology, The University of Chicago, 920 East 58th Street, Chicago, Illinois 60637

The island model with stochastically variable migration rate and immigrant gene frequency is investigated. It is supposed that the migration rate and the immigrant gene frequency are independent of each other in each generation, and each of them is independently and identically distributed in every generation. The treatment is confined to a single diallelic locus without mutation. If the diploid population is infinite, selection is absent and the immigrant gene frequency is fixed, then the gene frequency on the island converges to the immigrant frequency, and the logarithm of the absolute value of its deviation from it is asymptotically normally distributed.

The above implies that if you have two genes in some frequency in the immigrant population, that under one way migration that frequency becomes the frequency on the island.

From PDF, conclusion:

We investigated various cases of the island model with stochastic migration. If the population is infinite, the immigrants have a fixed gene frequency and the alleles are neutral, the gene frequency on the island converges to that of the immigrants.

What this means is that the genes initially on the island, in effect, disappear. But the West is the Island, and we don’t survive in this model. We are being voted off the island by the genes of the immigrants. This never stops. Every cohort of immigrants is voted off the island in genetic terms by the following cohorts.

WRIGHT S,. , 1931 Evolution in Mendelian populations. Genetics 16: 97-159. -, 1948 On
the roles of directed and random changes in gene frequency in the genetics of populations.
Evolution 2 : 279-294.

References with links from above paper were posted by NIH. Some are below. To see the original article on-line in this case does NOT require a subscription. Go to the link and in the middle of the page is Full Text Genetics Free. Click on that. This will open another page, and in a few seconds that page will itself open a pdf. If that doesn’t happen try clicking.

You don’t need to understand the math or the biology terms to get something out of the articles. Read the abstract, the introduction, the conclusion and look at figures and tables and their captions. There may be conclusions or explanations between equations or technical discussion that gives the conclusions.

Don’t let yourself get stuck on not understanding a word. Just skip around or pretend the word isn’t in the sentence and give it the meaning it needs. You can look up technical words in Wikipedia or with Google. Wikipedia is very good in math and science. Textbooks often have more errors or misinformation on the history of their subject and who discovered what than is found in Wikipedia science and math articles.

“This list contains those references that cite another article in PMC or have a citation in PubMed. It may not include all the original references for this article.”


  • Hartl, Daniel L. Mutation-Selection Balance with Stochastic Selection. Genetics. 1977 Jul;86(3):687–696. [PubMed]
  • Jensen L. Random selective advantages of genes and their probabilities of fixation. Genet Res. 1973 Jun;21(3):215–219. [PubMed]
  • Karlin S, Lieberman U. Random temporal variation in selection intensities: case of large population size. Theor Popul Biol. 1974 Dec;6(3):355–382. [PubMed]
  • Kimura, Motoo. Process Leading to Quasi-Fixation of Genes in Natural Populations Due to Random Fluctuation of Selection Intensities. Genetics. 1954 May;39(3):280–295. [PubMed]
  • Latter BDH. The Island Model of Population Differentiation: A General Solution. Genetics. 1973 Jan;73(1):147–157. [PubMed]
  • Levikson B, Karlin S. Random temporal variation in selection intensities acting on infinite diploid populations: diffusion method analysis. Theor Popul Biol. 1975 Dec;8(3):292–300. [PubMed]
  • Maruyama T. Effective number of alleles in a subdivided population. Theor Popul Biol. 1970 Nov;1(3):273–306. [PubMed]
  • Wright, Sewall. Evolution in Mendelian Populations. Genetics. 1931 Mar;16(2):97–159. [PubMed]

“island model” population genetics

“island model” migration

“theoretical biology”

Wright’s first paper is available online

1: Genetics. 1931 Mar;16(2):97-159.
Evolution in Mendelian Populations.

Wright S.

University of Chicago, Chicago, Illinois.

PMID: 17246615 [PubMed]

Page 128 “Irreversible recurrent mutation ”

—Previous Post:

Immigration Vanishing Survival Theorem

June 4th, 2007 Assume that

  1. Population is bounded from above
  2. The flow of immigrants is unbounded from above
  3. The survival probabilities of the genes of each immigrant are equal.


For any given cohort of immigrants at time t, the survival probability of their genes at T > t, p(t,T) must go to zero as T goes to infinity.

Mathematical Population Genetics
By W. J. (Warren John) Ewens,M1

1965 Immigration Act Causes U inverted U in Income Inequality and Fertility
==Omnia Cleansing Immigration Substitution Effect

Mathematically, immigration causes omnia cleansing. To review the math:

Suppose US population is stable at 300 million. If people live 75 years, 4 million die per year. If 2 million enter, and pop is stable, then there are 2 million births. 2 million births over 4 million deaths is a genetic survival ratio of 1/2. 25 years birth to parent, so in 75 years, 3 cycles leaves 1/8 genes. Even if pop goes to 450mm and 1 million enter, we get a fraction of 5/6 per cycle, which results in genetic extinction.

This happens by lowering wages and is happening already. There is a substitution effect from births to immigrants.


“Numbers Drop for the Married With Children
Institution Becoming The Choice of the Educated, Affluent

By Blaine Harden
Washington Post Staff Writer
Sunday, March 4, 2007; Page A03

PORTLAND, Ore. — Punctuating a fundamental change in American family life, married couples with children now occupy fewer than one in every four households — a share that has been slashed in half since 1960 and is the lowest ever recorded by the census.

As marriage with children becomes an exception rather than the norm, social scientists say it is also becoming the self-selected province of the college-educated and the affluent.

end quote

== Some historical analysis is here:
Search Catholics Immigration Intense Feelings
=Key words

Unpleasant Immigration Arithmetic, Omnia Cleansing.


Samuel Karlin

Sewall Green Wright ForMemRS (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory. Along with R. A. Fisher and J.B.S. Haldane, he was a founder of theoretical population genetics. Evolutionary biologists argue as to whether Fisher or Wright made the greater contribution. He is the discoverer of the inbreeding coefficient and of methods of computing it in pedigrees. He extended this work to populations, computing the amount of inbreeding of members of populations as a result of random genetic drift, and he and Fisher pioneered methods for computing the distribution of gene frequencies among populations as a result of the interaction of natural selection, mutation, migration and genetic drift. The work of Fisher, Wright, and Haldane on theoretical population genetics was a major step in the development of the modern evolutionary synthesis of genetics with evolution. Wright also made major contributions to mammalian genetics and biochemical genetics.

==gap decay math

The gap between the current value and a target value decays in these models. The gap this period is a fraction less than one of its value last period. Suppose the fraction is one-half. Then after 2 periods the gap is 1/4 its size, and in 3 periods it is one-eighth.

The decay of a set of atoms or molecules follows the same math. This type of arithmetic is common.

==Life becomes hard and then our genes die

These theorems don’t happen by themselves. They have mechanisms. For humans, wages fall and they lose job security so that they pay more for security things like prestige education. As this goes on, they lose their chances to have kids when they are young.

== Young adults lose feeling of security

Young adults lose the feeling of security. Its the confidence of young adulthood that lets young adults get married, have kids, stay married and have more kids. When that confidence goes, they pull back at the time their biology says to have kids. So they don’t. The result is below replacement fertility.

There are estimates that up to 1/3 of the women who go to college will never have children. Ths is job insecurity at the time biology tells them to have children. By the time they feel secure, its too late. The same is happening to men.

==London Telegraph Women losing feeling of security
Third of graduate women will be childless

By Ben Leapman, Home Affairs Correspondent, Sunday Telegraph

Last Updated: 6:46am BST 24/04/2007

A third of women graduates will never have children, research has concluded.

The number of highly educated women who are starting families has plummeted in the past decade, according to findings that provide the most detailed insight yet into education and fertility.

While some women are making a conscious decision not to have children, others are simply leaving it too late after taking years to build their careers, buy a home and find the right partner.


Overall population decline is only being prevented by immigration and a higher birth rate among non-graduate women.

Actually wrong. Its immigration that creates the economic insecurity. Economic insecurity doesn’t grow spontaneously from nowhere.

The findings come from a ground-breaking study into more than 5,000 women born in 1970 and tracked throughout their lives by researchers at the Centre for Longitudinal Studies, based at the Institute of Education in London.

Of a panel of older graduate women born in 1958, only 32.7 per cent were childless at 35.

The 1958 group were less impacted by immigration and diversity. Diversity sends the message of insecurity and that stops reproductivity. Colleges also tend to be more diverse themselves, thus sending that wrong message at the wrong time.

== Immigration level is at extinction level in US.

Legal immigration itself is as high as between 3 to 4 million per year in the US according to Senator Sessions if one counts every form of guest worker, temporary arrival, etc. Immigration is displacing replacement fertility.

At 300 million for US population, with a life of 75 years, 4 million die per year. Thus with zero immigration and zero population growth, replacement fertility is 4 million births. But immigration is almost at that level. Thus immigration is at the full immediate extinction level.

This is why women are not having children. This is why men are not either. Legal immigration is a democaust, a demographic holocaust. This is omnia cleansing. Every gene that comes here goes through this as well. So every gene that comes here goes extinct, and every gene here at a point in time goes extinct.

We have to set legal immigration to zero. We have to eliminate all guest worker, asylum, refugee, family reunification, student visa, H-1B, and tourism or business travel from any country whose visitors overstay visas. Until visa overstay is reduced to zero, all visas must be canceled.

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