One Source Group and Vanishing Survival for rest

We define a source group as a group that has a fertility rate above replacement. If we assume one group is a source group and continues its above replacement fertility what stops it?

Lets assume there is a bound on global population. When the bound is reached, total fertility has to be at or below replacement. If one group continues above replacement then it will have to stop when all other groups have reached zero.

Given a population bound, no group can be a source group indefinitely. At some point it has to either eliminate all other groups and then its fertility is the global fertility at or below replacement or other groups have to stop the source group from having above replacement fertility.

If a group in one land is a source, and another land accepts immigration, the target land will experience complete genetic replacement assuming some positive fertility by the immigrants bounded above some epsilon above zero.

This is math. Sticking one’s head in the sand doesn’t change it. We as a civilization have to recognize math and deal with it.

==Added Sep 16 2007

The Wright Island Model is criticized on the grounds that its assumptions are too restrictive.

One assumption is one way migration. We can fix that with a source group. The source group really substitutes for the geographical boundary. A source group emits into the target population, but itself does not absorb.

The joint set of the target group and the emission then have some interaction or linkage. In particular, the survival probabilities are linked. We can assume they have the same survival probability. This is neutrality.

But we can instead assume that some multiple of the emitted group’s survival probability is greater than the survival probability of the target group. There can be intermarriage or none. It doesn’t matter.

It is also enough to assume that the asymptotic survival probabilities are related in this way. Asymptotic hear means the limit as time increases without bound. So if the asymptotic survival probability of the emitted genes times some number is greater than the survival probability of the original population, then we can apply the logic of the Island Model.

We can also view this as the paradigm of the Immigration Vanishing Survival Theorem. Either way, we can link into either of these paradigms, viewed as different or the same with modifications. The IVST tries to work from a population bound, whereas the Island Model works from an assumed substitution rate. The IVST tries to deduce a substitution effect, so it is more tuned to our needs in studying immigration.

So if we assume a source group, that doesn’t absorb, but emits at above replacement forever, and if the asymptotic survival probability of the emissions times some constant is greater than the asymptotic survival probability of the original target population, then the asymptotic survival probability of the emissions and the target are both zero. This is the focus of the Immigration Vanishing Survival Theorem.

Moreover, asymptotically, the gene frequency of the union of emissions and original population equals the gene frequency of the emissions from the source. This is the focus of the Wright Island Model, finding this asymptotic frequency, i.e. the frequency as the time goes to infinity.

Immigration Vanishing Survival Theorem.

Wright Island Model (with links to academic papers including Nagylaki.)

==James Pinkerton

http://www.amconmag.com/2007/2007_09_10/cover.html

If demography is the author of destiny, then the danger of Europe falling within dar al-Islam is real. And in addition to the teeming Muslim lumpen already within the gates, plenty more are coming. According to United Nations data, the population of the Arab world will increase from 321 million in 2004 to 598 million in 2050. Are those swarming masses really going to hang back in Egypt and Yemen when Europe beckons?

In other words, if present trends continue, the green flag of Islam—bearing the shahada, the declaration of faith, “There is no god but God; Muhammad is the Messenger of God”—could be fluttering above Athens and Rotterdam in the lifespan of a youngster today. If so, then the glory of Europe as the hub of Greco-Roman and Christian civilization would be extinguished forever.

If this Muslimization befalls Europe, the consequences would be catastrophic for Americans as well.

The above link was from the thread at

http://www.jihadwatch.org/archives/018147.php

found by DP111.  There is criticism of this article at that thread by some posters.  This is addressed there and at the article

Is the West too anti-geek to survive?