Some muddled thinking is evident among those who think rapid Islamification of a nation cannot occur.  They perhaps look at graphs of exponential growth of the Muslim percentage in the general population and think the rate surely must slow down and stop, either before a Muslim majority is reached or at least well before 100%.

Not so.

These incomplete arguments are based on assuming that the only factors that can meaningfully contribute to the growth in the Muslim proportion of the population are new births of Muslims and Muslim immigrants, which collectively must far outpace births and immigration from non-Muslims.

What these views overlook are the equally important mechanisms of conversion and mass migration, which often "kick in" once some critical mass of a Muslim population is reached.

Conversion means we do not need to create or import new Muslims to very quickly increase their population.  And once a tipping point is reached toward Islamification, conversion will be forced (see, e.g., ISIS-controlled territory).

But even before that, large-scale conversion can occur voluntarily.  To Osama bin Laden is attributed an appropriate quote:

When people see a strong horse and a weak horse, they will naturally want to side with the strong horse. When people of the world look upon the confusion and atheism of the West, they see that Islam is the strong horse.

A self-fulfilling prophecy, or more generally a positive feedback loop, is set up.  The more popular Islam is, the more popular it becomes and the more converts it attracts.  Voluntary conversion can also occur to avoid the jizyah (poll tax) against dhimmis.

Mass population influxes and effluxes also take place during and after an Islamic revolution.  Such revolutions can be triggered at Muslim proportions far less than 100%, and they act to rapidly drive up the Muslim percentage of the general population from the point of revolution (say, 50%) to a value near 100%.

We see evidence of these mechanisms at work throughout the historical record, clearly overwhelming any type of traditional birth/death and/or normal immigration/emigration impacts.

Between 1960 and 1978, the percentage of Muslims within the total population for North Cyprus increased from 18% to >98%, with most of the increase taking place between 1973 (32%) and 1978 (>98%).

In Turkey, the Muslim proportion of the general population increased from 80% to >97% between 1914 and 1927.

From 1941 to 1951, the percentage of Muslims in Pakistan increased from 79% to >97%.

In Mali, the Muslim proportion went from just 30% in 1910 to 93% in 1987.

Over a half-century between 1910 and 1960, Niger's Muslim proportion increased from 56% to 99%.

Tunisia saw a move from 90% to effectively 100% in less than a decade during the 1950s and 1960s.

Burkina Faso went from 1% to 61% in a little over a century.  Senegal increased from 45% to 75% between 1910 and 1921, moving up to 90% by 1961.  Sierra Leone transitioned from 35% Muslim in 1963 to 60% by 1980 and 77% by 2004.

An abundance of mechanisms exist to continue rapidly expanding the Muslim proportion of the population after the relative influence of the early stage birth/death and net immigration factors begin to wane.  Consider these other mechanisms the second- and third-stage rockets that propel the Muslim population up past the majority benchmark and toward totality.  They are real, they have been active throughout history, and they are active today.