There is no significant evidence of high rates of conversion of non-Muslims to Muslims. My response was concerning the the claim of the high rate of growth. The spreading of Islam is by far dominantly related to migration of Muslims from Islamic countries.
From:
Fastest Growing Religion - WikiIslam
Other Factors to Consider
Worth noting is the fact that apostates will rarely advertise leaving Islam due to the death sentence it imposes on its followers, and that most Islamic countries do not acknowledge conversions out of Islam.
Systematic
persecution of religious minorities has been documented in almost
every Muslim majority country, leading to some
converts to Islam being coerced or forced into their conversion.
For example, following the 2010 murder of a leading Muslim politician who called for modifications to
Pakistan’s blasphemy law, it had been reported that at least 20 Pakistani Christians were converting to Islam each week out of fear.
[36] Also according to the Society for the Protection of the Rights of the Child (SPARC), there were as many as 2,000 women and girls who were
forcibly converted in 2011 to Islam through
rape, torture and kidnappings in Pakistan.
[37]
This is not limited to Muslim-majority countries. In the United Kingdom, it was reported in 2007 that police were working with universities to clamp down on "aggressive conversions" to Islam, during which vulnerable teenage girls are beaten up by Muslims and forced to abandon university courses.
[38][39]
Conclusion
All the actual data available reveals that Islam is neither the fastest growing religion by number of adherents or the fastest growing religion by percentage-increase.
The growing number of Muslims in the world is due primarily to the higher than average birth-rates, and consequent population growths of Muslim countries and communities. And their growing presence in non-Muslim societies such as Europe and the Americas is overwhelmingly due to immigration.
Furthermore, converts to Islam are vastly outnumbered by those who choose to leave the religion and embrace another faith or worldview. And the majority of converts that Islam does manage to attract, decide to leave within the first few years of practicing it.
Finally, even if Islam were to be the fastest growing religion in the world, it would be an
Argumentum ad populum to claim that this makes it the correct religion.