Question: Was this Arabic outlook that passed to Latin America the result of the vestiges of the Islamic Invasion of the Iberian Penninsula? In other words, would Quigley say that this outlook has been bread into the Latin American Gene Pool from the many centuries of Islamic Domination of the Iberian Penninsula?
Yes, that's exactly what Quigley claims. We sometimes forget that the Iberian Peninsula was invaded by Muslims in the early 700s, and that the last vestiges of Islamic domination were not expelled from Spain until the late 1400s. 700 years of cultural domination will leave a lasting impression on the conquered culture. When and if a subject culture ever re-emerges, it will not be the same; it will have taken on some aspects of the subjugating culture.
Recent genetic studies have shown that invaders, even those who dominate for long periods, generally have remarkably little impact on the gene pool of the area. Since the Muslim invaders of Spain were not genetically based, but were rather based on religion, and also were by all accounts very few in number, I would expect the genetic impact to be even less than usual.
But cultural patterns are probably minimally, if at all, based in the genetic code. Which doesn't mean they aren't persistent and critically important. Only that a Japanese boy brought up from birth in 10th century Spain by Moslem parents, and fully accepted by his compatriots, would be difficult to tell apart by his actions from his friends of Arab, Berber, Gothic, Celtic and Roman ancestry.