The people who lived on La Palma before the Spanish arrived in 1493 called the island Benahoare, and themselves Benahorita. (Or according to some people, Benawara and Benawaritas. They insist their spelling is correct. I find this odd, because to me the correct spelling would be the one the people themselves used, only they didn’t write.)
The Benahorita probably arrived on La Palma somewhere between 1000 BC and 100 BC, and the best guess is that they were Berbers from North Africa, or related to Berbers. (Of course if that’s where they came from, they left well before the Arab invasion of North Africa, which changed the Berber gene pool.) Modern DNA analysis suggests that 42 – 73% of the modern gene pool is Berber. Since this is maternal DNA only, it’s probably skewed towards women who survived the Spanish invasion and away from the invading men. Come to that, it’s also skewed away from the sailors who spent stopovers in Santa Cruz de la Palma when it was the biggest port in the Canaries, and towards the women who gave them a good time while they were here.
A study of DNA from the teeth of 38 Benahorita shows 70% north African, 7% sub-Saharan origin, and something they haven’t found outside the Canaries. They also found a high gene diversity, which suggests that the Benahorita didn’t stay isolated once they got here.
You can read the abstract itself here.