There was quite a bit of sex going on, enough that censors and editors of the account of Bougainville and Cook edited down the sheer amount of galavanting that went on between island women and european men (just as they made no mentioned of 'impolite' acts between men on the ship). Whether all or most of this sex was consensual seems open to some debate-- Historian Anne Salmon's recent duology on Cook/Bligh in Tahiti makes a good case for at least some of those sexual liaisons occurring due to cultural misunderstandings. To boil it down a bit; when gifts were exchanged, a common gift from Tahitians to Europeans was long rolls of tapa cloth, sometimes the gift was presented by unwrapping the cloth off of a young teen, who was either naked under the cloth or wearing only a pareo around her waste. For Tahitians, who had far less restricted cultural taboos on nakedness, this was nothing extraordinary, it was part of the theatre of a gift exchange and not meant to be salacious. For European sailors this was a sex show and the girls were part of the gift. Anthropologist Serge Tcherkézoff uses this scene as the center of one of his own works on cultural exchanges-or misunderstandings, its title 'The young girls in tears' taken from an unedited description of such a gift scene, in which the young girls were visibly upset once they realized what was happening. Some of the journals of the explorers; that of Labillardiere comes to mind, also describe scenes of sexual violence and attempted rape on the part of the European sailors (which he of course steps in to stop). And while that story serves to promote Labillardiere's own good moral standing, he isn't the only observer to record such episodes, meaning they must have been occurring, and very likely more often than they bothered recording.

Remember a lot of these sailors arrived in Tahiti unwashed, unshaved, and suffering of scurvy-- which can cause bleeding gums, open sores, and jaundice. These sailors were not attractive figures-- they were half dead and suffering serious vitamin deficiencies.

That said, there were obvious consensual sexual relations, especially between elites. Officers and nobles, like Banks, who were on the ship. It wasn't hard to figure out who was in charge of a British or French naval ship and so the elites of the island and of the ship often spent their time together, and it was women from the elite of the island who might be most interested in having a child by an officer of a ship. The child was a way to anchor or take some of the power or spirit of the commanding officer and keep it on the island. This could also happen between lower ranking members of either ship or island society, but the best descriptions come from the top.

There is really know way to know if there was a population boom. No one was measuring demographic trends on the island until the London Missionary Society set up shop in 1796 (roughly 25 years after Banks). Missionaries were keen to begin keeping track of population in order to figure out how much of it they had converted and get some statistics to prove the efficacy of their mission. What they found by and large, and beyond just Tahiti, was a dramatic downward demographic trend- by 1800 the island had lost somewhere between 50-90% of its population (pre-European population of the island is estimated between 15,000 to 200,000 and even taking the lowest levels, by 1800 the population had dropped dramatically).

So while there is no way to tell if there was a baby boom, there was certainly a dramatic population decline. The British blamed the French and the French blamed the British for introducing venereal diseases into the population-- which contributed some to declining birth rates. Tuberculosis, small pox, and a whole host of other nasty bacteria and viruses were also introduced during this time, gradually causing the rising death rate to outstrip the declining birthrate.

Some reading I mentioned above:

• Tcherkézoff, Serge. Tahiti 1768: Jeunes Filles En Pleurs. La Face Cachée Des Premiers Contacts Et La Naissance Du Mythe Occidental (1595-1928). Singapore: Au vent des îles, 2004. [I know this book was being translated into English, but I'm not sure whatever happened to that project...]

• Salmond, Ann. Aphroditeʻs Island: The European Discovery of Tahiti. Berkeley: University of California Press, 2010.

• Salmond, Ann. Bligh; William Bligh in the South Seas. Berkeley: University of California Press, 2011.

• McArthur, Norma. Island Populations of the Pacific. Canberra: Australia National University Press, 1967.

• Rallu, Jean-Louis. “Population of the French Overseas Territories in the Pacific, Past, Present, Projected.” The Journal of Pacific History 26.2 (1991): 169-186.