The exact population of the Hawaiian Islands at the time of Captain James Cook's arrival is not known however the large range of estimates from 100,000 to 1,000,000 illustrate the controversial nature of the topic and disagreement over the best methods for calculating it. What is known is that the first voyaging canoes that landed on Hawaiian shores during the discovery and settlement of Hawaii cannot have carried more than a hundred people, and perhaps even fewer. For the purposes of this article, "ancient" Hawaii is defined as the period beginning with the first arrival of human settlers, around AD 1100, and ending with their initial contact with the first Western visitors. Constant population growth theory In the popular model of constant population growth, the human population of Hawaii expanded steadily from the first settlements until the arrival of Captain Cook, when growth halted because of the introduction of unfamiliar diseases. This theory was originally advanced by Robert C. Schmitt and Lynn Zane, and it is still used to support an estimate of 800,000 to 1,000,000 people in the Hawaiian Islands in 1778. However, this theory relies on a hypothetical settlement date of AD 500 along with a doubling of population every 110 years. Modern high-precision radiocarbon dating in Hawaii has since refuted that date, as well as the notion of linear population growth, as subsequent examination of habitation sites showed a peak population around 1450-1550 AD. Thereafter, population declined dramatically because of declining fertility, infanticide, and war between chiefs, well before Western contact. Arrested population growth The theory of constant population growth in Hawaii has scant support from the archaeological data and is contradicted by paleo-environmental evidence and radiocarbon dating of historical sites. The human imprint on the land increases along with population, as more and more people require more and more food, light, and heat. Thus there would be more fires and more wood charcoal produced, with increases correlated with population growth. Accordingly, the evidence indicates a rather complex model of arrested population growth, especially as a consequence of island life. This theory finds corroboration in archaeological censuses of abandoned habitation sites on leeward Hawai'i Island and Kaho'olawe Island, which indicate that the population peaked before Cook's arrival. The arrested growth model fits well with an estimated pre-contact population of between 100,000 and 150,000, derived primarily from the study of historical records. Population estimates based on an initial