JAMES A. BRANDER
University of British Columbia Vancouver, British Columbia, Canada
1. The Mystery of Easter Island
2. First Discovery and Early History
3. Resource Depletion and Collapse
4. Malthusian Population Dynamics
5. A Predator-Prey System with Unfortunate Parameter Values
6. The Role of Property Rights and Open Access
8. Lessons of Easter Island
core sample A specimen obtained in a long cylinder, taken from a physical site for subsequent study; used in many fields, including oil exploration and archaeology. In archaeology, elements in the core sample can be carbon dated, allowing a reconstruction of the implicit historical record.
Malthusian population dynamics A demographic theory originated by Thomas Malthus, suggesting that the human population has a natural tendency to grow sufficiently rapidly to offset and perhaps even overshoot productivity gains in food production. Malthus also made the related assertion that population growth will therefore be sensitive to per capita consumption— tending to increase when consumption rises and to decrease when consumption falls. Hence, the term refers to a situation in which population growth is positively related to per capita consumption. It is noteworthy that the term does not describe societies that have gone through the so-called demographic transition in which fertility tends to fall at sufficiently high income levels, it does seem to describe societies at the level of development of Easter Island prior to European contact.
market failure A situation in which markets fail to achieve economic efficiency. Open-access resources and, more broadly, difficulty in establishing property
rights constitute an important source of market failure.
open-access resource A resource to which any potential user can gain access. Various communities have sometimes had land to which everyone had access, e. g., a ‘‘common,’’ consisting of grazing land. It was commonly observed that such common land was often overgrazed. The tendency to overuse open-access resources is sometimes referred to as the ‘‘open-access’’ problem, which is an extreme version of ‘‘incomplete property rights,’’ arising when the owner or controller of an economic resource can exclude other users only at significant cost.
predator-prey system A system in which a ‘‘prey’’ forms an important part of the consumption for a ‘‘predator.’’ It has often been observed that predators and prey (such as lynx and rabbits) sometimes go through dramatic population cycles. In the early 20th century, Lotka and Volterra independently studied the formal properties of simple linear two-equation dynamic systems in an effort to shed light on predator-prey systems. They discovered that population cycles are a natural outcome of such systems for particular parameter values. Extinction and monotonic convergence to a steady state are also possible dynamic trajectories in predator-prey models.
Easter island (or rapa nui) is remarkable for being a small geographic entity that has generated enormous academic and popular interest. This interest arose primarily from the enormous stone statues, or moai, positioned at various locations around the island. These moai are sometimes referred to as ‘‘the mystery of Easter Island.’’ The mystery of the moai remained unsolved until the last decade of the 20th century, when it became clear that the statues were intimately connected to a story of resource depletion and collapse.