Easter Island's Collapse: A Tale of a Population Race

Abstract

We study different extended formulations for the set X = {x ∈ Z Z n | A = A § } in order to tackle the feasibility problem for the set X + = X∩ n + . Here the goal is not to find an improved polyhedral relaxation of conv(X + ), but rather to reformulate in such a way that the new variables introduced provide good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. For the case that A has one row a we analyze the reformulations in more detail. In particular, we determine the integer width of the extended formulations in the direction of the last coordinate, and derive a lower bound on the Frobenius number of a. We also suggest how a decomposition of the vector a can be obtained that will provide a useful extended formulation. Our theoretical results are accompanied by a small computational study.

The natalist bias of pollution control

“…10 Another possible extension of the model would consist in adding income heterogeneity among households within generations. This would allow us to study the distributive impact of the substitution effect.…”

Overlapping Generations

“…It occurs as soon as rearing children takes time 3 and is sensitive to the relative return of spending time on this or other activities. Various factors can affect this relative return: parents' income [5], child mortality [6,7], the absence of formal old age support schemes [8], cultural norms (Princeton European Fertility Project), the importance of increasing the relative power of one's community (see [9,10]), etc. In this paper we concentrate on the first of these factors.…”

Interconnections accelerate collapse in a socio-ecological metapopulation

“…Although logistic growth models and its variations are most widely used in ecology, the application of population growth models to resource-limited human populations has also received attention, perhaps on account of our growing awareness of the possible ramifications of resource over-exploitation, especially in the face of environmental change [13]. Mathematical models have been used to study phenomena such as human population collapse in a model with resource dynamics [14] and conflict among metapopulations arising over common resources [15, 16]. Models have also been used to study historical human population collapses such as in the people of Easter Island [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], the Kayenta Anasazi [28], and the Andean Tiwanaku civilization [29], as well as collapse of modern populations [30, 31, 32, 33].…”

“…With some exceptions [15, 16, 27, 34], most previous research on resource-limited population growth focuses on single populations and not on multi-population interactions. However, multi-population interactions through trade and other mechanisms are an inescapable feature of the world’s human metapopulation dynamic, and can have significant impacts on ecosystems and resource levels [35].…”

“…However, multi-population interactions through trade and other mechanisms are an inescapable feature of the world’s human metapopulation dynamic, and can have significant impacts on ecosystems and resource levels [35]. The literature on multi-population interactions has explored meta-population models involving migration of individuals between patches [28], or competing populations conflicting and bargaining over a common resource [15, 16]. A multi-patch model of human populations fitted to data from Easter Island has predicted that coupling human populations together through exchange of resources, migration and technology can stabilize the entire metapopulation [27].…”