An integrated stochastic economic-ecological-social model with stratified-population

There has been a growing interest on the study of the human-ecosystems sustainability from an integrated point of view. The recognition of sustainability as a complex long-term problem has led to the development of tools that address it from a multidisciplinary perspective. Several mathematical models have been developed to support the understanding of the interactions between human activities and natural resources, and the effect of economic and social issues on the sustainability of such ecosystems. However, only a few of them have considered these aspects holistically; even more, critical social aspects such as uneven distribution of goods and services have not been addressed. Developed countries have a larger pool of resources when facing environmental and social issues than developing countries, along with larger resilience to external threats, being able to rely on scientific and technological advances against poverty and inequity. Therefore, these developed societies are socially fairer and more capable to become sustainable. This work presents an integrated ecological-economical-social model which includes a crucial social aspect in the sustainability study such is inequity, having two sectors of a population with different economic distribution values; these two populations interact directly with each other representing a stratified society as an attempt to conceptually describe a real-world human ecosystem where goods and natural resources are not evenly distributed. Also, the system is under the influence of uncertain external instabilities due to the inclusion of real data series, captured in the model by stochastic processes incorporated in demographic variables. Four typical kinds of societies with different levels of development and inequity were analyzed. Over the sixty percent of the times simulations led to a system collapse, being the probability of collapse directly related to the inequity. Results suggest that societies with unevenly distributed economies are less sustainable than more equalitarian societies, proving that economic equality is an important factor to consider in sustainability studies. Additionally, a typical pattern for per capita wages was found in those cases where the system collapsed, similar from a macroeconomic behavior in real world economies under economic crisis.