Social-ecological system sustainability conditions : a mathematical modelling approach ; Conditions de durabilité d'un système écologique et social : une approche par modélisation mathématique

Renewable natural capital (RNC) exploitation by human activities allows human society's development, but may cause deterioration of their quality of life through ecosystem services loss. This paradox questions the compatibility between economic development and the preservation of natural resources. This thesis studies how does the properties of the economic and social-anthropological dimensions of a social-ecological system (SES) may influence its sustainability. To do so, we build a generic model in the ordinary differential equation framework. This model has three variables: human population size, the amount of the RNC and the manufactured good amount per capita (BMpi). This allows us to study its asymptotic and transient properties. We identify as sustainable a situation in which a special type of asymptotically stable steady state exists. We show the importance of return to scale, since this hypothesis changes drastically the results. In case of increasing return to scale, instability of the steady state of interest may be due to: 1) A RNC regeneration rate that is too weak compared to economic system properties; 2) not fulfilled subsistence requirement or 3) an over-production of BMpi that may cause boom and bust cycles for the population size, but also the RNC and the manufactured goods. We then study how does the asymptotically stable steady state vary in case of modification in sub-systems embedded in the SES. As expected, we find that increasing the RNC extraction rate provokes non sustainability of the SES. However, our work shows that, under some hypotheses, this instability may be avoided through task repartition changes in the society. Then, sustainability of a SES depends on the properties assumed for the ecological and economic systems. Moreover, we illustrate that stability does not mean viability: before stability disappears, viability is no more assured. Lastly, in increasing return to scale case, we show that an inner approximation of a capture basin, which lead to population disappearance can ...