Positive and Negative Feedbacks and Free-Scale Pattern Distribution in Rural-Population Dynamics

Depopulation of rural areas is a widespread phenomenon that has occurred in most industrialized countries, and has contributed significantly to a reduction in the productivity of agro-ecological resources. In this study, we identified the main trends in the dynamics of rural populations in the Central Pyrenees in the 20(th) C and early 21(st) C, and used density independent and density dependent models and identified the main factors that have influenced the dynamics. In addition, we investigated the change in the power law distribution of population size in those periods. Populations exhibited density-dependent positive feedback between 1960 and 2010, and a long-term positive correlation between agricultural activity and population size, which has resulted in a free-scale population distribution that has been disrupted by the collapse of the traditional agricultural society and by emigration to the industrialized cities. We concluded that complex socio-ecological systems that have strong feedback mechanisms can contribute to disruptive population collapses, which can be identified by changes in the pattern of population distribution.