Viability Analysis of Labor Force in an Agroforestry System

In the economic and social development of humanity, man has incorporated the exploitation of natural resources as a fundamental livelihood source and has made efforts to understand and calculate the limits that allow the rate at which the renewable resource is regenerated to be greater than or, at least, equal to the rate at which it is extracted. When these limits are exceeded, overexploitation of natural resources occurs, which could lead to non-return scenarios, in which in the medium and long term, it is not possible to ensure a sufficient supply to satisfy the population’s requirements and preserve the well-being of the ecosystems. A desired scenario must always, or at least for a period of time, ensure a population level that does not extract resources below a certain threshold; that is where the role of the viability theory is relevant. A determining factor for increasing the extraction rate of natural resources, which in this case are forestry, is the labor force dedicated to extractive activity, whose increase negatively affects the availability of resources at each moment of time. This chapter addresses a continuous dynamic system of a population that has agriculture and forest use as its main livelihood. The forest, as a renewable resource, is assumed to grow logistically, but at the same time, it is harvested by population through a production function that depends on the labor force. By using the viability theory and considering that the population dynamics is increasing and that of the resource is decreasing with respect to the selected control parameter, i.e., labor force, the thresholds for which there is an adequate workforce that guarantees the sustainable levels of the forest and population for a period of time were determined. In addition, it was found that the time interval in which this resource is sustained is determined by the dynamics of the human population. These analytical results are also presented numerically.