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Regime shifts in a socio-ecological model of farmland abandonment

Model Type
SES Library XPP model

This is a simple model with reciprocal feedbacks between social and ecological dynamics of farmland abandonment. With the rising urbanization, human migration to urban centers have increased significantly around the globe. One notable consequence of this migration pattern is that mountainous forests that had been traditionally cleared for farming are increasingly becoming abandoned. As a result, such lands likely become forests again through natural regeneration. These trends may induce two reinforcing feedbacks: (1) more migration means less farmlands due to forest regeneration and (2) less farmlands mean less economic incentives to stay in farming and more incentives to move to urban areas for better opportunities.

Reference

Figueiredo, J., & Pereira, H. M. (2011). Regime shifts in a socio-ecological model of farmland abandonment. Landscape Ecology, 26(5), 737-749. doi:10.1007/s10980-011-9605-3

Scenarios

The coupled system has five types of stable fixed points: (1) M=P and F=T, i.e., entire population migrates and all farmlands become forests, (2) M=0 and F=0, i.e., no migration happens and all forests are cleared for farming, (3) M=0 and F='a non-zero value', i.e., individuals do not migrate but do not deforest all of the area, (4) M=some value between 0 and 100 and F=0, i.e., a part of the population migrates but people still find a way to deforest all of the forests, and (5) M=some value between 0 and 100 and F=some value between 0 and 100, i.e., a part of the population migrates and a portion of the area still remains as forests. Hence, the possible system states encompass extreme cases, i.e., all of the population either migrates or stays and all of the forests remain or become clearned, as well as moderate cases, i.e., parts of the population and the forests still remain.

To explore the fixed points, a broad range of paramater combinations should be tested: (1) forest growth rate (epsilon) ranging from 0.1 to 5, residents' ability to deforest (lambda) ranging from 0 to 0.25, annual farmland utility (gamma) ranging from 1 to 5, and social bonding (s) ranging from 0.01 to 0.5. For the details, please see Figure 3 and Figure 4 in Figueiredo and Pereira (2011).

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$$\Large \frac{dF}{dt}=\epsilon F(1-\frac{F}{K})-\lambda RF$$
$$\Large \frac{dM}{dt}=\omega\left ( \frac{1}{1+e^{\frac{\mu-\frac{M}{P}}{s}}}-\frac{M}{P} \right )P$$
$$\Large R=T-M$$
$$\Large \mu=\frac{\frac{Ah}{P-M}}{2\gamma}$$
$$\Large \frac{Ah}{P-M}=\gamma \ \ extrm{holds when} \ \ \mu=0.5$$
$$\Large A=T-F$$
regime_shifts_in_a_socio-ecological_model_of_farmland_abandonment.ode
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