Spring Phenology Data

Spring Phenology Dat

Agricultural production and ecological resilience of the landscape as a function of agricultural pressure.

<p>Two cases are presented: (a) Borneo—moderate soil and (b) Madagascar—good soil. Results are shown for two values of the local recruitment rate: <i>r</i> = 0.3 and <i>r</i> = 0.5. Most values on the upper branch of the agricultural production function are the same regardless of the value of local recruitment rate.</p

Ecological resilience of the forested stable state as a function of agricultural pressure.

<p>The ‘ecological resilience’ is the proportion of forested land that can be converted to agriculture without pushing the socio-ecological system into the deforested stable state. Results are shown for two different values (0.3 and 0.5) of the local recruitment rate parameter (<i>r</i>).</p

A graphical representation of the forest-landscape model used in this paper.

<p>See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0137497#pone.0137497.t001" target="_blank">table 1</a> for additional explanation of symbols. Note that under the model, land used for agriculture becomes unproductive and must be left fallow during the next time step, so both of these values are indicated with the same symbol.</p

Stable states of the modeled shifting cultivation system.

<p>The stable states are shown here as a function of agricultural pressure and local forest recruitment rate. Region I has little forest cover (deforested stable state) while region II has extensive forest cover (forested stable state). In region III either the forested or deforested state is possible, depending on the previous forest and soil condition. The existence of two alternative stable states in this part of the model’s parameter space results in a hysteresis such that the current state of the system has two possible configurations depending on its previous state [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0137497#pone.0137497.ref030" target="_blank">30</a>].</p

Relative recovery time following a standardized disturbance as a function of agricultural pressure.

<p>Note that this value is not an absolute number of time steps as in our definition of engineering resilience, but is scaled to the recovery time in the absence of agricultural pressure for easy comparison among the cases. The level of agricultural pressure at which <i>f</i>₅ stage forest is no longer possible depends on the values of the forest recruitment rate and succession parameters. These plots are for a local recruitment rate (<i>r</i>) of 0.3; plots for <i>r</i> = 0.5 were virtually identical.</p

Brief explanations of symbols used for variables and parameters in this paper.

<p>Brief explanations of symbols used for variables and parameters in this paper.</p

An example of a system transition between stable states.

<p>This example is based on the Borneo (good soil) case with internal recruitment rate <i>r</i> = 0.3. Point ‘a’ is the initial system state; point ‘b’ is the state following a disturbance, which leads to a forest collapse to point ‘c’ as agricultural pressure has not changed. Only by reducing agricultural demand to point ‘d’ may the system evolve back to the forested state (point ‘e’) when agriculture may safely be increased while maintaining the system in the forested state. See main text for additional details.</p

Basins of attraction of the forested and deforested stable states.

<p>Data shown are for the Borneo (good soil) case, for internal recruitment rates <i>r</i> = 0.3 (a) and <i>r</i> = 0.5(b).</p

Forest condition as a function of agricultural pressure.

<p>The lines correspond to two different internal recruitment rates (<i>r</i> = 0.3 and <i>r</i> = 0.5). The diagonal lines correspond to the forested stable state and the horizontal lines the deforested state. Note that in the forested state, the lines for the two values of <i>r</i> overlap exactly for most values of agricultural pressure. For intermediate values of <i>A</i>_<i>P</i> two values of forest condition (<i>F</i>_<i>C</i>) are possible due to hysteresis in the system. These results are from the Borneo (good soil) case.</p