Ecological Archives A021-081-A2

Taal Levi, Glenn H. Shepard, Jr., Julia Ohl-Schacherer, Christopher C. Wilmers, Carlos A. Peres, and Douglas W. Yu. 2011. Spatial tools for modeling the sustainability of subsistence hunting in tropical forests. Ecological Applications 21:1802–1818.

Appendix B. Equations for rmax(θ), rmin(θ), θmax, and θmin.

Working in the first quadrant with x and y not equal to zero, to facilitate explanation, we can calculate the following values of rmax(θ), rmin(θ), θmax, and θmin using basic trigonometry. The formulae for rmax(θ), rmin(θ) vary depending on which edge of the square bin is hit first and last, which depends on the trajectory defined by θ (See Figure 1).

Using the above values in Equation 7 we find that the integral cannot be solved so we seek an approximation.


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