Computes the geometric volume (area in 2D, volume in 3D, hypervolume in higher dimensions) of a \(p\)-dimensional ellipsoid defined by its semi-axis lengths.
Details
For semi-axes \(a_1, \dots, a_p\), the volume is: $$ V_p = \frac{\pi^{p/2}}{\Gamma(p/2 + 1)} \prod_{i=1}^{p} a_i $$ where \(\pi^{p/2} / \Gamma(p/2 + 1)\) is the volume of the unit \(p\)-dimensional ball.
In probabilistic niche models, semi-axis lengths are typically derived from covariance eigenvalues and a chi-square cutoff.