Table 1.
Notation used in this paper.
| symbol | definition |
|---|---|
| variables | |
| z ∈ ℝx | the environment, a vector of environmental variables |
| x | dimension of environment |
| δ | order of the range-bagging model |
| v | number of votes used for the range-bagging model |
| n | number of occurrence records |
| Xi | bootstrap sample |
| w | tuning parameter |
| ε | tuning parameter |
| p = w/n | fraction of occurrence records used in the bootstrap sample |
| k | number of points in the convex hull |
| functions | |
| p(z) | probability density of environments |
| f(z) | probability density of environments occupied by species |
| q(z) | habitat selection function |
| gN(z) | mapping from environmental space to niche |
| hN(z) | zero net growth isocline, the boundary of the niche |
| hF(z) | boundary of the set of occupied environments |
|
niche centrality |
| sets | |
| P | set of realized environments |
| F | set of occupied environments |
| N | niche, the set of environments in which a species can persist |
| Δδ | marginal niche, a projection of n onto a δ-dimensional subspace Δ ⊂ N |
|
marginal niche model for the ith bootstrap sample |