Climatic variable contribution to squared niche distance change

Usage

variable_contribution(current, future, center, A)

Arguments

current: Current climate matrix in the fitted climate space.
future: Future climate matrix in the fitted climate space.
center: Current niche reference centre.
A: Niche metric matrix.

Value

Matrix whose rows sum to future minus current squared niche distance.

Details

For centred current and future climatic vectors $z_{0i}$ and $z_{1i}$, the contribution of variable $j$ is $$V_{ij} = z_{1ij}(A z_{1i})_j - z_{0ij}(A z_{0i})_j.$$ Consequently, $$\sum_j V_{ij} = \psi_{1i} - \psi_{0i} = (r_{1i} - r_{0i})(r_{1i} + r_{0i}),$$ where $r_{0i}$ and $r_{1i}$ are current and future niche distances. These values therefore decompose the squared-distance change underlying Niche Distance Shift. They are not SDM variable importance or causal effects.