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Appendix A. Definitions of the Matrushka property, and the 1D and 2D means and quantiles.

Appendix B. Proof that the elliptic distortion model function is well defined, and extensions of the function.

Appendix C. Proof that contour lines in the full elliptic distortion model are non-concentric ellipses and that the elliptic distortion distance fulfils the Matrushka property.

Appendix D. Proof of the form of the two-dimensional dispersal kernel pELL for the elliptic distortion model.

Appendix E. Principles of the inverse modelling procedure, applied to the elliptic distortion model.

Appendix F. Methods for quantifying directional variability in the elliptic distortion model.

Appendix G. Proofs that the anisotropic models incorporating Von Mises distributions presented in Tufto et  al. (1997), Wagner et  al. (2004) and Staelens et  al. (2003) are special cases of our framework.

Appendix R. R-code for maximum-likelihood fitting of anisotropic dispersal kernels, specifically elliptic distorted-distance kernels, through inverse modelling.

Appendix S. R-code for simulating datasets similar to the case study dataset, for fitting these datasets and for calculating fit statistics.

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