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.

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

MEE3_208_sm_Appendices.pdf166KSupporting info item

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.