Bulletin of Mathematical Biology

, Volume 69, Issue 8, pp 2723–2735

Toward the Human Genotope

Origianal Article

DOI: 10.1007/s11538-007-9244-7

Cite this article as:
Huggins, P., Pachter, L. & Sturmfels, B. Bull. Math. Biol. (2007) 69: 2723. doi:10.1007/s11538-007-9244-7


The human genotope is the convex hull of all allele frequency vectors that can be obtained from the genotypes present in the human population. In this paper, we take a few initial steps toward a description of this object, which may be fundamental for future population based genetics studies. Here we use data from the HapMap Project, restricted to two ENCODE regions, to study a subpolytope of the human genotope. We study three different approaches for obtaining informative low-dimensional projections of this subpolytope. The projections are specified by projection onto few tag SNPs, principal component analysis, and archetypal analysis. We describe the application of our geometric approach to identifying structure in populations based on single nucleotide polymorphisms.


ENCODE project Genotope Human variation Polytope Single nucleotide polymorphism 

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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