Inbreeding depression in a zygotic algebra

Abstract

We study the algebraic behavior of a three dimensional zygotic algebra in the presence of parameters 0 < s < 1 and 0 < g < 1; s for selfing and g which reflects its associated inbreeding depression. We also study the dynamics of the system for which this algebra is a model. Our methods lean towards commutative algebra and algebraic geometry and find support on the computer program Macaulay2.Our results are best understood through the geometry of a rational function of the projective plane.

Keywords:

• Selfing
• inbreeding depression
• zygotic algebra
• mixed mating
• natural selection
• generic methods
• semiinvariants
• projective plane
• rational function

1991 Mathematics Subject Classification:

• Primary: 17D92
• Secondary: 14E05