A Note on the Reduction of the Dynamics of Multilocus Diploid Genetic Systems with Multiplicative Fitness

Epistasis in Predator-Prey Relationships

“…x x x x x x x x x x x = + + + + + + + + + where • 1 x is the size of the population of type AABB (expected phenotype AB ), • 2 x is the size of the population of type AABb (expected phenotype AB ), • 3 x is the size of the population of type AAbb (expected phenotype Ab ), • 4 x is the size of the population of type AaBB (expected phenotype AB ), • 5 x is the size of the population of type AaBb (expected phenotype AB ), • 6 x is the size of the population of type Aabb (expected phenotype Ab ), • 7 x is the size of the population of type aaBB (expected phenotype aB ), • 8 x is the size of the population of type aaBb (expected phenotype aB ) and …”

“…Table A1 in the Appendix shows the expected ratio of offspring produced by each i j x x − combination. Refer to articles like Braselton et al [7], or Szathmáry [8], for details regarding these and similar calculations.…”

“…We are unable to compute the eigenvalues of J at 1 E or 2 E . However, for the remaining rest points (equilibrium points), 4 E , 5 E ,  , 12 E , the eigenvalues of J evaluated at i E are 1,2 0 λ = , 3,4,5,6,7 a λ = − , 8 2 a λ = − , and 9,10 i ac λ = ± . Thus, we expect the rest points to usually be "center-like", which is illustrated in the computations.…”