TABLE 1

Cytoplasmic and nuclear effective population sizes in gynodioecious populations with simple sex determination systems

Sex determination
Nuclear gynodioecy (w > 2)Cytoplasmic gynodioecy (w = 1)Dioecy (w → ∞)
ParametersGeneral caseDominant male sterilityRecessive male sterility
ψfEmbedded Image Embedded Image Embedded Image → 10 ≤ ψf ≤ 1
ψhEmbedded Image 1Embedded Image →1Not defined
1 − hEmbedded Image Embedded Image Embedded Image Embedded Image ψf
ψcf (Equation Al)f1Embedded Image Embedded Image 1
ψch (Equation Al)Embedded Image Embedded Image Embedded Image ψh if ψf ≠ 1; 1 if ψr = 10
ψnf (Equation A2)ψfEmbedded Image ψfEmbedded Image Embedded Image
ψnh (Equation A2)Embedded Image Embedded Image Embedded Image Embedded Image Embedded Image
Embedded Image (Equation B4)Embedded Image Embedded Image Embedded Image 0Embedded Image
Embedded Image Embedded Image Embedded Image Embedded Image → ∞1
Nec (Equation 5)Embedded Image N(1 − h)Embedded Image NN(1 − h)
Embedded Image (Equation B4)000Embedded Image Embedded Image
Embedded Image 4h2Embedded Image 1
Nen (Equation 5)NNNNh4h(1 − h)N
  • Assuming equilibrium for the frequency of females, the sex-inheritance parameter (ψf, ψh) and the frequency of females (1 − h) are given for five sex determination systems. From these, the parameters ψf, ψh, the variances of fitness, σ2., the cumulative effects of selection, (1 /[2 − ψcfψch]2) and the effective population sizes, Ne*, were deduced, assuming complete outcrossing of hermaphrodites.

  • –, no simplification.