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Thus, the equilibrium variance doubles at z = -1, it rises fourfold at z = -1.5 and is unbounded at z = -2.
The equilibrium variance of genomic EBV follows from substituting σ Mt+ 1 = σ M,t and solving for σ M,t, which yields (3) σ M e q. 2 = σ M 0 2 1 + k.
We see from Table 1 that if we require a bound on the equilibrium variance of 0.1 then the Poisson τ-leap method must take | z ⋅ | ≤ 2 11 while for the RK methods the bounds on | z| are approximately 4 and 10, respectively with s = 3, 5.
For example, for a phenotypic variance of σ P = 1, and a heritability of the unselected base-generation of h0 = 0.3, an initial accuracy of genomic EBV of r g g ˆ 0 = 0.8, and a selected proportion of 5%, so that k = 0.86, the initial variance of genomic EBV equals 0.8 × 0.3 × 1 = 0.192 and the equilibrium variance of genomic EBV equals 0.192/1.86 = 0.103.
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There are other approaches to understanding the approach to equilibrium at variance with the approaches that rely on mixing phenomena.
We find that (1) analytical results are accurate in a large parameter space; (2) epistasis always reduces the equilibrium genetic variance, as predicted in earlier studies that exclude drift; (3) large-scale stochastic fluctuations and non-equilibrium phenomena like adaptive inertia can strongly influence the evolution of the genetic architecture of the trait.
If a population is at mutation-drift equilibrium, the variance at an STR locus is proportional to the (effective) mutation rate [17].
In equilibrium, the variance ratio between penta/hexa and tri/tetra STRs times a mutation rate of tri- and tetranucleotide markers would give a mutation rate of penta- and hexanucleotide STRs.
In migration – drift equilibrium the variance of the genetic distance measure is further expected to increase with geographic distance [ 26].
At this equilibrium, the trait variance is maintained by mutation, which increases variance, and by genetic drift and stabilizing selection, which decrease variance.
Denote the equilibrium mean and variance of as and, respectively.
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