The infinitesimal model is extended to cover linkage in finite
populations. General equations to
predict the dynamics of the genetic variation under the joint effects
of mutation, selection and drift
are derived. Under truncation and stabilizing selection, the quadratic
equations for the asymptotic genetic variance (VG)
are respectively
V2G(1+kS)+VG
(Ve−2NeVm)
−2NeVmVe=0
and
V2G(1+S)+VG
(Ve+γ−2NeVm)
−2NeVm(Ve+γ)=0,
where Ne is the effective population size,
Vm is the mutational variance, Ve
is the environmental
variance, γ is the parameter that measures the spread of fitness
around the optimum under
stabilizing selection, k is equal to i(i−x)
where i is the selection intensity and x is the cut-off
point
under truncation selection. The term S is a function of the
number of chromosomes (v) and the average chromosome length (l):
formula here
These predictions are accurate when compared with results of
simulations of small populations
unless the number of genes is small. The infinitesimal model reduces
to the continuum of alleles
model if there is no recombination between homologous chromosomes.