The problem of genetic hitch-hiking in a geographically subdivided population is analysed under the assumption that migration rates among populations are relatively small compared with the selection coefficient for a newly arising advantageous allele. The approximate method used in the paper is valid when the number of emigrants per generation (Nm) is less than one. The approximate analysis shows that hitch-hiking can result in substantial differences among populations in the frequencies of neutral alleles closely linked to the advantageous allele. Thus, in cases for which genetic hitch-hiking is thought to be responsible for low levels of genetic variability in regions of the genome with restricted crossing over, it might be possible to find confirmatory evidence for that hypothesis by finding unusual patterns of geographic differentiation in the same regions of the genome.

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.

We present a multipoint algorithm to map quantitative trait loci (QTLs) using families from outbred populations with a variable number of sibs. The algorithm uses information from all markers on a chromosome simultaneously to extract information of QTL segregation. A previous multipoint method (Kruglyak & Lander (1995) American Journal of Human Genetics57, 439–454) extracts information using a hidden Markov model. However, this method is restricted to small families (<10 sibs). We present an approximate hidden Markov model approach that can handle large sibships while retaining similar efficiency to the previous method. Computer simulations support the notion that data sampled from a small number of large families provide more power than data obtained from a large number of small families, under the constraint that the total number of individuals for the two schemes is the same. This is further reflected in simulations with variable family sizes, where variance in family size improves the statistical power of QTL detection relative to a constant size control.

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) by interval mapping was investigated using simulation. Confidence intervals were created using a non-parametric (resampling method) and parametric (resimulation method) bootstrap for a backcross population derived from inbred lines. QTLs explaining 1%, 5% and 10% of the phenotypic variance were tested in populations of 200 or 500 individuals. Results from the two methods were compared at all locations along one half of the chromosome. The non-parametric bootstrap produced results close to expectation at all non-marker locations, but confidence intervals when the QTL was located at the marker were conservative. The parametric method performed poorly; results varied from conservative confidence intervals at the location of the marker, to anti-conservative intervals midway between markers. The results were shown to be influenced by a bias in the mapping procedure and by the accumulation of type 1 errors at the location of the markers. The parametric bootstrap is not a suitable method for constructing confidence intervals in QTL mapping. The confidence intervals from the non-parametric bootstrap are accurate and suitable for practical use.

The magnitude of inbreeding depression in Drosophila melanogaster appears too large to be accounted for by mutational load with multiplicative fitness interactions among loci, if current estimates of mutation and selection parameters are valid. One possible explanation for this discrepancy is synergistic epistasis among the fitness effects of deleterious mutations. A simple model of the effect of synergistic epistasis on the inbreeding load is developed. This model is used to show that deleterious mutations could account for the Drosophila data on the effects of inbreeding on components of fitness such as viability.