Quantification of inbreeding due to distant ancestors and its detection using dense single nucleotide polymorphism data

Abstract

Inbreeding depression, which refers to reduced fitness among offspring of related parents, has traditionally been studied using pedigrees. In practice, pedigree information is difficult to obtain, potentially unreliable, and rarely assessed for inbreeding arising from common ancestors who lived more than a few generations ago. Recently, there has been excitement about using SNP data to estimate inbreeding (F) arising from distant common ancestors in apparently "outbred" populations. Statistical power to detect inbreeding depression using SNP data depends on the actual variation in inbreeding in a population, the accuracy of detecting that with marker data, the effect size, and the sample size. No one has yet investigated what variation in F is expected in SNP data as a function of population size, and it is unclear which estimate of F is optimal for detecting inbreeding depression. In the present study, we use theory, simulated genetic data, and real genetic data to find the optimal estimate of F, to quantify the likely variation in F in populations of various sizes, and to estimate the power to detect inbreeding depression. We find that F estimated from runs of homozygosity (Froh), which reflects shared ancestry of genetic haplotypes, retains variation in even large populations (e.g., SD=0.5% when Ne=10,000) and is likely to be the most powerful method of detecting inbreeding effects from among several alternative estimates of F. However, large samples (e.g., 12,000-65,000) will be required to detect inbreeding depression for likely effect sizes, and so studies using Froh to date have probably been underpowered.

Figure 1

Procedure for deriving 10 samples from each of three effective population sizes. Circles represent populations, arrows represent evolution and splitting/combining of each population, and squares represent samples of size 1000 derived from each population. The sizes of the shapes correspond to population (circles and arrows) or to sample (squares) sizes. See text for details.

Figure 2

Shown is the probability that mates share no common ancestors in the most recent g generations as a function of population size (see text). The x’s are the same values, derived empirically from simulations, for up to 5 generations in the past, and show good agreement with the expected probabilities. Even in large, randomly breeding populations (e.g., 1 million), it is almost certain that at least one ancestor exists in common between two pedigrees within 11 generations.

Figure 3

Contribution to var(F_ped) from previous generations. Most of the variance in F_ped at all population sizes is attributable to recent inbreeding. For example, the variance in F_ped due to spouses sharing common ancestors five generations in the past makes up only ∼0.2% of the total variance in F_ped at all population sizes.

Figure 4

Variance of F (±1 SE) as a function of N_e. The variance of F_ped is the lowest at all population sizes and the variance of F_roh is intermediate. Comparing the variance of genomic measures of F in simulated data to the equivalent variances in real SNP data (from an outbred Caucasian sample) suggests that the effective population size of Caucasians is ∼10,000 with respect to these statistics.

Figure 5

Prediction error variance (PEV) of genomic estimates of F as a function of N_e. PEV decreases as a function of population size for all genomic estimates of F, but does so most rapidly for F_roh.

Figure 6

Correlations between F_ped and genomic estimates of F as a function of N_e. All correlations between genomic estimates of F and F_ped decrease as a function of N_e, but F_roh is consistently correlated most highly with F_ped.

Figure 7

Correlations between F and homozygous mutation load as a function of N_e. F_roh correlates most highly with the homozygous mutation load at all population sizes, and this advantage increases at larger population sizes (where inbreeding becomes more ancient).

Figure 8

Correlations between alternative thresholds of F_roh and the homozygous mutation load as a function of N_e. Runs of homozygosity (ROHs) are defined as stretches of 0.5-Mb, 1.5-Mb, or 5-Mb homozygous SNPs. Long thresholds are optimal for detecting autozygosity in highly inbred populations, whereas shorter thresholds are optimal for detecting autozygosity in outbred populations.

Figure 9

Variance of F (±1 SE) as a function of generations since population expansion. Whereas F_ped drops immediately following a population expansion, the variance in genomic measures of F requires hundreds of generations to reach equilibrium levels.

Figure 10

Correlations between F and homozygous mutation load as a function of generations since population expansion. The relationship between the homozygous mutation load and F_roh increases the most quickly following a population expansion.

Figure 11

Estimated power to detect inbreeding effects on a human complex trait using F_roh. Higher levels of real inbreeding (smaller N_e) lead to higher variance in F_roh and thus greater statistical power to detect an inbreeding effect. Large (solid lines) and small (dashed lines) inbreeding effect sizes were derived from a review on the effects of consanguinity on IQ (see text). Arrows show predicted sample sizes required to achieve ∼80% power. When inbreeding is high (N_e = 100), sample sizes of ∼400 are adequate, but in outbred populations (N_e = 10,000 or real SNP data), samples sizes >20,000 may be required.