Detecting inbreeding depression in structured populations

Abstract

Measuring inbreeding and its consequences on fitness is central for many areas in biology including human genetics and the conservation of endangered species. However, there is no consensus on the best method, neither for quantification of inbreeding itself nor for the model to estimate its effect on specific traits. We simulated traits based on simulated genomes from a large pedigree and empirical whole-genome sequences of human data from populations with various sizes and structures (from the 1,000 Genomes project). We compare the ability of various inbreeding coefficients ([Formula: see text]) to quantify the strength of inbreeding depression: allele-sharing, two versions of the correlation of uniting gametes which differ in the weight they attribute to each locus and two identical-by-descent segments-based estimators. We also compare two models: the standard linear model and a linear mixed model (LMM) including a genetic relatedness matrix (GRM) as random effect to account for the nonindependence of observations. We find LMMs give better results in scenarios with population or family structure. Within the LMM, we compare three different GRMs and show that in homogeneous populations, there is little difference among the different [Formula: see text] and GRM for inbreeding depression quantification. However, as soon as a strong population or family structure is present, the strength of inbreeding depression can be most efficiently estimated only if i) the phenotypes are regressed on [Formula: see text] based on a weighted version of the correlation of uniting gametes, giving more weight to common alleles and ii) with the GRM obtained from an allele-sharing relatedness estimator.

Keywords: inbreeding; inbreeding depression; population structure.

Fig. 1.

Comparison of the estimation of ID strength ($b$) among different $F$ estimates and two models in the PEDIGREE population. Each column represents a regression model. The first column depicts the simple linear regression (LM), and the second column depicts the LMM with the allele sharing relatedness matrix as a random component (LMM_AS). The first row represents the complete simulated population (11,924 individuals, A and B). The second row shows the random subsampling (2,500 individuals, C and D). The third row shows the ranged subsampling (2,500 individuals, E and F). Inbreeding estimates presented in this graph are $F_{\mathrm{PED}}$, $F_{\mathrm{AS}}$, $F_{\mathrm{UNI}}^U$, $F_{\mathrm{UNI}}^W$, $F_{{\mathrm{HBD}}_{100\mathrm{KB}}}$, $F_{{\mathrm{ROH}}_{100\mathrm{KB}}}$, $F_{{\mathrm{HBD}}_{1\mathrm{MB}}}$, and finally $F_{{\mathrm{ROH}}_{1\mathrm{MB}}}$. For A and B, violin plots show the distribution of the ID strength estimates ($b$) among the 100 simulation replicates. For C–F, violin plots represent the distribution of the ID strength estimates ($b$) for the 10,000 simulation and subsampling replicates (100 subsampling replicates for each of the 100 simulation replicates). The solid dark gray line is the true strength of ID ($b$$=-$3). The dashed red line represents the absence of ID ($b=$0), meaning that we failed to detect ID in any replicate above this line. Note that all panels are in $lo{g}_{10}$ scale and that all replicates converged.

Fig. 2.

Comparison of the estimation of ID strength ($b$) among different $F$ estimates and two models in the three populations from the 1,000 Genomes project. Each column represents a regression model. The first column depicts the simple linear regression (LM) and the second column depicts the LMM with the allele-sharing relatedness matrix as a random component (LMM_AS). The three rows correspond to the three populations from the 1,000 Genomes project: EAS on A and B, AFR on C and D, and WORLD on E and F. Inbreeding estimates presented in this graph are $F_{\mathrm{AS}}$, $F_{\mathrm{UNI}}^U$, $F_{\mathrm{UNI}}^W$, $F_{{\mathrm{HBD}}_{100\mathrm{KB}}}$, $F_{{\mathrm{ROH}}_{100\mathrm{KB}}}$, $F_{{\mathrm{HBD}}_{1\mathrm{MB}}}$, and finally $F_{{\mathrm{ROH}}_{1\mathrm{MB}}}$. Violin plots show the distribution of the ID strength estimates ($b$) among the simulation 100 replicates. The solid dark gray line is the true strength of ID ($b=-$3). The dashed red line represents the absence of ID ($b=$0), meaning that we failed to detect ID in any replicate above this line. Note that all panels are in $lo{g}_{10}$ scale and that all replicates converged.

Fig. 3.

Comparison of the ID strength estimates ($b$) with $F_{\mathrm{UNI}}^W$ in the four populations with four different models. The four models are i) the simple linear regression (LM), ii) the LMM with the allele-sharing relatedness matrix as a random factor, iii) the LMM with the weighted GCTA relatedness matrix as a random factor, and iv) the LMM with the unweighted GCTA relatedness matrix as a random factor. Panel A shows the simulated PEDIGREE population, panel B the EAS population, panel C the AFR population and finally panel D the WORLD population. Note that all panels are in $lo{g}_{10}$ scale. Also note that LMM did not converge for some replicates (yielding estimated $b$ values above 1,000 or below $-$1,000). Percentages of replicates which did not converge: panel D (WORLD): 21% for $GR{M}_{{\mathrm{GCTA}}^{\mathrm{W}}}$; 20% for $GR{M}_{{\mathrm{GCTA}}^{\mathrm{U}}}$.