A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Abstract

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.

Figure 1

Configurations of identity by descent between two diploids. In each subfigure, the two upper dots represent the two alleles of one individual, whereas the other two represent the alleles of the second individual. The lines indicate alleles that are IBD.

Figure 2

Distribution of r̂ estimates between autotetraploids using six different methods (ML, MOM and RI for exact genotypes, ML*, MOM* and RI* for ambiguous genotypes) for four relationships (PO for parent–offspring, FS for full-sibs, HS for half-sibs and UN for unrelated). Each distribution was based on a sample of 200 000 estimates taken from five loci, each segregating for eight alleles with their frequencies drawn from the triangular distribution.

Figure 3

Multilocus RMSE of r̂ between autotetraploids as a function of the number of alleles under a triangular allele frequency distribution. Six estimators were compared, including the polyploid maximum-likelihood estimator (ML, first row), the truncated polyploid method-of-moment estimator (MOM, second row), the truncated Ritland (1996) estimator (RI, third row) and their respective modified versions that support ambiguous genotypes (denoted by an asterisk after the estimator abbreviation). Two kinds of loci were simulated: (1) penta-allelic (n=5, two leftmost columns) and (2) deca-allelic loci (n=10, two rightmost columns). Results were obtained by generating 15 000–100 000 pairs of four relationships including parent–offspring (‘—'), full-sibs (‘– –'), half-sibs (‘– .') and unrelated (‘…') using Monte Carlo simulations.

Figure 4

The minimal number of loci required to obtain a 95% confidence interval±0.05 units of r in half-sibs showed in Figure 3. Three estimators were compared in diploids (‘—'), tetraploids (‘– –'), hexaploids (‘– .') and octoploids (‘…'). Results were obtained by the split-half method and 30 000 Monte Carlo simulations per attempt.

Figure 5

Marker-based estimated relatedness (r̂) as a function of pedigree-based true relatedness (r) in a finite population. Twenty unlinked loci were used in the estimation, each initially segregating with 10 alleles under triangular distribution. Each figure shows 4000 points randomly selected from 402 000 dyads. The top two rows show results for a population without double reduction, the bottom two rows show a population with double reduction. The second and fourth rows include genotype ambiguity. The trend lines for truncated (‘—') and original (‘– –') estimators were obtained by weighted least-squares regression.