Overt and concealed genetic loads revealed by QTL mapping of genotype-dependent viability in the Pacific oyster Crassostrea gigas

Abstract

Understanding the genetic bases of inbreeding depression, heterosis, and genetic load is integral to understanding how genetic diversity is maintained in natural populations. The Pacific oyster Crassostrea gigas, like many long-lived plants, has high fecundity and high early mortality (type-III survivorship), manifesting a large, overt, genetic load; the oyster harbors an even greater concealed genetic load revealed by inbreeding. Here, we map viability QTL (vQTL) in six interrelated F₂ oyster families, using high-density linkage maps of single nucleotide polymorphisms generated by genotyping-by-sequencing (GBS) methods. Altogether, we detect 70 vQTL and provisionally infer 89 causal mutations, 11 to 20 per family. Genetic mortality caused by independent (unlinked) vQTL ranges from 94.2% to 97.8% across families, consistent with previous reports. High-density maps provide better resolution of genetic mechanisms, however. Models of one causal mutation present in both identical-by-descent (IBD) homozygotes and heterozygotes fit genotype frequencies at 37 vQTL; consistent with the mutation-selection balance theory of genetic load, 20 are highly deleterious, completely recessive mutations and 17 are less deleterious, partially dominant mutations. Another 22 vQTL require pairs of recessive or partially dominant causal mutations, half showing selection against recessive mutations linked in repulsion, producing pseudo-overdominance. Only eight vQTL appear to support the overdominance theory of genetic load, with deficiencies of both IBD homozygotes, but at least four of these are likely caused by pseudo-overdominance. Evidence for epistasis is absent. A high mutation rate, random genetic drift, and pseudo-overdominance may explain both the oyster’s extremely high genetic diversity and a high genetic load maintained primarily by mutation-selection balance.

Introduction

The topics of inbreeding depression, heterosis, and genetic load are integral to debates about the factors maintaining genetic diversity in natural populations. Two fundamentally different views of genetic diversity co-exist, the balance and classical models (Dobzhansky 1970). The classical model views genetic diversity as the result, largely, of the balance between mutation and purifying selection against mutations, which are mostly deleterious or detrimental. “The greatest part of the continuing genetic variation observed within a genetically united population must usually have been caused by multiple genes each of which, mutating separately, has given rise to its own small mutation load before the mutants are eliminated by selection… . Of course, this variation is in evolution a very necessary ‘evil’, since it allows natural selection a grasp by which in time of changed needs or opportunities the constitution of the population may be altered adaptively” (Muller and Kaplan 1966, as quoted by Dobzhansky 1970). The balance model, on the other hand, views genetic diversity as the outcome of various forms of balancing selection: “The balance model of the genetic population structure acknowledges genetic diversity as a fundamental phenomenon of nature” (Dobzhansky 1970). The discovery of widespread polymorphism at the molecular level appeared initially to support the balance model but could be explained by the theory that most mutations in DNA were actually selectively neutral or nearly so, rather than harmful or beneficial, giving rise to transient polymorphism undergoing random genetic drift in populations of finite size (Kimura 1983).

Inbreeding depression, the reduction in survival and fertility of offspring produced by related parents, and heterosis, the superior fitness or performance of hybrids between inbred lines or divergent populations, have long been observed in both natural and domesticated populations of animals and plants (Darwin 1876; Crow 1948, 1998; Shull 1948; Charlesworth and Willis 2009). The genetic causes of these phenomena continue to be debated, after a century or more, precisely because they reflect the contention between the classical and balance models of genetic diversity in natural populations. Illuminating which holds sway over variants that do affect fitness, dominance of “normal type” alleles over mostly recessive, deleterious mutations or overdominance, the superior fitness of heterozygotes, is important for fundamental understanding of population genetic structure as well as for progress in applied fields, such as agriculture and conservation (Charlesworth and Willis 2009). Closely allied to the question of what maintains genetic diversity is the concept of genetic load, “the proportion by which the population fitness (or whatever other trait is being considered) is decreased in comparison with an optimum genotype” (Crow 1958). Genetic load can be classified in a number of ways (Wallace 1987), primarily into mutational load—the reduced relative fitness owing to recurrent mutation to deleterious or detrimental alleles, which depends on the mutation rate rather than the degree of detriment (Haldane 1937)—and segregation load—the loss of fitness in sexually reproducing populations owing to segregation of less fit homozygotes maintained by heterotic balancing selection. Dobzhansky (1970) classified genetic load in a way that is particularly relevant to this study into overt genetic load, which is expressed in outcrossing natural populations as the result of segregating partially dominant mutations and overdominant alleles, and concealed genetic load, which becomes evident in inbred progenies or populations, as inbreeding depression caused by homozygosis for recessive mutations or heterotic alleles.

Although a variety of observational and experimental methods has been used to detect and measure inbreeding depression and genetic load (Morton et al. 1956; Wallace 1956; Simmons and Crow 1977; Carr and Dudash 2003; Charlesworth and Willis 2009; Plough 2016), examining segregation of genetic markers in pedigreed families, using quantitative-trait loci (QTL) mapping methods, has several advantages for resolving the genetic causes: (1) integration of information from multiple markers to localize positions in the genome (viability QTL or vQTL), where segregation ratios are statistically significantly distorted from their Mendelian expectations (Luo and Xu 2003; Luo et al. 2005; Hu and Xu 2009); (2) estimation of selection and dominance coefficients at vQTL, aided by identification of identical-by-descent (IBD) homozygotes in F₂ families initiated from partially inbred lines; (3) identification of cases of pseudo-overdominance caused by separate but linked vQTL, at which segregating deleterious mutations in repulsion phase mimic overdominance or heterozygote advantage; and (4) testing for epistasis. Potential disadvantages of vQTL mapping are distinguishing between gametic and zygotic causes of distorted segregation ratios and the absence of a phenotype, other than distortion of genotypic ratios, which prevents typical approaches, such as multiple regression, for demonstrating the statistical independence of linked QTL.

Marker-based approaches have been widely used to study genetic load and the causes of inbreeding depression, especially in plants (Carr and Dudash 2003) and marine animals (Plough 2016). For bivalve mollusks, in particular, this interest was stimulated by widespread observations in experimental crosses of distorted Mendelian segregation ratios for allozyme and DNA polymorphisms (Wada 1975; Wilkins 1976; Beaumont et al. 1983; Gaffney and Scott 1984; Foltz 1986; Thiriot-Quiévreux et al. 1992; Hu et al. 1993; Hu and Foltz 1996; McGoldrick and Hedgecock 1997; Launey 1998; McGoldrick et al. 2000). Early work with oysters revealed that marker distortions were zygotic, not gametic, caused by linkage to genes affecting early viability, that the number of lethal equivalents was potentially high, and that highly deleterious mutations were heritable across generations and likely not components of lethal gene-interactions (Bierne et al. 1998; Launey and Hedgecock 2001; Bucklin 2003). Improvements in linkage maps for the Pacific oyster Crassostrea gigas (Hubert and Hedgecock 2004; Hedgecock et al. 2015) enabled subsequent application of vQTL mapping methods, which confirmed early marker-based results and provide a more detailed understanding of genetic load in this species (Plough and Hedgecock 2011; Plough 2012; Plough et al. 2016). Families typically have from 8 to 15 vQTL, suggesting that each oyster gamete carries 3 to 4 lethal equivalents, among the highest genetic loads reported for an animal (Plough 2016). A minority of vQTL in F₂ families show selection against both parent-line IBD homozygotes, suggesting a portion of genetic load could owe to either overdominance or pseudo-overdominance. The mortality ascribed to genetic inviability, in both inbred and random-bred families, ranges from 85% to 99%, accounting for much of the mortality observed in experimental cultures and according with the type-III survivorship curves characteristic of the life histories of many marine animals. Finally, statistical tests of dependence of genotypic proportions in pairwise comparisons of markers or vQTL show no evidence for epistasis. This high genetic load, accounting for early mortality in a highly fecund species, was predicted by G. C. Williams’s (1975) “Elm-Oyster” model, drawing attention to an interesting parallel between the population genetics of plants, particularly conifers, and bivalve mollusks (Plough 2016).

In this study, we extend this QTL-mapping approach with six interrelated F₂ families of Pacific oysters, using high-density linkage maps, which were made using genotyping-by-sequencing (GBS) methods (Yin et al. 2020) and which are aligned, here, with a chromosome-level assembly of the C. gigas genome (Qi et al. 2021). While aiming to confirm features of genetic load that have been previously reported for the Pacific oyster, we seek to provide a more thorough, systematic, genome-wide examination of vQTL and their genetic bases, with the goal of shedding light on the relative importance of dominance, overdominance, and epistasis in maintaining genetic diversity in this highly fecund marine animal. The estimates of mortality derived from vQTL mapping are, again, high and consistent with high early mortality and type-III survivorship in natural populations.

Materials and methods

Biological materials

Our study was based on six interrelated F₂ families (sire × dam), 23 × 31, 23 × 40, 31 × 23, 40 × 92, 47 × 92, and 92 × 40. Each F₂ family was derived from an intercross of full-sib F₁ hybrids, which, in turn, were produced by crosses, in 2009, of partially inbred lines 23, 31, 40, 47, and 92. The pedigrees are shown in Figure  1, and rearing information is described in Yin et al. (2020). We made these F₂ families in May and June of 2011; in June and July of 2012, we tagged a total of 1514 individuals with Floy FTF-69 oval, numbered vinyl tag and reared them through the summer of 2012 in Thorndyke Bay, WA, USA.

Figure 1.

Pedigrees of six, interrelated families.

Data collection

The six F₂ families were harvested in September or October of 2012 and shipped to the University of Southern California, where adductor muscle tissue was dissected and preserved in 70% ethanol for later DNA extraction. Sixty-one of the tagged oysters (4%) died between planting and harvest, indicating that major mortality did not occur during the second summer post fertilization. We determined genotypes of the 12, F₁ hybrid parents and progeny from the six F₂ families through GBS and bioinformatics analyses guided by Genome Analysis Toolkit (GATK, https://www.broadinstitute.org/gatk/) (Bentley et al. 2008; Elshire et al. 2011). We remapped all SNPs called with the previously released C. gigas genome (Zhang et al. 2012; GenBank assembly accession: GCA_000297895.1; hereafter, the v9 genome assembly) to the recently assembled, chromosome-level assembly (Qi et al. 2021; GenBank assembly accession: GCA_011032805.1; hereafter, the Chr_v1 genome assembly). Details on GBS, GATK analysis, and SNP remapping are described in Yin et al. (2020). Finally, we conducted vQTL analysis with the 12 parent oysters from six F₁ families and 1041 offspring from six F₂ families (i.e., 23 × 31: n = 208; 23 × 40: n = 181; 31 × 23: n = 142; 40 × 92: n = 258; 47 × 92: n = 127; 92 × 40: n = 125).

Data analyses

Analysis of Mendelian segregation ratios

Since the grandparents of the families in this study were not completely inbred, our F₂ families were produced by three possible cross types, ab × ab, aa × ab, and ab × aa. We tested whether progeny genotype proportions deviate from an expected Mendelian segregation ratio, using goodness-of-fit chi-square tests with standard, α = 0.05, significance threshold as well as the conservative, α/n Bonferroni threshold for n simultaneous tests for each cross type. Since cross types aa × ab and ab × aa had the same expected Mendelian segregation ratio, they were taken as one cross type in the adjustment of significance thresholds. Numbers of markers showing Mendelian segregation distortion (i.e., distorted markers) at α = 0.05 and at the α level adjusted via Bonferroni correction for the number of markers within each cross type are reported. Since some markers were removed from linkage maps (see below), we only conducted Mendelian segregation distortion analysis on markers that were kept for vQTL mapping.

Viability QTL mapping

We constructed high-density linkage maps for the six F₂ families and obtained the phase of markers on parental haplotypes using JoinMap 4.1 according to methods and for reasons given in Yin et al. (2020). Since Yin et al. (2020) found good correspondence between linkage maps and the Chr_v1 C. gigas genome assembly, we standardized the six maps by converting genomic positions of SNPs to map positions, using recombination rates appropriate to each chromosome in each family. We first calculated least-squares means for family × chromosome recombination rates (from raw data generated by MareyMap, Rezvoy et al. 2007; see Yin et al. 2020) and then categorized these means into four groups: (1) within the 95% confidence limit (CL) of the grand mean (n = 34; mean, 1.105 cM/Mbp), (2) significantly below the lower 95% CL (n = 12; mean, 0.704 cM/Mbp), (3) significantly above the upper 95% confidence limit (UCL) but less than 2 cM/Mbp (n = 8; mean, 1.581 cM/Mbp), and (4) significantly above the UCL but greater than 2 cM/Mbp (n = 6; mean, 2.262 cM/Mb), using a post-hoc analysis of means, followed by a partitioning of the UCL group according to P-values for differences between means, as implemented in SAS (PROC GLM, version 9.4). We then calculated map positions of SNPs by dividing their physical positions on the Chr_v1 genome assembly by the mean recombination rate for their family × chromosome group.

With the reconstructed linkage maps, we mapped vQTL based on a viability QTL model developed by Luo and Xu (2003), which is implemented in PROC QTL (Hu and Xu 2009), a user-defined procedure in SAS (version 9.4). Inputs for vQTL mapping included phased parent genotypes, progeny genotypes, and linkage maps. In running PROC QTL, we encountered “Floating Point Zero Divide” errors, which caused the program to stop and were likely caused by the small spacing between markers (Z. Hu, University of California-Riverside Department of Botany and Plant Sciences, personal communication), and we obtained, in all six families, negative likelihood ratio test (LRT) values, which were likely driven by extreme distortions of Mendelian segregation ratios. We rectified these errors by removing markers at the point in the data where the error was generated or increasing the convergence criterion, MAXERR, from e⁻⁸ to up to 1. Since there is no phenotype for viability, PROC QTL generates a random dummy variable for each individual as the trait for vQTL mapping. Genomes were scanned in 1-cM increments using the maximum likelihood method with distortion analysis. Since original parent lines were not completely inbred, we set the mating type of each F₂ family to the four-way cross, AB × CD. An LRT statistic and estimated proportions of progeny genotypes (i.e., AC, AD, BC, and BD) were generated for each increment on the genome. We approximated genomewise significance thresholds, at the α = 0.05 level, by the method of Piepho (2001).

Identifying “parent-line” and “hybrid” genotypes in the F₂ families

With the phase information for parent genotypes, we determined grandparental haplotypes to establish the possibilities for identity-by-descent (IBD) in F₂ progeny. Since we do not have genotypic data on the grandparental inbred lines, we calculated genetic similarity among the four phased F₁ parent haplotypes (i.e., A, B, C, and D) as the number of loci with identical alleles divided by the total number of loci. The four phased F₁ haplotypes should comprise two pairs of haplotypes derived from the two inbred grandparents (either AC, BD or AD, BC), with the haplotypes derived from one grandparent being more similar to each other than to either of the haplotypes derived from the other grandparent. We tested the three-way interaction of the numbers of markers with identical and nonidentical alleles across the four combinations of parental haplotypes in a 2 × 2 × 2 log-linear analysis in SAS PROC CATMOD (version 9.4, SAS Institute Inc., Cary, NC, USA). Because many tables contained a large percentage of cells with zeros or fewer than five observations, we found it necessary to add 0.5 to all cells to allow estimation of the interaction term; for tables that ran without this addition, test results were the same.

We extended this reasoning to try to determine which phased haplotypes in different but related F₂ families (e.g., 40 × 92, 47 × 92, 92 × 40) might have originated from a shared inbred grandparent line. Knowing the grandparental origin of phased haplotypes might allow us to assign a mutation affecting viability back to the inbred grandparent line of origin. We calculated and compared genetic similarity at shared markers between pairs of phased haplotypes (i.e., A₁ vs. A₂, B₂, C₂, D₂; B₁ vs. A₂, B₂, C₂, D₂, and so on, in which subscripts denote different but related F₂ families).

Identifying separate vQTL

In many instances, multiple major and minor peaks were evident on the LRT profiles for chromosomes. As viability is not an explicit phenotype, typical methods for resolving separate QTL, such as multiple regression, cannot be used to identify statistically independent vQTL. Thus, we first did pairwise 2 × 4 contingency chi-square tests between estimated genotype frequencies at all positions, adjusting significance for the false discovery rate (FDR; Benjamini and Hochberg 1995), to visualize underlying patterns in genotype frequencies. Then, we fit genetic models to multiple peaks in order to evaluate similarity and differences in the underlying genetic causes of distortions in genotypic frequencies.

We used the approach of Hedrick and Muona (1990), as modified by Launey and Hedgecock (2001), to estimate parameters of genetic models fit to genotypic frequencies at vQTL by maximum likelihood methods. The primary model was a recessive or partially dominant deleterious mutation affecting viability with one parental genotype being an IBD homozygous. Since we have the genotypic frequencies at putative vQTL, we need not estimate the recombination distance, c, between a marker and the mutation; we need only estimate the selection coefficient, s, and the dominance, h, to maximize the LOD score for the comparison of this model to a neutral, 1:1:1:1 Mendelian model. The genotypic proportions, P_i, assuming that the IBD mutation is on the A and C chromosomes, are:

$$P_{AC}=\left(1-s\right)/\left(4-s\left(2h+1\right)\right)$$

$$P_{AD}=P_{BC}=\left(1-hs\right)/(4-s(2h+1\left)\right)$$

$$P_{BD}=1/(4-s(2h+1\left)\right)$$

The LOD score is calculated as $z=\sum N_i{\log }_{10}\left(P_i/P_i^{\mathrm{\varnothing }}\right)$, where $N_i$ is the observed proportion of genotype i and $P_i$ and $P_i^{\mathrm{\varnothing }}$ are the proportions expected under the selection model and the Mendelian model, respectively. We then calculated the goodness-of-fit chi-square between observed genotype proportions and those expected under the genetic model, with one degree of freedom.

While this model fit genotypic proportions at most putative vQTL quite well, it did not fit a minority of cases, which yielded significant goodness-of-fit tests and which, therefore, required different explanations. A majority of these cases appeared to fit a model of selection against two recessive IBD deleterious mutations linked to each of the parental genotypes. This model requires two selection coefficients and often a recombination distance, since one mutation may not be located at the focal vQTL. Genotypic proportions in this model of two recessive deleterious mutations—one IBD homozygous on AC, the other IBD homozygous on BD at a recombination of distance, c, from the vQTL—are:

$$P_{AC}=\left(1-s_1\right)/\left(4-s_1-s_2{\left(1-c\right)}^2\right)$$

$$P_{AD}=P_{BC}=1/(4-s_1-s_2{(1-c)}^2)$$

$$P_{BD}=1-s_2{\left(1-c\right)}^2/(4-s_1-s_2{\left(1-c\right)}^2).$$

LOD scores for these models were calculated, as above, but with genotypic proportions from the first model of selection against a single, recessive, deleterious mutation substituted for the neutral, Mendelian proportions, $P_i^{\mathrm{\varnothing }}$. Alternative models were required for other cases; the most common of these models were mutations linked to one haplotype with partial dominance, often in combination with selection against an IBD homozygote on the other parental chromosome. Because each goodness-of-fit test has only three degrees of freedom, it is not possible to test models with three or more parameters. Nevertheless, maximum-likelihood estimates of parameters provide hypotheses about the number of mutations underlying vQTL and their mode of action on viability. In the case of the model of two recessive mutations linked to each of the parental haplotypes, the recombinational distance of the second mutation from the focal vQTL, c, can be compared to the map distance from the focal vQTL to another vQTL, where the second mutation has maximal effect.

Following the fitting of genetic models, we re-visited the identification of separate vQTL, combining the results of pairwise contingency chi-square tests with the genetic models to identify a minimum number of vQTL to explain LRT profiles. In many cases, adjacent minor peaks in the LRT profile were explained by nearly identical genetic models, leading us to reject many putative vQTL.

Genetic mortality, shared vQTL, epistasis, and candidate genes

Following Plough and Hedgecock (2011), we calculated average relative survival at each vQTL as $\overline{S}=1/{4w}_{\max }$, where $w_{\mathit{max}}$ is the relative frequency of the most abundant genotype. This estimate of survival will be less than one in finite samples, even when there is no selection and genotype frequencies conform to Mendelian ratios. To adjust for such sampling error, we used multinomial modeling in SAS/IML 14.2 (SAS Institute Inc., Cary, NC, USA) to generate 1000 genotype arrays with ratios of 1:1:1:1, assuming the sample size for each family. The median of 1000 maximum values, divided by family sample size, was used to represent $w_{\mathrm{m}ax\mathrm{\varnothing }}$, the expected frequency of the most abundant genotype with no selection. Adjusted survival for each QTL was then calculated as ${\overline{S}}_{\mathrm{adj}}=1/(4{(w}_{\max }-(w_{\max \mathrm{\varnothing }}-0.25\left)\right))$, following Plough and Hedgecock (2011).

We identified vQTL shared by related families by first checking whether confidence limits defined by genomic positions corresponding to a drop in LRT of at least 4.6 on either side of both vQTL peaks overlapped. If so, we then examined whether the genetic models for these vQTL were the same and whether the two mutations originated from the same inbred parent line.

To test whether epistasis between unlinked vQTL located on different chromosomes may at least partially account for genetic mortality, we conducted contingency chi-square tests on genotype associations between all pairs of markers within each family (Plough and Hedgecock 2011; Plough et al. 2016). We pooled comparisons by segregation types and controlled the FDR by the method of Benjamini and Hochberg (1995).

We identified candidate genes with mutations causing early mortality and their positions in the chromosome-level genome assembly, Chr_v1. Focusing on vQTL peaks with the narrowest confidence intervals, we took all genes in those genomic regions as candidates for genetic mortality. We retrieved candidate genes using BEDTools/2.29.0, determined unique genes by eliminating redundant gene-name identifiers regardless of species, and examined them for expression in early life stages (Supplementary Table S14 in Zhang et al. 2012), when most genotype-dependent mortality is thought to occur (Launey and Hedgecock 2001; Plough and Hedgecock 2011).

Results

Distortions of Mendelian segregation ratios

We scored from 429 to 657 SNP markers in each of six F₂ families (Table  1). From 56.7% to 91.9% of the markers in a family are distorted at the α = 0.05 level of significance, and 27% to 56.6% are distorted after adjusting for multiple testing. Mating type ab × ab accounts for the majority of segregation patterns in all families except 23 × 40. Likewise, at both the α = 0.05 and the adjusted α-level, the proportion of markers distorted is higher for mating type ab × ab than for either mating type aa × ab or ab × aa.

Table 1.

Segregation results for SNP markers in six, F₂ families

Family	Cross type	No. scored markers	No. distorted markers	% distorted markers
23 × 31	aa × ab	29	16 (2)	55.2% (6.9%)a
	ab × aa	15	4 (1)	26.7% (6.7%)
	ab × ab	613	584 (260)	95.3% (42.4%)
	Total	657	604 (263)	91.9% (40%)
23 × 40	aa × ab	85	49 (34)	57.6% (40%)
	ab × aa	149	120 (71)	80.5% (47.7%)
	ab × ab	195	176 (138)	90.3% (70.8%)
	Total	429	345 (243)	80.4% (56.6%)
31 × 23	aa × ab	53	31 (13)	58.5% (24.5%)
	ab × aa	53	27 (8)	50.9% (15.1%)
	ab × ab	361	269 (137)	74.5% (38%)
	Total	467	327 (158)	70% (33.8%)
40 × 92	aa × ab	67	27 (12)	40.3% (17.9%)
	ab × aa	36	17 (0)	47.2% (0%)
	ab × ab	394	378 (246)	95.9% (62.4%)
	Total	497	422 (258)	84.9% (51.9%)
47 × 92	aa × ab	14	0 (0)	0% (0%)
	ab × aa	9	1 (0)	11.1% (0%)
	ab × ab	412	332 (183)	80.6% (44.4%)
	Total	435	333 (183)	76.6% (42.1%)
92 × 40	aa × ab	51	18 (4)	35.3% (7.8%)
	ab × aa	58	18 (4)	31% (6.9%)
	ab × ab	369	235 (121)	63.7% (32.8%)
	Total	478	271 (129)	56.7% (27%)

^aNumbers in parentheses are test results adjusted for simultaneous multiple testing at Bonferroni adjusted-α level.

Mapping of viability QTL

The LRT profiles produced by PROC QTL reveal widespread vQTL across the genomes of the six F₂ families (Figure  2), consistent with the pervasive distortions of Mendelian segregation ratios at individual markers. From seven to nine of the 10 chromosomes in each family have peaks of LRT scores above their respective genomewise thresholds of significance (slightly greater than an LRT of 20 in all families), indicating the presence of one or more vQTL per chromosome. LRT scores range as high as 262 with a median of 67, reflecting very strong distortions of Mendelian segregation ratios. LRT profiles comprise both very sharp, tall, isolated peaks, such as those on chromosomes 1, 3, and 8 of 23 × 31, and broader, often lower peaks, such as those on chromosomes 2, 3, and 5 of 23 × 40.

Figure 2.

Viability QTL in six, F₂ families. Genomic position (Mbp) is the cumulative position across chromosomes on the C. gigas genome in Mbp. The symbol “×” and numerals indicate the locations of 70 separate vQTL.

We detect three instances—in the LRT profiles for chromosomes 6, 8, and 10 of 23 × 31, 47 × 92, and 92 × 40, respectively—in which LRT peaks appear to have been split by the alignment of vQTL maps with the chromosome-level, genome assembly used for Figure  2. In these cases, single peaks based on the original linkage maps become separate, though nearby peaks, of equal height and with essentially identical genetic models. These cases suggest structural differences between the linkage maps for these families and the reference genome, and we have counted each of these cases as a single vQTL.

“Parent-line” and “Hybrid” genotypes in the F₂ families

In F₂ families, individuals that are homozygous IBD for a recessive viability mutation show reduced survival compared to other genotypes (Launey and Hedgecock 2001; Plough and Hedgecock 2011). The two haplotypes originating from the same partially inbred grandparent should be more similar to each other than to those from the other grandparent. Therefore, to shed light on which F₂ genotypes might possibly be IBD homozygous, we infer that the F₁ haplotypes with the highest genetic similarity come from the same inbred grandparent line. Chromosome 1 in family 23 × 31 illustrates the dependence of numbers of markers with identical or nonidentical alleles on haplotype combination (Table  2), with AC and BD being implicated as the parent-line genotypes. Genetic similarity depends on the pair of phased F₁ haplotypes being compared in 57 out of 60 contingency tables (i.e., ten chromosomes in six F₂ families; Supplementary Table S1). Apart from nonsignificant tests for chromosomes 3, 8, and 9 in 23 × 40, the parent-line genotype determined for chromosome 1 in 92 × 40, AD, conflicts with the observed pattern of viability at vQTL1 in this family (Table  3), in which AC is the least frequent genotype. We are, thus, able to identify parent-line genotypes and, therefore, the possibility of IBD homozygosity for putative vQTL for 56 of the 60 chromosomes screened. Distributions of genetic similarity, as a proportion, for the two haplotypes in parent-line and in hybrid genotypes are nearly nonoverlapping (Figure  3), with a mode of one for parent-line and a mode of zero for hybrid haplotype combinations, suggesting that haplotype similarity is a reliable guide to provenance. Extending this approach to similarity of phased haplotypes between related families, we successfully determined the origin of parent-line haplotypes for chromosome 6 in all six families, for chromosome 10 in 23 × 31, 23 × 40, and 31 × 23, for chromosome 9 in 40 × 92 and 47 × 92, and for chromosome 3 in 92 × 40 (Supplementary Table S2). This enables us to attribute mutations to the inbred parent lines from which they were inherited in these cases and to evaluate whether vQTL at similar genomic positions in different families might be shared by descent.

Table 2.

Chi-square test of the three-way interaction in a 2 × 2 × 2 contingency table of numbers of markers with identical or nonidentical alleles across four combinations of parent haplotypes for chromosome 1 in family 23 × 31

Sire haplotype	Identical in dam		Nonidentical in dam		χ2	Probability
	C	D	C	D
Aa	42	0	0	42
B	2	40	40	2	42.68	<0.0001

^a A and B (C and D) stand for two phased haplotypes from the F₁ paternal (maternal) parent.

Table 3.

Viability QTL in six, F₂ families

Family	Viability locus	Chra	Positionb (Mbp)	LRT	Markerc	Genotype frequencyd				# mute	$\overline{\mathit{S}}$ adj f
						AC	AD	BC	BD
23 × 31	vQTL1	1	51.89	123.46	chr01-51886430	0.00	0.35	0.38	0.27	1	0.7247
23 × 31	vQTL2	2	86.96	21.17	chr02-8043532	0.35	0.20	0.15	0.30	2	0.7821
23 × 31	vQTL3	3	173.83	124.63	chr03-33136167	0.33	0.40	0.28	0.00	1	0.6871
23 × 31	vQTL4	3	193.05	42.54	chr03-52356629	0.32	0.31	0.29	0.08	1	0.8666
23 × 31	vQTL5	5	306.48	49.18		0.05	0.26	0.42	0.26	2	0.6453
23 × 31	vQTL6	6	354.55	148.93	chr06-27173929	0.17	0.44	0.39	0.00	2	0.6118
23 × 31	vQTL7	7	411.44	27.69	chr07-27219004	0.11	0.29	0.29	0.31	1	0.9123
23 × 31	vQTL8	8	485.35	107.33		0.37	0.00	0.33	0.30	1	0.7381
23 × 31	vQTL9	9	547.60	21.78	chr09-54462900	0.22	0.38	0.15	0.24	1	0.7179
23 × 31	vQTL10	10	558.13	117.92		0.00	0.25	0.35	0.40	1	0.6830
						# mutations per family				13
						Genotype-dependent mortality					0.9492
23 × 40	vQTL1	2	92.28	66.23	chr02-13369610	0.35	0.39	0.04	0.22	1	0.7043
23 × 40	vQTL2	3	193.50	40.74	chr03-52804373	0.23	0.43	0.10	0.24	1	0.6360
23 × 40	vQTL3	5	302.25	147.89	chr05-35833008	0.57	0.25	0.18	0.00	1	0.4706
23 × 40	vQTL4	6	352.94	101.82		0.27	0.39	0.34	0.00	1	0.7120
23 × 40	vQTL5	6	377.67	51.31	chr06-50294215	0.14	0.43	0.32	0.11	1	0.6307
23 × 40	vQTL6	7	401.64	111.85	chr07-17418104	0.36	0.00	0.40	0.24	1	0.6855
23 × 40	vQTL7	7	424.65	52.54	chr07-40424487	0.32	0.05	0.30	0.33	1	0.8548
23 × 40	vQTL8	8	468.94	21.82	chr08-29532019	0.35	0.32	0.20	0.14	1	0.8057
23 × 40	vQTL9	9	524.28	29.26	chr09-31143900	0.16	0.18	0.25	0.42	1	0.6492
23 × 40	vQTL10	10	570.42	27.74		0.13	0.31	0.18	0.38	1	0.7235
23 × 40	vQTL11	10	578.25	22.35		0.18	0.25	0.16	0.41	1	0.6651
						# mutations per family				11
						Genotype-dependent mortality					0.9611
31 × 23	vQTL1	1	31.80	85.52	chr01-31799445	0.23	0.35	0.42	0.00	1	0.6594
31 × 23	vQTL2	1	52.43	36.21	chr01-52425370	0.18	0.36	0.37	0.08	1	0.7486
31 × 23	vQTL3	1	75.50	80.69	chr01-75496894	0.28	0.42	0.31	0.00	1	0.6598
31 × 23	vQTL4	5	286.45	80.35		0.01	0.20	0.36	0.43	1	0.6329
31 × 23	vQTL5	5	308.12	31.95	chr05-41705024	0.08	0.16	0.46	0.30	1	0.5993
31 × 23	vQTL6	6	352.17	100.82		0.27	0.28	0.45	0.00	2	0.6039
31 × 23	vQTL7	6	379.26	29.20		0.38	0.23	0.30	0.09	1	0.7420
31 × 23	vQTL8	7	409.69	21.01		0.24	0.41	0.11	0.24	1	0.6677
31 × 23	vQTL9	8	447.56	29.23	chr08-8147273	0.27	0.32	0.33	0.08	1	0.8729
31 × 23	vQTL10	8	485.77	49.53	chr08-46360488	0.30	0.32	0.34	0.04	1	0.8212
31 × 23	vQTL11	9	496.30	28.35	chr09-3160289	0.21	0.30	0.39	0.10	1	0.7141
31 × 23	vQTL12	9	518.29	87.25		0.16	0.39	0.45	0.00	1	0.6026
31 × 23	vQTL13	9	531.17	117.01		0.00	0.50	0.38	0.11	1	0.5382
31 × 23	vQTL14	10	585.01	76.99	chr10-36770061	0.00	0.35	0.35	0.30	1	0.7978
						# mutations per family				15
						Genotype-dependent mortality					0.9509
40 × 92	vQTL1	1	17.98	112.15	chr01-17982413	0.28	0.32	0.38	0.02	1	0.7064
40 × 92	vQTL2	1	67.71	141.40	chr01-67707426	0.14	0.46	0.38	0.02	2	0.5796
40 × 92	vQTL3	2	100.27	167.15	chr02-21356899	0.00	0.29	0.36	0.34	1	0.7545
40 × 92	vQTL4	2	121.99	167.76	chr02-43073437	0.00	0.20	0.46	0.34	2	0.5809
40 × 92	vQTL5	5	268.64	149.97	chr05-2222854	0.00	0.38	0.29	0.33	1	0.7145
40 × 92	vQTL6	5	303.94	89.59	chr05-37524497	0.04	0.32	0.41	0.23	2	0.6598
40 × 92	vQTL7	6	333.14	97.79	chr06-5763042	0.31	0.03	0.37	0.29	1	0.7289
40 × 92	vQTL8	6	360.18	40.71	chr06-32807501	0.18	0.14	0.26	0.41	2	0.6526
40 × 92	vQTL9	7	394.03	40.68	chr07-9802186	0.21	0.42	0.22	0.15	2	0.6347
40 × 92	vQTL10	7	427.27	34.56	chr07-43048118	0.33	0.35	0.20	0.12	1	0.7764
40 × 92	vQTL11	9	511.23	66.90	chr09-18089122	0.29	0.36	0.06	0.28	1	0.7457
40 × 92	vQTL12	9	521.80	54.06		0.40	0.28	0.06	0.27	2	0.6793
40 × 92	vQTL13	10	567.34	261.96	chr10-19100499	0.02	0.06	0.73	0.18	2	0.3543
						# mutations per family				20
						Genotype-dependent mortality					0.9706
47 × 92	vQTL1	1	30.98	93.05	chr01-30975265	0.00	0.55	0.26	0.18	2	0.4903
47 × 92	vQTL2	1	74.26	79.89	chr01-74261613	0.01	0.55	0.15	0.30	2	0.4944
47 × 92	vQTL3	2	104.07	30.09	chr02-25161785	0.13	0.41	0.33	0.13	1	0.6835
47 × 92	vQTL4	2	111.94	36.49	chr02-33030032	0.15	0.38	0.38	0.09	1	0.7420
47 × 92	vQTL5	4	264.99	84.53	chr04-61217776	0.22	0.39	0.39	0.00	2	0.7174
47 × 92	vQTL6	5	270.37	25.54	chr05-3948786	0.15	0.36	0.36	0.13	1	0.7813
47 × 92	vQTL7	5	304.39	79.91	chr05-37974398	0.23	0.39	0.39	0.00	1	0.7239
47 × 92	vQTL8	6	339.03	90.85	chr06-11658772	0.08	0.44	0.44	0.03	1	0.6206
47 × 92	vQTL9	6	356.73	85.06	chr06-29357983	0.00	0.40	0.40	0.21	1	0.7033
47 × 92	vQTL10	7	411.09	41.80		0.26	0.25	0.45	0.05	2	0.6142
47 × 92	vQTL11	8	481.47	72.94	chr08-42064424	0.34	0.33	0.33	0.00	1	0.8318
47 × 92	vQTL12	9	507.42	31.70		0.06	0.33	0.33	0.28	1	0.8651
47 × 92	vQTL13	10	585.01	82.26	chr10-36770094	0.19	0.41	0.41	0.00	2	0.6855
						# mutations per family				18
						Genotype-dependent mortality					0.9645
92 × 40	vQTL1	1	21.19	29.60	chr01-21190392	0.09	0.44	0.23	0.23	2	0.6325
92 × 40	vQTL2	2	81.67	25.36	chr02-2754564	0.35	0.08	0.27	0.30	1	0.8243
92 × 40	vQTL3	3	168.71	41.24		0.29	0.37	0.03	0.31	1	0.7661
92 × 40	vQTL4	5	299.73	136.29		0.00	0.50	0.50	0.00	2	0.5522
92 × 40	vQTL5	6	350.69	73.04	chr06-23319107	0.00	0.37	0.31	0.32	1	0.7789
92 × 40	vQTL6	6	382.97	20.60	chr06-55590369	0.10	0.32	0.33	0.26	1	0.8766
92 × 40	vQTL7	7	410.89	35.86	chr07-26667613	0.18	0.35	0.39	0.08	2	0.7223
92 × 40	vQTL8	8	488.66	171.69	chr08-49251530	0.59	0.41	0.00	0.00	1	0.4586
92 × 40	vQTL9	10	579.01	55.58	chr10-30773245	0.24	0.42	0.32	0.02	1	0.6764
						# mutations per family				12
						Genotype-dependent mortality					0.9615

^aChr stands for chromosome.

^bPosition stands for genomic position in Mbp.

^cMarkers are only shown for vQTL at which a marker is located at the position with the highest LRT.

^dGenotype frequency is estimated by PROC QTL for AC, AD, BC, and BD.

^e# mut stands for the number of mutations.

^f $\overline{S}$ _adj stands for the adjusted survival for each vQTL. Bold numbers are $\overline{S}$_adj for independent, unlinked vQTL; for linked vQTL (<50 cM apart), we choose the adjusted survival of the one with the highest LRT to calculate genotype-dependent mortality.

Figure 3.

Distributions of genetic similarity for parent-line, hybrid, and undetermined genotypes. Categories are determined by results of contingency chi-square tests (Supplementary Table S1).

Separating individual vQTL

LRT profiles for many chromosomes have numerous major and minor peaks above the genomewise threshold for significance (Figure  2), so identifying the number of independent vQTL is a nontrivial task, especially when relative viability is not amenable to typical methods for evaluating statistical dependence, such as multiple regression. To resolve independent vQTL, we first used contingency chi-square tests of genotype frequencies between all pairs of positions on a chromosome to reveal broad and statistically conservative patterns of variation (Supplementary Figure S1). We then fit genetic models to all putative peaks along each chromosome and compared their parameters.

We illustrate the approach with reference to chromosomes 1 and 6 of 31 × 23 (Figure  2, Supplementary Figure S1 and Table S2). There are potentially three LRT peaks on chromosome 1 in this family, the last being a bicuspid peak with two points of LRTs near 80 separated by a shallow valley with LRTs above 70 (Figure  2). Contingency chi-square test results (Supplementary Figure S1A) show that the chromosome is broken up into three alternating regions, in which genotypic proportions first conform to Mendelian ratios (M) and then are significantly distorted near LRT peaks (P), with the overall pattern being M₁/P₁/M₂/P₂/M₃/P₃ (cf. Figure  2 with Supplementary Figure S1A). Positions in region P₃, which encompasses the bicuspid peak, have homogeneous genotypic frequencies among themselves and in comparisons to positions under region P₁. These results suggest three, independent vQTL. At both P₁ and P₃, there appears to have been strong selection against a recessive IBD mutation on the BD parent-line chromosome, which explains the homogeneity of their genotypic frequencies; however, these mutations are separated by 70 cM and intervening regions, M₂/P₂/M₃, and appear, therefore, to be independent (vQTL1 and vQTL3, Supplementary Table S2). The intervening peak, P₂, has a genetic model suggesting a third vQTL, with distortions owing, evidently, to linkage with the recessive IBD mutation under P₃, as well as to weaker selection, at the P₂ position, against a recessive, IBD mutation on the AC parental chromosome. Altogether, on this chromosome, we count three vQTL, each with an independent mutation (Supplementary Table S2).

The LRT profile for chromosome 6 of 31 × 23 shows a very tall peak (LRT = 100) with broad, above threshold-level shoulders, extending over nearly the entire chromosome (Figure  2). A small putative peak at genome position 380 Mbp (LRT = 29) is not separated from the main peak by any position falling below the genomewise threshold LRT. Contingency chi-square test results clearly separate these two peaks on the basis of their genotypic proportions (Supplementary Figure S1B). Their genetic models, moreover, are quite distinct. At the tallest peak (vQTL6, Supplementary Table S2), a highly deleterious, IBD recessive mutation linked to the BD parent-line chromosome acts in concert with a partially dominant deleterious mutation on the A chromosome; these two mutations together cause the massive distortions of Mendelian ratios reflected by the LRT of 100. At the lesser peak (vQTL7, Supplementary Table S2), distortions of genotypic proportions are also attributable to a mutation linked to BD, but one which is less deleterious, partially dominant, and thus seemingly independent from the other distant mutation on this parental haplotype.

On several chromosomes, such as on chromosome 9 in 31 × 23 (Figure  4), broad peaks in LRT scores, giving rise to correspondingly broad regions of statistically homogeneous but non-Mendelian genotype frequencies, are evidently the result of selection against two, independent, recessive viability mutations in replusion phase. In Figure  4, the peak in the LRT profile is at genomic position 526, where distortion from Mendelian ratios is maximized, between the positions of minimum (zero) frequency in parental genotypes AC and BD, at 531 and 518, respectively, where the viability mutations are presumably located.

Figure 4.

Viability QTL on chromosome 9 in family 31 × 23. The maximum in LRT scores (heavy solid line) occurs between the genomic positions of maximum selection against (minimum frequencies of) parental genotypes AC (long dash and dot line) and BD (dotted line), which have Mendelian expected frequencies of 0.25.

Altogether, in this fashion, we resolve 70 vQTL peaks (Table  3; marked by “×” and numbered in Figure  2). The vQTL are not distributed evenly among chromosomes (F_9,50 = 2.74; P = 0.011), but chromosome 4 accounts for all the variation, having a vQTL in only one family, 47 × 92. The genomic positions of vQTL are, for the majority of cases, not consistent across the six families (Table  3 and Figure  2). Still, similarity in the location of six pairs of vQTL across related families (i.e., vQTL1 in 23 × 31 and vQTL2 in 31 × 23; vQTL7 in 23 × 31 and vQTL8 in 31 × 23; vQTL6 in 23 × 40 and vQTL8 in 31 × 23; vQTL8 in 23 × 31 and vQTL10 in 31 × 23; vQTL3 in 40 × 92 and vQTL3 in 47 × 92; vQTL5 in 40 × 92 and vQTL6 in 47 × 92; vQTL11 in 40 × 92 and vQTL12 in 47 × 92) suggests some shared inheritance of mutations present in a common grandparent.

Genetic models, number of deleterious mutations, epistasis, and candidate genes

We sequentially fit genetic models by maximum likelihood to genotypic proportions at all 70 vQTL, starting with the simple model of a single recessive or partially dominant deleterious mutation affecting viability that is co-inherited by the F₁ parents from one of the inbred grandparent lines. This model, which has two estimated parameters, the selection coefficient, s, and the dominance coefficient, h, fits 40 of the 70 vQTL, with goodness-of-fit, chi-square probabilities greater than or equal to 0.05 (Supplementary Table S2). Two of these vQTL (vQTL5 and vQTL7 in 47 × 92), with goodness-of-fit probabilities between 0.05 and 0.1, are fit significantly better by a model of selection against two, independent, recessive mutations (Supplementary Table S2); vQTL4 in 23 × 40, which fits the simple model but clearly has small residual effects from selection against another parent-line genotype at vQTL5, is not regarded as an isolated case. Of the 37 vQTL fit by the single-mutation model, 20 are fit by a model with zero dominance—symbolized by a sparkline,, showing frequencies for AC, AD, BC and BD, where {AC, BD} are parent-line and AC is linked to an IBD recessive deleterious mutation—and 17 require dominance ranging from 0.1 to 0.89—symbolized by, where the mutation on AC is partially dominant, reducing the frequencies of AD and BC. For models with no dominance, s ranges from 0.67 to 1.0, with an average of 0.9; for models with dominance, s ranges from 0.57 to 1.0, with an average of 0.79 (Supplementary Table S2). There is a significant negative relationship between selection and dominance coefficients for viability mutations (linear regression, adjusted r² = 0.27, P = 0.001; Figure  5). We count all vQTL fit by this first model as evidence for the inheritance of a single recessive or partially dominant mutation with deleterious effects on viability.

Figure 5.

Distribution of selection and dominance coefficients in genetic models fit to genotypic frequencies at 37 vQTL; diameter of circle is proportional to the LOD score of the genetic model.

Thirty-three vQTL have genotypic proportions that are not fit well by the simple model of a single recessive deleterious mutation affecting viability (Supplementary Table S2; P ≤ 0.05 in the 1 d.f. goodness-of-fit chi-square test plus the three exceptions mentioned above). We attempted to fit alternative models to these cases, recognizing that most of these alternative models required three parameters, leaving no degrees of freedom for testing goodness-of-fit to observed genotypic proportions. Nevertheless, we take models with LOD scores greater than 1.3 over the simple model as reasonable support for assuming two mutations at or near each of the vQTL fit by these more complex models.

The most common alternative model, accounting for 19 of 70 genetic models (Supplementary Table S2), is one with two recessive IBD mutations, as symbolized by the sparkline,, in which parent-line genotypes AC and BD are each linked to IBD recessive deleterious mutations. Such a model is also illustrated by Figure  4 (vQTL12 and vQTL13 in family 31 × 23, Supplementary Table S2). In this example, each vQTL is fit with a model involving an IBD recessive associated with one parent-line genotype at that position (BD for vQTL12, AC for vQTL13) plus an IBD recessive mutation on the other parent-line genotype but at an estimated map-distance. The selection coefficients, s₁ and s₂, are both 1.0 at these vQTL and the recombination distance, which is actually 14 cM on the linkage map, is estimated as 20.5 cM at vQTL12 and 14 cM at vQTL13 in the two models. In Supplementary Table S2 (column BI), 11 genetic models like this example are noted as showing the position of maximum selection against one parent-line genotype. An additional eight models in Supplementary Table S2 are designated as showing selection against the two IBD recessive mutations, but the second mutation is either at the same position as the first or is not associated with another mapped vQTL and may lie in an unmapped genomic region.

The second most common alternative model, accounting for 11 of 70 vQTL models (Supplementary Table S2), is one with an IBD recessive mutation linked to a parent-line genotype and a partially dominant mutation on another haplotype. Above, we noted how such a model explains the major QTL on chromosome 6 in family 31 × 23 (Supplementary Table S2). The pattern of genotype frequencies in these cases is illustrated by a sparkline,, depicting selection against an IBD recessive mutation on AC and a partially dominant mutation on D, affecting the survival of AD and BD. The genotype with the highest frequency, BC, is not a parent-line genotype, which distinguishes this pattern from that of a simple, partially dominant mutation that is IBD homozygous in one parent-line genotype and affects the viability of both hybrid genotypes.

Based on the results of fitting genetic models, we infer provisionally that the 70 separate vQTL reflect a total of 89 mutations, having deleterious effects on early viability (Table  3). The number of mutations per family ranges from 11 to 20, with a mean of 14.8; were these derived equally from inbred grandparents, then each inbred line was carrying 7.5 deleterious mutations. Although we successfully traced the grandparental origins of 23 mutations underlying 19 vQTL (Supplementary Table S2), the information is insufficient for determining the provenance of most mutations and the variance in mutational load among inbred grandparent lines.

Average relative survival of genotypes at vQTL, $\overline{S}$_adj, ranges from a low of 0.35, at vQTL13 in 40 × 92, to a high of 0.91, at vQTL7 in 23 × 31 (Table  3). We estimate overall relative survival in each family as the product of the relative survival estimates across unlinked vQTL, assuming that these are independent causes of mortality; when there is more than one vQTL on a chromosome, we use the relative survival of the vQTL with the lowest value (bold values in Table  3). Genotype-dependent mortality, $1-\prod {\overline{S}}_{\mathrm{adj}}$, ranges from 94.9% to 97.1% over the six families (Table  3).

We conducted tests for epistasic interactions over a total of 153,181 to 398,278 pairs of markers across six families (23 × 31, n = 398,278; 23 × 40, n = 153,181; 31 × 23, n = 207,690; 40 × 92, n = 240,471; 47 × 92, n = 159,330; 92 × 40, n = 190,653). Of these pairwise comparisons, an average of 89% is between unlinked markers on different chromosomes and an average of 11% is between linked markers on the same chromosomse. On average, within a family, 72% of linked marker-pairs show significant interaction of genotype frequencies, while only 0.4% of unlinked marker-pairs show significant association of genotype frequencies, suggesting the absence of epistasis between unlinked vQTL.

Confidence intervals for 69 of the 70 vQTL are bounded by the genomic positions corresponding to a drop of 4.6 in LRT from the peak LRT (Supplementary Table S2). These genomic intervals range in length from 0.09 to 14.7 Mbp, averaging 3.7 ± 3.4 Mbp (SD), but their length depends on the genetic basis of the QTL. Genetic models for 66 vQTL fit into four categories: (1) one completely recessive mutation affecting a presumptively, IBD homozygous, parent-line genotype (n = 19); (2) a partially dominant mutation affecting one parent-line homozygote and both hybrid genotypes (n = 17); (3) two recessive mutations, one in each parent-line genotype (n = 19); and (4) one recessive mutation in a parent-line genotype plus a partially dominant mutation in another haplotype (n = 11). The categories have significantly different vQTL confidence intervals (F_{3, 62} = 3.71; P = 0.016), with the single and double recessive mutation models having mean genomic confidence intervals (2.4 and 2.8 Mbp, respectively) that are significantly smaller than those for either the models with a single, partially dominant mutation or the models with both a recessive and a partially dominant mutation (5.0 and 5.4 Mbp, respectively). Thus, vQTL with tall, sharp peaks in the LRT profiles (Figure  2) are mostly caused by completely recessive mutations, while vQTL with broader peaks in the LRT profile are caused by partially dominant mutations, whether alone or in combination with other recessive mutations.

We identify 12 vQTL driven by one IBD recessive mutation with confidence intervals less than 2 Mbp. These relatively short vQTL confidence intervals contain an average of 21 genes each and a total of 313 genes, of which 264 are uniquely identified (Supplementary Table S3). One hundred and sixty-eight of the 264 uniquely identified genes are expressed well before the juvenile stage (from fertilized eggs to spats; Zhang et al. 2012) and are, therefore, candidates for the genes harboring the mutations causing the vQTL detected in our study.

Discussion

QTL mapping provides important insights into the genetic basis of inbreeding depression, by localizing regions of the genome affecting fitness and allowing study of modes of gene action. Here, we map viability QTL causing distortions of Mendelian ratios at SNP markers in F₂ families of the Pacific oyster. Like many plants, the oyster shows dramatic heterosis for growth (Hedgecock et al. 1995; Hedgecock and Davis 2007) and large genetic loads (Williams 1975; Plough 2016). The Pacific oyster also has genomic and genetic resources, aside from the well-developed linkage maps employed here (Hedgecock et al. 2005; Zhang et al. 2012; Peñaloza et al. 2021; Qi et al. 2021), which will eventually enable identification of genes affecting early mortality.

Early work (cited in the Introduction) showed that distortions of Mendelian ratios, such as those detected in this study, are widespread among bivalve mollusks. Subsequent studies showed that these distortions result from genotype-dependent mortality early in the life cycle, during larval stages or metamorphosis (Bierne et al. 1998; Launey and Hedgecock 2001; Plough and Hedgecock 2011), even in random-bred families (Plough et al. 2016), and can be mapped using the viability QTL model (Luo and Xu 2003; Luo et al. 2005). Early genotype-dependent mortality in the oyster corresponds with and may account for much of the type-III survivorship characteristic of highly fecund, broadcast spawning, marine invertebrates (Korringa 1946; Rumrill 1990). Type-III survivorship thus manifests an overt genetic load, which is absorbed by early life stages without great ecological cost and perhaps, even with some ecological benefit in the planktonic phase of the life cycle, such as satiation of predators (Wallace 1987; Agrawal and Whitlock 2012). QTL mapping in F₂ families derived from partially inbred parent lines exposes a concealed genetic load causing inbreeding depression.

Parsing the causes of genetic load revealed by this study, we find strong support for Charlesworth’s and Willis’s (2009) conclusion that “inbreeding depression is predominantly caused by the cumulative effects of deleterious mutations at many loci, probably with a contribution from overdominance at a few loci.” Twenty of 70 vQTL (28.6%) are caused by single, completely recessive, highly deleterious mutations, with selection coefficients, s, ranging from 0.67 to 1.0 (lethal, 10 cases) and averaging 0.9. In addition, 11 vQTL (15.7%) are attributable to pairs of highly deleterious, recessive mutations, which are linked in repulsion, i.e., at different genomic locations on opposite parent-line chromosomes, giving rise to pseudo-overdominance for viability. These vQTL are characterized by an excess of hybrid genotypes among survivors, over the chromosomal region bounded by the separate mutations (see Figure  4 for an example). Eleven of the 22 mutations involved in these pseudo-overdominant pairs are lethal, with s greater than 0.9 in three more cases. Thus, nearly half of the vQTL detected are caused by recessive lethal or highly deleterious mutations, in accord with the dominance hypothesis for inbreeding depression.

Support for the overdominance hypothesis of inbreeding depression comes potentially from eight vQTL (11.4%), which appear to show selection against both parent-line homozygotes. At only four of these cases, however, are minimum frequencies for both parent-line homozygotes precisely at the peak in the LRT profile, consistent with true overdominance. Displacements in the apparent sites of maximum selection against alternative parent-line homozygotes at the remaining vQTL could owe to sampling errors but could also indicate additional cases of pseudo-overdominance rather than true overdominance.

The remaining 31 vQTL provide evidence for genotype-dependent mortality caused by partially dominant deleterious mutations. For 17 vQTL (24.3%), we model single, partially dominant, deleterious mutations, with s averaging 0.79 and dominance coefficients, h, ranging from 0.1 to 0.89. Hybrid carriers of these mutations have an average viability, 1-hs, of 0.67 relative to the viability of apparently unaffected parent-line homozygotes. The negative correlation between s and h observed across viability mutations (Figure  5) is in line with extensive observations from Drosophila species that dominance of lethal mutations averages 0.02, while dominance of new detrimental mutations is in the range 0.35–0.5 (Simmons and Crow 1977). We detect a slightly higher percentage of partially dominant viability QTL than that reported by Launey and Hedgecock (2001; 3 of 20 or 15%) or by Plough and Hedgecock (2011; 2 of 11 or 18%). Such partially dominant mutations likely contribute through mortality of heterozygous carriers to type-III survivorship in natural, outcrossing populations, as shown by Plough et al. (2016), but they also contribute to inbreeding depression in the F₂ mapping families, owing to the lower relative viabilities of IBD homozygotes. At another 11 vQTL (15.7%), we model a recessive mutation from one parent-line chromosome and a second partially dominant mutation that is not inherited homozygous IBD from the other parent. Though we lack degrees of freedom to estimate dominance coefficients and contributions to genetic load and inbreeding depression, selection coefficients against IBD homozygotes are greater than 0.9 in most cases, suggesting a contribution to hidden genetic load from these more complicated vQTL. Finally, three vQTL are caused by partially dominant mutations on non-IBD parent chromosomes; these contribute to overt genetic load but not to inbreeding depression.

As in our previous studies (Bucklin 2003; Plough and Hedgecock 2011; Plough 2012; Plough et al. 2016), we find no evidence for dependence of genotype frequencies among unlinked markers, which would suggest an absence of strong epistatic interactions affecting viability. That the statistical dependence of physically linked genetic markers is detected in 72% of pairwise tests suggests that contingency chi-square tests have sufficient power to detect associations between markers when they exist, owing to linkage. The absence of evidence for viability epistasis in F₂ families of the Pacific oyster contrasts sharply with a report of seven pairs of epistatic segregation distortion loci in a family of double haploid Japanese flounder (Zhao et al. 2018). What role the extremely low viability of double haploid flounder derived from mitotic gynogenesis might play in this difference is unknown; double haploids have not been produced in any bivalve mollusk, but meiotic gynogenesis has been induced in Pacific oysters (Guo et al. 1993) and could provide a way to test for epistasis after severe selection on homozygous genotypes.

High-density linkage maps made possible by GBS sequencing methods aided inferences about the genetic basis of genetic load and inbreeding depression in two ways. First, a greater number of genetic markers, compared to previous studies (Launey and Hedgecock 2001; Plough and Hedgecock 2011), enabled us to identify parent-line chromosomes, through analysis of genetic similarity, which, in turn, supported the likelihood of IBD. Second, higher map densities helped to resolve multiple vQTL on the same chromosome, a task made difficult by the absence of a phenotype amenable to standard methods for resolving statistical independence of multiple peaks. On the other hand, the GBS maps only cover an average of 86% of the genome, suggesting that we may be missing vQTL and underestimating genetic mortality.

Average genotype-dependent mortality in the six F₂ families ranges from 94.9% to 97.1%, a remarkable genetic load that is consistent, nevertheless, both with previous reports and with estimates of early mortality of oysters (Plough and Hedgecock 2011; Plough 2016). Not all of this genotype-dependent mortality is strictly attributable to inbreeding depression, as a portion of it owes to selection against the heterozygous carriers of partially dominant mutations, a residuum in F₂ families derived from incompletely inbred parent lines of the overt genetic load normally expressed in natural populations. Still, we are likely underestimating genotype-dependent mortality and, thus, inbreeding depression for at least two reasons: (i) we have incomplete coverage of the genome, noted above, and (ii) we calculate mortality only over unlinked vQTL, to be conservative, and thus do not account fully for the contributions of linked vQTL to mortality.

The numbers of mutations per family, 11–20, are remarkably consistent with previous reports for the Pacific oyster (8–14, Launey and Hedgecock 2001; 11–15, Plough and Hedgecock 2011), confirming a high genetic load in this marine invertebrate (Plough 2016). Direct evidence of the factors that maintain this large genetic load in oysters is still lacking and needed. From the average number of partially dominant lethal mutations carried by wild-caught oysters, Plough et al. (2016) calculated that the average frequency of such mutations, ${\overline{q}}_e$, must be low in natural populations (7.25 × 10⁻⁴) but that the partially dominant lethal mutation rate, $\mu \approx {\overline{q}}_e\times hs$, must be high (3.6 × 10⁻⁴). An elevated rate of mutation may simply be a by-product of high fecundity (Williams 1975) and a likely source of observed variation in the oyster genome. The sequence polymorphism rate of 2.3% in the oyster genome (Sauvage et al. 2007; Zhang et al. 2012) is among the highest reported for animals, high enough to cause practical problems, for example, in designing PCR primers that do not generate “null,” nonamplifying alleles (Hedgecock et al. 2004, 2015; Sun et al. 2015). Direct estimates of mutation rates could be made by sequencing the genomes of parent-offspring trios (Yoder and Tiley 2021).

Another factor to be considered in explaining the maintenance of a large genetic load in the oyster is the relatively small effective population sizes, compared to census sizes of natural populations (Sun and Hedgecock 2017; Hedgecock and Pan 2021), as predicted by the hypothesis of high variance in reproductive success (Hedgecock and Pudovkin 2011). Small populations can have higher genetic loads than larger populations, owing to genetic drift (Kimura et al. 1963), and mildly deleterious and partially dominant mutations may not be purged as readily as in large populations (Glémin 2003). Finally, the extent of pseudo-overdominance for viability, the coupling in repulsion phase of highly deleterious mutations, revealed here could also maintain substantial amounts of variation, including deleterious mutations (Gilbert et al. 2020), extending the ‘grasp’ of natural selection on useful variation, perhaps even promoting heterotic genotypes, which could be maintained with essentially no additional genetic burden.

Data availability

Datasets (i.e., genotype and marker information) used in the analysis and supplemental materials are available via figshare (https://doi.org/10.25386/genetics.16565973).