Segregation Analysis of a Sex Ratio Distortion Locus in Congenic Mice

Abstract

The congenic HG.CAST-(D17Mit196-D17Mit190) (HQ17^hg/hg) mouse strain showed a significant departure on the expected 50%/50% offspring sex ratio in more than 2400 progeny (55.7% females). The entire pedigree file included data from 13 nonoverlapping purebred generations and an F₂ cross with the C57BL/6J inbred strain. Offspring sex ratio data were analyzed on the basis of 40 purebred HQ17^hg/hg sires and 29 F₁ HQ17^hg/hg × B6 sires under a Bayesian Binomial segregation model accounting for 4 different autosomal inheritance models of gene action (i.e., additive, dominance, recessive, and overdominance) and X-linked and Y-linked loci. For each model, the segregation effect was evaluated as a single regression coefficient for all sires or assuming 2 independent regression coefficients accounting for offspring sex ratio departures in purebred and F₁ sires, respectively. The deviance information criterion clearly favored the autosomal dominance model with different regression coefficients for the 2 groups of sires. Under this model, the dominance effect increased the percentage of female offspring by 4.3% (HQ17^hg/hg purebred sires) and 8.2% (F₁ sires) with the highest posterior density regions ranging from 0.5% to 10.6% and from 1.3% to 14.4%, respectively. This article provides significant evidence of genetic determinism for sex ratio distortion in the HQ17^hg/hg strain and develops new analytical tools to perform segregation studies on dichotomous traits.

Long before the chromosomal mechanism for sex determination was recognized, there was an interest in developing a means to predetermine the sex of offspring, not only in domestic livestock but also in our own species as well. These efforts evolved during the 20th century with multiple controversial results (Hohenboken 1981) and some evidence concerning the environmental (King 1927; Roche et al. 2006) and genetic (King 1918; Weir 1976; de la Casa-Esperón et al. 2000) contributions to offspring sex ratio. Theoretically, the chromosomal sex determination acts as a constraint that precludes control of offspring sex ratio in mammals (Charnov 1982); offspring sex ratio being expected to be 1:1 with a substantial variance inherent to the binomial distribution of the phenotype. Nevertheless, this assumption has been weakened by a few breeds and strains showing significant departures from the expected sex ratio (Cook and Vlcek 1961; Schlager and Roderick 1968; de la Casa-Esperón et al. 2000). These kinds of animal models are of special interest for sex ratio distortion research where the identification of causal loci could be of economic relevance in livestock species (Cunningham 1975; Van Vleck and Everett 1976) and of sociologic importance in humans (Charnov 1982).

The presence of polymorphic sex ratio distortion loci can be detected using segregation analysis (Elston and Stewart 1971; Morton and Maclean 1974); an analytical tool to model both phenotypic and genealogic information and to determine whether the inheritance of a certain phenotype is (clearly) dominated by one gene with a large effect (Janss et al. 1997). Segregation analysis techniques have recently been adapted to accommodate complex pedigrees under linear models (Janss et al. 1995) using Markov chain Monte Carlo methods (Geman and Geman 1984; Gelfand and Smith 1990), although further research is required in order to adapt them to dichotomous variables such as sex ratio. This methodology has been systematically applied in livestock and laboratory populations, providing the first insights into new mutations with a relevant contribution to the phenotype (Janss et al. 1997; Walling et al. 2002; Argente et al. 2003; Janutta et al. 2006).

The HQ17^hg/hg congenic mouse strain was created at the University of California, with contributions from both C57BL/6J and CAST/EiJ backgrounds and including the high growth mutation on chromosome 10 (Horvat and Medrano 2001; Wong et al. 2002). This strain showed a significant increase in the percentage of female offspring in more than 2400 offspring from 13 generations (55.7%). This article focused on the segregation analysis of this inbred mouse strain to determine if the observed pattern of sex ratio distortion was due to a major locus. We also developed a modification of Janss et al. (1995) segregation model to accommodate binomial data and different inheritance patterns through Bayesian inference.

Materials and Methods

Congenic Mice Data Source

The congenic HG.CAST-(D17Mit196-D17Mit190) (HQ17^hg/hg; MGI reference: 3771215) mouse strain was created in our vivarium at the University of California, Davis, during years 2002 and 2003. These HQ17^hg/hg mice harbored CAST/EiJ (CAST) alleles on chromosome 17 between microsatellites D17Mit196 to D17Mit190 and C57BL/6J^hg/hg (B6^hg/hg) alleles in the rest of the genome (Farber et al. 2006). Note that the B6^hg/hg strain was isogenic to C57BL/6J (B6), except for the high growth mutation on mouse chromosome 10 (Horvat and Medrano 2001; Wong et al. 2002) and a stretch of AKR/J sequence around this mutation (Horvat and Medrano 1996). After its development, the HQ17^hg/hg strain was maintained for 13 nonoverlapping generations from March 2004 to March 2008 (generations G₁–G₁₃; Table 1). Additionally, an F₂ cross was generated by mating one HQ17^hg/hg male from generation 4 with 31 B6 females (F₀), and subsequently mating 29 F₁ males with 91 F₁ females (Table 1). Sire, dam, date of mating, date of birth, and number of pups at birth were recorded for each litter, and pups were individually marked by ear notching at weaning (3 weeks after birth). Sex was checked by visual inspection during the first days after birth and at weaning (3 weeks after birth). The data set included 860 purebred pups (474 females and 386 males) and 1615 F₂ HQ17^hg/hg × B6 pups (905 females and 710 males) born in 338 litters from 69 sires and 192 dams.

Table 1.

Summary of sex ratio data in the HQ17^hg/hg strain

	Breeding individuals			Pups
Generations	Sires	Dams	Parturitions	Born	♀	♂	%♀a
G1	3	7	10	64	25	28	47.2NS
G2	6	8	12	66	33	31	51.6NS
G3	1	3	5	37	20	15	57.1NS
G4	2	5	6	39	19	14	57.6NS
G5	2	4	5	26	14	11	56.0NS
G6	2	5	10	48	29	16	64.4*
G7	3	6	11	61	33	26	55.9NS
G8	4	13	13	93	47	46	50.5NS
G9	4	11	15	105	57	47	54.8NS
G10	3	7	8	63	36	26	58.1NS
G11	4	11	11	88	51	37	58.0NS
G12	2	7	8	60	36	24	60.0NS
G13	4	14	21	140	74	65	53.2NS
G1–G13	40	101	135	890	474	386	55.1**
F1	29	91	203	1,620	905	710	56.0***
Overall	69	192	338	2,510	1379	1096	55.7***

^aPercentage of females. Departures from the expected 50% were checked by a χ² test with 1 df (NS, not significant, P > 0.1; *P < 0.1; **P < 0.01; ***P < 0.001).

All mice were housed in polycarbonate cages and maintained under controlled conditions of temperature (21 ± 2 °C), humidity (40–70%), and lighting (14 h light, 10 h dark, lights on at 7 AM). Mice were fed with Purina Laboratory Rodent Diet 5008 (Labdiet, Purina Mills, Inc, San Louis, MO; 23.5% protein, 6.5% fat, 3.3 kcal/g), and water was ad libitum. All mouse protocols were managed according to the guidelines of the American Association for Accreditation of Laboratory Animal Care (http://www.aaalac.org).

Segregation Analysis

Sex of the progeny can be viewed as a dichotomous variable with 2 possible phenotypes, male or female, that are determined by inheritance of the sex chromosomes from the heterogametic parent, that is, the father in mammals. This suggests that genetic (and environmental) determinants of the sex ratio in mammals could be appropriately analyzed on the basis of each male and the sex of its progeny (Toro et al. 2006). Note that the genetic determinants could modify offspring sex ratio at several biological levels by altering the ratio of male and female determining alleles, changing the fertilization success of male or female determining gametes, or causing differential survival in the 2 sexes during embryo, fetal, or neonatal periods. All these mechanism will converge to the same phenotypic end, producing a departure of offspring sex ratio.

In order to assess genetic and environmental influences on HQ17^hg/hg mice sex ratio, the hierarchical segregation analysis developed by Janss et al. (1995) for linear phenotypic traits was adapted to the dichotomous framework. For a given male i with n_i(m) sons and n_i(f) daughters $(n_i=n_{i\left(\mathrm{f}\right)}+n_{i\left(\mathrm{m}\right)})$, each offspring can be viewed as an independent Bernoulli trial with (female) probability π_i. These multiple Bernoulli variables generalize to a Binomial process with probability

$n_{i\left(\mathrm{f}\right)}$ being the number of successes (females). If we assume an unknown autosomal locus with 2 alleles, A₁ and A₂, and allelic frequencies in the founder generation of p and 1 − p, respectively, the effect of this locus on the π_i parameter could be modeled under the following hierarchical structure,

where μ is the overall mean, s_i is the permanent environmental effect of the ith sire, g_i is the autosomal genotype of the ith sire $\left(A_j{A}_k\right)$, θ is the appropriate regression coefficient, ${\mathrm{\kappa }}_{A_j{A}_k}$ is the inheritance coefficient as defined in Table 2, and $\text{I(}\hspace{0.5em}\text{)}$ is an indicator function as defined within parentheses. This indicator function has a value of 1 if the evaluated expression is true and a value of 0 otherwise.

Table 2.

Coefficients for the different autosomal Inheritance models

Autosomal	Genotypea
Inheritance model	$A_1{A}_1$	$A_1{A}_2$ or $A_2{A}_1$	$A_2{A}_2$
Additive	1	1/2	0
Recessive	1	0	0
Dominant	1	1	0
Overdominant	0	1	0

^aTwo alleles, A₁ and A₂, were assumed.

Under a standard Bayesian development, this segregation model can be generalized as

where m is the number of animals in the pedigree, y is the o × 2 matrix storing the number of offspring (n_i; first column) and number of daughters (n_i(f); second column) from o sires with sex-evaluated progeny, s is the vector of permanent environmental sire effects, ${\mathrm{\sigma }}_s^2$ is the permanent environmental variance, and ${\mathbf{g}}_{-l}$ is vector g after excluding its lth element. The Bayesian likelihood was modeled under the Binomial process defined above, $p\left(\mathbf{y}\right|\mathrm{\mu },\mathrm{\theta },\mathbf{g})={\displaystyle \prod _{i=1}^{o}B\left(n_{i\left(\mathrm{f}\right)}\right|n_i,{\mathrm{\pi }}_i)}$, whereas permanent environmental sire effects were modeled under a multivariate normal process,

I being a o × o identity matrix. Our a priori knowledge about sex ratio distortion in HQ17^hg/hg mice was restricted to the higher percentage of female offspring observed and thus, flat priors between 0 and appropriate higher bounds were defined for μ, θ, and p,

and an improper flat prior between 0 and +∞ was assumed for ${\mathrm{\sigma }}_s^2$. Following Janss et al. (1995), the sampling probability of g_l for a founder individual without known parents can be stated as

whereas this probability can be generalized to

for subsequent offspring, where ${\mathrm{\rho }}_{A_{m,\mathrm{Sire}}}$ $\mathrm{(}{\mathrm{\rho }}_{A_{m,\mathrm{Dam}}})$ is the probability that the lth individual will inherit allele A_m from its father (mother; Janss et al. 1995). This Binomial segregation model was also extended to a segregating locus in the X or Y chromosomes (Appendix 1, Supplementary Material).

Analytical Models, Markov Chain Monte Carlo Sampling and Model Comparison

In addition to the putative sex ratio distortion locus, the ratios in progeny of purebred and F₁ HQ17^hg/hg males could differ based on the maternal genetic contribution of their HQ17^hg/hg and B6 dams, respectively. The HQ17^hg/hg was isogenic to B6 with the exception of the presence of the high growth locus having a few flanking AKR/J sequences in chromosome 10 (Horvat and Medrano 1996, 2001) and the CAST congenic region on chromosome 17, although additional spontaneous mutations cannot be discarded (Casellas and Medrano 2008). This framework allowed testing 2 opposite hypotheses regarding the genetic behavior of the sex ratio distortion locus. First, the segregation analysis was performed as described above, assuming that the causal locus (θ) had the same effect in both purebred and F₁ sires (one genetic effect model) and thus, it did not interact with the remaining mouse genome. Six independent analyses were performed under this hypothesis by accounting for the 4 autosomal inheritance patterns reported in Table 2, as well as for an X-linked and Y-linked locus model (Appendix 1, Supplementary Material). Second, independent allelic effects were modeled for HQ17^hg/hg purebred and HQ17^hg/hg × B6 F₁ sires (θ₁ and θ₂, respectively; 2 genetic effects model) (Appendix 2, Supplementary Material) allowing for different epistatic interactions between the sex ratio distortion locus and the remaining mouse genome in both genetic backgrounds. The X-linked and Y-linked segregation model and the 4 autosomal inheritance patterns shown in Table 2 were independently analyzed by assuming the same inheritance pattern for both purebred and F₁ sires. An additional nongenetic model with centrality parameter μ and all variability in offspring sex ratio accounted for by s was analyzed by arbitrarily fixing θ = 0 (or θ₁ = 0 and θ₂ = 0) (Model Null). At the end, 13 independent analyses were performed assuming null (one analysis), homogeneous (6 analyses), and heterogeneous (6 analyses) effects of the segregating sex distortion locus in the 2 genetic backgrounds. Note that the genotype for the B6 dams of the HQ17^hg/hg × B6 F₁ sires was fixed as wild-type homozygous given that sex ratio departures in B6 have not been reported in the scientific literature nor in our vivarium (6629 males and 6542 females after 46 nonoverlapping generations; see Casellas and Medrano (2008) for a detailed description of this data set).

For each analysis, autocorrelated samples from the marginal posterior distribution of all unknowns in the model were obtained by Metropolis–Hastings sampling (Metropolis et al. 1953; Hastings 1970) with the exception of ${\mathrm{\sigma }}_s^2$ that was updated by Gibbs sampling (Gelfand and Smith 1990). A uniform proposal distribution between 0 and 1 was used during the sampling process for μ and p, whereas the proposal distribution for θ was uniform between 0 and μ. In a similar way, a 1/3 proposal probability was assumed for each genotype during sampling for (1/2 probability for male genotypes under X-linked and Y-linked models), and a uniform proposal distribution with mathematical expectation at the current value of s_i was used for Metropolis–Hastings sampling of s. The range of the proposed distribution was determined in a preliminary analysis, with an acceptance rate greater than 25% for all levels of s. A unique chain of 250 000 rounds was launched for each analysis and the first 50 000 were discarded as burn-in (Raftery and Lewis 1992). Given the high autocorrelation between successive samples related to the Metropolis–Hasting method, a lag interval of 10 iterations was applied and 20 000 samples of model parameters were used to calculate the posterior distribution of each parameter using the ergodic property of the chain (Gilks et al. 1996).

Models were compared through the deviance information criterion (DIC; Spiegelhalter et al. 2002). Models with smaller DIC were favored as this indicated a better fit and lower degree of model complexity. In general, differences larger than 3–5 DIC units are assumed as statistically relevant (Spiegelhalter et al. 2002). Additionally, Verdinelli and Wasserman (1995) Bayes factor (BF) was adapted to check the statistical relevance of θ parameters (Appendix 3, Supplementary Material). The BF provides the ratio of posterior probabilities between 2 competing models avoiding the calculation of significance levels and without any requirement to define the null or the alternative hypothesis. In this case, each model developed above was compared with a competing model with θ = 0 (or θ₁ = 0, or θ₂ = 0). A BF > 1 suggested that θ was significantly different from zero whereas a BF < 1 favored the model with null θ.

Results and Discussion

The HQ17^hg/hg inbred strain was an attractive animal model because of the empirical observation of an overall sex ratio distortion in the progeny of both pure (474 daughters vs. 386 sons) and B6-crossed sires (905 daughters vs. 710 sons). Both groups of sires had a highly significant (P value < 0.001; χ² test with 1 degrees of freedom [df]) departure from the expected 1:1 ratio between offspring females and males (1.23:1 and 1.28:1, respectively), with an overall percentage of offspring females born of 55.7%. Generations G₂–G₁₃ showed a greater-than-50% offspring female percentage, although these values did not reach statistical significance due to sample size (Table 1). A substantial degree of within-generation variability was observed, with offspring female percentages ranging between 33.8% and 75.6% (Figure 1). These across-sires discrepancies were maximum in the F₁ population where 6 sires reported suggestive (60.9% ♀; n = 69; P = 0.071), significant (61.1% ♀, 69.7% ♀, and 64.9% ♀; n = 95, 33, and 74; P = 0.031, 0.023, and 0.011) and highly significant (69.4% ♀ and 75.6% ♀; n = 72 and 45; both P < 0.001) offspring sex ratio departures, whereas the remaining 23 sires did not statistically differ from the 1:1 expected sex ratio (offspring female percentages ranged from 37.1% to 66.7%). Note that only 35 of the 2510 pups died before sexing (1.39%), whereas the remaining 1379 females and 1096 males contributed phenotypic data to our analyses (Table 1). Obviously, these 35 early neonatal deaths did not explain the large difference of 283 pups between the observed number of male and female offspring. These results suggest that biological mechanisms involved in increasing the percentage of female offspring in HQ17^hg/hg mice must act during conception or gestation, although influencing effects during gametogenesis cannot be completely discarded.

Figure 1.

Empirical distribution of the HQ17^hg/hg purebred (a) and HQ17^hg/hg×B6 F₁ sires (b) in relation to their offspring sex ratio phenotype (percentage of female offspring).

The main objective of this research was to determine the genetic and environmental factors influencing sex ratio in the HQ17^hg/hg strain. The segregation analyses examined 3 main sources of sex ratio distortion, 1) systematic departures from the 1:1 expected sex ratio for all individuals $(\mathrm{\mu }\ne 0.5)$, 2) environmental variability greater than the one inherent to the Bernoulli process $({\mathrm{\sigma }}_s^2>0)$, and 3) genetic variability linked to a segregating locus (θ > 0, θ₁ > 0, or θ₂ > 0). Note that a $\mathrm{\mu }\ne 0.5$ could be due to both environmental and genetic effects, whereas ${\mathrm{\sigma }}_s^2>0$ and θ > 0 must be specifically linked to environmental and genetic contributions, respectively. Therefore, maternal contributions to offspring sex ratio (Trivers and Willard 1973; Rosenfeld and Roberts 2004) could be partially accumulated in μ and ${\mathrm{\sigma }}_s^2$ parameters, or alternatively, contribute to the Binomial residual term. Because all the females in our study were kept in the same vivarium room and fed the same diet, the relevance of maternal variability in our population must be very small. As shown in Table 3, Model Null (i.e., systematic sex ratio departure and/or environmental variability), X-linked and Y-linked segregation models and the autosomal segregation models with one genetic effect did not showed statistically relevant divergences, with average differences lower than 3 DIC units. It is important to note that the small dispersion of the DIC estimates for each model (standard error < 0.06) provided a high confidence of the average DIC estimates and model stability. Moreover, the BF for θ parameters agreed with these DIC estimates with lower-than-one or close-to-1 values (Table 4). Focusing on the second subset of autosomal segregation models (2 genetic parameters for sires from generations G₁–G₁₃ and F₁, respectively), the recessive inheritance pattern was discarded with a DIC larger (3,919,512.34) than the one for the Model Null (3,919,512.31), whereas overdominance, additive, and dominance inheritance models reduced DIC in 7.25, 9.11, and 11.67 units, suggesting a reduction in ${\mathrm{\sigma }}_s^2$, and showing high BF, larger than 25 for θ₂ under additive and dominance models (Table 4). Note that these DIC differences were clearly larger than the 3–5 DIC units suggested by Spiegelhalter et al. (2002), discarding the Model Null and advocating for a complex framework of environmental and genetic variability. The DIC differences between additive, dominance, and overdominance inheritance patterns favored the dominance model, although the additive one cannot be completely discarded. Indeed, differences between additive and dominance models could be highly related to the structure of our data set, given that F₁ males could not be homozygous for the sex ratio distortion allele (note that the F₀ B6 female was assumed wild-type homozygous) and there was no relevant information to differentiate between additive and dominance contributions in the F₁ population of sires. Within this context, differences between additive and dominance model performances were mainly predicted with G₁–G₁₃ sires, suggesting a slight advantage for the dominance inheritance pattern with 2 regression coefficients (Figure 2).

Table 3.

Model comparison through the DIC (Spiegelhalter et al. 2002)

	DIC
Model	Chain 1	Chain 2	Chain 3	Average ± standard error	Differencea
Nullb	3,919,512.36	3,919,512.28	3,919,512.29	3,919,512.31 ± 0.02	0.00
One genetic effectc
Additive	3,919,511.47	3,919,511.47	3,919,511.58	3,919,511.50 ± 0.03	−0.80
Recessive	3,919,512.37	3,919,512.33	3,919,512.36	3,919,512.35 ± 0.01	0.04
Dominant	3,919,510.88	3,919,510.90	3,919,510.89	3,919,510.89 ± 0.00	−1.42
Overdominance	3,919,510.12	3,919,510.12	3,919,510.13	3,919,510.12 ± 0.00	−2.19
X-linkedd	3,919,513.12	3,919,513.07	3,919,513.11	3,919,513.11 ± 0.03	0.80
Y-linkede	3,919,512.81	3,919,512.82	3,919,512.89	3,919,512.84 ± 0.04	0.53
Two genetic effectsf
Additive	3,919,503.19	3,919,503.32	3,919,503.09	3,919,503.20 ± 0.06	−9.11
Recessive	3,919,512.37	3,919,512.32	3,919,512.34	3,919,512.34 ± 0.01	0.03
Dominant	3,919,500.69	3,919,500.57	3,919,500.65	3,919,500.63 ± 0.03	−11.67
Overdominance	3,919,505.09	3,919,504.97	3,919,505.13	3,919,505.06 ± 0.04	−7.25
X-linked	3,919,513.98	3,919,513.93	3,919,513.94	3,919,513.95 ± 0.03	1.64
Y-linked	3,919,514.09	3,919,514.02	3,919,514.01	3,919,514.04 ± 0.03	1.73

^aDIC difference from Model Null.

^bNull model with the θ parameter arbitrarily fixed to 0.

^cGenetic model assuming a unique θ parameter for all sires.

^dGenetic model assuming a X-linked segregating locus.

^eGenetic model assuming a Y-linked segregating locus.

^fGenetic models assuming a different θ parameter for purebred HQ17^hg/hg (generation G₁–G₁₃) and F₁ HQ17^hg/hg × B6 sires.

Table 4.

Mode (and highest posterior density region at 95%) of the analyzed parameters under each autosomal inheritance model

	Parametera
Model	μ	p	σs2	θ (or θ1)	θ2
Nullb	0.557 (0.538–0.577)		0.018 (0.009–0.027)
One genetic effectc
Additive	0.546 (0.514–0.570)	0.433 (0.242–0.740)	0.016 (0.007–0.026)	0.043NR (0.001–0.187)
Recessive	0.556 (0.536–0.575)	0.380 (0.238–0.723)	0.018 (0.010–0.030)	0.117NR (0.002–0.413)
Dominant	0.543 (0.508–0.569)	0.456 (0.244–0.746)	0.015 (0.007–0.025)	0.027NR (0.001–0.090)
Overdominance	0.540 (0.503–0.568)	0.498 (0.248–0.752)	0.015 (0.007–0.024)	0.039d (0.003–0.120)
Two genetic effectse
Additive	0.525 (0.485–0.558)	0.429 (0.241–0.739)	0.012 (0.003–0.021)	0.059f (0.005–0.181)	0.156g (0.022–0.283)
Recessive	0.556 (0.536–0.576)	0.371 (0.238–0.718)	0.018 (0.008–0.026)	0.122NR (0.002–0.414)	0.223d (0.012–0.434)
Dominant	0.522 (0.480–0.556)	0.451 (0.244–0.743)	0.010 (0.002–0.021)	0.043f (0.005–0.106)	0.082g (0.013–0.144)
Overdominance	0.526 (0.489–0.558)	0.501 (0.256–0.747)	0.013 (0.003–0.023)	0.038d (0.002–0.095)	0.077f (0.011–0.140)

Note that the statistical relevance of θ parameters was characterized through Jeffreys (1984) scale of evidence for BF (NR, not relevant, BF < 1).

^aμ, overall mean for the frequency of daughters; p, allelic frequency of A₁ allele in founder generation; σ_s², permanent environmental variance; θ, θ₁, and θ₂, regression coefficients of the genetic effect for all sires (θ, models with 1 genetic effect), pure HQ17^hg/hg sires (θ₁) and B6-crossed sires (θ₂, models with 2 genetic effects).

^bModel with the θ parameter arbitrarily fixed to 0.

^cModels assuming a unique θ parameter for all sires.

^d1 ≤ BF < 3.16.

^eModels assuming a different θ parameter for pure (generation G₁–G₁₃) and B6-crossed sires (generation F₁).

^f3.16 ≤ BF < 10.

^g10 ≤ BF < 31.62.

Figure 2.

Pedigree and predicted genotype for an underlying locus regulating sire offspring sex ratio under the dominance model with 2 genetic effects (generations 2–10). The left box shows the HQ17^hg/hg purebred pedigree between generations 2 and 10 (sires are marked with a rectangular box and the number of sons and daughters is specified), whereas the vertical right box shows the F₁ HQ17^hg/hg × B6 sires and their offspring sex ratio phenotype. Two alleles were assumed (+, wild type; D, sex ratio distortion) and the horizontal bar characterizes the predicted probability of each genotype (+/+, white; +/D or D/+, gray; D/D, black).

It is very important to highlight the large DIC differences between segregation models with one and 2 genetic effects (Table 2). These DIC discrepancies supported relevant differences between HQ17^hg/hg and B6 genetic backgrounds and different effects of the sex ratio-related underlying locus in each genetic environment. Known genetic differences between HQ17^hg/hg and B6 strains relied on the CAST congenic segment on chromosome 17 (Farber et al. 2006), the high growth locus on chromosome 10 (Horvat and Medrano 2001), and the few AKR/J sequences flanking the high growth locus (Horvat and Medrano 2001), although the relevant and continuous uploading of new mutations reported in the B6 strain (Casellas and Medrano 2008) could suggest larger genetic departures between both strains.

As shown in Table 4, the modal estimate (and highest posterior density region at 95%; HPD95) for the frequency of offspring females under Model Null was 0.557 (0.538–0.577), fitting the 55.7% of daughters observed in the overall data set. This parameter showed a slight reduction under segregation models, although the HPD95 overlapped in all cases. It is important to note that only the HPD95 of the additive, dominance, and overdominance models with 2 genetic effects included the 0.5 value. Although the modal estimates suggested a slight advantage for daughters of ∼2.5%, the HPD95 discarded a statistically significant systematic departure from the 1:1 expected sex ratio, whereas environmental and genetic sources of variation were corroborated (Table 4). The estimated genetic effects suggested a similar pattern across models, with a larger modal estimate for the recessive model than for the 3 remaining segregation models. Focusing on the autosomal models with 2 genetic effects, modal estimates were larger for F₁ sires than for G₁–G₁₃ sires, agreeing with the DIC differences shown in Table 3, and the modal estimates in the additive segregation model approximately doubled modal estimates under the dominance model. The dominance model with 2 genetic effects predicted an increase in the percentage of female offspring of 3.8% (56.4%; G₁–G₁₃ sires) and 7.7% (60.3%; F₁ sires) for heterozygous and sex ratio distortion allele homozygous sires. Note that HQ17^hg/hg purebred and F₁ sires were reared in the same mouse colony and overlapped during years 2005 and 2006. Although some differences between these sires could be attributed to uncontrolled environmental effects, these sources of variation were accounted for by the permanent environmental sire effect in our models (s); estimated genetic effects must be free from biases due to uncontrolled environmental perturbations.

Although several systematic sex ratio departures have been reported in invertebrate experimental strains (Sweeny and Barr 1978; Cazemajor et al. 1997; Tao, Araripe, et al. 2007; Tao, Masly, et al. 2007), data on unequal sex ratios in mammals are not common. The increased percentage of female offspring in the HQ17^hg/hg strain agrees with the pattern in some rabbit strains (Sawin and Gadbois 1947), in PHL mice (Weir 1960, 1976), and in C, C57BR/cd, and LAC albino mice (Cook and Vlcek 1961), whereas inverse departures were reported in DDK mice (de la Casa-Esperón et al. 2000; Lee 2002), PHH mice (Weir 1960, 1976), CE mice (Cook and Vlcek 1961), and some congenic histocompatibility mouse strains (Beamer and Whitten 1991). Additionally, some controversial sex ratio departures have been reported in mice (Schlager and Roderick 1968) and domestic species of livestock (Kennedy and Moxley 1978; Skjervold 1979; Skjervold and James 1979). The HQ17^hg/hg strain joins this small collection of mammalian strains with sex ratio departures. Moreover, the main question for the HQ17^hg/hg strain is the underlying genetic mechanism involved in the offspring sex ratio departure or, at least, the location of the segregating locus. Our analyses suggested a major autosomal locus, whereas contributions from sex chromosomes were discarded. These results partially agrees with the ones from the PHL strain where both Y-linked and autosomal contributions were suggested (Weir 1976). This segregation pattern could be possibly due to a new mutation arising elsewhere in the HQ17^hg/hg genome (Casellas and Medrano 2008). Although the generation of this congenic strain could have left a few polymorphic loci segregating at the boundary of the CAST congenic region, the dominance effect revealed by the segregation analyses must be observed as a systematic departure in the strain of origin, B6^hg/hg or CAST. To our best knowledge, systematic offspring sex ratio departures have not been reported for the CAST strain, whereas B6^hg/hg inbred strain showed a percentage of female offspring of 50.5% in our vivarium during the last 42 generations (1976 females and 1939 males; P value = 0.554, χ² test with 1 df). Unfortunately, the segregation analysis does not allow elucidating the biological mechanisms involved in the offspring sex ratio departure, where disturbances during meiosis, sperm capacitation, fecundation, and the embryonic and fetal stages could be responsible for the observed offspring sex ratio distortion in the HQ17^hg/hg strain.

The current implementation of segregation models has adapted the Janss et al. (1995) approach to the dichotomous traits framework. This methodology provides the first insights into the inheritance model involved in the phenotypic determination of this trait. Besides the inheritance pattern, the Binomial segregation analysis characterizes the genetic configuration of each individual for the segregating locus in terms of probabilities for each competing genotype (Figure 2). This prediction of the genotype is performed on the basis of the genotypic information of parents and offspring, and phenotypic data if available. As shown in Figure 2, the posterior probability favoring each genotype depends on the available information. For example, the founder male for the F₁ population had the highest probability to be heterozygous (97%), mainly inferred from the 29 F₁ offspring with phenotypic data that indirectly contributed to the prediction of its genotype. In a similar way, the genotypic probabilities in the F₁ males clearly varied depending on the realized sex ratio departure and the number of offspring (Figure 2).

This research has 2 principal scientific contributions. First, we have provided evidence for the genetic regulation sex of the offspring in HQ17^hg/hg mice, that is, most likely linked to a new mutation locus in the autosomal genome. Second, Janss et al. (1995) segregation models were adapted to Binomial traits, providing a useful statistical tool for the identification of underlying loci with large effects on discrete phenotypic traits.

Supplementary Material

Supplementary material can be found at http://www.jhered.oxfordjournals.org/.

Funding

National Research Initiative grant, from the United States Department of Agriculture Cooperative State Research, Education, and Extension Service (2005-35205-15453); National Institute of Health (DK69978); Spain's Ministerio de Ciencia e Innovación (programs Juan de la Cierva and José Castillejo) (to J.C.).