Livestock Science 277 (2023) 105354 Contents lists available at ScienceDirect Livestock Science journal homepage: www.elsevier.com/locate/livsci Evidential segregation analysis for offspring sex ratio in rabbit and sheep populations Joaquim Casellas a, *, Marta Vázquez-Gómez b, Samir Id-Lahoucine c, Melani Martín de Hijas- Villalba a a Departament de Ciència Animal i dels Aliments, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain b Sorbonne Université, INSERM, Nutrition and Obesities: Systemic Approach Research Group, Nutriomics, Paris, F-75013, France c Department of Animal and Veterinary Sciences, Scotland’s Rural College, Easter Bush Campus, Midlothian, EH25 9RG, United Kingdom H I G H L I G H T S • Evidential inference provided a robust paradigm to analyze quantitative traits in livestock populations. • Segregation analysis could be effectively implemented on offspring sex ratio whatever the origin of the mutation. • Offspring sex ratio was significantly influenced by inbreeding, dam age, year and season of birth in rabbit and sheep populations. • A major mutation increasing the percentage of daughters was revealed in the Ripollesa sheep breed. A R T I C L E I N F O A B S T R A C T Keywords: Offspring sex ratio has been found to be altered by environmental and genetic distortions in multiple species, Evidential statistics against the Mendelian inheritance rules. However, little is known in livestock populations where it is essential to Inbreeding validate whether a polymorphic major gene with relevant effects may segregate in the target population. Logistic regression However, the current analytical tool (model FREQ) cannot handle new mutations in non-founder individuals, Mutation Sex ratio reducing the chance of detecting them. Our new analytical approach aimed to overcome this limitation in the context of evidential inference, a statistical framework based on the likelihood function as a robust objective measure of the strength of statistical evidence without variation from the sample size. Two field data sets from sheep and rabbit populations were used. Models evaluated environmental and inbreeding effects in both species. Our new approach assumed that the mutation primarily arose in an individual of the analyzed data set (model MUTj). Each sire was individually analyzed to determine the most plausible source for the new mutation, if any. The likelihood ratio (LR) against a reference parametrization without mutations (model NULL) was used to test the statistical relevance of systematic effects (LR ≥ 8) and models (LR ≥ 32). Both species revealed relevant departures for offspring sex ratio along the analyzed time frame with strong evidence for the year (LR = 1.4 × 109 in Ripollesa sheep and LR = 85.7 in MARET rabbits) and season (LR = 12.6 in MARET rabbits), although with a fluctuating pattern. The age of the dam reported weak evidence in both species (LR < 4). Inbreeding had a relevant linear impact on both sheep (LR = 60.7) and rabbit (LR = 780.4) populations, whereas the quadratic effect only showed strong evidence in MARET rabbits (LR = 8.3). Regarding the segregation analysis, most models showed an almost homozygous pattern of weak or lacking evidence of new mutations influencing offspring sex ratio. The only species showing strong evidence for the MUTj model (LR > 32) was the Ripollesa sheep, with a ram three to six generations from the founders as the most likely source for a new mutation increasing the odds of daughters. The additive genetic effect of this model for the mutant allele also had strong evidence (LR = 1,195). Therefore, the MUTj parametrization can be a valuable analytical tool to check for the possibility of new mutations along the pedigree files, not only before the founders. * Corresponding author. E-mail address: joaquim.casellas@uab.cat (J. Casellas). https://doi.org/10.1016/j.livsci.2023.105354 Received 9 January 2023; Received in revised form 4 September 2023; Accepted 6 October 2023 Available online 7 October 2023 1871-1413/© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). J. Casellas et al. Livestock Science 277 (2023) 105354 1. Introduction analytical approach for sex ratio data was tested in two different live­ stock data sets such as sheep and rabbit populations. Moreover, model fit Chromosomal mechanisms for sex determination were indepen­ was compared to the standard segregation analysis approach (Janss dently proposed more than a century ago (Stevens, 1905; Wilson, 1905). et al., 1995) to elucidate the most plausible source for new mutations, if In almost every mammalian species, sex is determined by the differential any (i.e., the new mutation appeared (1) before founder individuals, or inheritance of sex chromosomes (i.e., X and Y chromosomes), with (2) from founders onward). daughters inheriting two X chromosomes and sons inheriting both an X and a Y. According to Mendel’s (1866) inheritance rules, this would 2. Materials and methods anticipate a 1:1 sex ratio in the offspring of each sire, although with substantial variability inherent to the binomial distribution pattern of Animal Care and Use Committee approval was not necessary for this this biological outcome (Toro et al., 2006). However, both environ­ study because analyses were performed on existing field data obtained mental (King, 1927; Trivers and Willard, 1973; Roche et al., 2006) and under standard farm management. genetic distortions (King, 1918; Weir, 1976; de la Casa-Esperón et al., 2000) have been reported in multiple species. There exist some mice 2.1. Sex data from livestock populations strains with systematic departures in offspring sex ratio (Cook and Vlcek, 1961; Schlager and Roderick, 1968; Casellas et al., 2010). This The Servei de Granges i Camps Experimentals of the Universitat opens the door to scanning for genetic mutations affecting the sex ratio Autònoma de Barcelona (Bellaterra, Spain) has kept a sheep flock of in livestock, although little is known about this topic in domestic species ~100 Ripollesa ewes since its foundation in 1986. It is a medium-sized (Kennedy and Moxley, 1978; Skjervold, 1979; Skjervold and James, sheep breed (rams, 75 to 90 kg of live weight; ewes, 45 to 65 kg) 1979). characterized by white animals with black or dark brown marks on head Genetic laboratory technologies allow genome-wide screening for and legs, and semi-fine wool with closed fleece. The Ripollesa breed is polymorphisms at a reasonable cost. However, prior to this economic native from Catalonia (a north-east region of Spain) and should be investment, it is crucial to validate whether a polymorphic major gene considered as a representative example of the meat-type sheep industry with relevant effects on the phenotype of interest may be segregating in from the Mediterranean basin, producing pascual-type lambs (22 to 24 the target population. This preliminary survey could be carried out kg of live weight at slaughter; Esquivelzeta et al., 2011). The analyses through segregation analysis, as originally developed by Elston and included sex data at birth (both born alive and dead) from 3731 lambs Stewart (1971) and Morton and Maclean (1974) in humans, and later (males, 50.3 %) born between 1988 and 2022 from 49 sires and 561 adapted to livestock by Janss et al. (1995). This analytical approach ewes. Each ram contributed between two and 229 lambs (mean, 76.1 explored field and pedigree data and has been applied to livestock lambs; Fig. 1a) distributed between one and four lambing seasons. This (Janss et al., 1997; Walling et al., 2002; Argente et al., 2003), pet flock was maintained under standard semi-intensive management (Janutta et al., 2006) and laboratory species (Casellas et al., 2010), practices, with lambings concentrated in late summer and fall until 2006 where some major mutations were suggested. It is important to note that the standard parametrization assumed a single mutation that arose some time ago in the population and currently segregated among founder individuals of the analyzed data set at a given frequency. Although this could be viewed as a reasonable assumption, the emergence of new mutations in non-founder individuals could not be properly accommo­ dated unless they arose in a founder individual itself. This limitation precluded a proper analysis of all relevant mutations segregating in the population (i.e., both arising before and after founder individuals) and reduced the chance of detecting them. Segregation analyses in livestock populations have been previously implemented through the two main statistical frameworks of inference, frequentist (van Arendonk et al., 1989; Knott et al., 1992) and Bayesian (Janss et al., 1995, 1997; Casellas et al., 2010). Both rested on solid decision-theoretic foundations. The frequentist null hypothesis was rejected depending on a p-value falling below a fixed significance level that strictly controlled type-I error (Bickel, 2012). Bayesian posterior probabilities led to a measure of belief regarding how much one would wager on its truth (i.e., prior knowledge) given the available data and model (Jeffreys, 1948). Attempts have been made to adapt them to scenarios looking for the strength of evidence favoring one hypothesis over another rather than rejecting one hypothesis in a black-or-white choice. However, those attempts were controversial and highlighted evidential statistics as an appealing alternative focused on the objective quantification of statistical evidence (Edwards, 1972). This principle stated that all the statistical evidence was contained in the likelihood function once the data and the analytical model were accounted for. Within this context, the likelihood function must be viewed as a robust measure of the strength of statistical evidence that did not vary from one researcher to another (objectivity criterion) and has the same practical interpretation whatever the sample size of the data set (interpretability criterion; Bickel, 2012). This research focused on generalizing segregation analysis to new Fig. 1. Distribution of the offspring sex ratio against the number of offspring mutations arising in founder individuals and subsequent generations for each sire of the Ripollesa sheep breed (a) and the MARET rabbit popula­ within the context of evidential inference (Bickel, 2012). The developed tion (b). 2 J. Casellas et al. Livestock Science 277 (2023) 105354 and in spring from 2008 onward (no lambings in 2007). bucks (9.7 %), were not inbred, they contributing 10 % of offspring. On the other hand, the MARET rabbit population was founded be­ Remaining breeders had an inbreeding coefficient between 18.2 % and tween 1992 and 1999 from four unrelated rabbit farms located in the 74.7 %. I the preliminary analysis we found that there was a high degree Girona province (Catalonia, Spain) that contributed with one doe and of colinearity among inbreeding coefficients (i.e., offspring-sire-dam). four bucks (Casellas et al., 2011). This rabbit population was maintained Their joint inclusion in the same analytical model led to sever conver­ under standard farm conditions (Sant Gregori, Spain) to produce rabbits gence issues and, therefore, could not be applied. for the slaughterhouse. Its data set contained sex data from 2607 rabbits The statistical relevance of each fixed effect of the model was tested at weaning (males, 50.2 %) from 400 litters born between 2002 and within the context of evidential inference (Edwards, 1972). This is a 2022. The pedigree included 36 bucks and 39 does, where 31 males sired well-known paradigm relying on the likelihood function as a mathe­ between five and 296 offspring with relevant sex data (Fig. 1b). The matical structure that encompasses all statistical evidence from the data remaining five bucks contributed relevant pedigree relationships, relevant to the analytical model assumed (Birnbaum, 1962). Within this although without available offspring sex data. context, a given effect of the model (θ) could be tested by calculating the All relevant productive and reproductive data were systematically ratio (LR) between the likelihood of the full model (numerator model) registered in both livestock populations by the stockbreeders who made against the likelihood of a reduced model without θ (denominator it available to this study. model; Hacking, 1965). This ratio advocated for the superiority of the numerator model (LRθ > 1) or the denominator one (LRθ < 1), also ac­ 2.2. Analysis of binomial offspring sex data counting for an intermediate scenario where both models could not be properly discriminated (LRθ = 1). Small departures from LRθ = 1 provide Sex is determined by the sex chromosome inherited from the sire as a weak evidence in favor of either hypothesis, and Royall (1997) proposed dichotomous variable with two possible outcomes, male and female, a benchmark of LRθ > 8 (or <1/8) for a simple hypothesis (this roughly although some additional genetic and environmental distortion factors corresponded to a frequentist type-I error of 0.05 as demonstrated by have been reported (King, 1918, 1927; Weir, 1976; Roche et al., 2006; Blume [2002]). Within this context, both data sets were analyzed with de la Casa-Esperón et al., 2000). These factors may influence offspring the full model accounting for all sources of variation, and effects with sex ratio at several biological levels (e.g., fertilization success of X- and LRθ < 8 were removed from the final model (model NULL) used as the Y-bearing gametes [Sweeny and Barr, 1978], differential implantation reference for further segregation analyses. Confidence interval-like [Cameron, 2004] and differential survival during embryo or fetal and estimation could also be used in evidential statistics by properly neonatal periods [McMillen, 1979]) and cause departures from the ex­ defining likelihood intervals at 1/8 (LI8) such as the set of θ values with pected 1:1 ratio at different stages between fertilization (primary sex higher than 1/8 likelihood ratio when comparing against the maximum ratio), birth (secondary sex ratio; Berry et al., 2011), at puberty or likelihood θ estimate (Royall, 1997). among sexually mature individuals (tertiary sex ratio), and among in­ dividuals that can no longer expect to produce offspring (quaternary sex 2.4. Segregation analysis by evidential inference ratio; Ancona et al., 2017). Within this context, the offspring sex ratio can be appropriately analyzed based on each sire and the sex of its Model NULL expanded to segregation analysis by including two progeny (Toro et al., 2006). Sex of a given offspring i can be viewed as a additional linear covariates (i.e., additive and dominance) inherent to an phenotypic record (yi) with two possible values, yi = 1 (female) or yi = ungenotyped major gene that potentially segregates in the population 0 (male). This was an independent Bernoulli trial with female (male) (Janss et al., 1995). Assuming only two alleles with null (wild allele) and probability πi (1 - πi) as typically defined for logistic regression model non-null effects (mutant allele) on offspring sex ratio, the additive co­ (Berkson, 1944), variate accumulated the number of mutant copies in sires’ genome, π i = 1/[1 +exp(− xi b)], where b was the vector of fixed effects and xi whereas the dominance covariate was 1 for heterozygous sires and was an appropriate vector of incidences. Random infinitesimal additive 0 otherwise (Falconer and Mackay, 1996). Nevertheless, genotypes must genetic effects were discarded, as previously suggested by Toro et al. be updated as unknown parameters of the model by Kerr and Kinghorn (2006). The joint probability of n observed data (yT = [y1 y2 … yn]T) as a (1996). function of b and the chosen statistical model (i.e., the likelihood) The original parametrization of the segregation analysis (Janss et al., generalized top(y|b) = Πi [yi πi + (1 − yi )(1 − πi )] 1996) assumed that the mutation arose some time ago in the population This logistic regression model was fitted by maximum likelihood and was currently segregating in the founder individuals of the analyzed estimation implemented through a gradient descent algorithm (Cou­ data set at a given allelic frequency (model FREQ). Neither recurrent (i. rant, 1943). e., wild to mutant) nor reverse (i.e., mutant to wild) mutations were allowed. 2.3. Operational models Alternatively, the segregation analysis could assume that the new mutation primarily arose in the jth individual of the analyzed data set The analysis of lamb data accounted for three discrete effects and (model MUTj); i.e., this individual was arbitrarily fixed as heterozygous, two continuous covariates. The model included the population mean (a and remaining genotype probabilities were calculated following Kerr single level influencing all records), the year of lambing (34 levels from and Kinghorn (1996). Additional recurrent and reverse mutations were 1988 to 2022), and the age of the dam at lambing (<3 years, 3–4 years, not allowed again. An independent analysis was required for each sire 5–6 years, 7–8 years, and >8 years) as discrete effects following in part contributing offspring sex ratio data with model MUTj to determine the Arun Kumar et al. (2021), and the linear and quadratic effect of most plausible source for the new mutation, if any. Given that the inbreeding as continuous covariates. Only 15 out of 49 sires (30.6 %) analysis focused on a sire-linked trait, this approach could not were inbred with inbreeding coefficients fluctuating between 1.6 % and discriminate between a sire with offspring sex data and its dam when 12.5 %. These sires contributed with 1.132 lambs (30.3 % of the lambs trying to elucidate the real origin of the mutation unless the dam had under study). more than one son with similar departures in their offspring sex ratio. As The model for MARET rabbit data evaluated four discrete effects, for model NULL, both model FREQ and MUTj were solved by a gradient such as the populational mean, the season of birth (four levels), the year descent algorithm (Courant, 1943), although with the peeling approach of birth (10 levels grouping years by pairs to guarantee a minimum of 50 developed by Kerr and Kinghorn (1996) to update genotype offspring per year), the age of the doe at parturition (<12 months, 12 to probabilities. 24 months, and >24 months), and two regression coefficients involving Comparisons between models NULL, FREQ, and MUTj were carried the linear and quadratic effect of inbreeding. In this case, only three out by the ratio of their likelihood probabilities (Hacking, 1965). The 3 J. Casellas et al. Livestock Science 277 (2023) 105354 total number of pairwise comparisons was equal to the triangular number of s + 1 (Ts+1), such as Ts+1 = (s + 1)(s + 2)/2, where s was the number of sires with offspring sex ratio data. In order to account for multiple comparisons, the benchmark for strong evidence favoring the numerator (denomi­ nator) model was raised to LR > 32 (LR < 1/32) as proposed by Royall (1997) and Blume (2002). This value equaled 15 deciban units, a base-10 logarithmic unit that measures information and entropy (Good, 1979). 3. Results 3.1. Environmental and genetic factors influencing sex ratio Both species revealed relevant departures for offspring sex ratio along the analyzed time frame with strong evidence for the year effect in Fig. 2. Odds ratio estimates (black dot) and their 1/8 likelihood intervals the Ripollesa sheep (LR = 1.4 × 109), and both season (LR = 12.6) and (whiskers) for year of lambing effect on the analysis of offspring sex ratio in the year (LR = 85.7) effects in MARET rabbits (Table 1). Although odds Ripollesa sheep breed (upper-than-one estimates indicated an increase of fe­ ratios (i.e., the ratio of the odds of having a daughter in a given level of male offspring). the fixed effect of the model to the odds of it occurring in the reference level of the same effect) for the year effect did not show a clear tendency across the parametric space in the Ripollesa breed, they fluctuated around the unity and even several LI8 did not include this estimate by excess (years 1995, 1996, 2005, 2006, 2009 and 2013) or shortage (year 1997; Fig. 2). It is important to note that LI8 characterized the range of estimates guaranteeing a likelihood estimate of (at least) 1/8 of the likelihood probability at maximum likelihood estimates, and where roughly comparable to the 95 % confidence intervals (Blume, 2002). A similar fluctuating pattern was revealed in MARET rabbits, although a top estimate in the first (i.e., reference) level generated odds ratios lower than one for the remaining levels and a positive odds ratio estimate for the population mean of 1.20 (LI8, 1.11 to 1.31). On the other hand, the season effect suggested a fluctuating pattern one-year around, with the top odds ratio for daughters during spring (1,19; LI8, 1.13 to 1.29), and the lowest in autumn (0.84; LI8, 0.75 to 0.97; Fig. 3). The age of the dam reported weak evidence in both species, with LR Fig. 3. Odds ratio estimates (black dot) and their 1/8 likelihood intervals values lower than the relevant benchmark (LR < 8), although larger than (whiskers) for season (W, winter; Sp, spring; Su, summer; A, autumn) and year the unity (Table 1). Inbreeding had a relevant linear impact on the of birth effects (years in pairs from 2002 to 2003 to 2018 and 2019 and a final offspring sex ratio of both sheep (LR = 60.7) and rabbit (LR = 780.4) estimate for 2020 to 2022) on the analysis of offspring sex ratio in the MARET populations, whereas the quadratic effect only over-passed the evidence rabbit population (upper-than-one estimates indicated an increase of fe­ male offspring). boundary in MARET rabbits (LR = 8.3). As shown in Fig. 4, the linear regression coefficient for inbreeding depression in the Ripollesa sheep breed was 0.25 (LI8, 0.07 to 0.42), which increases the odds for daughters when increasing inbreeding. Similarly, inbreeding depression in the MARET rabbit population revealed a positive linear coefficient of 0.32 (LI8, 0.24 to 0.41) and a negative quadratic coefficient of -0.24 (LI8, -0.38 to -0.11). Likelihood intervals discarded negative odds (i.e., male offspring) for low and in­ termediate inbreeding coefficients until an inbreeding of 62.7 % (Fig. 4). 3.2. Segregation analysis Most pairwise model comparisons did not discriminate among Table 1 Statistical relevance for each fixed factor involved in the analysis of offspring sex ratio data (i.e., likelihood ratio (LR) between the full model against the model discarding the factor itself). Fig. 4. Odds ratio estimate (black line) and its 1/8 likelihood intervals (whis­ Ripollesa sheep data set MARET rabbit data set kers) for inbreeding depression on offspring sex ratio (upper-than-one estimates Factor LR Factor LR indicated an increase of female offspring). Population mean 1.1 Population mean 1.5 × 105 Year 1.4 × 109 Season 12.6 competing parametrizations. Indeed, the NULL model must be viewed as Ewe age 3.5 Year 85.7 the reference one. The heatmap shown in Fig. 5 provided an almost Inbreeding (linear) 60.7 Doe age 1.7 homozygous pattern of weak or even lacking evidence of new mutations Inbreeding (quadratic) 1.3 Inbreeding (linear) 780.4 Inbreeding (quadratic) 8.3 influencing offspring sex ratio. The only species showing strong 4 J. Casellas et al. Livestock Science 277 (2023) 105354 Fig. 5. Heatmap for the likelihood ratio (columns, numerator model; rows, denominator model) of segregation models on offspring sex ratio data of the Ripollesa sheep breed (a) and MARET rabbit population (b). Comparisons included the model without mutations (NULL), the model with a mutation already segregating in the founder generation (FREQ), and models with a new mutation arising in the jth individual (MUTj). evidence for the MUTj model (LR > 32) was the Ripollesa sheep, where a ram born in 1997 was revealed as the most probable source for a new mutation increasing the percentage of daughters. This model had a likelihood of 183.1 and 102.5 times greater than the ones from the NULL and FREQ models, respectively. Moreover, this model outperformed remaining MUTj models with an LR ≥ 27.6, except for direct compari­ sons with its father (LR = 2.7) and two grandsons (LR = 2.9 and 9.7) who generate the dark green columns flanking the fair green one in Fig. 5a. Focusing on the MUTj model with the highest likelihood in the Ripollesa breed, there was strong evidence supporting the additive ge­ netic effect for the mutant allele (LR = 1195.0) and null evidence for the dominance effect (LR = 1.0). The additive genetic effect reached an odds ratio of 2.23 for daughter offspring (LI8, 1.43 to 3.53), which is consistent with the departed 50:50 ratios shown in Fig. 5a for some sires. This specific MUTj model highlighted a ram born in 1997 as the first carrier of a new mutation departing offspring sex ratio (Fig. 6), with 57 daughters (62.6 %) and 34 sons (37.4 %). Three out of its four male sons/grandsons retained for breeding purposes inherited the mutation with a higher-than-0.5 probability, although those lineages did not contributed rams since 2013 (Fig. 6). Unfortunately, MARET rabbits did not suggest relevant segregation patterns influencing offspring sex ratio (Fig. 5b). 4. Discussion 4.1. Analytical framework The segregation analysis model developed in this manuscript (MUTj) must be viewed as a relevant example where the mutation source must Fig. 6. Maximum likelihood predicted genotypes (green, homozygous wild- be evaluated along the pedigree file with multiple hypotheses to be type; orange, heterozygous wild-type/mutant) under the MUTj model with maximum likelihood probability in Ripollesa data set (i.e., the model assumed a compared in terms of probability instead of being accepted or discarded. new mutation arising in a non-founder sire placed on the top of the figure). This relied on an evidential inference approach (Birnbaum, 1962) as Note that the size of the ♂ symbol characterized the number of offspring (from opposed to both Bayesian and frequentist inferential frameworks. 39 to 109 offspring; not applicable to ♀) and included the percentage of Bayesian inferential procedures failed to satisfy the objectivity criterion daughters. Only descendants from the sire carrying the first mutation (on the because of the inclusion of researcher-specific a priori distributions to top) were included. obtain the relevant joint posterior distribution (Bickel, 2012). On the other hand, the interpretability of frequentist tests was impaired due to the invariable boundary for type-I errors, characterizing the probability of observing misleading evidence. This parameter must tend to zero with 5 J. Casellas et al. Livestock Science 277 (2023) 105354 increasing the sample size, whereas it is typically fixed to 0.05, whatever Further efforts must focus on active ewes descending from the 1997 ram. the amount of data involved in the analysis (Bickel, 2012). Predicted genotype probabilities must be viewed as a key tool to identify descendants with the highest heterozygote probabilities, they being 4.2. Factors influencing offspring sex ratio target dams to provide a new generation of rams to be tested in terms of offspring sex ratio. Environmental factors inherent to year and/or season of birth The whole data set involved deep pedigree files rooted more than influenced the offspring sex ratio in both species, as previously reported three decades ago and with a minimum of ten generations (results not in sheep (Kent, 1996; Thiruvenkadan et al., 2008; Hossein-Zadeh, 2016; shown). Within this context, the MUTj parametrization must be viewed Kumar et al., 2021) and discarded in rabbits, although under research as a relevant analytical tool to check for the possibility of new mutations maintenance conditions (Sawin and Gadbois, 1947). Indeed, seasonal along the pedigree files, where Janss et al. (1995) model would fail due departures were also described in other mammalian species such as seals to the inherent restriction about the mutational event happening before (Stirling, 1971). These variations were previously linked to resource founders. availability and the Trivers and Willard’s (1973) hypothesis, an argu­ ment that suggested higher chance to produce sons from mothers in 4.4. Mutation in offspring sex ratio superior body condition, and vice-versa. The same rationale must apply to the age of the dam effect, which slightly increased the percentage of Scientific literature about sex ratio departures was scarce and daughters from young and old females, and males from intermediate controversial in livestock species (Sawin and Gadbois, 1947; Kennedy ages. These results were previously reported in sheep (Kent, 1996) and and Moxley, 1978; Skjervold, 1979; Skjervold and James, 1979), pigs (Toro et al., 2006). whereas they were more frequently reported in laboratory rodents Inbreeding was also revealed as a relevant source of variation for (Weir, 1960, 1976; Cook and Vlcek, 1961; Beamer and Whitten, 1991; offspring sex ratio. The higher inbreeding, the higher chance of daughter de la Casa-Esperón et al., 2000; Lee, 2002), and experimental inverte­ offspring as reported in Irish Holstein–Friesian cattle (Mc Parland et al., brate strains (Sweeny and Barr, 1978; Cazemajor et al., 1997; Tao et al., 2007), pygmy hippopotamus in zoological gardens (Graczyk et al., 2007a,b). The additive mutation increasing the odds of female offspring 2015), eastern bongo (Tragelaphus eurycerus isaaci; Malo et al., 2019), in the Ripollesa sheep breed must join this small collection of Arabian oryx (Oryx leucoryx) and red wolf (Canis rufus; Frankham and mammalian populations with sex ratio departures. Indeed, this Wilcken, 2006). These results could be due to sex-linked deleterious female-biased pattern agreed with deviations previously reported in recessive alleles, although other genetic influences could not be rabbits (Sawin and Gadbois, 1947) and laboratory mice (Weir, 1960, discarded. 1976; Cook and Vlcek, 1961; Casellas et al., 2010). Our analyses sug­ gested a major autosomal locus, although the lack of homozygous 4.3. New parametrization for segregation analysis wild-type individuals in Fig. 6 did not completely discard contributions from the sex chromosome X. Indeed, research in mice over the last few Janss et al. (1995) assumed a previous mutation already segregating years has found sex chromosome-linked gene families associated with in the founder individuals of the analyzed data set, and Casellas et al. sex ratio distortions (Prssly, Sly & Slx/Slx1; Kruger et al., 2019 and (2010) adapted the original segregation analysis (Elston and Stewart, Hughes et al., 2022), mainly from the chromosome X. These genes have 1971; Morton and Maclean, 1974) to a dichotomous trait. The current been related to sperm production and release and may be critical for research takes a step ahead to generalize the analysis to a new scenario male fertility. where the new mutation on the binary trait arose in one individual of the analyzed population. One main criticism would focus on the lack of 5. Conclusions reference to the very low chance of new mutations in the genome, typically around 10− 8 per base pair (Lipson et al., 2015). The odds of a Segregation analysis on binary traits can be performed within the new mutational event in the subset of analyzed sires departing their context of evidential inference, which involves the degree of statistical offspring sex ratio would be minimal, if any. Nevertheless, the same low evidence regarding each mutational source. This statistical tool must be chance must apply to the recent ancestors of founder individuals under viewed as useful to check for new mutations affecting traits of interest in Janss et al. (1995) approach, where both mutation and genetic drift livestock populations and laboratory species. The MARET rabbit popu­ played a key role. It must be highlighted that both parametrizations took lation did not provide evidence supporting offspring sex ratio departures the same assumption about the mutational event, conditioning all the due to new mutations. In contrast, the Ripollesa sheep breed revealed a subsequent analysis to the premise of a new mutation that happens with new mutation increasing the odds of female offspring. This mutation full probability in the jth individual (model MUTj) or some recent arose in an intermediate generation (year 1997) of the pedigree file and ancestor (model FREQ; Janss et al., 1995). As a consequence, this segregated with high probability until 2013. canceled in likelihood functions and did not bias the LR. Model FREQ did not reveal statistical evidence favoring a mutation CRediT authorship contribution statement already segregating neither in the Ripollesa breed nor in the MARET population when compared against the NULL model (LR = 3.2 and 1.7, Joaquim Casellas: Conceptualization, Data curation, Software, respectively). Nevertheless, the MUTj model succeeds in the Ripollesa Writing – original draft. Marta Vázquez-Gómez: Methodology, Writing breed with an LR of almost 200 compared to NULL and FREQ. It is – review & editing. Samir Id-Lahoucine: Methodology, Writing – re­ important to highlight the contradictory behavior of FREQ and MUTj view & editing. Melani Martín de Hijas-Villalba: Methodology, models on the same data set. One would expect some absorption of the Writing – review & editing. new mutation in the founders’ generation when analyzed under the FREQ model. Nevertheless, the new mutant shown in Fig. 6 was between Declaration of Competing Interest three and six generations away from the founders, and its father and grandfathers had offspring sex ratios between 47 % and 52 % with 70 to There are no known conflicts of interest associated with this publi­ 134 offspring. It is important to note that current analytical approaches cation and there has been no significant financial support for this work cannot discriminate between this ram and its mother as the first known that could have influenced its outcome. carrier of the segregating mutation. Unfortunately, this paternal lineage was unconsciously removed from the UAB experimental flock after the 2021 breeding season, by culling the two rams born in 2019 (Fig. 6). 6 J. Casellas et al. 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