Likelihood-based association analysis for nuclear families and unrelated subjects with missing genotype data

Missing data occur in genetic association studies for several reasons including missing family members and uncertain haplotype phase. Maximum likelihood is a commonly used approach to accommodate missing data, but it can be difficult to apply to family-based association studies, because of possible loss of robustness to confounding by population stratification. Here a novel likelihood for nuclear families is proposed, in which distinct sets of association parameters are used to model the parental genotypes and the offspring genotypes. This approach is robust to population structure when the data are complete, and has only minor loss of robustness when there are missing data. It also allows a novel conditioning step that gives valid analysis for multiple offspring in the presence of linkage. Unrelated subjects are included by regarding them as the children of two missing parents. Simulations and theory indicate similar operating characteristics to TRANSMIT, but with no bias with missing data in the presence of linkage. In comparison with FBAT and PCPH, the proposed model is slightly less robust to population structure but has greater power to detect strong effects. In comparison to APL and MITDT, the model is more robust to stratification and can accommodate sibships of any size. The methods are implemented for binary and continuous traits in software, UNPHASED, available from the author.     

Performance of Markov chain-Monte Carlo approaches for mapping genes in oligogenic models with an unknown number of loci

Markov chain-Monte Carlo (MCMC) techniques for multipoint mapping of quantitative trait loci have been developed on nuclear-family and extended-pedigree data. These methods are based on repeated sampling-peeling and gene dropping of genotype vectors and random sampling of each of the model parameters from their full conditional distributions, given phenotypes, markers, and other model parameters. We further refine such approaches by improving the efficiency of the marker haplotype-updating algorithm and by adopting a new proposal for adding loci. Incorporating these refinements, we have performed an extensive simulation study on simulated nuclear-family data, varying the number of trait loci, family size, displacement, and other segregation parameters. Our simulation studies show that our MCMC algorithm identifies the locations of the true trait loci and estimates their segregation parameters well-provided that the total number of sibship pairs in the pedigree data is reasonably large, heritability of each individual trait locus is not too low, and the loci are not too close together. Our MCMC algorithm was shown to be significantly more efficient than LOKI (Heath 1997) in our simulation study using nuclear-family data.     

Mapping disease genes: family-based association studies.

With recent rapid advances in mapping of the human genome, including highly polymorphic and closely linked markers, studies of marker associations with disease are increasingly relevant for mapping disease genes. The use of nuclear-family data in association studies was initially developed to avoid possible ethnic mismatching between patients and randomly ascertained controls. The parental marker alleles not transmitted to an affected child or never transmitted to an affected sib pair form the so-called AFBAC (affected family-based controls) population. In this paper, the theoretical foundation of the AFBAC method is proved for any single-locus model of disease and for any nuclear family-based ascertainment scheme. In a random-mating population, when there is a marker association with disease, the AFBAC population provides an unbiased estimate of the overall population (control) marker alleles when the recombination fraction (theta) between the marker and disease genes is sufficiently small that it can be taken as zero (theta = 0). With population stratification, only marker associations present in the subpopulations will be detected with family-based analyses. Of more importance, however, is the fact that, when theta not equal to 0, differences between transmitted parental (patient) marker allele frequencies and non- or never-transmitted parental marker allele frequencies (implying a marker association with disease) can only be observed for marker genes linked to a disease gene (theta < 1/2). Thus, associations of unlinked marker loci with disease at the population level, caused by population stratification, migration, or admixture, are eliminated. This validates the use of family-based association tests as an appropriate strategy for mapping disease genes.     

Allowing for missing data at highly polymorphic genes when testing for maternal, offspring and maternal-fetal genotype incompatibility effects

Genes can be associated with disease through an individual's inherited genotype, the maternal genotype or the interaction between these two. When the gene is highly polymorphic, it is more difficult to identify the gene's functional role than for less polymorphic loci, because different alleles at the locus may be associated with the disease through separate and joint effects from maternal and offspring genotypes. Family-based studies are used to test genetic associations because of their robustness to population stratification. However, parental genotype data are often missing, and omitting incompletely genotyped families is inefficient. Methods have been proposed to accommodate incomplete families in family-based association studies. They are not easily generalized to allow simultaneous examination of offspring allelic, maternal allelic and maternal-fetal genotype (MFG) incompatibility effects. Since many MFG incompatibility effects occur through matching between maternal and offspring's genotypes, we present an identity-by-state (IBS) framework to incorporate incomplete families in the MFG test when modeling genetic effects produced by a polymorphic gene. Using simulations, we examine the MFG test's performance with incomplete parental genotype data and an IBS framework. The MFG test using the IBS framework is immune to population stratification and efficiently uses information from incomplete families.     

Predicting parental genotypes and gene segregation for tetrasomic inheritance

Recent genome mapping projects in tetraploid plant species require a method for analysing the segregation patterns of molecular marker loci in these species. The present study presents a theoretical model and a statistical analysis for predicting the genotypes of a pair of tetraploid parents at a codominant (for example, RFLPs, microsatellites) or dominant (for example, AFLPs, RAPDs) molecular marker locus based on their and their progeny’s phenotypes scored at that locus (gel-band patterns). The theory allows for null alleles and for any degree of double-reduction to be modelled. A simulation study was performed to investigate the properties of the theoretical model. This showed that in many circumstances both the parental genotypes can be correctly identified with a probability of nearly 1, even when the molecular data were complicated by null alleles or double-reduction. Configurations where the parental genotype cannot be identified are discussed. The power to detect double-reduction varies considerably, depending on the proportion of identical alleles carried and shared by the parents, and the number of null alleles. Incorrect deductions of the occurrence of double-reduction were rare. The method was applied to data on a microsatellite locus segregating in the parents and 74 offspring of a tetraploid potato cross. Twentyfour parental configurations were consistent with the parental gel pattern, but only one of these was compatible with all the phenotypic data on the offspring. The feasibility for extending the present model to predict segregation of several linked loci, and particularly the linkage phase, is briefly discussed. Received: 7 June 1999 / Accepted: 28 September 1999     

Weak evidence for anticipatory parental effects in plants and animals

The evolution of adaptive phenotypic plasticity relies on the presence of cues that enable organisms to adjust their phenotype to match local conditions. Although mostly studied with respect to nonsocial cues, it is also possible that parents transmit information about the environment to their offspring. Such ‘anticipatory parental effects’ or ‘adaptive transgenerational plasticity’ can have important consequences for the dynamics and adaptive potential of populations in heterogeneous environments. Yet, it remains unknown how widespread this form of plasticity is. Using a meta‐analysis of experimental studies with a fully factorial design, we show that there is only weak evidence for higher offspring performance when parental and offspring environments are matched compared with when they are mismatched. Estimates of heterogeneity among studies suggest that effects, when they occur, are subtle. Study features, environmental context, life stage and trait categories all failed to explain significant amounts of variation in effect sizes. We discuss theoretical and methodological reasons for the limited evidence for anticipatory parental effects and suggest ways to improve our understanding of the prevalence of this form of plasticity in nature.     

Maternal care,mother–offspring aggregation and age‐dependent coadaptation in the European earwig

Benefits and costs of parental care are expected to change with offspring development and lead to age‐dependent coadaptation expressed as phenotypic (behavioural) matches between offspring age and parental reproductive stage. Parents and offspring interact repeatedly over time for the provision of parental care. Their behaviours should be accordingly adjusted to each other dynamically and adaptively, and the phenotypic match between offspring age and parental stage should stabilize the repeated behavioural interactions. In the European earwig (Forficula auricularia), maternal care is beneficial for offspring survival, but not vital, allowing us to investigate the extent to which the stability of mother–offspring aggregation is shaped by age‐dependent coadaptation. In this study, we experimentally cross‐fostered nymphs of different age classes (younger or older) between females in early or late reproductive stage to disrupt age‐dependent coadaptation, thereby generating female–nymph dyads that were phenotypically matched or mismatched. The results revealed a higher stability in aggregation during the first larval instar when care is most intense, a steeper decline in aggregation tendency over developmental time and a reduced developmental rate in matched compared with mismatched families. Furthermore, nymph survival was positively correlated with female–nymph aggregation stability during the early stages when maternal care is most prevalent. These results support the hypothesis that age‐related phenotypically plastic coadaptation affects family dynamics and offspring developmental rate.     

Proximate causes and consequences of intergenerational influences of salient sensory experience

Salient sensory environments experienced by a parental generation can exert intergenerational influences on offspring. While these data provide an exciting new perspective on biological inheritance, questions remain about causes and consequences of intergenerational influences of salient sensory experience. We previously showed that exposing male mice to a salient olfactory experience, like olfactory fear conditioning, resulted in offspring demonstrating a sensitivity to the odor used to condition the paternal generation and possessing enhanced neuroanatomical representation for that odor. In this study, we first injected RNA extracted from sperm of male mice that underwent olfactory fear conditioning into naïve single‐cell zygotes and found that adults that developed from these embryos had increased sensitivity and enhanced neuroanatomical representation for the odor (Odor A) with which the paternal male had been conditioned. Next, we found that female, but not male offspring sired by males conditioned with Odor A show enhanced consolidation of a weak single‐trial Odor A + shock fear conditioning protocol. Our data provide evidence that RNA found in the paternal germline after exposure to salient sensory experiences can contribute to intergenerational influences of such experiences, and that such intergenerational influences confer an element of adaptation to the offspring. In so doing, our study of intergenerational influences of parental sensory experience adds to existing literature on intergenerational influences of parental exposures to stress and dietary manipulations and suggests that some causes (sperm RNA) and consequences (behavioral flexibility) of intergenerational influences of parental experiences may be conserved across a variety of parental experiences.     

Male-biased mutation rates and the overestimation of extrapair paternity: problem, solution, and illustration using thick-billed murres (Uria lomvia, Alcidae)

The widespread utility of hypervariable loci in genetic studies derives from the high mutation rate, and thus the high polymorphism, of these loci. Recent evidence suggests that mutation rates can be extremely high and may be male biased (occurring in the male germ-line). These two factors combined may result in erroneous overestimates of extrapair paternity, since legitimate offspring with novel alleles will have more mismatches with respect to the biological father than the biological mother. As mutations are male driven, increasing the number of hypervariable loci screened may simply increase the number of mismatches between fathers and their legitimate offspring. Here we describe a simple statistic, the probability of resemblance (PR), to distinguish between mismatches due to parental misassignment versus mutation in either sex or null alleles. We apply this method to parentage data on thick-billed murres (Uria lomvia), and demonstrate that, without considering either mutations or male-biased mutation rates, cases of extrapair paternity (7% in this study) would be grossly overestimated (14.5%-22%). The probability of resemblance can be utilized in parentage studies of any sexually reproducing species when allele or haplotype frequency data are available for putative parents and offspring. We suggest calculating this probability to correctly categorize legitimate offspring when mutations and null alleles may cause mismatches.     

Informative missingness in genetic association studies: case-parent designs

We consider the effect of informative missingness on association tests that use parental genotypes as controls and that allow for missing parental data. Parental data can be informatively missing when the probability of a parent being available for study is related to that parent's genotype; when this occurs, the distribution of genotypes among observed parents is not representative of the distribution of genotypes among the missing parents. Many previously proposed procedures that allow for missing parental data assume that these distributions are the same. We propose association tests that behave well when parental data are informatively missing, under the assumption that, for a given trio of paternal, maternal, and affected offspring genotypes, the genotypes of the parents and the sex of the missing parents, but not the genotype of the affected offspring, can affect parental missingness. (This same assumption is required for validity of an analysis that ignores incomplete parent-offspring trios.) We use simulations to compare our approach with previously proposed procedures, and we show that if even small amounts of informative missingness are not taken into account, they can have large, deleterious effects on the performance of tests.     

The evolution of indicator traits for parental quality: the role of maternal and paternal effects

In systems where individuals provide material resources to their mates or offspring, mate choice based on traits that are phenotypically correlated with the quality of resources provided is expected to be adaptive. Several models have explored the evolution of mating preference where there are direct benefits to choice, but few have addressed how a phenotypic correlation can be established between a male indicator trait and the degree of parental investment. We present a model with three quantitative traits: male and female parental investment and a potential male indicator trait. In our model, the expression of the "indicator" trait in offspring is affected by parental investment. These effects are referred to as maternal or paternal effects, or as "indirect genetic effects" when parental investment is heritable. With genetic variation for degree of parental investment, offspring harbor genes for parental investment that are unexpressed before mating but will affect the investment that they provide when expressed. Because the investment received from the parents affects the expression of the indicator trait, there will be a correlation between the genes for parental investment inherited and the degree of expression of the indicator trait in the offspring. The indicator trait is thus an "honest" signal for the degree of paternal investment.     

Models of parent-offspring conflict. IV. Suppression: Evolutionary retaliation by the parent

We have earlier analysed ESSs for the amount of parental investment (PI) that offspring are expected to solicit from their parents, given that parents acquiesce to offspring demands. The present paper considers evolutionary retaliation by the parent for species where only one parent provides PI. Two genetic loci are envisaged: one (the ‘conflictor’ locus) determines the extent of offspring solicitation; the other (the ‘suppressor’ locus) determines how parents retaliate. Solicitation is assumed to carry a cost which may affect a particular offspring uniquely if time and energy are the major costs, or may affect all offspring in a brood equally if the main cost is predation risk. Two kinds of parental retaliation are possible. Parents may supply PI in proportion to offspring demands, or may ignore solicitation altogether and give a fixed PI. Analytical models of conflict in which the parent supplies PI in proportion to solicitation yield pure ESSs with PI at a compromise level between parent and offspring interests. These are termed ‘pro rata’ ESSs. Where solicitation costs are high, an ‘offspring wins’ ESS (offspring get all they ‘want’) is possible especially for forms of conflict that affect future sibs, and a ‘parent wins’ ESS (parent supplies its optimum) is possible especially for conflict that affects contemporary sibs. When parental retaliation takes the form of ignoring offspring solicitation, this can lead to a ‘parent wins’ ESS if costs of ignoring solicitation are negligible, but where parental insensitivity carries costs, the result is an unresolvable evolutionary chase with cycling frequencies of alleles coding for parent and offspring strategies. ‘Pro rata’ ESSs cannot be invaded by ‘ignore solicitation’ mutants but ‘pro rata’ mutants can often invade at certain stages in ‘ignore solicitation’ limit cycles. We therefore conclude that the probable evolutionary end product for most species will be the ‘pro rata’ ESS in which the parent supplies more PI than would be optimal in the absence of conflict, but less PI than would be an ESS for the offspring in the absence of parental retaliation. Such ESSs will be characterized by solicitation costs; offspring will ‘ask’ for more PI than they get. In nature, under similar conditions, highest conflict will occur when both parents sustain equally the effects of conflict, or when conflict affects contemporary rather than future sibs.     

Male "mixed" reproductive strategies in biparental species: Trivers was probably right, but why?

Trivers proposed that, if parental care by both sexes is advantageous, males should practice a "mixed" strategy of seeking extrapair copulations, while restricting their parental investment to offspring of social mates. We explore circumstances under which males should limit their parental care in the predicted manner. We find that Trivers's "mixed" strategy will generally be evolutionarily stable so long as either socially monogamous or polygynous males usually sire more offspring per brood from a social mate than they typically sire in broods of extrapair mates. Polygynous males should spread investment across their home nests unless the expected number of chicks sired in them differs widely. Whether polygynous males should restrict paternal care to social mates' offspring hinges additionally on resident male investment in broods containing extrapair young: if resident males contribute minimally, some investment by a polygynous extrapair male becomes more advantageous. Recently reviewed data on extrapair fertilization distributions within monogamous and polygynous passerines suggest that extrapair offspring often predominate numerically within their broods, consistent with sperm expenditure theory. Nevertheless, most species conform to the model's criterion regarding relative parentage levels in broods of social versus extrapair mates. Patterns of extrapair parentage thus appear sufficient to stabilize biparental care systems.     

中国对虾微卫星家系鉴定的模拟分析与应用

本研究基于中国对虾群体所获的微卫星标记等位基因频率进行了计算机模拟分析,并选择5个微卫星标记,就单独养殖家系群体微卫星标记家系鉴定的准确性及混养家系群体微卫星标记家系鉴定的应用价值做了研究.模拟分析表明4个微卫星标记可以鉴定95%的后裔.而单独养殖的家系鉴定准确率达到92.9%,在30个可能的父母对,215尾中国对虾组成的混养家系群体中,90.7%的后裔可以鉴定其父母.本研究结果表明微卫星分子标记可以应用于中国对虾的家系鉴定.模拟分析与实际应用的差异及父母与子代间的错配部分原因是由于无效等位基因的出现,基因分型错误也是一个重要原因.基于父母LOD值的分析可以降低错配的几率.     

Sex‐specific pathways of parental age effects on offspring lifetime reproductive success in a long‐lived seabird

The conditions under which individuals are reared vary and sensitivity of offspring to such variation is often sex‐dependent. Parental age is one important natal condition with consequences for aspects of offspring fitness, but reports are mostly limited to short‐term fitness consequences and do not take into account offspring sex. Here we used individual‐based data from a large colony of a long‐lived seabird, the common tern Sterna hirundo, to investigate longitudinal long‐term fitness consequences of parental age in relation to both offspring and parental sex. We found that recruited daughters from older mothers suffered from reduced annual reproductive success. Recruited sons from older fathers were found to suffer from reduced life span. Both effects translated to reductions in offspring lifetime reproductive success. Besides revealing novel sex‐specific pathways of transgenerational parental age effects on offspring fitness, which inspire studies of potential underlying mechanisms, our analyses show that reproductive senescence is only observed in the common tern when including transgenerational age effects. In general, our study shows that estimates of selective pressures underlying the evolution of senescence, as well as processes such as age‐dependent mate choice and sex allocation, will depend on whether causal transgenerational effects exist and are taken into account.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

On the detection of imprinted quantitative trait loci in line crosses: effect of linkage disequilibrium

Imprinted quantitative trait loci (QTL) are commonly reported in studies using line-cross designs, especially in livestock species. It was previously shown that such parent-of-origin effects might result from the nonfixation of QTL alleles in one or both parental lines, rather than from genuine molecular parental imprinting. We herein demonstrate that if linkage disequilibrium exists between marker loci and nonfixed QTL, spurious detection of pseudo-imprinting is increased by an additional 40–80% in scenarios mimicking typical livestock situations. This is due to the fact that imprinting can be tested only in F₂ offspring whose sire and dam have distinct marker genotypes. In the case of linkage disequilibrium between markers and QTL, such parents have a higher chance to have distinct QTL genotypes as well, thus resulting in distinct padumnal and madumnal allele substitution effects, i.e., QTL pseudo-imprinting.     

COEVOLUTIONARY FEEDBACKS BETWEEN FAMILY INTERACTIONS AND LIFE HISTORY

Families with parental care show a parent–offspring conflict over the amount of parental investment. To date, the resolution of this conflict was modeled as being driven by either purely within‐brood or between‐brood competition. In reality the partitioning of parental resources within‐ versus between‐broods is an evolving life history trait, which can be affected by parent–offspring interactions. This coevolutionary feedback between life history and family interactions may influence the evolutionary process and outcome of parent–offspring coadaptation. We used a genetic framework for a simulation model where we allowed parental parity to coevolve with traits that determine parental investment. The model included unlinked loci for clutch size, parental sensitivity, baseline provisioning, and offspring begging. The simulation showed that tight coadaptation of parent and offspring traits only occurred in iteroparous outcomes whereas semelparous outcomes were characterized by weak coadaptation. When genetic variation in clutch size was unrestricted in the ancestral population, semelparity and maximal begging with poor coadaptation evolved throughout. Conversely, when genetic variation was limited to iteroparous conditions, and/or when parental sensitivity was treated as an evolutionarily fixed sensory bias, coadapted outcomes were more likely. Our findings show the influence of a feedback between parity, coadaptation, and conflict on the evolution of parent–offspring interactions.     

Models of parent-offspring conflict. V. Effects of the behaviour of the two parents

In the absence of any parent-offspring conflict, the total parental investment per offspring should be less when two parents collaborate in caring for the offspring than when only one parent invests. This does not necessarily mean that offspring fare less well when both parents invest. The ‘ideal’ amount of parental investment for an offspring to take is always greater than is ‘ideal’ for the parent to allocate (Trivers 1974). The offspring's optimum is higher if the offspring's action affects the reproductive success of only one parent and lower if both parents are affected (e.g. two-parent investment, or lifelong monogamy). The difference between the parental optimum and the offspring optimum depends on the mating system and on the form of conflict (between successive broods, or within broods), and prescribes a ‘conflict range’. The extent of conflict cannot be deduced solely from a knowledge of the average relatedness between siblings. The conflict is likely to be resolved by an ESS in which intermediate (compromise) levels of investment are paid out to offspring, which nevertheless continue to make costly demands for yet more investment. The degree of conflict can be measured by the extent to which offspring subject their parents to aggressive demands for extra investment, and is likely to be greater when two parents collaborate equally over investment than when only one parent invests. When only one parent invests, conflict is higher if sibling-competition is between siblings in the same broods (intra-brood) than when it is between progeny in successive broods (inter-brood). However, the reverse will tend to be the case when both parents invest equally.