Allowing for missing parents in genetic studies of case-parent triads

In earlier work, my colleagues and I described a log-linear model for genetic data from triads composed of affected probands and their parents. This model allows detection of and discrimination between effects of an inherited haplotype versus effects of the maternal haplotype, which presumably would be mediated by prenatal factors. Like the transmission disequilibrium test (TDT), the likelihood-ratio test (LRT) based on this model is not sensitive to associations that are due to genetic admixture. When used as a method for testing for linkage disequilibrium, the LRT can be regarded as an alternative to the TDT. When one or both parents are missing, the resulting incomplete triad must be discarded to ensure validity of the TDT, thereby sacrificing information. By contrast, when the problem is set in a likelihood framework, the expectation-maximization algorithm allows the incomplete triads to contribute their information to the LRT without invalidation of the analysis. Simulations demonstrate that much of the lost statistical power can be recaptured by means of this missing-data technique. In fact, power is reasonably good even when no triad is complete-for example, when a study is designed to include only mothers of cases. Information from siblings also can be incorporated to further improve the statistical power when genetic data from parents or probands are missing.     

A log-linear approach to case-parent-triad data: assessing effects of disease genes that act either directly or through maternal effects and that may be subject to parental imprinting.

We describe a log-linear method for analysis of case-parent-triad data, based on maximum likelihood with stratification on parental mating type. The method leads to estimates of association parameters, such as relative risks, for a single allele, and also to likelihood ratio chi2 tests (LRTs) of linkage disequilibrium. Hardy-Weinberg equilibrium need not be assumed. Our simulations suggest that the LRT has power similar to that of the chi2 "score" test proposed by Schaid and Sommer and that both can outperform the transmission/disequilibrium test (TDT), although the TDT can perform better under an additive model of inheritance. Because a restricted version of the LRT is asymptotically equivalent to the TDT, the proposed test can be regarded as a generalization of the TDT. The method that we describe generalizes easily to accommodate maternal effects on risk and, in fact, produces powerful and orthogonal tests of the contribution of fetal versus maternal genetic factors. We further generalize the model to allow for effects of parental imprinting. Imprinting effects can be fitted by a simple, iterative procedure that relies on the expectation-maximization algorithm and that uses standard statistical software for the maximization steps. Simulations reveal that LRT tests for detection of imprinting have very good operating characteristics. When a single allele is under study, the proposed method can yield powerful tests for detection of linkage disequilibrium and is applicable to a broader array of causal scenarios than is the TDT.     

A hybrid design for studying genetic influences on risk of diseases with onset early in life

Studies of genetic contributions to risk can be family-based, such as the case-parents design, or population-based, such as the case-control design. Both provide powerful inference regarding associations between genetic variants and risks, but both have limitations. The case-control design requires identifying and recruiting appropriate controls, but it has the advantage that nongenetic risk factors like exposures can be assessed. For a condition with an onset early in life, such as a birth defect, one should also genotype the mothers of cases and the mothers of controls to avoid potential confounding due to maternally mediated genetic effects acting on the fetus during gestation. The case-parents approach is less vulnerable than the case-mother/control-mother approach to biases due to population structure and self-selection. The case-parents approach also allows access to epigenetic phenomena like imprinting, but it cannot evaluate the role of nongenetic cofactors like exposures. We propose a hybrid design based on augmenting a set of affected individuals and their parents with a set of unaffected, unrelated individuals and their parents. The affected individuals and their parents are all genotyped, whereas only the parents of unaffected individuals are genotyped, although exposures are ascertained for both affected and unaffected offspring. The proposed hybrid design, through log-linear, likelihood-based analysis, allows estimation of the relative risk parameters, can provide more power than either the case-parents approach or the case-mother/control-mother approach, permits straightforward likelihood-ratio tests for bias due to mating asymmetry or population stratification, and admits valid alternative analyses when mating is asymmetric or when population stratification is detected.     

Grandparental Effects on Fertility Vary by Lineage in the United Kingdom

Grandparental presence is known to correlate with the number of grandchildren born, and this effect may vary according to grandparental sex and lineage. However, existing studies of grandparental effects on fertility mostly concern traditional subsistence societies, while evidence from contemporary developed societies is both scarce and mixed. Here, we explore how grandparents affect the transition to second and subsequent children in the contemporary United Kingdom. The longitudinal Millennium Cohort Study (n = 10,295 families) was used to study the association between grandparental investment and parents’ probability of having a new child within 4.5 years. Results show that contact with paternal grandparents is associated with higher probability of parents having a second child. In contrast, contact with maternal grandparents is associated with lower probability of having a third or subsequent child. Kin may have opposite effects on fertility even in contemporary societies, which may explain the lack of consistent effects of grandparental investment on fertility in previous studies.     

Adaptive transgenerational plasticity in an annual plant: grandparental and parental drought stress enhance performance of seedlings in dry soil

Stressful parental (usually maternal) environments can dramatically influence expression of traits in offspring, in some cases resulting in phenotypes that are adaptive to the inducing stress. The ecological and evolutionary impact of such transgenerational plasticity depends on both its persistence across generations and its adaptive value. Few studies have examined both aspects of transgenerational plasticity within a given system. Here we report the results of a growth-chamber study of adaptive transgenerational plasticity across two generations, using the widespread annual plant Polygonum persicaria as a naturally evolved model system. We grew five inbred Polygonum genetic lines in controlled dry vs. moist soil environments for two generations in a fully factorial design, producing replicate individuals of each genetic line with all permutations of grandparental and parental environment. We then measured the effects of these two-generational stress histories on traits critical for functioning in dry soil, in a third (grandchild) generation of seedling offspring raised in the dry treatment. Both grandparental and parental moisture environment significantly influenced seedling development: seedlings of drought-stressed grandparents or parents produced longer root systems that extended deeper and faster into dry soil compared with seedlings of the same genetic lines whose grandparents and/or parents had been amply watered. Offspring of stressed individuals also grew to a greater biomass than offspring of nonstressed parents and grandparents. Importantly, the effects of drought were cumulative over the course of two generations: when both grandparents and parents were drought-stressed, offspring had the greatest provisioning, germinated earliest, and developed into the largest seedlings with the most extensive root systems. Along with these functionally appropriate developmental effects, seedlings produced after two previous drought-stressed generations had significantly greater survivorship in very dry soil than did seedlings with no history of drought. These findings show that plastic responses to naturalistic resource stresses experienced by grandparents and parents can "preadapt" offspring for functioning under the same stresses in ways that measurably influence realized fitness. Possible implications of these environmentally-induced, inherited adaptations are discussed with respect to ecological distribution, persistence under novel stresses, and evolution in natural populations.     

Assortative mating and grandparental transmission facilitate the persistence of a sign language.

Conditions for the persistence (i.e., protection from loss) of a sign language are investigated assuming monogenic recessive inheritance of deafness, assortative mating for deafness or hearing, and cultural transmission of the sign language to deaf individuals from their deaf parents and deaf maternal grandparents. A new method is introduced to deal with the problem of grandparental transmission in which the basic variables are the frequencies of triplets comprising a mother, a father, and their daughter of permissible phenogenotypes. Usual stability analysis is then done on the system of linear recursions in the frequencies of these triplets, derived on the assumption that signers (users of the sign language) are rare. It is shown that assortative mating is the most important factor contributing to persistence, but that grandparental transmission can also have a significant effect when assortment is as strong as observed in England and the United States.     

Ancestral feeding and survival of offspring in European corn borer

Experiments were conducted to evaluate the influence of ancestral adult feeding by European corn borer, Ostrinia nubilalis (Hübner) (Lepidoptera: Crambidae), on larval survival in the field and neonate movement behavior in laboratory. Larval survival was higher when either the grandparental or parental generation had fed, but the feeding sites of the surviving larvae were not affected by ancestral feeding condition. This is the first evidence that grandparental feeding could influence larval survival in the field. Larval movement was observed in the laboratory. Silking speed of neonates was faster when either grandparents or parents had fed, while walking speed was faster only when parents had fed. No broad-sense genetic correlation was found between silking speed and walking speed. Broad-sense heritability among feeding histories were not significant for silking speed, but was significantly greater than zero for walking speed when grandparents fed and parents did not. These intergenerational effects could induce complex population dynamics in this species.     

The use of case-parent triads to study joint effects of genotype and exposure

Most noninfectious disease is caused by low-penetrance alleles interacting with other genes and environmental factors. Consider the simple setting where a diallelic autosomal candidate gene and a binary exposure together affect disease susceptibility. Suppose that one has genotyped affected probands and their parents and has determined each proband's exposure status. One proposed method for assessment of etiologic interaction of genotype and exposure, an extension of the transmission/disequilibrium test, tests for differences in transmission of the variant allele from heterozygous parents to exposed versus unexposed probands. We show that this test is not generally valid. An alternative approach compares the conditional genotype distribution of unexposed cases, given parental genotypes, versus that of exposed cases. This approach provides maximum-likelihood estimators for genetic relative-risk parameters and genotype-exposure-interaction parameters, as well as a likelihood-ratio test (LRT) of the no-interaction null hypothesis. We show how to apply this approach, using log-linear models. When a genotype-exposure association arises solely through incomplete mixing of subpopulations that differ in both exposure prevalence and allele frequency, the LRT remains valid. The LRT becomes invalid, however, if offspring genotypes do not follow Mendelian proportions in each parental mating type-for example, because of genotypic differences in survival-or if a genotype-exposure association reflects an influence of genotype on propensity for exposure-for example, through behavioral mechanisms. Because the needed assumptions likely hold in many situations, the likelihood-based approach should be broadly applicable for diseases in which probands commonly have living parents.     

Discriminative grandparental solicitude as reproductive strategy

1,857 adults rated the grandparental solicitude they received in childhood. Through a simple model based on the evolutionary concepts of ontogenetically differentiated reproductive strategy and paternity confidence, an ordered discriminative pattern of grandparental caregiving was predicted and confirmed by solid main effects, based on 603 complete cases. The maternal grandmother was the most caring. Unlike prevalent gender stereotypes, she was followed by the maternal grandfather, the paternal grandmother, and the paternal grandfather. The preferential grandparental solicitude was not influenced by residential distance, grandparent age, and availability of other grandparents. A predicted higher correlation for male than for female progenitors between solicitude and phenotypic resemblance could be confirmed.     

Males and Females Contribute Unequally to Offspring Genetic Diversity in the Polygynandrous Mating System of Wild Boar

The maintenance of genetic diversity across generations depends on both the number of reproducing males and females. Variance in reproductive success, multiple paternity and litter size can all affect the relative contributions of male and female parents to genetic variation of progeny. The mating system of the wild boar (Sus scrofa) has been described as polygynous, although evidence of multiple paternity in litters has been found. Using 14 microsatellite markers, we evaluated the contribution of males and females to genetic variation in the next generation in independent wild boar populations from the Iberian Peninsula and Hungary. Genetic contributions of males and females were obtained by distinguishing the paternal and maternal genetic component inherited by the progeny. We found that the paternally inherited genetic component of progeny was more diverse than the maternally inherited component. Simulations showed that this finding might be due to a sampling bias. However, after controlling for the bias by fitting both the genetic diversity in the adult population and the number of reproductive individuals in the models, paternally inherited genotypes remained more diverse than those inherited maternally. Our results suggest new insights into how promiscuous mating systems can help maintain genetic variation.     

Methods for detection of parent-of-origin effects in genetic studies of case-parents triads.

When affected probands and their biological parents are genotyped at a candidate gene or a marker, the resulting case-parents-triad data enable powerful tests for linkage in the presence of association. When linkage disequilibrium has been detected in such a study, the investigator may wish to look further for possible parent-of-origin effects. If, for example, the transmission/disequilibrium test restricted to fathers is statistically significant, whereas that restricted to mothers is not, the investigator might interpret this as evidence for nonexpression of the maternally derived disease gene-that is, imprinting. This report reviews existing methods for detection of parent-of-origin effects, showing that each can be invalid under certain scenarios. Two new methods are proposed, based on application of likelihood-based inference after stratification on both the parental mating type and the inherited number of copies of the allele under study. If there are no maternal genetic effects expressed prenatally during gestation, the parental-asymmetry test is powerful and provides valid estimation of a parent-of-origin parameter. For diseases for which there could be maternal effects on risk, the parent-of-origin likelihood-ratio test provides a robust alternative. Simulations based on an admixed population demonstrate good operating characteristics for these procedures, under diverse scenarios.     

Grandparental effects in marine sticklebacks: transgenerational plasticity across multiple generations

Nongenetic inheritance mechanisms such as transgenerational plasticity (TGP) can buffer populations against rapid environmental change such as ocean warming. Yet, little is known about how long these effects persist and whether they are cumulative over generations. Here, we tested for adaptive TGP in response to simulated ocean warming across parental and grandparental generations of marine sticklebacks. Grandparents were acclimated for two months during reproductive conditioning, whereas parents experienced developmental acclimation, allowing us to compare the fitness consequences of short‐term vs. prolonged exposure to elevated temperature across multiple generations. We found that reproductive output of F1 adults was primarily determined by maternal developmental temperature, but carry‐over effects from grandparental acclimation environments resulted in cumulative negative effects of elevated temperature on hatching success. In very early stages of growth, F2 offspring reached larger sizes in their respective paternal and grandparental environment down the paternal line, suggesting that other factors than just the paternal genome may be transferred between generations. In later growth stages, maternal and maternal granddam environments strongly influenced offspring body size, but in opposing directions, indicating that the mechanism(s) underlying the transfer of environmental information may have differed between acute and developmental acclimation experienced by the two generations. Taken together, our results suggest that the fitness consequences of parental and grandparental TGP are highly context dependent, but will play an important role in mediating some of the impacts of rapid climate change in this system.     

Beyond animals and plants: dynamic maternal effects in the fungus Neurospora crassa

Maternal effects are widely documented in animals and plants, but not in fungi or other eukaryotes. A principal cause of maternal effects is asymmetrical parental investment in a zygote, creating greater maternal vs. paternal influence on offspring phenotypes. Asymmetrical investments are not limited to animals and plants, but are also prevalent in fungi and groups including apicomplexans, dinoflagellates and red algae. Evidence suggesting maternal effects among fungi is sparse and anecdotal. In an experiment designed to test for maternal effects across sexual reproduction in the model fungus Neurospora crassa, we measured offspring phenotypes from crosses of all possible pairs of 22 individuals. Crosses encompassed reciprocals of 11 mating‐type ‘A’ and 11 mating‐type ‘a’ wild strains. After controlling for the genetic and geographic distances between strains in any individual cross, we found strong evidence for maternal control of perithecia (sporocarp) production, as well as maternal effects on spore numbers and spore germination. However, both parents exert equal influence on the percentage of spores that are pigmented and size of pigmented spores. We propose a model linking the stage‐specific presence or absence of maternal effects to cellular developmental processes: effects appear to be mediated primarily through the maternal cytoplasm, and, after spore cell walls form, maternal influence on spore development is limited. Maternal effects in fungi, thus far largely ignored, are likely to shape species' evolution and ecologies. Moreover, the association of anisogamy and maternal effects in a fungus suggests maternal effects may also influence the biology of other anisogamous eukaryotes.     

Asymmetry in Family History Implicates Nonstandard Genetic Mechanisms: Application to the Genetics of Breast Cancer

Genome-wide association studies typically target inherited autosomal variants, but less studied genetic mechanisms can play a role in complex disease. Sex-linked variants aside, three genetic phenomena can induce differential risk in maternal versus paternal lineages of affected individuals: 1. maternal effects, reflecting the maternal genome''s influence on prenatal development; 2. mitochondrial variants, which are inherited maternally; 3. autosomal genes, whose effects depend on parent of origin. We algebraically show that small asymmetries in family histories of affected individuals may reflect much larger genetic risks acting via those mechanisms. We apply these ideas to a study of sisters of women with breast cancer. Among 5,091 distinct families of women reporting that exactly one grandmother had breast cancer, risk was skewed toward maternal grandmothers (p<0.0001), especially if the granddaughter was diagnosed between age 45 and 54. Maternal genetic effects, mitochondrial variants, or variant genes with parent-of-origin effects may influence risk of perimenopausal breast cancer.     

Paternity uncertainty overrides sex chromosome selection for preferential grandparenting

With respect to autosomal genes, a grandparent is equally related to male and female grandchildren. Because males are heterozygous for sex chromosomes, however, grandparents are asymmetrically related to male and female grandchildren via the sex chromosomes. For example, the Y chromosome from the paternal grandfather passes directly down to grandsons. This asymmetry leads to a prediction that genes on the sex chromosomes could drive differential grandparental care. Alternatively, the paternity uncertainty hypothesis for differential grandparent care brings about a different set of predictions. A grandfather, for example, has two degrees of uncertainty to his son's children but only one to his daughter's children. Thus, under high extra-pair paternity rates, paternity uncertainty predicts that a grandfather will favor his daughter's children over his son's children. A paternity uncertainty vs. a genetic relatedness hypothesis was tested using data from questionnaires asking adult grandchildren to rate the amount and quality of care of their various grandparents. We found no support for preferential care based on expected sex chromosome similarities. Instead, our data were in general accord with the predictions of the paternity uncertainty hypothesis of grandparental care. A model is presented to predict the rates of extra-pair paternity required in a population to have the effects of paternity uncertainty outweigh sex chromosome effects.     

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.     

Predictors of Grandparental Investment Decisions in Contemporary Europe: Biological Relatedness and Beyond

Across human cultures, grandparents make a valued contribution to the health of their families and communities. Moreover, evidence is gathering that grandparents have a positive impact on the development of grandchildren in contemporary industrialized societies. A broad range of factors that influence the likelihood grandparents will invest in their grandchildren has been explored by disciplines as diverse as sociology, economics, psychology and evolutionary biology. To progress toward an encompassing framework, this study will include biological relatedness between grandparents and grandchildren, a factor central to some discipline''s theoretical frameworks (e.g., evolutionary biology), next to a wide range of other factors in an analysis of grandparental investment in contemporary Europe. This study draws on data collected in the Survey of Health, Ageing and Retirement in Europe from 11 European countries that included 22,967 grandparent–child dyads. Grandparents reported biological relatedness, and grandparental investment was measured as the frequency of informal childcare. Biological and non-biological grandparents differed significantly in a variety of individual, familial and area-level characteristics. Furthermore, many other economic, sociological, and psychological factors also influenced grandparental investment. When they were controlled, biological grandparents, relative to non-biological grandparents, were more likely to invest heavily, looking after their grandchildren almost daily or weekly. Paradoxically, however, they were also more likely to invest nothing at all. We discuss the methodological and theoretical implications of these findings across disciplines.     

Inherited non-autosomal effects on body fat in F2 mice derived from an AKR/J × SWR/J cross

In this study we describe the contribution of matrilineal and patrilineal effects on the adiposity, body weight, and on the weights of individual fat pads in F₂ male mice derived from an SWR/J × AKR/J cross. AKR/J mice become obese after 12 weeks on a high-fat diet, whereas SWR/J mice remain relatively lean. Here we report that mice with AKR maternal and AKR paternal grandmothers have significantly larger epidydimal and retroperitoneal fat pads than those with SWR maternal and paternal grandmothers. However, grandparental strain had no effect on the overall adiposity (AI) or the weights of the inguinal, subcutaneous or mesenteric fat pads. The strain of the paternal grandparents had a small but significant effect on body weight. These effects can be attributed to in utero effects, imprinting effects, cytoplasmic and/or Y chromosome transmission of factors controlling body fat. We also describe the presence of a quantitative trait locus (QTL) on Chromosome X, close to DXMit174, which is linked to adiposity, body weight, and to the weights of the individual fat depots. However, this QTL is not responsible for the grandparental strain effects described above. Received: 3 March 1997 / Accepted: 5 May 1997     

COMPLEX INTERACTIONS BETWEEN PATERNAL AND MATERNAL EFFECTS: PARENTAL EXPERIENCE AND AGE AT REPRODUCTION AFFECT FECUNDITY AND OFFSPRING PERFORMANCE IN A BUTTERFLY

Parental effects can greatly affect offspring performance and are thus expected to impact population dynamics and evolutionary trajectories. Most studies have focused on maternal effects, whereas fathers are also likely to influence offspring phenotype, for instance when males transfer nutrients to females during mating. Moreover, although the separate effects of maternal age and the environment have been documented as a source of parental effects in many species, their combined effects have not been investigated. In the present study, we analyzed the combined effects of maternal and paternal age at reproduction and a mobility treatment in stressful conditions on offspring performance in the butterfly Pieris brassicae. Both paternal and maternal effects affected progeny traits but always via interactions between age and mobility treatment. Moreover, parental effects shifted from male effects expressed at the larval stage to maternal effects at the adult stage. Indeed, egg survival until adult emergence significantly decreased with father age at mating only for fathers having experienced the mobility treatment, whereas offspring adult life span decreased with increasing mother age at laying only for females that did not experience the mobility treatment. Overall, our results demonstrate that both parents’ phenotypes influence offspring performance through nongenetic effects, their relative contribution varying over the course of progeny's life.     

Body height in relation to rural-urban migration in Poland

A survey was conducted among 2800 students studying in Wroc?aw, Poland. The questionnaire included questions on the body height of the students and their parents, and place of residence and migration patterns of the students themselves, their parents and their grandparents. Body height in both students and their parents was positively correlated with the size of their place of residence. This was particularly true for male students and their fathers. Body height in students and parents from mobile families was not significantly different from that of their peers from non-mobile families. Body height in mobile individuals was generally between that of non-mobile individuals from rural areas and that of non-mobile individuals from large urban centres. Students from families that had migrated from smaller urban centres to larger ones were taller than students from families that had migrated from rural areas to urban centres. Body height in students was also correlated with the kind of migration that took place. In the students' mothers, body height was higher if the maternal grandparents moved from smaller urban centres to larger urban centres than if the maternal grandparents moved from rural areas to urban centres. In female students, body height depended on whether their mothers had migrated from smaller places of residence to larger places of residence, but was not affected by the degree of migration. Intra-generational migration during the generation of the students' grandparents was associated with increased body height in the students' mothers. On the other hand, intergenerational migration during the generations of the students' grandparents and parents was associated with increased body height in the students' fathers and in female students. Body height was not a reliable indicator of whether an individual migrated from rural areas to Wroc?aw. Far more reliable indicators were the size of the place the student lived their whole life and whether the family had lived in an urban environment for at least two generations.