Hemoglobin concentration of high-altitude Tibetans and Bolivian Aymara

Elevated hemoglobin concentrations have been reported for high-altitude sojourners and Andean high-altitude natives since early in the 20th century. Thus, reports that have appeared since the 1970s describing relatively low hemoglobin concentration among Tibetan high-altitude natives were unexpected. These suggested a hypothesis of population differences in hematological response to high-altitude hypoxia. A case of quantitatively different responses to one environmental stress would offer an opportunity to study the broad evolutionary question of the origin of adaptations. However, many factors may confound population comparisons. The present study was designed to test the null hypothesis of no difference in mean hemoglobin concentration of Tibetan and Aymara native residents at 3,800–4,065 meters by using healthy samples that were screened for iron deficiency, abnormal hemoglobins, and thalassemias, recruited and assessed using the same techniques. The hypothesis was rejected, because Tibetan males had a significantly lower mean hemoglobin concentration of 15.6 gm/dl compared with 19.2 gm/dl for Aymara males, and Tibetan females had a mean hemoglobin concentration of 14.2 gm/dl compared with 17.8 gm/dl for Aymara females. The Tibetan hemoglobin distribution closely resembled that from a comparable, sea-level sample from the United States, whereas the Aymara distribution was shifted toward 3–4 gm/dl higher values. Genetic factors accounted for a very high proportion of the phenotypic variance in hemoglobin concentration in both samples (0.86 in the Tibetan sample and 0.87 in the Aymara sample). The presence of significant genetic variance means that there is the potential for natural selection and genetic adaptation of hemoglobin concentration in Tibetan and Aymara high-altitude populations. Am J Phys Anthropol 106:385–400, 1998. © 1998 Wiley-Liss, Inc.     

Ventilation and hypoxic ventilatory response of Tibetan and Aymara high altitude natives

Newcomers acclimatizing to high altitude and adult male Tibetan high altitude natives have increased ventilation relative to sea level natives at sea level. However, Andean and Rocky Mountain high altitude natives have an intermediate level of ventilation lower than that of newcomers and Tibetan high altitude natives although generally higher than that of sea level natives at sea level. Because the reason for the relative hypoventilation of some high altitude native populations was unknown, a study was designed to describe ventilation from adolescence through old age in samples of Tibetan and Andean high altitude natives and to estimate the relative genetic and environmental influences. This paper compares resting ventilation and hypoxic ventilatory response (HVR) of 320 Tibetans 9–82 years of age and 542 Bolivian Aymara 13–94 years of age, native residents at 3,800–4,065 m. Tibetan resting ventilation was roughly 1.5 times higher and Tibetan HVR was roughly double that of Aymara. Greater duration of hypoxia (older age) was not an important source of variation in resting ventilation or HVR in either sample. That is, contrary to previous studies, neither sample acquired hypoventilation in the age ranges under study. Within populations, greater severity of hypoxia (lower percent of oxygen saturation of arterial hemoglobin) was associated with slightly higher resting ventilation among Tibetans and lower resting ventilation and HVR among Aymara women, although the associations accounted for just 2–7% of the variation. Between populations, the Tibetan sample was more hypoxic and had higher resting ventilation and HVR. Other systematic environmental contrasts did not appear to elevate Tibetan or depress Aymara ventilation. There was more intrapopulation genetic variation in these traits in the Tibetan than the Aymara sample. Thirty-five percent of the Tibetan, but none of the Aymara, resting ventilation variance was due to genetic differences among individuals. Thirty-one percent of the Tibetan HVR, but just 21% of the Aymara, HVR variance was due to genetic differences among individuals. Thus there is greater potential for evolutionary change in these traits in the Tibetans. Presently, there are two different ventilation phenotypes among high altitude natives as compared with sea level populations at sea level: lifelong sustained high resting ventilation and a moderate HVR among Tibetans in contrast with a slightly elevated resting ventilation and a low HVR among Aymara. Am J Phys Anthropol 104:427–447, 1997. © 1997 Wiley-Liss, Inc.     

Tibetan and Andean patterns of adaptation to high-altitude hypoxia

Understanding the workings of the evolutionary process in contemporary humans requires linking the evolutionary history of traits with their current genetics and biology. Unusual environments provide natural experimental settings to investigate evolution and adaptation. The example of high-altitude hypoxia illustrates some of the progress and many of the remaining challenges for studies of evolution in contemporary populations. Current studies exemplify the frequently encountered problem of determining whether large, consistent population differences in mean values of a trait reflect genetic differences. In this review I describe 4 quantitative traits that provide evidence that indigenous populations of the Tibetan and Andean plateaus differ in their phenotypic adaptive responses to high-altitude hypoxia. These 4 traits are resting ventilation, hypoxic ventilatory response, oxygen saturation, and hemoglobin concentration. The Tibetan means of the first 2 traits were more than 0.5 standard deviation higher than the Aymara means, whereas the Tibetan means were more than 1 standard deviation lower than the Aymara means for the last 2 traits. Quantitative genetic analyses of within-population variance revealed significant genetic variance in all 4 traits in the Tibetan population but only in hypoxic ventilatory response and hemoglobin concentration in the Aymara population. A major gene for oxygen saturation was detected among the Tibetans. These findings are interpreted as indirect evidence of population genetic differences. It appears that the biological characteristics of sea-level humans did not constrain high-altitude colonists of the 2 plateaus to a single adaptive response. Instead, microevolutionary processes may have operated differently in the geographically separated Tibetan and Andean populations exposed to the same environmental stress. Knowledge of the genetic bases of these traits will be necessary to evaluate these inferences. Future research will likely be directed toward determining whether the population means reflect differences identified at the chromosomal level. Future research will also likely consider the biological pathways and environmental influences linking genotypes to phenotypes, the costs and benefits of the Tibetan and Andean patterns of adaptation, and the question of whether the observed phenotypes are indeed adaptations that enhance Darwinian fitness.     

Developmental components of resting ventilation among high- and low-altitude Andean children and adults

This paper evaluates the age-associated changes of resting ventilation of 115 high- and low-altitude Aymara subjects, of whom 61 were from the rural Aymara village of Ventilla situated at an average altitude of 4,200 m and 54 from the rural village of Caranavi situated at an average altitude of 900 m. Comparison of the age patterns of resting ventilation suggests the following conclusions: 1) the resting ventilation (ml/kg/min) of high-altitude natives is markedly higher than that of low-altitude natives; 2) the age decline of ventilation is similar in both lowlanders and highlanders, but the starting point and therefore the age decline are much higher at high altitude; 3) the resting ventilation that characterizes high-altitude Andean natives is developmentally expressed in the same manner as it is at low altitude; and 4) the resting ventilation (ml/kg/min) of Aymara high-altitude natives is between 40–80% lower than that of Tibetans. Am J Phys Anthropol 109:295–301, 1999. © 1999 Wiley-Liss, Inc.     

藏香猪放牧对滇西北高原湿地土壤CO2通量的影响

高原湿地是生态系统中重要的碳汇。土壤CO_2通量作为高原湿地生态系统碳收支的重要组成部分,碳的释放对区域碳平衡发挥着重要的作用。藏香猪放牧是我国高海拔藏区一种特有的放牧方式,是导致高原湿地土壤退化的重要干扰因素之一,并影响着土壤CO_2通量的变化。采用土壤CO_2通量自动测量系统(LI-8100A,LI-COR,USA),分别在不同季节对滇西北布伦、哈木谷、伊拉草原上藏香猪干扰和对照(非干扰土壤)CO_2通量变化进行监测,研究发现,藏香猪干扰型放牧降低了土壤CO_2排放通量,且表现出明显的日波动变化特征。相比旱季,雨季不同放牧方式影响下的土壤CO_2通量差异性更为明显,其中布伦、哈木谷、伊拉草原较对照分别降低了70.4%、87.5%、60.7%。CO_2排放通量与土壤理化性状及植物生物量的回归分析表明,对照样地的土壤容重、孔隙度、pH、总活性碳、植物生物量与土壤CO_2通量具有显著的相关性(P0.01)。通过植物-土壤指数(plant-soil index,PSI)分析了藏香猪干扰型放牧对高原湿地的影响,总体来看,对照样地中土壤CO_2通量与PSI之间具有较好的线性关系,可以用来很好的预测未来高原湿地土壤CO_2通量的变化。该研究结果不仅有效估算了强干扰放牧影响下的高原湿地土壤碳排放量,而且为加强藏香猪放牧的科学管理,高原湿地生态系统的保护、恢复及重建提供了理论支持。     

Genetic and Environmental Contributions to BMI in Adolescent and Young Adult Women

The objective of this study was to determine the genetic and environmental contributions to variation in BMI over time in European‐American (EA) and African‐American (AA) adolescent and young adult women. Self‐reported BMI (kg/m²) data from 2,816 EA (1,306 twin pairs, 56.5% monozygotic (MZ)) and 404 AA (178 twin pairs, 42.7% MZ) women at baseline (T1; median age 15 years) and 3,225 EA (1,511 twin pairs, 55.3% MZ) and 539 AA (252 pairs, 43.3% MZ) women at follow‐up (T2; median age 22 years) from a Midwestern US, population‐based twin registry were used to construct biometrical genetic models. For EA women, the majority of the variance in BMI was attributable to additive genetic effects at both time points (82% for each), with the remaining variance attributable to nonshared environment. Genetic and nonshared environment correlations between adolescent and young adult BMI were 0.87 and 0.23, respectively. Among AA women, nonadditive genetic effects comprised 68% of the variance at T1 and 73% at T2, and were highly correlated (r_D = 0.94). The proportions of variance attributable to nonshared environment at T1 (29%) and T2 (25%) were more modestly correlated (r_E = 0.31). The remaining variance in AA women could be attributed to additive genetic effects. Additive vs. nonadditive genetic effects contribute differentially to BMI in AA vs. EA adolescent and young adult women. Additional research is needed to better characterize the environmental and genetic factors related to BMI in persons of different races to aid understanding of the complex determinants of body weight in individuals.     

EPISTASIS AND THE EVOLUTION OF ADDITIVE GENETIC VARIANCE IN POPULATIONS THAT PASS THROUGH A BOTTLENECK

Traditional models of genetic drift predict a linear decrease in additive genetic variance for populations passing through a bottleneck. This perceived lack of heritable variance limits the scope of founder-effect models of speciation. We produced 55 replicate bottleneck populations maintained at two male-female pairs through four generations of inbreeding (average F = 0.39). These populations were formed from an F₂ intercross of the LG/J and SM/J inbred mouse strains. Two contemporaneous control strains maintained with more than 60 mating pairs per generation were formed from this same source population. The average level of within-strain additive genetic variance for adult body weight was compared between the control and experimental lines. Additive genetic variance for adult body weight within experimental bottleneck strains was significantly higher than expected under an additive genetic model This enhancement of additive genetic variance under inbreeding is likely to be due to epistasis, which retards or reverses the loss of additive genetic variance under inbreeding for adult body weight in this population. Therefore, founder-effect speciation processes may not be constrained by a loss of heritable variance due to population bottlenecks.     

Major gene for percent of oxygen saturation of arterial hemoglobin in Tibetan highlanders

This report employs a statistical genetic approach to analyze quantitative oxygen transport variables in a high-altitude (4,850–5,450 m) native Tibetan population and demonstrates the presence of a major gene influencing % O₂ saturation of arterial hemoglobin. This result suggests the hypothesis that individuals with the dominant allele for higher % O₂ saturation have a selective advantage at high altitude. Studies of the biologically distinctive Himalayan and Andean populations have greatly influenced thinking about ongoing human evolution and adaptation; this is the first statistical evidence for a major gene enhancing oxygen transport in a highaltitude native population. © 1994 wiley-Liss, Inc.     

Between‐family variation and quantitative genetics of developmental instability of long bones in rabbit foetuses

The genetic basis of developmental instability (DI) remains largely unknown as a result of its morphological expression, fluctuating asymmetry (FA), poorly reflecting DI, especially if few traits are studied. The typically low values of heritability of FA (h²_FA) can be translated into higher values of DI (h²_DI) by the hypothetical repeatability, yet leading to wide confidence intervals. Thus, high sample sizes and/or several traits are indispensible for reaching meaningful conclusions. To obtain more insights into quantitative genetic variation of DI, we investigated between‐family variance in DI in six long bones of 1126 foetuses of the New Zealand white rabbit from a full‐sib experiment. We applied different approaches to obtain genetic parameters for DI. Heritabilities and the coefficients of between‐family variation (CVB) were calculated for six individual traits and composite indices. The results obtained, despite a likely upward bias as a result of maternal and non‐additive effects, lend support to the presence of moderate additive genetic variance for DI. It is suggested that, in foetal traits, the environmental variance was minimal, leading to a high likelihood of detecting genetic variation in DI, thus creating an ideal model system for studying the genetic basis of DI. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 109 , 33–42.     

Genetic studies in an exotic population of corn (Zea mays L.) grown under two plant densities

Summary Progenies of a Design II [Comstock and Robinson (1948)] using random S ₁ lines from an exotic population of corn (Zea mays L.) were evaluated in a randomized incomplete block design with two replications at two plant-population densities (1 7,222 plants/ha and 68,888 plants/ha) in 1970 and 1971, at Lincoln, Nebraska. Five traits were studied i.e. grain weight, number of ears, days to flower, plant height and ear height.Under both densities the estimates of additive genetic variance were much larger than those of dominance genetic variance for all traits. The ratio of dominance to additive genetic variance estimates was less than 0.5 suggesting that for the majority of loci controlling the traits, partial to complete dominance is likely.The estimates of additive genetic x year interaction variance were high and significantly different from zero under both densities, indicating that estimates of additive genetic variance in this population obtained from experiments conducted in only one year may be seriously biased. The estimates of dominance genetic x year interaction variance were not significant and most of them were negative.Under both densities high genetic inter-relationships were indicated between grain weight and number of ears, days to flower and plant height, days to flower and ear height, and plant height and ear height.Even though there was a large difference between the two densities used in the study, the differences between the estimates of genetic parameters were not significant in all cases.The sample size of S ₁ plants representing each S₀ parent in the crossing nursery used in the present study (11.75) caused a small upward bias in the estimates of additive genetic variance, but it caused an upward bias in the estimates of dominance genetic variance of 6–7% of the total genetic variance.It is suggested that a trait such as grain weight should be expressed on a unit area basis when genetic parameters (except for correlation and the ratio between two values) obtained from experiments with different plant-population densities are to be compared.Published as Paper Number 3542, Journal Series, Nebraska Agricultural Experimental Station. Part of a thesis submitted by the senior author in partial fulfillment of the requirements for the Ph. D. degree.A. I. D. Participant.The work was supported in part by a grant from the Rockefeller Foundation.     

Genetic diversity and structure of Lilium pumilum DC. in southeast of Qinghai–Tibet plateau

Lilium pumilum DC. is a valuable species not only for its showy flowers but also for its edible and medicinal values. As one of the distribution areas of L. pumilum, Qinghai–Tibet plateau has unique environmental features which have high impact on the evolution of the species. No population genetic studies have been done for L. pumilum so far. To provide the first reference data for evolutionary study and understanding the influence of eco-geographic factors on the distribution of genetic variation in L. pumilum, interspecific simple sequence repeat markers were used to investigate genetic diversity and population structure of 28 populations sampled from southeast of Qinghai–Tibet plateau. Fifteen selected primers generated a total of 147 polymorphic bands. The genetic diversity was low within populations (average He = 0.173), but higher at the species level (He = 0.392). A clear population structure and high level of genetic differentiation (F _ST = 0.518) were detected by unweighted pair group method for arithmetic averages, principle coordinate analysis and Bayesian clustering. All clustering approaches supported a division of the 28 populations into 4 major groups for which analysis of molecular variance confirmed a significant variation among groups (34.3 %). These population genetic parameters suggest limited gene flow among populations and evidence for isolation by distance (r = 0.272, P < 0.0001) was found in this study. Altitude, AMT and AMP explained 9.5, 11.5 and 14.0 % of the total variance among populations indicating that eco-geographic factors have a significant effect. Considering the low within-population genetic diversity, high differentiation among populations and the increasing anthropogenic pressure on the species, in situ conservation measures were recommended to preserve L. pumilum in Qinghai–Tibet plateau.     

Spatial genetic structuring in a widespread wetland plant on a plateau: Effects of elevation-driven geographic isolation and environmental heterogeneity

1. Highlands are ideal research areas for improving our understanding of the influence of ecological factors on the diversity and spatial patterns of natural species. Elevation-driven physical and environmental isolation greatly affect the evolution of plants. The mechanisms and essential drivers underlying these processes may differ among research scales, habitats and landscapes. Wetlands are important elements of the Qinghai–Tibetan Plateau, which is the highest plateau in the world, and these habitats harbour high aquatic organismal diversity. However, how the environments shape the genetic variation and structure of hydrophilous plants is poorly understood.
2. Using microsatellite markers and a chloroplast fragment, we quantified the genetic diversity and spatial genetic pattern of Stuckenia filiformis, one of the most widespread aquatic plants on the plateau. The relative contributions of geography, climate and local conditions to intra- and interpopulation variation were estimated. The results showed that intrapopulation genetic variation of the plant is moderate to high and not constrained by high-altitude environments. Topographical isolation mainly contributes to the genetic structure of S. filiformis, as inferred by simple sequence repeats and chloroplast DNA data. Significant effects of environmental variables on the spatial genetic patterns of this freshwater species were also suggested by landscape genetic analysis.
3. Infrequent long-distance dispersal, sexual recruitment and annual growth are probably important for the maintenance and distribution of this variation. Our findings imply a combined effect of geography and elevation-driven environmental heterogeneity on the evolution of aquatic organisms in highlands.

     

Environmental and genetic influences on body mass and resting metabolic rates (RMR) in a natural population of weasel Mustela nivalis

Body mass (BM) and resting metabolic rates (RMR) are two inexorably linked traits strongly related to mammalian life histories. Yet, there have been no studies attempting to estimate heritable variation and covariation of BM and RMR in natural populations. We used a marker‐based approach to construct a pedigree and then the ‘animal model’ to estimate narrow sense heritability (h²) of these traits in a free‐living population of weasels Mustela nivalis—a small carnivore characterised by a wide range of BM and extremely high RMR. The most important factors affecting BM of weasels were sex and habitat type, whereas RMR was significantly affected only by seasonal variation of this trait. All environmental factors had only small effect on estimates of additive genetic variance of both BM and RMR. The amount of additive genetic variance associated with BM and estimates of heritability were high and significant in males (h² = 0.61), but low and not significant in females (h² = 0.32), probably due to small sample size for the latter sex. The results from the two‐trait model revealed significant phenotypic (r_P = 0.62) and genetic correlation (r_A = 0.89) between BM and whole body RMR. The estimate of heritability of whole body RMR (0.54) and BM corrected RMR (0.45) were lower than estimates of heritability for BM. Both phenotypic and genetic correlations between BM corrected RMR and BM had negative signals (r_P = ?0.42 and r_A = ?0.58). Our results indicate that total energy expenditures of individuals can quickly evolve through concerted changes in BM and RMR.     

Genetic analysis of salt tolerance during germination in Lycopersicon

Summary The salt-tolerant cultivated tomato (Lycopersicon esculentum) accession, PI174263, and a sensitive cv, UCT5, were crossed to develop reciprocal F₁, F₂ and BC₁ populations for genetic analysis of salt tolerance in tomatoes during seed germination. Variation was partitioned into embryo, endosperm and maternal (testa and cytoplasmic) components. Generation means analysis indicated that there were no significant embryo (additive, dominance or epistatic) effects on germination performance under salt stress. Highly significant endosperm additive and testa dominance effects were detected. The proportion of the total variance explained by the model containing these two components was R²=98.2%. Variance component analysis indicated a large genetic variance with additive gene action as the predominant component. Furhter inspection indicated that this variance was attributable to endosperm additive effects on germinability under salt stress. Narrow-sense heritability was estimated as moderately high. Implications for breeding procedures are discussed.     

High intra-population genetic variability and inter-population differentiation in a plateau specialized fish, <Emphasis Type="BoldItalic">Triplophysa orientalis</Emphasis>

Triplophysa orientalis (Herzenstein) is one of the Nemacheilinae (Cypriniformes: Balitoridae) fish species distributed in the Tibetan Plateau area. In order to understand the impact of plateau uplift on population history and the isolation effect of plateau lakes on T. orientalis, we examined its genetic structure and phylogenetic relationships. A total of 98 individuals from five wild populations, three from plateau lakes and two from branch rivers in upper reaches of the Yangtze River, in the eastern peripheral of the Tibetan Plateau were sampled. An 848 base pair fragment from the mitochondrial DNA (mtDNA) control region was sequenced for analyses. Overall, very high intra-population genetic variability was found in all populations except for one lake population (Rannicuo); nucleotide diversity ranged from 0.0025 to 0.0159 and haplotype diversity ranged from 0.641 to 0.879. Furthermore, the genetic distance between river populations (0.0326) was much higher than that among lake populations (Rannicuo and Barencuo 0.0035, Bannicuo and Yibicuo 0.0038, Rannicuo and Yibicuo 0.0049). Additionally, the analysis of molecular variance demonstrated that most of the observed genetic variability occurred among populations, accompanied with significant Fst values except for that between the Yibicuo and Barencuo populations. This evidence suggested a strong population structure of the species and a lack of inter-population connection. Lastly, the rate of migration indicated there were large historic gene flows among lake populations. Demographic analysis also indicated there were bottlenecks or expansions in three lake populations, suggesting a potential isolation effect of plateau lakes on population differentiation. Molecular dating of intra-specific divergence showed the plateau uplift has shaped the genetic structure of T. orientalis.     

Genetic determination of head-size-related anthropometric traits in an ethnically homogeneous sample of 373 Indian pedigrees of West Bengal

The substantial involvement of genetic factors in the determination of head-size and head-shape traits has been firmly established. However, there has been a lack of agreement on a number of specific issues concerning the pattern of inheritance of craniofacial features. In this study we examined some of these issues in a large, ethnically homogeneous sample of Indian pedigrees. The data included 1,263 individuals belonging to 373 nuclear families. Eleven raw head-size traits and two synthetic phenotypes, interpreted as horizontal and vertical head-size components (HOC and VEC, respectively), were used in the analysis. To establish the pattern of inheritance of head traits, we carried out univariate and bivariate analyses. Maximum heritability estimates ranged from 0.41 to 0.83 for the studied head-size phenotypes. The portion of the total residual variance attributable to putative additive genetic factors was 68.3% and 70.3% for HOC and VEC, respectively, and common familial factor effects were found to be nonsignificant. The extent of genetic influences did not differ significantly with respect to sex or between HOC and VEC. The results of bivariate variance decomposition analysis strongly suggest the existence of common genetic factors simultaneously affecting HOC and VEC; 41.8% of the two traits' total residual variance was attributable to the effect of these common genetic factors.     

Differences in physical growth of Aymara and Quechua children living at high altitude in Peru

Physical growth of Amerindian children living in two Aymara and three Quechua peasant communities in the Andean highlands of southern Peru (altitude 3,810–3,840 m) was studied, taking into account differences in the microclimate, agronomic situation, and sociodemographic variables. Anthropometric measurements were taken in 395 children aged under 14 years of age in a sample of 151 families in these communities, who were surveyed for sociodemographic variables as well. Data on the land system were available for 77 families. In comparison with reference populations from the United States (NCHS) and The Netherlands, stature, weight, head circumference, and midupper arm circumference (but not weight for stature) in the sample children were reduced. Growth retardation increased after the age of 1 year. Stature and weight in the present sample were very similar compared with previously published data on growth of rural Aymara children living near Lake Titicaca in Bolivia. Head circumference, midupper arm circumference, and weight for stature were significantly larger in Aymara children compared with Quechua children. Land was significantly more fragmented in Aymara compared with Quechua families, but amount of land owned was not different. Perinatal and infant mortality was elevated in Aymara vs. Quechua communities. Most families in Aymara communities used protected drinking water. One Quechua community had a severe microclimate, grim economic outlook, and weak social cohesion. Children in this community showed significant reductions in weight and midupper arm circumference compared with their peers in the other communities. We conclude that (presumably nutritionally mediated) intervillage and Aymara-Quechua differences in childhood physical growth existed in this rural high-altitude population in Peru and were associated with microclimate and the village economy, sociodemographic factors, and differences in the land system. © 1993 Wiley-Liss, Inc.     

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

Background

Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞ genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞ model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).

Results

In this paper, we further explore the differences and links between the F_∞ and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞ models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞ model. A new way of linking the Cockerham and F_∞ model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞ models are applied.

Conclusion

The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞ regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞ model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞ model can then be calculated by translating formulas derived for the Cockerham models.