Bayesian inference on age-specific survival for censored and truncated data

1. Traditional estimation of age-specific survival and mortality rates in vertebrates is limited to individuals with known age. Although this subject has been studied extensively using effective capture-recapture and capture-recovery models, inference remains challenging because of large numbers of incomplete records (i.e. unknown age of many individuals) and because of the inadequate duration of the studies. 2. Here, we present a hierarchical model for capture-recapture/recovery (CRR) data sets with large proportions of unknown times of birth and death. The model uses a Bayesian framework to draw inference on population-level age-specific demographic rates using parametric survival functions and applies this information to reconstruct times of birth and death for individuals with unknown age. 3. We simulated a set of CRR data sets with varying study span and proportions of individuals with known age, and varying recapture and recovery probabilities. We used these data sets to compare our method to a traditional CRR model, which requires knowledge of individual ages. Subsequently, we applied our method to a subset of a long-term CRR data set on Soay sheep. 4. Our results show that this method performs better than the common CRR model when sample sizes are low. Still, our model is sensitive to the choice of priors with low recapture probability and short studies. In such cases, priors that overestimate survival perform better than those that underestimate it. Also, the model was able to estimate accurately ages at death for Soay sheep, with an average error of 0.94 years and to identify differences in mortality rate between sexes. 5. Although many of the problems in the estimation of age-specific survival can be reduced through more efficient sampling schemes, most ecological data sets are still sparse and with a large proportion of missing records. Thus, improved sampling needs still to be combined with statistical models capable of overcoming the unavoidable limitations of any fieldwork. We show that our approach provides reliable estimates of parameters and unknown times of birth and death even with the most incomplete data sets while being flexible enough to accommodate multiple recapture probabilities and covariates.     

Age-related changes of digital endocranial volume during human ontogeny: results from an osteological reference collection

Endocranial volume (EV) estimation is widely used in physical anthropology for assessing brain size differences between taxa and monitoring the emergence of brain growth patterns in modern humans. However, to date, no reference data are available for modern human EV ontogeny. We measured 94 skulls with known sex and age (ranging from 0 to 7.5 years) from the osteological collection of Strasbourg University (OCSU) by using an accurate digital active contour model algorithm on 3D virtual models, reconstructed by CT. The OCSU data also allow us to propose improved equations for estimating EV in immature individuals from dry skull diameters (length, width, and height). Aside from the EV, the average proportional endocranial volume (PEV), corresponding to the ratio of EV at a given age to the average EV in the corresponding adult population, was also computed. EV nearly doubles during the first year of life, and later continues to expand more slowly, at least until 7 years of age. No sex differences can be demonstrated between the EV distributions of boys and girls in this sample. However, although PEV at birth is identical in girls and boys, it later displays significantly higher values in the girls of our series. PEV obtained at birth is 22%, which is quite different from values established for the brain itself from autopsied individuals, or MRI data. This suggests that assessments of EV and PEV values in fossil specimens should be conducted by using identical measures in comparative samples of extant humans and apes.     

Heritability of age at first birth in captive olive baboons

The evolution of life history traits is a topic of growing interest in primatology. Traits associated with fertility, such as age at menarche and age at first birth, have great significance for natural selection, and knowing the genetic basis of such demographic traits may improve our understanding of population dynamics. Knowledge of the heritability of reproductive traits may also have practical implications for the management of captive breeding colonies. A maximum likelihood method was used to estimate heritability of age at first birth for a sample of female olive baboons resident at the Southwest Foundation for Biomedical Research. Only animals born at the Foundation that were caged in mixed sex groups and that had previously given birth were included in the sample (n = 316). There were 117 independent individuals and 199 individuals in 35 pedigrees composed of 2 to 26 members. Age at first birth ranged from 3.85 years to 13.11 years. Age at first birth is highly heritable (h² = 0.87) with no evidence for maternal effects or a dominance genetic component. This level of genetic variability in a fitness-related trait is contrary to evolutionary expectation and may reflect the uniform environment of a captive breeding situation. Thus, the heritability observed in this population may be taken as an upper bound for that in natural populations. © 1995 Wiley-Liss, Inc.     

Testing the value of skeletal samples in demographic research: a comparison with vital registration samples

Critics of paleodemography have suggested that the science is so fraught with error that its demise must be close at hand. Among the problems suggested as unsolvable are representativeness of skeletal samples and inaccuray of skeletal aging techniques. A historical skeletal sample with supportive vital registration might afford the opportunity to test the validity of such criticism or at least to examine the extent of the above problems. In 1984, a skeletal sample of 296 individuals was excavated from a 19th century American poorhouse cemetery. Age at death was determined by macroscopic multivariate examination. Mortality records of 247 individuals who died during four years of the poorhouse's operation provide data for demographic comparisons with the skeletal sample. A comparison of life tables generated from each sample demostrates that there are no significant differences in the age at death structure, life expectancy (at birth: 30.7 in the mortality records and 32.6 from the skeletal sample), or survivorship between the two samples. Skeletal aging techniques can, therefore, provide a demographic picture that is similar in accuracy to that presented by vital registration records.     

Generational effects and gender height dimorphism in contemporary Spain

We examine the influence of socio-environmental (and birth cohort specific) effects on both adult height and gender dimorphism (height gap). Our data set is from contemporary Spain, a country governed by an authoritarian regime for about 40 years. Both OLS and quantile regression approaches are used to examine these patterns. Furthermore, we then draw upon a Blinder-Oaxaca decomposition approach to explain the influence of socio-political environment in explaining gender dimorphism. Our findings point to a significant increase in adult height in the generations that benefited from the country's economic liberalization in the 1950s, and especially among those brought up after the transition to democracy in the 1970s. In contrast, individual heterogeneity suggests that only in recent generations has "height increased more among the tallest". We also find that the effects of education on height are greater among shorter individuals. Although the mean gender difference in height is 11.7cm, birth cohort and capabilities effects along with other controls explain on average roughly 4% of the gender height dimorphism, irrespective of the quantile considered.     

Inference of population structure using multilocus genotype data

We describe a model-based clustering method for using multilocus genotype data to infer population structure and assign individuals to populations. We assume a model in which there are K populations (where K may be unknown), each of which is characterized by a set of allele frequencies at each locus. Individuals in the sample are assigned (probabilistically) to populations, or jointly to two or more populations if their genotypes indicate that they are admixed. Our model does not assume a particular mutation process, and it can be applied to most of the commonly used genetic markers, provided that they are not closely linked. Applications of our method include demonstrating the presence of population structure, assigning individuals to populations, studying hybrid zones, and identifying migrants and admixed individuals. We show that the method can produce highly accurate assignments using modest numbers of loci-e.g. , seven microsatellite loci in an example using genotype data from an endangered bird species. The software used for this article is available from http://www.stats.ox.ac.uk/ approximately pritch/home. html.     

Spurious linkage between markers in QTL mapping

Selective genotyping of extreme progeny is a powerful method to increase the information content per individual when looking for quantitative trait loci (QTLs) using molecular markers for which a map is known. However, if marker information from the selected individuals is used to construct the map of the markers, this can lead to distorted segregation of the markers that in turn can lead to the estimation of a spurious linkage between independently inherited markers. The mistaken estimation of linkage between independently inherited markers will occur when there are two (or more) independently inherited QTLs linked to two (or more) markers and the same individuals are used to estimate the map of the markers and to do the QTL estimation. The incorrect linkage occurs because in selecting individuals from the tails of the phenotypic distribution we will also be selecting certain combinations of the markers instead of obtaining a random sample of the true distribution of the marker genotypes. Analytical results are outlined and the analyses of a simulated data set illustrate the problems that could arise when data from individuals chosen by selective genotyping are incorrectly employed to construct a marker map. A strategy is proposed to remedy this problem.     

Body mass prediction from stature and bi-iliac breadth in two high latitude populations, with application to earlier higher latitude humans

Previous studies have indicated that body mass can be estimated from stature and bi-iliac (maximum pelvic) breadth with reasonable accuracy in modern humans, supporting the use of this method to estimate body mass in earlier human skeletal samples. However, to date the method has not been tested specifically on high latitude individuals, whose body form in some ways more closely approximates that of earlier higher latitude humans (i.e., large and broad-bodied). In this study, anthropometric data for 67 Alaskan Inupiat and 54 Finnish adults were used to test the stature/bi-iliac body mass estimation method. Both samples are very broad-bodied, and the Finnish sample is very tall as well. The method generally works well in these individuals, with average directional biases in body mass estimates of 3% or less, except in male Finns, whose body masses are systematically underestimated by an average of almost 9%. A majority of individuals in the total pooled sample have estimates to within +/-10% of their true body masses, and more than three-quarters have estimates to within +/-15%. The major factor found to affect directional bias is shoulder to hip breadth (biacromial/bi-iliac breadth). Male Finns have particularly wide shoulders, which may in part explain their systematic underestimation. New body mass estimation equations are developed that include the new data from this study. When applied to a sample of earlier (late middle Pleistocene to early Upper Paleolithic) higher latitude skeletal specimens, differences between previous and new body estimates are small (less than 2%). However, because the Finns significantly extend the range of morphological variation beyond that represented in the original world-wide reference sample used in developing the method, thereby increasing its generality, it is recommended that these new formulas be used in subsequent body mass estimations.     

Optimization of genomic selection training populations with a genetic algorithm

In this article, we imagine a breeding scenario with a population of individuals that have been genotyped but not phenotyped. We derived a computationally efficient statistic that uses this genetic information to measure the reliability of genomic estimated breeding values (GEBV) for a given set of individuals (test set) based on a training set of individuals. We used this reliability measure with a genetic algorithm scheme to find an optimized training set from a larger set of candidate individuals. This subset was phenotyped to create the training set that was used in a genomic selection model to estimate GEBV in the test set. Our results show that, compared to a random sample of the same size, the use of a set of individuals selected by our method improved accuracies. We implemented the proposed training selection methodology on four sets of data on Arabidopsis, wheat, rice and maize. This dynamic model building process that takes genotypes of the individuals in the test sample into account while selecting the training individuals improves the performance of genomic selection models.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0116-6) contains supplementary material, which is available to authorized users.     

Decline of height with age in adults in a general population sample: estimating maximum height and distinguishing birth cohort effects from actual loss of stature with aging

The decline in stature with age among adults is well documented. Although part of this represents a birth cohort effect, actual height declines among older individuals are known to contribute to the effect. In this study we used longitudinal changes in the heights of adults in a general population sample to determine the rate of decline in height over time in individuals of different ages. This allowed an estimation of the age at which decline in height begins, a value close to age 40 in both sexes. It also allowed derivation of equations from which the maximum height of subjects can be estimated on the basis of their sex, current height, and age. These equations should prove useful when examining the effect of aging per se on physiological measurements that are height dependent. The data also allow one to compare the magnitude of the effect of year of birth with that of the actual decline in height seen among the elderly. We estimate that approximately 60% of the smaller stature of older male subjects and 45% of the smaller stature of older female subjects is a birth cohort effect deriving from the secular trend toward greater stature; the remainder is a result of an actual decrement in height after the age of 40.     

Optimal breeding-value prediction using a sparse selection index

Genomic prediction uses DNA sequences and phenotypes to predict genetic values. In homogeneous populations, theory indicates that the accuracy of genomic prediction increases with sample size. However, differences in allele frequencies and linkage disequilibrium patterns can lead to heterogeneity in SNP effects. In this context, calibrating genomic predictions using a large, potentially heterogeneous, training data set may not lead to optimal prediction accuracy. Some studies tried to address this sample size/homogeneity trade-off using training set optimization algorithms; however, this approach assumes that a single training data set is optimum for all individuals in the prediction set. Here, we propose an approach that identifies, for each individual in the prediction set, a subset from the training data (i.e., a set of support points) from which predictions are derived. The methodology that we propose is a sparse selection index (SSI) that integrates selection index methodology with sparsity-inducing techniques commonly used for high-dimensional regression. The sparsity of the resulting index is controlled by a regularization parameter (λ); the G-Best Linear Unbiased Predictor (G-BLUP) (the prediction method most commonly used in plant and animal breeding) appears as a special case which happens when λ = 0. In this study, we present the methodology and demonstrate (using two wheat data sets with phenotypes collected in 10 different environments) that the SSI can achieve significant (anywhere between 5 and 10%) gains in prediction accuracy relative to the G-BLUP.     

Detecting sample misidentifications in genetic association studies

Genetic association studies require that the genotype data from a given person can be correctly linked to the phenotype data from the same person. However, sample misidentification errors sometimes happen, whereby the link becomes invalid for some of the subjects in a study. This can have substantial consequences in terms of power to detect truly associated variants. In family-based studies, Mendelian inconsistencies can be used to detect sample misidentification. Genome-wide association studies (GWAS), however, typically use unrelated individuals, making error detection more problematic. Here we present a method for identifying potential sample misidentifications in GWAS and other genetic association studies building on ideas from forensic sciences. A widely used ad-hoc method for error detection is to check if the sex of an individual matches its X-linked genotype. We generalize this idea to less stringent associations between known genotypes and phenotypes, and show that if several known associations are combined, the power to detect misidentifications increases substantially. Individuals with an unlikely set of phenotypes given their genotypes are flagged as potential errors. We provide analytical and simulation results comparing the odds that the genotype and phenotype are both from the same individual for different numbers of available genotype-p henotype associations and for different information content of the associations. Our method has good sensitivity and specificity with as few as ten moderately informative genotype-phenotype associations. We apply the method to GWAS data from the Danish National Birth Cohort.     

Estimating the number of founder lineages from haplotypes of closely linked SNPs

We consider an isolated population founded by a small number of individuals randomly chosen from a source population of known genetic composition at a known time in the past. We develop a Monte-Carlo maximum-likelihood method for estimating the number of founding individuals from the haplotype frequencies at several SNP (single nucleotide polymorphism) loci in a sample. We assume the isolated population was founded recently enough that that mutation can be ignored and that haplotype frequencies in the source population have not changed. We apply the method to simulated data and show that it is unbiased. With a reasonable number of individuals sampled, it is possible to estimate the number of founders within a factor of 2. We show that the performance of the method is not degraded substantially if the frequencies of the rare haplotypes in the source are not known precisely and if there is some recombination. We illustrate the use of our method by applying it to a previously published data set from a recently founded population of wolves (Canis lupus) in Scandinavia.     

Allele-sharing methods for estimation of population size

Genetic data are becoming increasingly important in ecology and conservation biology. This article presents a novel method for estimating population size from DNA profiles obtained from a random sample of individuals. The underlying idea is that the degree of biological relationship between individuals in the sample reflects the size of the population and that DNA profiles provide information about relatedness. A pseudolikelihood approach is taken, involving pairwise comparison of individuals. The main field of applications is seen to be catch data, and as an example, the method is applied to DNA profiles (10 microsatellite loci) from 334 North Atlantic minke whales. It is concluded that the sample size is too small for the method to give useful results. The question about the required sample size is investigated by simulation.     

Identifying chromosomal fragile sites from individuals: a multinomial statistical model

The inability to identify fragile sites from data for single individuals remains the major obstacle to determining whether these chromosomal loci are predisposed to cancer-causing and evolutionary rearrangements. We describe a novel statistical model that is amenable to data from single individuals and that establishes site-specific chromosomal breakage as nonrandom with respect to the distribution of total breakage. Our method tests incrementally smaller subsets of the data for homogeneity under a multinomial model that assigns equal probabilites to a maximal set of nonfragile sites and unrestricted probabilities to the remaining fragile sites with significantly higher numbers of breaks. We show how standardized Pearson's chi-square (X ²) and likelihood-ratio (G ²) statistics can be appropriately used to measure goodness-of-fit for sparse contingency (individual-based) data in this model. A sample application of this approach indicates extensive variation in fragile sites among individuals and marked differences in fragile-site inferences from pooled as opposed to per-individual data.     

Smoothing population size estimates for time-stratified mark-recapture experiments using Bayesian P-splines

Petersen-type mark-recapture experiments are often used to estimate the number of fish or other animals in a population moving along a set migration route. A first sample of individuals is captured at one location, marked, and returned to the population. A second sample is then captured farther along the route, and inferences are derived from the numbers of marked and unmarked fish found in this second sample. Data from such experiments are often stratified by time (day or week) to allow for possible changes in the capture probabilities, and previous methods of analysis fail to take advantage of the temporal relationships in the stratified data. We present a Bayesian, semiparametric method that explicitly models the expected number of fish in each stratum as a smooth function of time. Results from the analysis of historical data from the migration of young Atlantic salmon (Salmo salar) along the Conne River, Newfoundland, and from a simulation study indicate that the new method provides more precise estimates of the population size and more accurate estimates of uncertainty than the currently available methods.     

Neonatal weight in gibbons (Hylobates spp.)

Neonatal and birth weights of gibbons have mostly been reported for single individuals, and larger samples (n = 2–8) have apparently been published for only two species of gibbons (Hylobates lar and H. syndactylus). In addition, a critical examination of the few published neonatal weights of gibbons shows that several of them should not be used. Neonatal weights are here defined as weights taken on infants up to seven days old, whereas birth weights include only those taken on the day of birth. This paper presents neonatal weights for six representative species of gibbons (H. lar, H. leucogenys, H. moloch, H. muelleri, H. pileatus, H. syndactylus) and some of their hybrids. Most of our data stem from surviving animals that were subsequently hand-reared and include 80 infants, thus making the previously available dataset 5 times larger. Our neonatal weights fall roughly into three different classes: neonates of the lar group (about 390 g, n = 27), the concolor group (about 510 g, n = 7), and the siamang (about 540 g, n = 46). This grouping corresponds not only to taxonomic units within the hylobatids, but also to grouping of gibbons by adult body weight. No weight difference between males and females is evident in our sample, and hybrids of the lar group do not appear to differ in weight from pure species. True birth weights (i.e., weights recorded on the day of birth) are available for only a few individuals. These weights are, on average, 7% higher than neonatal weights, but the difference is not statistically significant. Additional samples of neonatal weights suggest that infants that die on the day of birth weigh, on average, 17% less, twins weigh 29% less, and infants born by Cesarean section weigh 19% more than our reference sample of neonates. © 1995 Wiley-Liss, Inc.     

Characteristics that predict locating and interviewing mothers identified by a state birth defects registry and vital records

BACKGROUND: State vital records are often used to select population-based controls in record-linkage studies of birth defects. However, locating and contacting individuals based on these data sources to collect additional data can be a challenge. METHODS: A large case-control study of air quality and birth defects was conducted in 7 Texas counties in which cases were selected from the Texas Birth Defects Registry and controls from state vital records. In 2004, data from these sources were used to trace mothers of cases and controls who delivered babies in the year 2000 (n=2477) for participation in a computer-assisted telephone interview. A number of factors that predicted whether an individual would be located and interviewed were identified. RESULTS: Between March and August 2004, 38% of the mothers were located, and 38% of the located mothers were interviewed. Case mothers were more likely than control mothers to be located (44 vs. 30%) and, if located, to be interviewed (43 vs. 31%). We compared the characteristics of mothers who were not located (case n=760; control n=777), mothers who were located but not interviewed (case n=344; control n=236), and mothers who were interviewed (case n=256; control n=104). Among both cases and controls, older mothers (>or=30 years) were more likely than younger mothers to be located, and non-Hispanic black mothers were least likely to be located and interviewed. CONCLUSIONS: Despite the utility of vital records as a source of population-based controls in record-linkage analyses, the poor response rate discourages the use of these data sources to contact individuals for a follow-up study 4 years after delivery.     

Strategies for selecting subsets of single-nucleotide polymorphisms to genotype in association studies

In genetic association studies, linkage disequilibrium (LD) within a region can be exploited to select a subset of single-nucleotide polymorphisms (SNPs) to genotype with minimal loss of information. A novel entropy-based method for selecting SNPs is proposed and compared to an existing method based on the coefficient of determination (R2) using simulated data from Genetic Analysis Workshop 14. The effect of the size of the sample used to investigate LD (by estimating haplotype frequencies) and hence select the SNPs is also investigated for both measures. It is found that the novel method and the established method select SNP subsets that do not differ greatly. The entropy-based measure may thus have value because it is easier to compute than R2. Increasing the sample size used to estimate haplotype frequencies improves the predictive power of the subset of SNPs selected. A smaller subset of SNPs chosen using a large initial sample to estimate LD can in some instances be more informative than a larger subset chosen based on poor estimates of LD (using a small initial sample). An initial sample size of 50 individuals is sufficient in most situations investigated, which involved selection from a set of 7 SNPs, although to select a larger number of SNPs, a larger initial sample size may be required.     

Enhanced Localization of Genetic Samples through Linkage-Disequilibrium Correction

Characterizing the spatial patterns of genetic diversity in human populations has a wide range of applications, from detecting genetic mutations associated with disease to inferring human history. Current approaches, including the widely used principal-component analysis, are not suited for the analysis of linked markers, and local and long-range linkage disequilibrium (LD) can dramatically reduce the accuracy of spatial localization when unaccounted for. To overcome this, we have introduced an approach that performs spatial localization of individuals on the basis of their genetic data and explicitly models LD among markers by using a multivariate normal distribution. By leveraging external reference panels, we derive closed-form solutions to the optimization procedure to achieve a computationally efficient method that can handle large data sets. We validate the method on empirical data from a large sample of European individuals from the POPRES data set, as well as on a large sample of individuals of Spanish ancestry. First, we show that by modeling LD, we achieve accuracy superior to that of existing methods. Importantly, whereas other methods show decreased performance when dense marker panels are used in the inference, our approach improves in accuracy as more markers become available. Second, we show that accurate localization of genetic data can be achieved with only a part of the genome, and this could potentially enable the spatial localization of admixed samples that have a fraction of their genome originating from a given continent. Finally, we demonstrate that our approach is resistant to distortions resulting from long-range LD regions; such distortions can dramatically bias the results when unaccounted for.