Combining capture–recapture data and known ages allows estimation of age‐dependent survival rates

In many animal populations, demographic parameters such as survival and recruitment vary markedly with age, as do parameters related to sampling, such as capture probability. Failing to account for such variation can result in biased estimates of population‐level rates. However, estimating age‐dependent survival rates can be challenging because ages of individuals are rarely known unless tagging is done at birth. For many species, it is possible to infer age based on size. In capture–recapture studies of such species, it is possible to use a growth model to infer the age at first capture of individuals. We show how to build estimates of age‐dependent survival into a capture–mark–recapture model based on data obtained in a capture–recapture study. We first show how estimates of age based on length increments closely match those based on definitive aging methods. In simulated analyses, we show that both individual ages and age‐dependent survival rates estimated from simulated data closely match true values. With our approach, we are able to estimate the age‐specific apparent survival rates of Murray and trout cod in the Murray River, Australia. Our model structure provides a flexible framework within which to investigate various aspects of how survival varies with age and will have extensions within a wide range of ecological studies of animals where age can be estimated based on size.     

Estimating infection prevalence: Best practices and their theoretical underpinnings

Accurately estimating infection prevalence is fundamental to the study of population health, disease dynamics, and infection risk factors. Prevalence is estimated as the proportion of infected individuals (“individual‐based estimation”), but is also estimated as the proportion of samples in which evidence of infection is detected (“anonymous estimation”). The latter method is often used when researchers lack information on individual host identity, which can occur during noninvasive sampling of wild populations or when the individual that produced a fecal sample is unknown. The goal of this study was to investigate biases in individual‐based versus anonymous prevalence estimation theoretically and to test whether mathematically derived predictions are evident in a comparative dataset of gastrointestinal helminth infections in nonhuman primates. Using a mathematical model, we predict that anonymous estimates of prevalence will be lower than individual‐based estimates when (a) samples from infected individuals do not always contain evidence of infection and/or (b) when false negatives occur. The mathematical model further predicts that no difference in bias should exist between anonymous estimation and individual‐based estimation when one sample is collected from each individual. Using data on helminth parasites of primates, we find that anonymous estimates of prevalence are significantly and substantially (12.17%) lower than individual‐based estimates of prevalence. We also observed that individual‐based estimates of prevalence from studies employing single sampling are on average 6.4% higher than anonymous estimates, suggesting a bias toward sampling infected individuals. We recommend that researchers use individual‐based study designs with repeated sampling of individuals to obtain the most accurate estimate of infection prevalence. Moreover, to ensure accurate interpretation of their results and to allow for prevalence estimates to be compared among studies, it is essential that authors explicitly describe their sampling designs and prevalence calculations in publications.     

Semiparametric method for estimating paleodemographic profiles from age indicator data.

This paper addresses the problem of estimating an age-at-death distribution or paleodemographic profile from osteological data. It is demonstrated that the classical two-stage procedure whereby one first constructs estimates of age-at-death of individual skeletons and then uses these age estimates to obtain a paleodemographic profile is not a correct approach. This is a consequence of Bayes' theorem. Instead, we demonstrate a valid approach that proceeds from the opposite starting point: given skeletal age-at-death, one first estimates the probability of assigning the skeleton into a specific osteological age-indicator stage. We show that this leads to a statistically valid method for obtaining a paleodemographic profile, and moreover, that valid individual age estimation itself requires a demographic profile and therefore is done subsequent to its construction. Individual age estimation thus becomes the last rather than the first step in the estimation procedure. A central concept of our statistical approach is that of a weight function. A weight function is associated with each osteological age-indicator stage or category, and provides the probability that a specific age indicator stage is observed, given age-at-death of the individual. We recommend that weight functions be estimated nonparametrically from a reference data set. In their entirety, the weight functions characterize the relevant stochastic properties of a chosen age indicator. For actual estimation of the paleodemographic profile, a parametric age distribution in the target sample is assumed. The maximum likelihood method is used to identify the unknown parameters of this distribution. As some components are estimated nonparametrically, one then has a semiparametric model. We show how to obtain valid estimates of individual age-at-death, confidence regions, and goodness-of-fit tests. The methods are illustrated with both real and simulated data.     

A fast, powerful method for detecting identity by descent

We present a method, fastIBD, for finding tracts of identity by descent (IBD) between pairs of individuals. FastIBD can be applied to thousands of samples across genome-wide SNP data and is significantly more powerful for finding short tracts of IBD than existing methods for finding IBD tracts in such data. We show that fastIBD can detect facets of population structure that are not revealed by other methods. In the Wellcome Trust Case Control Consortium bipolar disorder case-control data, we find a genome-wide excess of IBD in case-case pairs of individuals compared to control-control pairs. We show that this excess can be explained by the geographical clustering of cases. We also show that it is possible to use fastIBD to generate highly accurate estimates of genome-wide IBD sharing between pairs of distant relatives. This is useful for estimation of relationship and for adjusting for relatedness in association studies. FastIBD is incorporated in the freely available Beagle software package.     

Age estimation in a long‐lived seabird (Ardenna tenuirostris) using DNA methylation‐based biomarkers

Age structure is a fundamental aspect of animal population biology. Age is strongly related to individual physiological condition, reproductive potential and mortality rate. Currently, there are no robust molecular methods for age estimation in birds. Instead, individuals must be ringed as chicks to establish known‐age populations, which is a labour‐intensive and expensive process. The estimation of chronological age using DNA methylation (DNAm) is emerging as a robust approach in mammals including humans, mice and some non‐model species. Here, we quantified DNAm in whole blood samples from a total of 71 known‐age Short‐tailed shearwaters (Ardenna tenuirostris) using digital restriction enzyme analysis of methylation (DREAM). The DREAM method measures DNAm levels at thousands of CpG dinucleotides throughout the genome. We identified seven CpG sites with DNAm levels that correlated with age. A model based on these relationships estimated age with a mean difference of 2.8 years to known age, based on validation estimates from models created by repeated sampling of training and validation data subsets. Longitudinal observation of individuals re‐sampled over 1 or 2 years generally showed an increase in estimated age (6/7 cases). For the first time, we have shown that epigenetic changes with age can be detected in a wild bird. This approach should be of broad interest to researchers studying age biomarkers in non‐model species and will allow identification of markers that can be assessed using targeted techniques for accurate age estimation in large population studies.     

Impact of and Correction for Outcome Misclassification in Cumulative Incidence Estimation

Cohort studies and clinical trials may involve multiple events. When occurrence of one of these events prevents the observance of another, the situation is called “competing risks”. A useful measure in such studies is the cumulative incidence of an event, which is useful in evaluating interventions or assessing disease prognosis. When outcomes in such studies are subject to misclassification, the resulting cumulative incidence estimates may be biased. In this work, we study the mechanism of bias in cumulative incidence estimation due to outcome misclassification. We show that even moderate levels of misclassification can lead to seriously biased estimates in a frequently unpredictable manner. We propose an easy to use estimator for correcting this bias that is uniformly consistent. Extensive simulations suggest that this method leads to unbiased estimates in practical settings. The proposed method is useful, both in settings where misclassification probabilities are known by historical data or can be estimated by other means, and for performing sensitivity analyses when the misclassification probabilities are not precisely known.     

Application of the anatomical method to estimate the maximum adult stature and the age‐at‐death stature

This study focuses on the age adjustment of statures estimated with the anatomical method. The research material includes 127 individuals from the Terry Collection. The cadaveric stature (CSTA)–skeletal height (SKH) ratios indicate that stature loss with age commences before SKH reduction. Testing three equations to estimate CSTA at the age at death and CSTA corrected to maximum stature from SKH indicates that the age correction of stature should reflect the pattern of age‐related stature loss to minimize estimation error. An equation that includes a continuous and linear age correction through the entire adult age range [Eq. (1)] results in curvilinear stature estimation error. This curvilinear stature estimation error can be largely avoided by applying a second linear equation [Eq. (2)] to only individuals older than 40 years. Our third equation [Eq. (3)], based on younger individuals who have not lost stature, can be used to estimate maximum stature. This equation can also be applied to individuals of unknown or highly uncertain age, because it provides reasonably accurate estimates until about 60/70 years at least for males. Am J Phys Anthropol 152:96–106, 2013. © 2013 Wiley Periodicals, Inc.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

Differentiation of animals from different age classes by means of pellet size: Assessment of a field method in European rabbits

Estimating population age structures by faecal pellets sizes is a commonly used field method in some mammal species. We examined the validity of this method in European rabbits based on 1113 pellets from 226 animals with known age, by measuring the intra-individual variation in pellet size and studying the explained variance of calibration curves describing the relation between pellet size and individual age. In addition, we applied a simulation model in order to estimate the accuracy of this method. Pellet size showed a high intra-individual variation and was only moderately correlated with the animals’ age. Modelling revealed that the population age structure assessed by this method deviated considerably from the given structure, indicating a systematic estimation error. We conclude that this method can lead to strongly biased results, restricting its validity. We provide estimation errors, which might be considered if estimates of age structure in wild rabbits populations based on faecal diameters are conducted.     

Age estimation in subadult Egyptian remains

In anthropological analyses of past populations, it is very important to be able to accurately reconstruct the palaeodemographic profile in order to interpret infant mortality as an indicator of the environmental, social and cultural conditions. There are various methods to evaluate the age of immature individuals but some of these methods are strongly influenced by the different rates of skeletal development observed in populations from various geographical areas and/or from various time periods, as well as between the sexes. Clearly, there is a need for adopting a method of estimation of age at death, which will be the one most suitable for analysing the particular skeletal sample.In this study we investigated subadults from the Egyptian osteological collection housed in the Museum of Anthropology and Ethnography of the University of Turin. For each individual, the age at death was estimated based on the degree of eruption and mineralisation of the teeth. Then the estimated age at death was correlated with the measurements of the long bones and ilium.We showed that greater regularity and constancy of rates of skeletal growth could be assessed with measurements, alternative to using maximum length of diaphysis. Moreover, using alternative characters, it was possible to markedly increase the number of individuals whose age at death could be estimated. Our study also showed the need to use a reference sample consistent with the sample being analysed and, which was derived from similar biological-environmental context. Therefore, our proposed method can be used for the estimation of age at death in pre/protohistorical populations from the Mediterranean region.     

年龄鉴定的转换分析法及其在月家庄墓地人骨中的应用

转换分析是一种基于贝叶斯统计的人骨年龄鉴定新方法,具有综合多种年龄标志物、不受参考样本影响、适用于老年个体等优势。本文将其用于陕西洛川月家庄墓地人骨年龄鉴定并与传统方法进行对比。结果表明,两种方法构建出的人群死亡年龄结构、生存过程有显著差异：转换分析得到的最高寿命、平均死亡年龄明显高于传统方法,更多个体可存活至中老年。两种方法鉴定出的年龄差值受样本保存状况、年龄阶段的影响,存在结构性差别。转换分析是人骨年龄鉴定方法的重大创新,使鉴定过程标准化、鉴定误差定量化。未来需使用一些年龄已知的个体开展更多验证研究,以评估该方法对我国人骨样本的适用性及不同软件间的差异。     

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.     

Segmented Bayesian calibration approach for estimating age in forensic science

Forensic age estimation is receiving growing attention from researchers in the last few years. Accurate estimates of age are needed both for identifying real age in individuals without any identity document and assessing it for human remains. The methods applied in such context are mostly based on radiological analysis of some anatomical districts and entail the use of a regression model. However, estimating chronological age by regression models leads to overestimated ages in younger subjects and underestimated ages in older ones. We introduced a full Bayesian calibration method combined with a segmented function for age estimation that relied on a Normal distribution as a density model to mitigate this bias. In this way, we were also able to model the decreasing growth rate in juveniles. We compared our new Bayesian‐segmented model with other existing approaches. The proposed method helped producing more robust and precise forecasts of age than compared models while exhibited comparable accuracy in terms of forecasting measures. Our method seemed to overcome the estimation bias also when applied to a real data set of South‐African juvenile subjects.     

Multilocus estimation of selfing and its heritability

We describe a new method of estimating the selfing rate (S) in a mixed mating population based on a population structure approach that accounts for possible intergenerational correlation in selfing rate, giving rise to an estimate of the upper limit for heritability of selfing rate (h(2)). A correlation between generations in selfing rate is shown to affect one- and two-locus probabilities of identity by descent. Conventional estimates of selfing rate based on a population structure approach are positively biased by intergenerational correlation in selfing. Multilocus genotypes of individuals are used to give maximum-likelihood estimates of S and h(2) in the presence of scoring artifacts. Our multilocus estimation of selfing rate and its heritability (MESH) method was tested with simulated data for a range of conditions. Selfing rate estimates from MESH have low bias and root mean squared error, whereas estimates of the heritability of selfing rate have more uncertainty. Increasing the number of individuals in a sample helps to reduce bias and root mean squared error more than increasing the number of loci of sampled individuals. Improved estimates of selfing rate, as well as estimates of its heritability, can be obtained with this method, although a large number of loci and individuals are needed to achieve best results.     

Variation in cortical bone histology within the human femur and its impact on estimating age at death

Histological methods for the estimation of age at death using cortical bone are based on the evaluation of microstructural changes over time. Since histological analysis is a destructive method, most techniques attempt to limit the amount of cortical bone needed for analysis. Sample location, however, can have a significant effect on the accuracy of these methods. Furthermore, research demonstrates that both intersection and intrasection variation is present at the midshaft of the femur, which is the primary location for estimating age at death in humans. This research determines the extent of regional variation within the adult human femur and its effect on age estimation. Secondary osteon lamellae and Haversian canal ratio and cortical thickness were quantified. Thompson's All Males Left Femur regression equation was used to estimate age. Results show that significant regional variation occurs in the estimated ages derived from the posterior aspect of the femoral shaft and significant intrasection variation occurs in age estimates from the mid and mid-distal cross-sections. Thus, the inter and intrasection variation that occurs in bone remodeling within the femoral cortex has the potential to produce significant differences amongst age estimates taken from various femoral diaphyseal locations compared to the age estimated from the standard location used in Thompson's core method (1978). The results indicate that the use of this histological method is dependant on the ability to correctly identify the four anatomical locations, but the extracted core used for age estimation is not necessarily confined to the anterior midshaft.     

Quick methods for evaluating survival of age-characterizable long-lived territorial birds

Survival is a key life-history trait in animals. However, most methods of survival estimation require substantial human and economic investment in the long term, particularly in species occurring in low densities, the case of most endangered species. An alternative to traditional recapture (CR) methods is estimation of adult survival based indirectly on either age ratios (AGR) or turnover rates (TOR) in territorial species. These 2 methods are applicable to bird species in which recruited individuals enter into the breeding population whilst still exhibiting the external traits that distinguish those animals from experienced adults. The main advantages of these methods are that survival can be easily estimated for all monitored individuals after just 1 or 2 breeding seasons and that disturbance to the species is minimized. The main constraints of indirect methods are that the assumptions are more restrictive than in CR methods, and survival estimates, although comparable between sites and years, may be biased. We used data from a long-term monitoring survey of 2 populations of the endangered Bonelli's eagle (Aquila fasciata), one in Catalonia (NE Spain) and the other in Provence and Languedoc-Roussillon (SE France). We evaluated survival estimates using the AGR and TOR methods and compared them with CR methods and provide suitable corrections for refining survival estimates based on indirect methods. In Catalonia (2002–2008), survival was estimated at 0.84 by CR methods (SE = 0.047; n = 25 radio tagged eagles), at 0.86 by the corrected AGR method (SE = 0.011; n = 558 bird * year), and at 0.86 by the corrected TOR method (SE = 0.022; n = 547 bird * year). In France (1999–2008), survival was estimated at 0.88 by CR methods (SE = 0.040; n = 45 darvic banded eagles), at 0.87 by the corrected AGR method (SE = 0.015; n = 443 bird * year), and at 0.87 by the corrected TOR method (SE = 0.015; n = 438 bird * year). All analyses suggest that females survive better than males and that individuals from the French population survive better than individuals from the Catalan population. We conclude that indirect methods, which should not be regarded as a substitute of CR methods, will allow wildlife managers and researchers to estimate accurately adult survival in a territorial species over a short period of time and to monitor survival across populations over large geographic ranges and over time. © 2011 The Wildlife Society.     

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.     

Inferring recent migration rates from individual genotypes

We present a novel and straightforward method for estimating recent migration rates between discrete populations using multilocus genotype data. The approach builds upon a two-step sampling design, where individual genotypes are sampled before and after dispersal. We develop a model that estimates all pairwise backwards migration rates ( m_ij , the probability that an individual sampled in population i is a migrant from population j ) between a set of populations. The method is validated with simulated data and compared with the methods of BayesAss and Structure. First, we use data for an island model and then we consider more realistic data simulations for a metapopulation of the greater white-toothed shrew ( Crocidura russula ). We show that the precision and bias of estimates primarily depend upon the proportion of individuals sampled in each population. Weak sampling designs may particularly affect the quality of the coverage provided by 95% highest posterior density intervals. We further show that it is relatively insensitive to the number of loci sampled and the overall strength of genetic structure. The method can easily be extended and makes fewer assumptions about the underlying demographic and genetic processes than currently available methods. It allows backwards migration rates to be estimated across a wide range of realistic conditions.     

Interval estimation of genetic susceptibility for retrospective case-control studies

Background

This article describes classical and Bayesian interval estimation of genetic susceptibility based on random samples with pre-specified numbers of unrelated cases and controls.

Results

Frequencies of genotypes in cases and controls can be estimated directly from retrospective case-control data. On the other hand, genetic susceptibility defined as the expected proportion of cases among individuals with a particular genotype depends on the population proportion of cases (prevalence). Given this design, prevalence is an external parameter and hence the susceptibility cannot be estimated based on only the observed data. Interval estimation of susceptibility that can incorporate uncertainty in prevalence values is explored from both classical and Bayesian perspective. Similarity between classical and Bayesian interval estimates in terms of frequentist coverage probabilities for this problem allows an appealing interpretation of classical intervals as bounds for genetic susceptibility. In addition, it is observed that both the asymptotic classical and Bayesian interval estimates have comparable average length. These interval estimates serve as a very good approximation to the "exact" (finite sample) Bayesian interval estimates. Extension from genotypic to allelic susceptibility intervals shows dependency on phenotype-induced deviations from Hardy-Weinberg equilibrium.

Conclusions

The suggested classical and Bayesian interval estimates appear to perform reasonably well. Generally, the use of exact Bayesian interval estimation method is recommended for genetic susceptibility, however the asymptotic classical and approximate Bayesian methods are adequate for sample sizes of at least 50 cases and controls.     

Applicability of Single-Camera Photogrammetry to Determine Body Dimensions of Pinnipeds: Galapagos Sea Lions as an Example

Morphological features correlate with many life history traits and are therefore of high interest to behavioral and evolutionary biologists. Photogrammetry provides a useful tool to collect morphological data from species for which measurements are otherwise difficult to obtain. This method reduces disturbance and avoids capture stress. Using the Galapagos sea lion (Zalophus wollebaeki) as a model system, we tested the applicability of single-camera photogrammetry in combination with laser distance measurement to estimate morphological traits which may vary with an animal’s body position. We assessed whether linear morphological traits estimated by photogrammetry can be used to estimate body length and mass. We show that accurate estimates of body length (males: ±2.0%, females: ±2.6%) and reliable estimates of body mass are possible (males: ±6.8%, females: 14.5%). Furthermore, we developed correction factors that allow the use of animal photos that diverge somewhat from a flat-out position. The product of estimated body length and girth produced sufficiently reliable estimates of mass to categorize individuals into 10 kg-classes of body mass. Data of individuals repeatedly photographed within one season suggested relatively low measurement errors (body length: 2.9%, body mass: 8.1%). In order to develop accurate sex- and age-specific correction factors, a sufficient number of individuals from both sexes and from all desired age classes have to be captured for baseline measurements. Given proper validation, this method provides an excellent opportunity to collect morphological data for large numbers of individuals with minimal disturbance.