The effects of prorating risk in the development of life‐tables

This study used computer models to investigate two different strategies for assessing risk in the development of age‐based life‐tables from studbook data sets. One methodology is similar to that currently employed in American Zoo and Aquarium Association population management, which prorates animals at risk within age‐classes. The other follows the method used in human life‐tables that assumes animals are at risk for the entire age‐class. This study concludes that prorating risk may invalidate population growth projections by significantly and unequally over‐estimating fecundity and mortality rates. This effect is most pronounced in species that have distinct breeding seasons (birth pulse populations), seasonal mortality, and small data sets. Recommendations include using a non‐prorated methodology, tabulating life‐tables using only completely known age‐class data, and combining population parameters for emigrations, releases, and deaths for population growth projections. Zoo Biol 20:279–291, 2001. © 2001 Wiley‐Liss, Inc.     

Hidden population size estimation and diagnostics using two respondent-driven samples with applications in Armenia

Estimating the size of hidden populations is essential to understand the magnitude of social and healthcare needs, risk behaviors, and disease burden. However, due to the hidden nature of these populations, they are difficult to survey, and there are no gold standard size estimation methods. Many different methods and variations exist, and diagnostic tools are needed to help researchers assess method-specific assumptions as well as compare between methods. Further, because many necessary mathematical assumptions are unrealistic for real survey implementation, assessment of how robust methods are to deviations from the stated assumptions is essential. We describe diagnostics and assess the performance of a new population size estimation method, capture–recapture with successive sampling population size estimation (CR-SS-PSE), which we apply to data from 3 years of studies from three cities and three hidden populations in Armenia. CR-SS-PSE relies on data from two sequential respondent-driven sampling surveys and extends the successive sampling population size estimation (SS-PSE) framework by using the number of individuals in the overlap between the two surveys and a model for the successive sampling process to estimate population size. We demonstrate that CR-SS-PSE is more robust to violations of successive sampling assumptions than SS-PSE. Further, we compare the CR-SS-PSE estimates to population size estimations using other common methods, including unique object and service multipliers, wisdom of the crowd, and two-source capture–recapture to illustrate volatility across estimation methods.     

Impacts of the Toba eruption and montane forest expansion on diversification in Sumatran parachuting frogs (Rhacophorus)

Catastrophic events, such as volcanic eruptions, can have profound impacts on the demographic histories of resident taxa. Due to its presumed effect on biodiversity, the Pleistocene eruption of super‐volcano Toba has received abundant attention. We test the effects of the Toba eruption on the diversification, genetic diversity, and demography of three co‐distributed species of parachuting frogs (Genus Rhacophorus) on Sumatra. We generate target‐capture data (~950 loci and ~440,000 bp) for three species of parachuting frogs and use these data paired with previously generated double digest restriction‐site associated DNA (ddRADseq) data to estimate population structure and genetic diversity, to test for population size changes using demographic modelling, and to estimate the temporal clustering of size change events using a full‐likelihood Bayesian method. We find that populations around Toba exhibit reduced genetic diversity compared with southern populations, and that northern populations exhibit a shift in effective population size around the time of the eruption (~80 kya). However, we infer a stronger signal of expansion in southern populations around ~400 kya, and at least two of the northern populations may have also expanded at this time. Taken together, these findings suggest that the Toba eruption precipitated population declines in northern populations, but that the demographic history of these three species was also strongly impacted by mid‐Pleistocene forest expansion during glacial periods. We propose local rather than regional effects of the Toba eruption, and emphasize the dynamic nature of diversification on the Sunda Shelf.     

Multivariate paired data analysis: multilevel PLSDA versus OPLSDA

Metabolomics data obtained from (human) nutritional intervention studies can have a rather complex structure that depends on the underlying experimental design. In this paper we discuss the complex structure in data caused by a cross-over designed experiment. In such a design, each subject in the study population acts as his or her own control and makes the data paired. For a single univariate response a paired t-test or repeated measures ANOVA can be used to test the differences between the paired observations. The same principle holds for multivariate data. In the current paper we compare a method that exploits the paired data structure in cross-over multivariate data (multilevel PLSDA) with a method that is often used by default but that ignores the paired structure (OPLSDA). The results from both methods have been evaluated in a small simulated example as well as in a genuine data set from a cross-over designed nutritional metabolomics study. It is shown that exploiting the paired data structure underlying the cross-over design considerably improves the power and the interpretability of the multivariate solution. Furthermore, the multilevel approach provides complementary information about (I) the diversity and abundance of the treatment effects within the different (subsets of) subjects across the study population, and (II) the intrinsic differences between these study subjects.     

Stacks 2: Analytical methods for paired‐end sequencing improve RADseq‐based population genomics

For half a century population genetics studies have put type II restriction endonucleases to work. Now, coupled with massively‐parallel, short‐read sequencing, the family of RAD protocols that wields these enzymes has generated vast genetic knowledge from the natural world. Here, we describe the first software natively capable of using paired‐end sequencing to derive short contigs from de novo RAD data. Stacks version 2 employs a de Bruijn graph assembler to build and connect contigs from forward and reverse reads for each de novo RAD locus, which it then uses as a reference for read alignments. The new architecture allows all the individuals in a metapopulation to be considered at the same time as each RAD locus is processed. This enables a Bayesian genotype caller to provide precise SNPs, and a robust algorithm to phase those SNPs into long haplotypes, generating RAD loci that are 400–800 bp in length. To prove its recall and precision, we tested the software with simulated data and compared reference‐aligned and de novo analyses of three empirical data sets. Our study shows that the latest version of Stacks is highly accurate and outperforms other software in assembling and genotyping paired‐end de novo data sets.     

Comparison of genetic (co)variance matrices within and between Scabiosa canescens and S. columbaria

In the current study, we used bootstrap analyses and the common principal component (CPC) method of Flury (1988) to estimate and compare the G ‐matrix of Scabiosa columbaria and S. canescens populations. We found three major patterns in the G ‐matrices: (i) the magnitude of the (co)variances was more variable among characters than among populations, (ii) different populations showed high (co)variance for different characters, and (iii) there was a tendency for S. canescens to have higher genetic (co)variances than S. columbaria. The hypothesis of equal G ‐matrices was rejected in all comparisons and there was no evidence that the matrices differed by a proportional constant in any of the analyses. The two ‘species matrices’ were found to be unrelated, both for raw data and data standardized over populations, and there was significant between‐population variation in the G ‐matrix in both species. Populations of S. canescens showed conservation of structure (principal components) in their G ‐matrices, contrasting with the lack of common structure among the S. columbaria matrices. Given these observations and the results from previous studies, we propose that selection may be responsible for some of the variation between the G ‐matrices, at least in S. columbaria and at the between‐species level.     

Analysis of covariance with pre-treatment measurements in randomized trials under the cases that covariances and post-treatment variances differ between groups

When primary endpoints of randomized trials are continuous variables, the analysis of covariance (ANCOVA) with pre-treatment measurements as a covariate is often used to compare two treatment groups. In the ANCOVA, equal slopes (coefficients of pre-treatment measurements) and equal residual variances are commonly assumed. However, random allocation guarantees only equal variances of pre-treatment measurements. Unequal covariances and variances of post-treatment measurements indicate unequal slopes and, usually, unequal residual variances. For non-normal data with unequal covariances and variances of post-treatment measurements, it is known that the ANCOVA with equal slopes and equal variances using an ordinary least-squares method provides an asymptotically normal estimator for the treatment effect. However, the asymptotic variance of the estimator differs from the variance estimated from a standard formula, and its property is unclear. Furthermore, the asymptotic properties of the ANCOVA with equal slopes and unequal variances using a generalized least-squares method are unclear. In this paper, we consider non-normal data with unequal covariances and variances of post-treatment measurements, and examine the asymptotic properties of the ANCOVA with equal slopes using the variance estimated from a standard formula. Analytically, we show that the actual type I error rate, thus the coverage, of the ANCOVA with equal variances is asymptotically at a nominal level under equal sample sizes. That of the ANCOVA with unequal variances using a generalized least-squares method is asymptotically at a nominal level, even under unequal sample sizes. In conclusion, the ANCOVA with equal slopes can be asymptotically justified under random allocation.     

Comparison of Parameters from Rhythmometric Models with Multiple Components on Hybrid Data

Population multiple components is a statistical tool useful for the analysis of time-dependent hybrid data. With a small number of parameters, it is possible to model and to predict the periodic behavior of a population. In this article, we propose two methods to compare among populations rhythmometric parameters obtained by multiple component analysis. The first is a parametric method based in the usual statistical techniques for comparison of mean vectors in multivariate normal populations. The method, through MANOVA analysis, allows comparison of the MESOR and amplitude-acrophase pair of each component among two or more populations. The second is a nonparametric method, based in bootstrap techniques, to compare parameters from two populations. This test allows one to compare the MESOR, the amplitude, and the acrophase of each fitted component, as well as the global amplitude, orthophase, and bathyphase estimated when all fitted components are harmonics of a fundamental period. The idea is to calculate a confidence interval for the difference of the parameters of interest. If this interval does not contain zero, it can be concluded that the parameters from the two models are different with high probability. An estimation of p-value for the corresponding test can also be calculated. Both methods are illustrated with an example, based on clinical data. The nonparametric test can also be applied to paired data, a special situation of great interest in practice. By the use of similar bootstrap techniques, we illustrate how to construct confidence intervals for any rhythmometric parameter estimated from population multiple components models, including the orthophase, bathyphase, and global amplitude. These tests for comparison of parameters among populations are a needed tool when modeling the nonsinusoidal rhythmic behavior of hybrid data by population multiple component analysis.     

Comparison of parameters from rhythmometric models with multiple components on hybrid data

Population multiple components is a statistical tool useful for the analysis of time-dependent hybrid data. With a small number of parameters, it is possible to model and to predict the periodic behavior of a population. In this article, we propose two methods to compare among populations rhythmometric parameters obtained by multiple component analysis. The first is a parametric method based in the usual statistical techniques for comparison of mean vectors in multivariate normal populations. The method, through MANOVA analysis, allows comparison of the MESOR and amplitude-acrophase pair of each component among two or more populations. The second is a nonparametric method, based in bootstrap techniques, to compare parameters from two populations. This test allows one to compare the MESOR, the amplitude, and the acrophase of each fitted component, as well as the global amplitude, orthophase, and bathyphase estimated when all fitted components are harmonics of a fundamental period. The idea is to calculate a confidence interval for the difference of the parameters of interest. If this interval does not contain zero, it can be concluded that the parameters from the two models are different with high probability. An estimation of p-value for the corresponding test can also be calculated. Both methods are illustrated with an example, based on clinical data. The nonparametric test can also be applied to paired data, a special situation of great interest in practice. By the use of similar bootstrap techniques, we illustrate how to construct confidence intervals for any rhythmometric parameter estimated from population multiple components models, including the orthophase, bathyphase, and global amplitude. These tests for comparison of parameters among populations are a needed tool when modeling the nonsinusoidal rhythmic behavior of hybrid data by population multiple component analysis.     

Effects of age‐based movement on the estimation of growth assuming random‐at‐age or random‐at‐length data

Simulation methods were used to generate paired data from a simulated population that included the age‐based process of movement and the length‐based process of gear selection. The age‐based process caused bias in the estimates of growth parameters assuming random at length, even when relatively few age classes were affected. Methods that assumed random at age were biased by the subsequent inclusion of the length‐based process of gear selection. Additional knowledge of the age structure of the sampled area is needed to ensure an unbiased estimate of the growth parameters when using the length‐conditional approach in the presence of age‐based movement. Estimates of the variability in the length‐at‐age relationship were better estimated with the length‐conditional than the traditional method even when the assumptions of random at length were violated. Inclusion of paired observations of length and associated age inside the population dynamics model may be the most appropriate way of estimating growth.     

EXTRA‐PAIR PATERNITY AND THE VARIANCE IN MALE FITNESS IN SONG SPARROWS (MELOSPIZA MELODIA)

The variance in fitness across population members can influence major evolutionary processes. In socially monogamous but genetically polygynandrous species, extra‐pair paternity (EPP) is widely hypothesized to increase the variance in male fitness compared to that arising given the socially monogamous mating system. This hypothesis has not been definitively tested because comprehensive data describing males’ apparent (social) and realized (genetic) fitness have been lacking. We used 16 years of comprehensive social and genetic paternity data for an entire free‐living song sparrow (Melospiza melodia) population to quantify and compare variances in male apparent and realized fitness, and to quantify the contribution of the variances in within‐pair reproductive success (WPRS) and extra‐pair reproductive success (EPRS) and their covariance to the variance in realized fitness. Overall, EPP increased the variance in male fitness by only 0–27% across different fitness and variance measures. This relatively small effect reflected the presence of socially unpaired males with zero apparent and low realized fitness, small covariance between WPRS and EPRS, and large variance in WPRS that was relatively unaffected by EPP. Therefore, although EPP altered individual males’ contributions to future generations, its impact on population‐level parameters such as the opportunity for selection and effective population size was limited.     

Limited plasticity in the phenotypic variance‐covariance matrix for male advertisement calls in the black field cricket,Teleogryllus commodus

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders’ equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent study, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance‐covariance matrix ( P ) stability are sparse, and largely focused on morphological traits. Here, we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild‐caught crickets from each of the populations and then a second subset after rearing crickets under common‐garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high‐ and low‐nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit.     

"Reverse ecology" and the power of population genomics

Rapid and inexpensive sequencing technologies are making it possible to collect whole genome sequence data on multiple individuals from a population. This type of data can be used to quickly identify genes that control important ecological and evolutionary phenotypes by finding the targets of adaptive natural selection, and we therefore refer to such approaches as "reverse ecology." To quantify the power gained in detecting positive selection using population genomic data, we compare three statistical methods for identifying targets of selection: the McDonald-Kreitman test, the mkprf method, and a likelihood implementation for detecting d(N)/d(S) > 1. Because the first two methods use polymorphism data we expect them to have more power to detect selection. However, when applied to population genomic datasets from human, fly, and yeast, the tests using polymorphism data were actually weaker in two of the three datasets. We explore reasons why the simpler comparative method has identified more genes under selection, and suggest that the different methods may really be detecting different signals from the same sequence data. Finally, we find several statistical anomalies associated with the mkprf method, including an almost linear dependence between the number of positively selected genes identified and the prior distributions used. We conclude that interpreting the results produced by this method should be done with some caution.     

‘True’ null allele detection in microsatellite loci: a comparison of methods,assessment of difficulties and survey of possible improvements

Null alleles are alleles that for various reasons fail to amplify in a PCR assay. The presence of null alleles in microsatellite data is known to bias the genetic parameter estimates. Thus, efficient detection of null alleles is crucial, but the methods available for indirect null allele detection return inconsistent results. Here, our aim was to compare different methods for null allele detection, to explain their respective performance and to provide improvements. We applied several approaches to identify the ‘true’ null alleles based on the predictions made by five different methods, used either individually or in combination. First, we introduced simulated ‘true’ null alleles into 240 population data sets and applied the methods to measure their success in detecting the simulated null alleles. The single best‐performing method was ML‐NullFreq_frequency. Furthermore, we applied different noise reduction approaches to improve the results. For instance, by combining the results of several methods, we obtained more reliable results than using a single one. Rule‐based classification was applied to identify population properties linked to the false discovery rate. Rules obtained from the classifier described which population genetic estimates and loci characteristics were linked to the success of each method. We have shown that by simulating ‘true’ null alleles into a population data set, we may define a null allele frequency threshold, related to a desired true or false discovery rate. Moreover, using such simulated data sets, the expected null allele homozygote frequency may be estimated independently of the equilibrium state of the population.     

Longitudinal analysis of pre- and post-treatment measurements with equal baseline assumptions in randomized trials

For continuous variables of randomized controlled trials, recently, longitudinal analysis of pre- and posttreatment measurements as bivariate responses is one of analytical methods to compare two treatment groups. Under random allocation, means and variances of pretreatment measurements are expected to be equal between groups, but covariances and posttreatment variances are not. Under random allocation with unequal covariances and posttreatment variances, we compared asymptotic variances of the treatment effect estimators in three longitudinal models. The data-generating model has equal baseline means and variances, and unequal covariances and posttreatment variances. The model with equal baseline means and unequal variance–covariance matrices has a redundant parameter. In large sample sizes, these two models keep a nominal type I error rate and have high efficiency. The model with equal baseline means and equal variance–covariance matrices wrongly assumes equal covariances and posttreatment variances. Only under equal sample sizes, this model keeps a nominal type I error rate. This model has the same high efficiency with the data-generating model under equal sample sizes. In conclusion, longitudinal analysis with equal baseline means performed well in large sample sizes. We also compared asymptotic properties of longitudinal models with those of the analysis of covariance (ANCOVA) and t-test.     

Interval estimates for the ratio of the means of two normal populations with variances related to the means

A procedure is given for estimating the ratio of the means of two populations using the data from two independent random samples when the observations are normally distributed with population variances that are related to the population means.     

Confidence intervals for the difference in the success rates of two treatments in the analysis of correlated binary responses

In clinical studies, we often compare the success rates of two treatment groups where post‐treatment responses of subjects within clusters are usually correlated. To estimate the difference between the success rates, interval estimation procedures that do not account for this intraclass correlation are likely inappropriate. To address this issue, we propose three interval procedures by direct extensions of recently proposed methods for independent binary data based on the concepts of design effect and effective sample size used in sample surveys. Each of them is then evaluated with four competing variance estimates. We also extend three existing methods recommended for complex survey data using different weighting schemes required for those three existing methods. An extensive simulation study is conducted for the purposes of evaluating and comparing the performance of the proposed methods in terms of coverage and expected width. The interval estimation procedures are illustrated using three examples in clinical and social science studies. Our analytic arguments and numerical studies suggest that the methods proposed in this work may be useful in clustered data analyses.     

Comparison of two methods for in vivo estimation of the glenohumeral joint rotation center (GH-JRC) of the patients with shoulder hemiarthroplasty

Determination of an accurate glenohumeral-joint rotation center (GH-JRC) from marker data is essential for kinematic and dynamic analysis of shoulder motions. Previous studies have focused on the evaluation of the different functional methods for the estimation of the GH-JRC for healthy subjects. The goal of this paper is to compare two widely used functional methods, namely the instantaneous helical axis (IHA) and symmetrical center of rotation (SCoRE) methods, for estimating the GH-JRC in vivo for patients with implanted shoulder hemiarthroplasty. The motion data of five patients were recorded while performing three different dynamic motions (circumduction, abduction, and forward flexion). The GH-JRC was determined using the CT-images of the subjects (geometric GH-JRC) and was also estimated using the two IHA and SCoRE methods. The rotation centers determined using the IHA and SCoRE methods were on average 1.47±0.62 cm and 2.07±0.55 cm away from geometric GH-JRC, respectively. The two methods differed significantly (two-tailed p-value from paired t-Test ～0.02, post-hoc power ～0.30). The SCoRE method showed a significant lower (two-tailed p-value from paired t-Test ～0.03, post-hoc power ～0.68) repeatability error calculated between the different trials of each motion and each subject and averaged across all measured subjects (0.62±0.10 cm for IHA vs. 0.43±0.12 cm for SCoRE). It is concluded that the SCoRE appeared to be a more repeatable method whereas the IHA method resulted in a more accurate estimation of the GH-JRC for patients with endoprostheses.