Evaluating Methods to Correct for Population Stratification when Estimating Paternity Indexes

The statistical interpretation of the forensic genetic evidence requires the use of allelic frequency estimates in the reference population for the studied markers. Differences in the genetic make up of the populations can be reflected in statistically different allelic frequency distributions. One can easily figure out that collecting such information for any given population is not always possible. Therefore, alternative approaches are needed in these cases in order to compensate for the lack of information. A number of statistics have been proposed to control for population stratification in paternity testing and forensic casework, Fst correction being the only one recommended by the forensic community. In this study we aimed to evaluate the performance of Fst to correct for population stratification in forensics. By way of simulations, we first tested the dependence of Fst on the relative sizes of the sub-populations, and second, we measured the effect of the Fst corrections on the Paternity Index (PI) values compared to the ones obtained when using the local reference database. The results provide clear-cut evidence that (i) Fst values are strongly dependent on the sampling scheme, and therefore, for most situations it would be almost impossible to estimate real values of Fst; and (ii) Fst corrections might unfairly correct PI values for stratification, suggesting the use of local databases whenever possible to estimate the frequencies of genetic profiles and PI values.     

Methods for Checking Assumptions in Regression Models

The usual assumptions in regression analysis are: The setup is true; the random errors are uncorre-lated (and normally distributed); and the data contain no outliers. Reasoning known recommendations to check these assumptions by inspection of the residuals new proposals are discussed and illustrated by an example.     

Asian Elephants in China: Estimating Population Size and Evaluating Habitat Suitability

We monitored the last remaining Asian elephant populations in China over the past decade. Using DNA tools and repeat genotyping, we estimated the population sizes from 654 dung samples collected from various areas. Combined with morphological individual identifications from over 6,300 elephant photographs taken in the wild, we estimated that the total Asian elephant population size in China is between 221 and 245. Population genetic structure and diversity were examined using a 556-bp fragment of mitochondrial DNA, and 24 unique haplotypes were detected from DNA analysis of 178 individuals. A phylogenetic analysis revealed two highly divergent clades of Asian elephants, α and β, present in Chinese populations. Four populations (Mengla, Shangyong, Mengyang, and Pu’Er) carried mtDNA from the α clade, and only one population (Nangunhe) carried mtDNA belonging to the β clade. Moreover, high genetic divergence was observed between the Nangunhe population and the other four populations; however, genetic diversity among the five populations was low, possibly due to limited gene flow because of habitat fragmentation. The expansion of rubber plantations, crop cultivation, and villages along rivers and roads had caused extensive degradation of natural forest in these areas. This had resulted in the loss and fragmentation of elephant habitats and had formed artificial barriers that inhibited elephant migration. Using Geographic Information System, Global Positioning System, and Remote Sensing technology, we found that the area occupied by rubber plantations, tea farms, and urban settlements had dramatically increased over the past 40 years, resulting in the loss and fragmentation of elephant habitats and forming artificial barriers that inhibit elephant migration. The restoration of ecological corridors to facilitate gene exchange among isolated elephant populations and the establishment of cross-boundary protected areas between China and Laos to secure their natural habitats are critical for the survival of Asian elephants in this region.     

Estimating Population Size and Density Using Line Transect Sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to a class of estimators with desirable characteristics. This work was given a basic and rigorous mathematica framework by BURNHAM and ANDERSON (1976). In the present article we use this mathematical framework to develop an estimator of population size and density using weighted least squares. The approach is a two-stage Method.     

Estimating Population Size for Continuous-Time Capture-Recapture Models Via Sample Coverage

An estimation procedure using the idea of sample coverage is proposed to estimate population size for capture-recapture experiments in continuous time. The capture rates (intensity) are allowed to vary by time and individuals (heterogeneity). Only capture frequency history are sufficient for estimating population size while capture times and sequential orders of animals caught are irrelevant for the analysis. An example is given for illustration. The performance of the proposed estimation procedure is also investigated by simulation.     

Estimating Litter Decomposition Rate in Single-Pool Models Using Nonlinear Beta Regression

Litter decomposition rate (k) is typically estimated from proportional litter mass loss data using models that assume constant, normally distributed errors. However, such data often show non-normal errors with reduced variance near bounds (0 or 1), potentially leading to biased k estimates. We compared the performance of nonlinear regression using the beta distribution, which is well-suited to bounded data and this type of heteroscedasticity, to standard nonlinear regression (normal errors) on simulated and real litter decomposition data. Although the beta model often provided better fits to the simulated data (based on the corrected Akaike Information Criterion, AIC_c), standard nonlinear regression was robust to violation of homoscedasticity and gave equally or more accurate k estimates as nonlinear beta regression. Our simulation results also suggest that k estimates will be most accurate when study length captures mid to late stage decomposition (50–80% mass loss) and the number of measurements through time is ≥5. Regression method and data transformation choices had the smallest impact on k estimates during mid and late stage decomposition. Estimates of k were more variable among methods and generally less accurate during early and end stage decomposition. With real data, neither model was predominately best; in most cases the models were indistinguishable based on AIC_c, and gave similar k estimates. However, when decomposition rates were high, normal and beta model k estimates often diverged substantially. Therefore, we recommend a pragmatic approach where both models are compared and the best is selected for a given data set. Alternatively, both models may be used via model averaging to develop weighted parameter estimates. We provide code to perform nonlinear beta regression with freely available software.     

Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.     

Sampling Methods for Estimating Breeding Population and Hunting Mortality of Game Birds

In this paper we will summarize some of the important sampling and non-sampling errors with special reference to the mail surveys on migratory game birds and aerial surveys on breeding birds in North America. Where possible, methods for controlling the errors will be indicated.     

Comparative Analysis of Methods for Estimating the Rate of Population Aging

Biophysics - The essence of aging is a decline in total vitality with age, being basic personal characteristics of human potential. Viability ( $${v}$$ ) is defined as the probability of surviving...     

On the Use of Bayesian Methods for Evaluating Compartmental Neural Models

Computational modeling is being used increasingly in neuroscience. In deriving such models, inference issues such as model selection, model complexity, and model comparison must be addressed constantly. In this article we present briefly the Bayesian approach to inference. Under a simple set of commonsense axioms, there exists essentially a unique way of reasoning under uncertainty by assigning a degree of confidence to any hypothesis or model, given the available data and prior information. Such degrees of confidence must obey all the rules governing probabilities and can be updated accordingly as more data becomes available. While the Bayesian methodology can be applied to any type of model, as an example we outline its use for an important, and increasingly standard, class of models in computational neuroscience—compartmental models of single neurons. Inference issues are particularly relevant for these models: their parameter spaces are typically very large, neurophysiological and neuroanatomical data are still sparse, and probabilistic aspects are often ignored. As a tutorial, we demonstrate the Bayesian approach on a class of one-compartment models with varying numbers of conductances. We then apply Bayesian methods on a compartmental model of a real neuron to determine the optimal amount of noise to add to the model to give it a level of spike time variability comparable to that found in the real cell.     

Estimating Competition in Cladocerans Using Data on Dynamics of Clutch Size and Population Density

Negative correlations between clutch size and population density are proposed to be considered as indices of intra- and interspecific competition in cladocerans if they are revealed while analyzing population dynamics and clutch size and time lags are taken into account. The proper correlation analysis of summer populations of Diaphanosoma brachyurum, Bosmina coregoni, Daphnia cucullata and D. galeata from mesotrophic Lake Glubokoye (Moscow Region) in 1975, 1978, and 1979 indicates the important role of competition of both types for the community studied. High niche overlap in food and space in the four populations was also observed.     

On Kernel Methods of Estimating Marginal Radial and Angular Probability Density Functions

Spatial point patterns which possess a natural origin are considered. Two ways of estimating the marginal radial and angular probability density functions associated with the stochastic process underlying such a pattern are presented. These methods are based on one and two-dimensional kernel functions respectively. The angular density estimate can be used to detect angular trend and to test for angular uniformity within a particular sector about the origin. The two methods of estimation produce essentially the same results. That based on the one-dimensional kernel is recommended because it is computationally simpler.     

Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure

We propose a method to estimate the regression coefficients in a competing risks model where the cause-specific hazard for the cause of interest is related to covariates through a proportional hazards relationship and when cause of failure is missing for some individuals. We use multiple imputation procedures to impute missing cause of failure, where the probability that a missing cause is the cause of interest may depend on auxiliary covariates, and combine the maximum partial likelihood estimators computed from several imputed data sets into an estimator that is consistent and asymptotically normal. A consistent estimator for the asymptotic variance is also derived. Simulation results suggest the relevance of the theory in finite samples. Results are also illustrated with data from a breast cancer study.     

Improving the Rank Precision of Population Health Measures for Small Areas with Longitudinal and Joint Outcome Models

Objectives

The University of Wisconsin Population Health Institute has published the County Health Rankings since 2010. These rankings use population-based data to highlight health outcomes and the multiple determinants of these outcomes and to encourage in-depth health assessment for all United States counties. A significant methodological limitation, however, is the uncertainty of rank estimates, particularly for small counties. To address this challenge, we explore the use of longitudinal and pooled outcome data in hierarchical Bayesian models to generate county ranks with greater precision.

Methods

In our models we used pooled outcome data for three measure groups: (1) Poor physical and poor mental health days; (2) percent of births with low birth weight and fair or poor health prevalence; and (3) age-specific mortality rates for nine age groups. We used the fixed and random effects components of these models to generate posterior samples of rates for each measure. We also used time-series data in longitudinal random effects models for age-specific mortality. Based on the posterior samples from these models, we estimate ranks and rank quartiles for each measure, as well as the probability of a county ranking in its assigned quartile. Rank quartile probabilities for univariate, joint outcome, and/or longitudinal models were compared to assess improvements in rank precision.

Results

The joint outcome model for poor physical and poor mental health days resulted in improved rank precision, as did the longitudinal model for age-specific mortality rates. Rank precision for low birth weight births and fair/poor health prevalence based on the univariate and joint outcome models were equivalent.

Conclusion

Incorporating longitudinal or pooled outcome data may improve rank certainty, depending on characteristics of the measures selected. For measures with different determinants, joint modeling neither improved nor degraded rank precision. This approach suggests a simple way to use existing information to improve the precision of small-area measures of population health.     

Models for Haplotype Evolution in a Nonstationary Population

Haplotype mapping has emerged in the past few years as a powerful tool for the fine mapping of disease genes. It is typically carried out on a sample of affected individuals from a population isolate. If the chromosome neighborhood of a disease gene is saturated with markers, then each new mutation in the population or existing mutation introduced by a population founder exhibits a unique haplotype signature at the time of its introduction. Partial disruptions of these signatures by recombination can be visualized in affecteds and provide important clues to the location of the disease gene. The current paper models haplotype evolution with the intention of clarifying the most favorable circumstances for haplotype mapping. Comparisons with linkage mapping are stressed. For dominant diseases, both deterministic and stochastic models are suggested. Numerical examples based on Finnish population parameters illustrate the general theory in the presence of the complications of selection, mutation, and slow, exponential growth of the isolate.     

Ecological and Genetic Models in Population Biophysics

Biophysics - Complex causal relationships occur between population dynamics and a change in a population genetic structure. In our study, a simple model was used to show that the evolutionary...