A Bayesian framework for comparative quantitative genetics

Bayesian approaches have been extensively used in animal breeding sciences, but similar approaches in the context of evolutionary quantitative genetics have been rare. We compared the performance of Bayesian and frequentist approaches in estimation of quantitative genetic parameters (viz. matrices of additive and dominance variances) in datasets typical of evolutionary studies and traits differing in their genetic architecture. Our results illustrate that it is difficult to disentangle the relative roles of different genetic components from small datasets, and that ignoring, e.g. dominance is likely to lead to biased estimates of additive variance. We suggest that a natural summary statistic for G-matrix comparisons can be obtained by examining how different the underlying multinormal probability distributions are, and illustrate our approach with data on the common frog (Rana temporaria). Furthermore, we derive a simple Monte Carlo method for computation of fraternity coefficients needed for the estimation of dominance variance, and use the pedigree of a natural Siberian jay (Perisoreus infaustus) population to illustrate that the commonly used approximate values can be substantially biased.     

Persistent Controversy in Statistical Approaches in Wildlife Sciences: A Perspective of Students

ABSTRACT The controversy over the use of null hypothesis statistical testing (NHST) has persisted for decades, yet NHST remains the most widely used statistical approach in wildlife sciences and ecology. A disconnect exists between those opposing NHST and many wildlife scientists and ecologists who conduct and publish research. This disconnect causes confusion and frustration on the part of students. We, as students, offer our perspective on how this issue may be addressed. Our objective is to encourage academic institutions and advisors of undergraduate and graduate students to introduce students to various statistical approaches so we can make well-informed decisions on the appropriate use of statistical tools in wildlife and ecological research projects. We propose an academic course that introduces students to various statistical approaches (e.g., Bayesian, frequentist, Fisherian, information theory) to build a foundation for critical thinking in applying statistics. We encourage academic advisors to become familiar with the statistical approaches available to wildlife scientists and ecologists and thus decrease bias towards one approach. Null hypothesis statistical testing is likely to persist as the most common statistical analysis tool in wildlife science until academic institutions and student advisors change their approach and emphasize a wider range of statistical methods.     

Probabilistic segmentation and intensity estimation for microarray images

We describe a probabilistic approach to simultaneous image segmentation and intensity estimation for complementary DNA microarray experiments. The approach overcomes several limitations of existing methods. In particular, it (a) uses a flexible Markov random field approach to segmentation that allows for a wider range of spot shapes than existing methods, including relatively common 'doughnut-shaped' spots; (b) models the image directly as background plus hybridization intensity, and estimates the two quantities simultaneously, avoiding the common logical error that estimates of foreground may be less than those of the corresponding background if the two are estimated separately; and (c) uses a probabilistic modeling approach to simultaneously perform segmentation and intensity estimation, and to compute spot quality measures. We describe two approaches to parameter estimation: a fast algorithm, based on the expectation-maximization and the iterated conditional modes algorithms, and a fully Bayesian framework. These approaches produce comparable results, and both appear to offer some advantages over other methods. We use an HIV experiment to compare our approach to two commercial software products: Spot and Arrayvision.     

Estimating hazard ratios in cohort data with missing disease information due to death

In clinical and epidemiological studies information on the primary outcome of interest, that is, the disease status, is usually collected at a limited number of follow‐up visits. The disease status can often only be retrieved retrospectively in individuals who are alive at follow‐up, but will be missing for those who died before. Right‐censoring the death cases at the last visit (ad‐hoc analysis) yields biased hazard ratio estimates of a potential risk factor, and the bias can be substantial and occur in either direction. In this work, we investigate three different approaches that use the same likelihood contributions derived from an illness‐death multistate model in order to more adequately estimate the hazard ratio by including the death cases into the analysis: a parametric approach, a penalized likelihood approach, and an imputation‐based approach. We investigate to which extent these approaches allow for an unbiased regression analysis by evaluating their performance in simulation studies and on a real data example. In doing so, we use the full cohort with complete illness‐death data as reference and artificially induce missing information due to death by setting discrete follow‐up visits. Compared to an ad‐hoc analysis, all considered approaches provide less biased or even unbiased results, depending on the situation studied. In the real data example, the parametric approach is seen to be too restrictive, whereas the imputation‐based approach could almost reconstruct the original event history information.     

Density estimates of two endangered nocturnal lemur species from northern Madagascar: new results and a comparison of commonly used methods

Very little information is known of the recently described Microcebus tavaratra and Lepilemur milanoii in the Daraina region, a restricted area in far northern Madagascar. Since their forest habitat is highly fragmented and expected to undergo significant changes in the future, rapid surveys are essential to determine conservation priorities. Using both distance sampling and capture-recapture methods, we estimated population densities in two forest fragments. Our results are the first known density and population size estimates for both nocturnal species. In parallel, we compare density results from four different approaches, which are widely used to estimate lemur densities and population sizes throughout Madagascar. Four approaches (King, Kelker, Muller and Buckland) are based on transect surveys and distance sampling, and they differ from each other by the way the effective strip width is estimated. The fifth method relies on a capture-mark-recapture (CMR) approach. Overall, we found that the King method produced density estimates that were significantly higher than other methods, suggesting that it generates overestimates and hence overly optimistic estimates of population sizes in endangered species. The other three distance sampling methods provided similar estimates. These estimates were similar to those obtained with the CMR approach when enough recapture data were available. Given that Microcebus species are often trapped for genetic or behavioral studies, our results suggest that existing data can be used to provide estimates of population density for that species across Madagascar.     

Modeling linkage disequilibrium between a polymorphic marker locus and a locus affecting complex dichotomous traits in natural populations

Linkage disequilibrium is an important topic in evolutionary and population genetics. An issue yet to be settled is the theory required to extend the linkage disequilibrium analysis to complex traits. In this study, we present theoretical analysis and methods for detecting or estimating linkage disequilibrium (LD) between a polymorphic marker locus and any one of the loci affecting a complex dichotomous trait on the basis of samples randomly or selectively collected from natural populations. Statistical properties of these methods were investigated and their powers were compared analytically or by use of Monte Carlo simulations. The results show that the disequilibrium may be detected with a power of 80% by using phenotypic records and marker genotype when both the trait and marker variants are common (30%) and the LD is relatively high (40-100% of the theoretical maximum). The maximum-likelihood approach provides accurate estimates of the model parameters as well as detection of linkage disequilibrium. The likelihood method is preferred for its higher power and reliability in parameter estimation. The approaches developed in this article are also compared to those for analyzing a continuously distributed quantitative trait. It is shown that a larger sample size is required for the dichotomous trait model to obtain the same level of power in detecting linkage disequilibrium as the continuous trait analysis. Potential use of these estimates in mapping the trait locus is also discussed.     

Comparison of Approaches for Developing Distributions for Carcinogenic Slope Factors

In recent years, risk assessors have increasingly been moving away from deterministic risk assessment approaches and are applying probabilistic approaches that incorporate distributions of possible values for each input parameter. This paper reviews several approaches that are being used or that could potentially be used to develop distributions for carcinogenic slope factors (CSFs). Based on the primary tool or framework that is applied, these approaches have been divided into the following three categories: the statistical framework, the decision analysis framework, and the biological framework. Work that has been done on each approach is summarized, and the aspects of variability and uncertainty that are incorporated into each approach are examined. The implications of the resulting distributional information for calculating risk estimates or risk-based concentrations is explored. The approaches differ in their stage of development, the degree to which they diverge from the U.S. Environmental Protection Agency's (EPA) current practice in establishing CSF values, their flexibility to accommodate varying data sets or theories of carcinogenicity, and their complexity of application. In some cases, wide ranges of potential potency estimates are indicated by these approaches. Such findings suggest widely divergent risk assessment implications and the need for additional evaluation of the goals of developing CSF distributions for use in risk assessment applications and the types of information that should be reflected in such distributions. Some combination of the features offered by these approaches may best support risk assessment and risk management decisions.     

Comparison of Methods for Estimating Bird Abundance and Trends From Historical Count Data

Abstract: The use of bird counts as indices has come under increasing scrutiny because assumptions concerning detection probabilities may not be met, but there also seems to be some resistance to use of model-based approaches to estimating abundance. We used data from the United States Forest Service, Southern Region bird monitoring program to compare several common approaches for estimating annual abundance or indices and population trends from point-count data. We compared indices of abundance estimated as annual means of counts and from a mixed-Poisson model to abundance estimates from a count-removal model with 3 time intervals and a distance model with 3 distance bands. We compared trend estimates calculated from an autoregressive, exponential model fit to annual abundance estimates from the above methods and also by estimating trend directly by treating year as a continuous covariate in the mixed-Poisson model. We produced estimates for 6 forest songbirds based on an average of 621 and 459 points in 2 physiographic areas from 1997 to 2004. There was strong evidence that detection probabilities varied among species and years. Nevertheless, there was good overall agreement across trend estimates from the 5 methods for 9 of 12 comparisons. In 3 of 12 comparisons, however, patterns in detection probabilities potentially confounded interpretation of uncorrected counts. Estimates of detection probabilities differed greatly between removal and distance models, likely because the methods estimated different components of detection probability and the data collection was not optimally designed for either method. Given that detection probabilities often vary among species, years, and observers investigators should address detection probability in their surveys, whether it be by estimation of probability of detection and abundance, estimation of effects of key covariates when modeling count as an index of abundance, or through design-based methods to standardize these effects.     

Optimizing trilateration estimates for tracking fine‐scale movement of wildlife using automated radio telemetry networks

A major advancement in the use of radio telemetry has been the development of automated radio tracking systems (ARTS), which allow animal movements to be tracked continuously. A new ARTS approach is the use of a network of simple radio receivers (nodes) that collect radio signal strength (RSS) values from animal‐borne radio transmitters. However, the use of RSS‐based localization methods in wildlife tracking research is new, and analytical approaches critical for determining high‐quality location data have lagged behind technological developments. We present an analytical approach to optimize RSS‐based localization estimates for a node network designed to track fine‐scale animal movements in a localized area. Specifically, we test the application of analytical filters (signal strength, distance among nodes) to data from real and simulated node networks that differ in the density and configuration of nodes. We evaluate how different filters and network configurations (density and regularity of node spacing) may influence the accuracy of RSS‐based localization estimates. Overall, the use of signal strength and distance‐based filters resulted in a 3‐ to 9‐fold increase in median accuracy of location estimates over unfiltered estimates, with the most stringent filters providing location estimates with a median accuracy ranging from 28 to 73 m depending on the configuration and spacing of the node network. We found that distance filters performed significantly better than RSS filters for networks with evenly spaced nodes, but the advantage diminished when nodes were less uniformly spaced within a network. Our results not only provide analytical approaches to greatly increase the accuracy of RSS‐based localization estimates, as well as the computer code to do so, but also provide guidance on how to best configure node networks to maximize the accuracy and capabilities of such systems for wildlife tracking studies.     

A comment on “Novel scavenger removal trials increase wind turbine-caused avian fatality estimates”

In a recent paper, Smallwood et al. (2010) conducted a study to compare their “novel” approach to conducting carcass removal trials with what they term the “conventional” approach and to evaluate the effects of the different methods on estimated avian fatality at a wind power facility in California. A quick glance at Table 3 that succinctly summarizes their results and provides estimated fatality rates and 80% confidence intervals calculated using the 2 methods reveals a surprising result. The confidence intervals of all of their estimates and most of the conventional estimates extend below 0. These results imply that wind turbines may have the capacity to create live birds. But a more likely interpretation is that a serious error occurred in the calculation of either the average fatality rate or its standard error or both. Further evaluation of their methods reveals that the scientific basis for concluding that “many estimates of scavenger removal rates prior to [their] study were likely biased low due to scavenger swamping” and “previously reported estimates of avian fatality rates … should be adjusted upwards” was not evident in their analysis and results. Their comparison to conventional approaches was not applicable, their statistical models were questionable, and the conclusions they drew were unsupported. © 2013 The Wildlife Society.     

An evaluation framework based on sustainability-related indicators for the comparison of conceptual approaches for ecological networks

Ecological networks (EN) are designed to maintain biodiversity and ecological processes by protecting habitats and their linkages. By considering the functional role of the landscape, EN can support the integration of ecological sustainability with human activities. Although all EN share the same general objectives, there are many different approaches for determining the spatial configuration of their components. The choice of an approach for the design of an EN has a major impact on the spatial configuration, ecological value, and ease of implementation of the resulting network. We applied different approaches to construct EN for the Saint-François River watershed (8700 km²) in southern Quebec, Canada. The approaches were based on single-species, multi-species, and landscape modeling categories. All of the resulting EN were evaluated using ecological, economic, and social spatial thematic indicators (TI) relevant to sustainable landscape management. This allowed us to quantitatively assess the impact of each approach and to establish their relative performance within a common framework. Our results showed that the conceptual approach for EN has a direct influence on their spatial configuration and performance. Single-species-, multi-species- and landscape-based categories produced very different EN. These results emphasize the importance of the selection of focal species and/or key environments for the design of EN. Our results also highlight the importance of adequately defining the desired objectives and expected functions of an EN, knowing that the results of the conceptual approach will be modified depending on the environment. Results are discussed in relation to the objectives sought by the implementation of the EN, spatial scale, and land use. Our evaluation framework is a useful tool for mitigating uncertainties associated with EN by facilitating the integration of stakeholders’ priorities and landscape management objectives.     

Distributed structure-searchable toxicity (DSSTox) public database network: a proposal.

The ability to assess the potential genotoxicity, carcinogenicity, or other toxicity of pharmaceutical or industrial chemicals based on chemical structure information is a highly coveted and shared goal of varied academic, commercial, and government regulatory groups. These diverse interests often employ different approaches and have different criteria and use for toxicity assessments, but they share a need for unrestricted access to existing public toxicity data linked with chemical structure information. Currently, there exists no central repository of toxicity information, commercial or public, that adequately meets the data requirements for flexible analogue searching, Structure-Activity Relationship (SAR) model development, or building of chemical relational databases (CRD). The distributed structure-searchable toxicity (DSSTox) public database network is being proposed as a community-supported, web-based effort to address these shared needs of the SAR and toxicology communities. The DSSTox project has the following major elements: (1) to adopt and encourage the use of a common standard file format (structure data file (SDF)) for public toxicity databases that includes chemical structure, text and property information, and that can easily be imported into available CRD applications; (2) to implement a distributed source approach, managed by a DSSTox Central Website, that will enable decentralized, free public access to structure-toxicity data files, and that will effectively link knowledgeable toxicity data sources with potential users of these data from other disciplines (such as chemistry, modeling, and computer science); and (3) to engage public/commercial/academic/industry groups in contributing to and expanding this community-wide, public data sharing and distribution effort. The DSSTox project's overall aims are to effect the closer association of chemical structure information with existing toxicity data, and to promote and facilitate structure-based exploration of these data within a common chemistry-based framework that spans toxicological disciplines.     

A new method for dealing with residual spatial autocorrelation in species distribution models

Species distribution modelling (SDM) is a widely used tool and has many applications in ecology and conservation biology. Spatial autocorrelation (SAC), a pattern in which observations are related to one another by their geographic distance, is common in georeferenced ecological data. SAC in the residuals of SDMs violates the ‘independent errors’ assumption required to justify the use of statistical models in modelling species’ distributions. The autologistic modelling approach accounts for SAC by including an additional term (the autocovariate) representing the similarity between the value of the response variable at a location and neighbouring locations. However, autologistic models have been found to introduce bias in the estimation of parameters describing the influence of explanatory variables on habitat occupancy. To address this problem we developed an extension to the autologistic approach by calculating the autocovariate on SAC in residuals (the RAC approach). Performance of the new approach was tested on simulated data with a known spatial structure and on strongly autocorrelated mangrove species’ distribution data collected in northern Australia. The RAC approach was implemented as generalized linear models (GLMs) and boosted regression tree (BRT) models. We found that the BRT models with only environmental explanatory variables can account for some SAC, but applying the standard autologistic or RAC approaches further reduced SAC in model residuals and substantially improved model predictive performance. The RAC approach showed stronger inferential performance than the standard autologistic approach, as parameter estimates were more accurate and statistically significant variables were accurately identified. The new RAC approach presented here has the potential to account for spatial autocorrelation while maintaining strong predictive and inferential performance, and can be implemented across a range of modelling approaches.     

The Relationship between Internalising Symptom Development and Academic Attainment in Early Adolescence

Evidence for the longitudinal associations between internalising symptom development and academic attainment is sparse and results from existing studies are largely inconclusive. The approaches that have been used in existing studies examining this relationship have in common the limitation of grouping together all individuals in the sample which makes the assumption that the relationship between time, symptoms and attainment across all individuals is the same. The current study aimed to use heterogeneous trajectories of symptom development to examine the longitudinal associations between internalising symptom development and change in academic attainment over a three years period in early adolescence, a key period for internalising symptom development. Internalising symptoms were assessed for 3 consecutive years in a cohort from age 11–14 years (n = 2647, mean age at T1 = 11.7 years). National standardised test scores prior to the first wave and subsequent to the last wave were used as measures of academic attainment. Heterogeneous symptom development trajectories were identified using latent class growth analysis and socio-demographic correlates, such as gender, SES and ethnicity, of the different trajectory groupings were investigated. Derived trajectory groupings were examined as predictors of subsequent academic attainment, controlling for prior attainment. Results demonstrate that symptom trajectories differentially predicted change in academic attainment with increasing trajectories associated with significantly worse academic outcomes when compared to pupils with low levels of symptoms in all waves. Hence, a trajectory based approach provides a more nuanced breakdown of complexities in symptom development and their differential relationships with academic outcomes and in doing so helps clarify the longitudinal relationship between these two key domains of functioning in early adolescence.     

Comparing three methods for variance estimation with duplicated high density oligonucleotide arrays

Microarray experiments are being increasingly used in molecular biology. A common task is to detect genes with differential expression across two experimental conditions, such as two different tissues or the same tissue at two time points of biological development. To take proper account of statistical variability, some statistical approaches based on the t-statistic have been proposed. In constructing the t-statistic, one needs to estimate the variance of gene expression levels. With a small number of replicated array experiments, the variance estimation can be challenging. For instance, although the sample variance is unbiased, it may have large variability, leading to a large mean squared error. For duplicated array experiments, a new approach based on simple averaging has recently been proposed in the literature. Here we consider two more general approaches based on nonparametric smoothing. Our goal is to assess the performance of each method empirically. The three methods are applied to a colon cancer data set containing 2,000 genes. Using two arrays, we compare the variance estimates obtained from the three methods. We also consider their impact on the t-statistics. Our results indicate that the three methods give variance estimates close to each other. Due to its simplicity and generality, we recommend the use of the smoothed sample variance for data with a small number of replicates. Electronic Publication     

Use of equivalent loss models under Section 316(b) of the Clean Water Act

Equivalent loss models encompass a variety of life table-based approaches that can be used to convert age- and life stage-specific estimates of entrainment and impingement loss to a common, easily understood currency. This common currency can be expressed in terms of numbers of individuals, yield to the fishery, or biomass to the ecosystem. These models have at least two key uses in the Section 316(b) assessment process: screening for adverse environmental impact (AEI) and determination of environmental benefits associated with intake alternatives. This paper reviews the various forms of equivalent loss models, their data input requirements, and their assumptions and limitations. In addition, it describes how these models can be used as a second-level screening tool as part of the assessment of the potential for AEI. Given their relative simplicity and ease of use, equivalent loss models should prove to be an important tool in the arsenal of impact assessment methods for Section 316(b).     

A comparison of Förster resonance energy transfer analysis approaches for Nanodrop fluorometry

Ensemble Förster resonance energy transfer (FRET) results can be analyzed in a variety of ways. Due to experimental artifacts, the results obtained from different analysis approaches are not always the same. To determine the optimal analysis approach to use for Nanodrop fluorometry, we have performed both ensemble and single-molecule FRET studies on oligomers of double-stranded DNA. We compared the single-molecule FRET results with those obtained using various ensemble FRET analysis approaches. This comparison shows that for Nanodrop fluorometry, analyzing the increase of the acceptor fluorescence is less likely to introduce errors in estimates of FRET efficiencies compared with analyzing the fluorescence intensity of the donor in the absence and presence of the acceptor.     

A reassessment of frequency estimates of PvuII-generated VNTR profiles in a Finnish, an Italian, and a general U.S. Caucasian database: no evidence for ethnic subgroups affecting forensic estimates.

Recently, Krane et al. addressed the effect of estimating various target DNA profile frequencies in Finnish, Italian, and general U.S. Caucasian databases. They observed that, when using an "inappropriate ethnic," or noncognate, database (e.g., a Finnish target profile frequency estimated in an Italian database, and vice versa), estimates were less common than when the target profile frequencies were estimated using their own ethnic, or cognate, database, and these estimates differed by more than one order of magnitude. These differences were attributed to the effects of subgroups. We demonstrate that the differences can be ascribed to statistical artifacts that induce large biases and correlations. Additionally, we show that the differences of estimates of any specific DNA profile frequency based on allelic size frequencies from different databases become smaller when the fixed-bin rather than a +/- 2.5% floating-bin approach is used.     

Estimating relatedness and relationships using microsatellite loci with null alleles

Relatedness is often estimated from microsatellite genotypes that include null alleles. When null alleles are present, observed genotypes represent one of several possible true genotypes. If null alleles are detected, but analyses do not adjust for their presence (ie, observed genotypes are treated as true genotypes), then estimates of relatedness and relationship can be incorrect. The number of loci available in many wildlife studies is limited, and loci with null alleles are commonly a large proportion of data that cannot be discarded without substantial loss of power. To resolve this problem, we present a new approach for estimating relatedness and relationships from data sets that include null alleles. Once it is recognized that the probability of the observed genotypes is dependent on the probabilities of a limited number of possible true genotypes, the required adjustments are straightforward. The concept can be applied to any existing estimators of relatedness and relationships. We review established maximum likelihood estimators and apply the correction in that setting. In an application of the corrected method to data from striped hyenas, we demonstrate that correcting for the presence of null alleles affect results substantially. Finally, we use simulated data to confirm that this method works better than two common approaches, namely ignoring the presence of null alleles or discarding affected loci.     

Walking the Walk to Teach the Talk: Implementing Ancestral Lifestyle Strategies as the Newest Tool in Evolutionary Studies

The learning of evolutionary theory typically takes place in the classroom or laboratory. Students of these traditional approaches often leave with the notion that applications of evolutionary theory have little bearing on their lives. The Evolutionary Studies Consortium (EvoS; ) has been extremely successful in overcoming these barriers and demonstrating the bridges across academic areas that can be created with the principles of evolution as a guide. While this is a fantastic means through which to educate students about the intricacies of evolution, we believe that the full potential of this approach has yet to be realized. Applications beyond strict academic contexts are still waiting to be mined. Here, we outline an approach that proposes the implementation of a nutrition and physical fitness program, alongside classroom pedagogy, as a means of helping students learn about evolution and how it can be used to increase their own quality of life.