Frequency spectra of neutral and deleterious alleles in a finite population

Summary One of the major goals of population genetics is to discover the nature and amount of genetic variation in natural populations. Various measures, including the population heterozygosity at any locus and the number of alleles extant at the locus, have been used for this purpose. An important task of theoretical population genetics is thus to provide expressions for the mean values of these two quantities (when calculated from a sample of genes) for various models of selection, mutation and random drift. This aim has been achieved for the selectively neutral case, where all alleles at the locus are assumed to be selectively equivalent. It is, however, generally agreed that classes of (evolutionarily unimportant) selectively deleterious alleles exist, so that the neutral theory calculations should be extended to cover this case. This has previously been done only for extremely weak selection. In this paper we obtain, via the confluent hypergeometric function and three allied functions, concise and simple exact and approximate formulae for the means of the above measures of population variation for arbitrary selective values. These all derive from the allelic frequency spectrum, which is of independent interest in assessing likely models of population variation.     

Microsatellite size homoplasies and null alleles do not affect species diagnosis and population genetic analysis in a fungal species complex

The suitability of 13 microsatellite loci for species diagnosis and population genetics in 11 species of the Phialocephala fortinii s.l.-Acephala applanata species complex (PAC) was assessed. Two data sets were compared to test possible biases in species typing and clone detection resulting from null alleles and size homoplasies. The first data set was based on fragment lengths derived from a multiplex polymerase chain reaction (PCR) assay and the second data set was received from singleplex PCR at lower stringency and sequencing. Most null alleles observed in the multiplex PCR assay could be amplified during singleplex PCR under less stringent conditions. Size homoplasies resulting from mutations in flanking regions and differences in microsatellite structures were observed. For example, Phialocephala uotolensis possessed a (CT)(13) in addition to the (GT)(x) motif at locus mPF_0644. Despite the occurrence of null alleles and size homoplasies, species diagnosis and population genetic analysis studies were not affected. These markers will facilitate studies on population biology, ecology and biogeography of PAC species.     

Microsatellite null alleles and estimation of population differentiation

Microsatellite null alleles are commonly encountered in population genetics studies, yet little is known about their impact on the estimation of population differentiation. Computer simulations based on the coalescent were used to investigate the evolutionary dynamics of null alleles, their impact on F(ST) and genetic distances, and the efficiency of estimators of null allele frequency. Further, we explored how the existing method for correcting genotype data for null alleles performed in estimating F(ST) and genetic distances, and we compared this method with a new method proposed here (for F(ST) only). Null alleles were likely to be encountered in populations with a large effective size, with an unusually high mutation rate in the flanking regions, and that have diverged from the population from which the cloned allele state was drawn and the primers designed. When populations were significantly differentiated, F(ST) and genetic distances were overestimated in the presence of null alleles. Frequency of null alleles was estimated precisely with the algorithm presented in Dempster et al. (1977). The conventional method for correcting genotype data for null alleles did not provide an accurate estimate of F(ST) and genetic distances. However, the use of the genetic distance of Cavalli-Sforza and Edwards (1967) corrected by the conventional method gave better estimates than those obtained without correction. F(ST) estimation from corrected genotype frequencies performed well when restricted to visible allele sizes. Both the proposed method and the traditional correction method have been implemented in a program that is available free of charge at http://www.montpellier.inra.fr/URLB/. We used 2 published microsatellite data sets based on original and redesigned pairs of primers to empirically confirm our simulation results.     

Non-Mendelian transmission of alleles at microsatellite loci: an example in Ixodes ricinus, the vector of Lyme disease

Microsatellite loci are usually considered to be neutral co-dominant and Mendelian markers. We undertook to study the inheritance of five microsatellite loci in the European Lyme disease vector, the tick Ixodes ricinus. Only two loci appeared fully Mendelian while the three others displayed non-Mendelian patterns that highly frequent null alleles could not fully explain. At one locus, IR27, some phenomenon seems to hinder the PCR amplification of one allele, depending on its origin (maternal imprinting) and/or its size (short allele dominance). DNA methylation, which appeared to be a possible explanation of this amplification bias, was rejected by a specific test comparing the amplification efficiency that did not differ between unmethylated and experimentally methylated DNA. The role of allele size in heterozygous individuals was then revealed from the data available on field collected ticks and consistent with the results of a theoretical approach. These observations highlight the need for prudence while inferring reproductive systems (selfing rates), parentage or even allelic frequencies from microsatellite markers, in particular for parasitic organisms for which molecular approaches often represent the only way for population biology inferences.     

Prospective studies of diagnostic test accuracy when disease prevalence is low

Prospective studies of diagnostic test accuracy have important advantages over retrospective designs. Yet, when the disease being detected by the diagnostic test(s) has a low prevalence rate, a prospective design can require an enormous sample of patients. We consider two strategies to reduce the costs of prospective studies of binary diagnostic tests: stratification and two-phase sampling. Utilizing neither, one, or both of these strategies provides us with four study design options: (1) the conventional design involving a simple random sample (SRS) of patients from the clinical population; (2) a stratified design where patients from higher-prevalence subpopulations are more heavily sampled; (3) a simple two-phase design using a SRS in the first phase and selection for the second phase based on the test results from the first; and (4) a two-phase design with stratification in the first phase. We describe estimators for sensitivity and specificity and their variances for each design, along with sample size estimation. We offer some recommendations for choosing among the various designs. We illustrate the study designs with two examples.     

Effects of antenna length and material on output power and detection of miniature radio transmitters

The optimal antenna of transmitters used in small aquatic animals is often a compromise between efficient radio wave propagation and effects on animal behavior. Radio transmission efficiency generally increases with diameter and length of the conductor, but increased antenna length or weight can adversely affect animal behavior. We evaluated the effects of changing antenna length and material on the subsequent tag output power, reception, and detection of tagged fish. In a laboratory, we compared the relative signal strengths in water of 150 MHz transmitters over a range of antenna lengths (from 6 to 30 cm) and materials (one weighing about half of the other). The peak relative signal strengths were at 20 and 22 cm, which are approximately one wavelength underwater at the test frequency. The peak relative signal strengths at these lengths were approximately 50% greater than those of 30 cm antennas, a length commonly used in fisheries research. Few significant differences were present in distances for the operator to hear or the telemetry receiver to decode transmitters from a boat-mounted receiving system based on antenna length, but the percent of tagged fish detected passing a hydroelectric dam fitted with an array of receiving systems was significantly greater at the antenna length with peak output power in laboratory tests. This study indicates careful choice of antenna length and material of small transmitters can be used to reduce weight and possible antenna effects on animal behavior, to maximize tag output power and detection, or to balance these factors based on the needs of the application.     

Sample Size Calculation for Intraclass Correlation in the Presence of Random Loss of Sampled Patients

When a trial involves an invasive laboratory test procedure or requires patients to make a commitment to follow a restrictive test schedule, we can often lose a great proportion of our sampled patients due to refusal of participation into our study. Therefore, incorporating the possible loss of patients into sample size calculation is certainly important in the planning stage of a study. In this paper, we have generalized the sample size calculation procedure for intraclass correlation by accounting for the random loss of patients in the beginning of a trial. We have demonstrated that the simple ad hoc procedure, that raises the estimated sample size in the absence of loss of patients by the factor 1/p_o, where p_o is the retention probability for a randomly selected patient, is adequate when p_o is large (=0.80). When p_o is small (i.e., a high refusal rate), however, use of this simple ad hoc procedure tends to underestimate the required sample size. Furthermore, we have found that if the individual retention probability varied substantially among patients, then the magnitude of the above underestimation could even be critical and therefore, the application of the simple direct adjustment procedure in this situation should be avoided.     

Experimental verification of microsatellite null alleles in Norway spruce (Picea abies [L.] Karst.): Implications for population genetic studies

Three stands ofPicea abies [L.] Karst. with different density in the Harz Mountains (Lower Saxony, Germany) were characterized at 4 microsatellite loci. An excess of homozygotes was observed in all 3 stands at 1 simple sequence repeat (SSR) locus, suggesting the presence of null alleles. To test for the segregation of a null allele, 24 openpollinated seeds (haploid megagametophytes and embryos) from apparently homozygous mother trees were analyzed. For 1 of 3 trees that could be identified as heterozygous for a null allele, no significant deviation from the expected 1∶1 segregation into marker absence (null allele) and marker presence of the second maternal allele could be observed in the haploid megagametophyte. Concordantly, the numbers of embryos heterozygous for the null allele and for the other maternal allele were not significantly different from each other. Inheritance analyses in seedlings and corresponding megagametophytes of gymnosperms were used as a direct experimental verification of microsatellite null alleles in single-tree progeny. Microsatellites with an abundance of null alleles should be discarded from further analysis because inclusion of these loci results in incorrect estimation of allele frequencies.     

On Choice of Subjects and Replicates in Estimating Among and Within Subject Variation

We consider the problem of choosing the number of replicates and number of subjects in a components of variance problem which optimizes various criteria. The case study here involves patients suffering from systemic sclerosis (Scleroderma), a form of rheumatic disease that is potentially disabling. Under the physical constraints imposed on the study, we find that using 2 or 3 replicates with as many patients as possible is the optimal strategy for several criteria.     

A benchmark test of accuracy and precision in estimating dynamical systems characteristics from a time series

Characteristics of dynamical systems are often estimated to describe physiological processes. For instance, Lyapunov exponents have been determined to assess the stability of the cardio-vascular system, respiration, and, more recently, human gait and posture. However, the systematic evaluation of the accuracy and precision of these estimates is problematic because the proper values of the characteristics are typically unknown. We fill this void with a set of standardized time series with well-defined dynamical characteristics that serve as a benchmark. Estimates ought to match these characteristics, at least to good approximation. We outline a procedure to employ this generic benchmark test and illustrate its capacity by examining methods for estimating the maximum Lyapunov exponent. In particular, we discuss algorithms by Wolf and co-workers and by Rosenstein and co-workers and evaluate their performances as a function of signal length and signal-to-noise ratio. In all scenarios, the precision of Rosenstein's algorithm was found to be equal to or greater than Wolf's algorithm. The latter, however, appeared more accurate if reasonably large signal lengths are available and noise levels are sufficiently low. Due to its modularity, the presented benchmark test can be used to evaluate and tune any estimation method to perform optimally for arbitrary experimental data.     

The Design and Use of Variance Component Models in the Analysis of Human Quantitative Pedigree Data

The use of variance components and multivariate linear models in genetics applications has a long history that dates back to (at least) Fisher's seminal 1918 paper “The correlation between relatives on the supposition of Mendelian inheritance” [Phil. Trans. 52: 399–433]. Although extensions and elaborations of Fisher's insights have been offered in recent times, relatively few studies exist which examine the theoretical and operational properties variance component models possess in complicated genetic analysis settings. In this paper variance component models, as well as some of their properties (e.g., power, efficiency, and sample size considerations) are discussed in the context of each of the following genetic analysis settings: 1. the detection of general polygenic additive and dominance effects; 2. the detection of genetic effects in the presence of environmental effects (and vice versa); 3. the detection of pleiotropic gene action; 4. aspects of the detection of genotype by environment interaction; and 5. sequential tests for general hypotheses framed in the context of settings 1 through 4. Exposition of the proposed methods and results are facilitated through a special emphasis placed on pedigree covariance structure modeling.     

Genetic evidence for linkage with the Z and W sex chromosomes of two distinct couples of alleles controlling larval and postmetamorphic skin pigmentation in salamander

In Pleurodeles waltl, progeny resulting from a cross between 2 individuals of the Z/W sexual genotype include 25% of W/W individuals, while those issued from crossing a Z/W neomale with a W/W thelygenous female include 50% of W/W individuals. W/W individuals can be identified through the peptidase-1 zymogram since, in P. waltl, this enzyme is controlled by codominant alleles which are linked to the sex chromosomes. In such progeny, we discovered 2 mutant phenotypes affecting larval and postmetamorphic skin pigmentation in W/W individuals. These phenotypes are described herein. The study of their inheritance in several offspring provides evidence that they are controlled by 2 distinct genes, the recessive mutant alleles of which are linked to the W sex chromosome; moreover, in thelygenous W/W females, the differential segment does not prevent the occurrence of meiotic recombinations between W sex chromosomes. Mutant skin pigmentary phenotypes are easily identified and constitute a tool for rapid, efficient selection of individuals of the W/W sexual genotype.     

Comparisons of site- and haplotype-frequency methods for detecting positive selection

In this report, we compare the differences between various site- and haplotype-frequency tests in their power to detect positive selection by doing computer simulations. Our results are the following. 1) Although haplotype-frequency tests that are conditional on the number of haplotypes (K) were developed for nonrecombining haplotypes, these tests are insensitive to recombination. Such tests, including the Ewens-Watterson (EW) test, can therefore be applied to recombining haplotypes. 2) Tests conditional on the number of segregating sites (S) become overly conservative in the presence of recombination. 3) The EW test is usually the most powerful test during the sweep phase, especially when the local recombination rate is high. 4) The "extended haplotype homozygosity" test relies heavily on the prior knowledge of the target of selection. With that knowledge, it is the most powerful test, whereas in the absence of this prior information, the test has little power. We also study the sensitivities of the haplotype-frequency tests to background selection and various demographic forces. We find that these tests are sensitive to some forces other than positive selection. To alleviate the problem of low specificity, compound tests, such as the DH test (Zeng et al. 2006), may be a solution. In the companion paper (Zeng K, Shi S, Wu C-I, in preparation), we use the EW test to devise 2 compound tests, which are more powerful in detecting positive selection than DH, but are also relatively insensitive to demography.     

A comparison of methods for fitting allometric equations to field metabolic rates of animals

We re-examined data for field metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for fitting the allometric equation can lead to very different estimates for the allometric coefficient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line fitted to logarithms of the data. Another two-parameter power function was then generated for each data-set by non-linear regression on values in the original arithmetic scale. Allometric equations obtained by non-linear regression described the metabolic rates of all animals in the samples. Equations estimated by back-transformation from logarithms, on the other hand, described the metabolic rates of small species but not large ones. Thus, allometric equations estimated in the traditional way for field metabolic rates of varanids and marsupials do not have general importance because they do not characterize rates for species spanning the full range in body size. Logarithmic transformation of predictor and response variables creates new distributions that may enable investigators to perform statistical analyses in compliance with assumptions underlying the tests. However, statistical models fitted to transformations should not be used to estimate parameters of equations in the arithmetic domain because such equations may be seriously biased and misleading. Allometric analyses should be performed on values expressed in the original scale, if possible, because this is the scale of interest.     

S-Sample Smooth Goodness of Fit Testing: Rederivation and Monte Carlo Assessment

S-sample smooth goodness of fit tests may be constructed using components from one sample goodness of fit testing. Each sample could be assessed for consistency with a target distribution using these components, although that is not our objective here. Contrasts in the components may be used to assess consistency of the samples with each other. If all the samples are consistent, we could then conveniently perform a one-sample goodness of fit test for the target distribution. If the samples are not consistent, an LSD-type analysis can be performed on the one-sample components to identify where the differences between occur. This approach gives a detailed and informative scrutiny of the data.     

Development of melting temperature-based SYBR Green I polymerase chain reaction methods for multiplex genetically modified organism detection

Commercialization of several genetically modified crops has been approved worldwide to date. Uniplex polymerase chain reaction (PCR)-based methods to identify these different insertion events have been developed, but their use in the analysis of all commercially available genetically modified organisms (GMOs) is becoming progressively insufficient. These methods require a large number of assays to detect all possible GMOs present in the sample and thereby the development of multiplex PCR systems using combined probes and primers targeted to sequences specific to various GMOs is needed for detection of this increasing number of GMOs. Here we report on the development of a multiplex real-time PCR suitable for multiple GMO identification, based on the intercalating dye SYBR Green I and the analysis of the melting curves of the amplified products. Using this method, different amplification products specific for Maximizer 176, Bt11, MON810, and GA21 maize and for GTS 40-3-2 soybean were obtained and identified by their specific Tm. We have combined amplification of these products in a number of multiplex reactions and show the suitability of the methods for identification of GMOs with a sensitivity of 0.1% in duplex reactions. The described methods offer an economic and simple alternative to real-time PCR systems based on sequence-specific probes (i.e., TaqMan chemistry). These methods can be used as selection tests and further optimized for uniplex GMO quantification.