Modeling Taxa-Abundance Distributions in Microbial Communities using Environmental Sequence Data

We show that inferring the taxa-abundance distribution of a microbial community from small environmental samples alone is difficult. The difficulty stems from the disparity in scale between the number of genetic sequences that can be characterized and the number of individuals in communities that microbial ecologists aspire to describe. One solution is to calibrate and validate a mathematical model of microbial community assembly using the small samples and use the model to extrapolate to the taxa-abundance distribution for the population that is deemed to constitute a community. We demonstrate this approach by using a simple neutral community assembly model in which random immigrations, births, and deaths determine the relative abundance of taxa in a community. In doing so, we further develop a neutral theory to produce a taxa-abundance distribution for large communities that are typical of microbial communities. In addition, we highlight that the sampling uncertainties conspire to make the immigration rate calibrated on the basis of small samples very much higher than the true immigration rate. This scale dependence of model parameters is not unique to neutral theories; it is a generic problem in ecology that is particularly acute in microbial ecology. We argue that to overcome this, so that microbial ecologists can characterize large microbial communities from small samples, mathematical models that encapsulate sampling effects are required.     

Maximum likelihood estimation of neutral model parameters for multiple samples with different degrees of dispersal limitation

In a recent paper, I presented a sampling formula for species abundances from multiple samples according to the prevailing neutral model of biodiversity, but practical implementation for parameter estimation was only possible when these samples were from local communities that were assumed to be equally dispersal limited. Here I show how the same sampling formula can also be used to estimate model parameters using maximum likelihood when the samples have different degrees of dispersal limitation. Moreover, it performs better than other, approximate, parameter estimation approaches. I also show how to calculate errors in the parameter estimates, which has so far been largely ignored in the development of and debate on neutral theory.     

New Statistical Tests of Neutrality for DNA Samples from a Population

The purpose of this paper is to develop statistical tests of the neutral model of evolution against a class of alternative models with the common characteristic of having an excess of mutations that occurred a long time ago or a reduction of recent mutations compared to the neutral model. This class of population genetics models include models for structured populations, models with decreasing effective population size and models of selection and mutation balance. Four statistical tests were proposed in this paper for DNA samples from a population. Two of these tests, one new and another a modification of an existing test, are based on EWENS'' sampling formula, and the other two new tests make use of the frequencies of mutations of various classes. Using simulated samples and regression analyses, the critical values of these tests can be computed from regression equations. This approach for computing the critical values of a test was found to be appropriate and quite effective. We examined the powers of these four tests using simulated samples from structured populations, populations with linearly decreasing sizes and models of selection and mutation balance and found that they are more powerful than existing statistical tests of the neutral model of evolution.     

Ion flux onto conducting and isolated surfaces in the beam-plasma discharge: Computer simulation

A physical model which allows the use of the program code KARAT for simulating the quasisteady state of the beam-plasma discharge with plasma regeneration from a neutral gas is developed. The results of simulation of the modes of discharge at different potentials at the discharge collector are reported. The results obtained for isolated and grounded ion collectors are compared.     

A flexible forward simulator for populations subject to selection and demography

This article introduces a new forward population genetic simulation program that can efficiently generate samples from populations with complex demographic histories under various models of natural selection. The program (SFS_CODE) is highly flexible, allowing the user to simulate realistic genomic regions with several loci evolving according to a variety of mutation models (from simple to context-dependent), and allows for insertions and deletions. Each locus can be annotated as either coding or non-coding, sex-linked or autosomal, selected or neutral, and have an arbitrary linkage structure (from completely linked to independent). AVAILABILITY: The source code (written in the C programming language) is available at http://sfscode.sourceforge.net, and a web server (http://cbsuapps.tc.cornell.edu/sfscode.aspx) allows the user to perform simulations using the high-performance computing cluster hosted by the Cornell University Computational Biology Service Unit.     

An examination of the factors involved in determining phosphatase activities in estuarine waters. 2: Sampling procedures

Sampling procedures which are significant in the assessment of phosphatase activities in water bodies have been studied. Variations in neutral phosphatase activities among sampling stations and over depth profiles were considered, as well as seasonal and diurnal variations. Large differences were found in neutral phosphatase activities between sampling stations, but the activities in water samples from within a sampling area varied by the less than 3%. Most frequently, phosphatase activity was constant throughout the water column until just above the sediment. Distinct diurnal patterns were always found, but the patterns were not consistent between either sampling stations or sampling dates. Phosphatase activity also varied seasonally. All of the above variations may reflect differences in biomass composition and concentration. The implications of such variations for setting up an adequate sampling program and for assessing data are stressed.     

Contrasting Patterns of Nucleotide Sequence Variation at the Glucose Dehydrogenase (Gld) Locus in Different Populations of Drosophila Melanogaster

We have analyzed nucleotide sequence variation at the Glucose dehydrogenase (Gld) locus from four populations of Drosophila melanogaster from four continents. All four population samples show a significant reduction in silent variation compared to the neutral expectation. The levels of silent variation across all four populations are consistent with the predictions of the background selection model; however, Zimbabwe has a remarkably low level of variation. In the face of dramatically reduced silent polymorphism, an amino acid variant, leading to the common allozyme polymorphism at Gld, remains in low to intermediate frequency in all non-African samples. In the Chinese population sample, the ratio of replacement to silent variation is significantly elevated compared to the neutral expectation. The difference in patterns of variation across these population samples suggests that selection on Gld (or the Gld region) has been different in the Chinese population than in the other three.     

A neutral sampling formula for multiple samples and an 'exact' test of neutrality

As the utility of the neutral theory of biodiversity is increasingly being recognized, there is also an increasing need for proper tools to evaluate the relative importance of neutral processes (dispersal limitation and stochasticity). One of the key features of neutral theory is its close link to data: sampling formulas, giving the probability of a data set conditional on a set of model parameters, have been developed for parameter estimation and model comparison. However, only single local samples can be handled with the currently available sampling formulas, whereas data are often available for many small spatially separated plots. Here, I present a sampling formula for multiple, spatially separated samples from the same metacommunity, which is a generalization of earlier sampling formulas. I also provide an algorithm to generate data sets with the model and I introduce a general test of neutrality that does not require an alternative model; this test compares the probability of the observed data (calculated using the new sampling formula) with the probability of model-generated data sets. I illustrate this with tree abundance data from three large Panamanian neotropical forest plots. When the test is performed with model parameters estimated from the three plots, the model cannot be rejected; however, when parameter estimates previously reported for BCI are used, the model is strongly rejected. This suggests that neutrality cannot explain the structure of the three Panamanian tree communities on the local (BCI) and regional (Panama Canal Zone) scale simultaneously. One should be aware, however, that aspects of the model other than neutrality may be responsible for its failure. I argue that the spatially implicit character of the model is a potential candidate.     

The identification of C-18 neutral steroids in normal stallion urine

As part of a continuing research program associated with the detection of anabolic steroid residues in horse urine, normal samples from entire male horses have now been investigated. Isomers of three C-18 neutral steroids; 4-estren-17-ol-3-one (1), estrane-3,17-diol (2) and an unsaturated estranediol having a possible structure (3), have been identified in urine samples from two male horses aged 8 and 14 years. Of these three steroids, compound (2) was not detected in the urine of a 2.5 yr old entire male nor in the majority of post-race urine samples from entire male horses average age 3.8 yrs (n = 34). Ten of these samples showed tentative indications of this compound. Although the isolation of isomers of estrane-3,17-diol from human non-pregnancy urine has been reported previously, analysis of non-pregnancy urine samples in the present study did not reveal the presence of these compounds.     

A Test of Neutrality Based on Interlocus Associations

The evolutionary processes governing variability within genomic regions of low recombination have been the focus of many studies. Here, I investigate the statistical properties of a measure of intrlocus genetic associations under the assumption that mutations are selectively neutral and sites are completely linked. This measure, denoted Z(nS), is based on the squared correlation of allelic identity at pairs of polymorphic sites. Upper bounds for Z(nS) are determined by simulations. Various deviations from the neutral model, including several different forms of natural selection, will inflate the value of Z(nS) relative to its neutral theory expectations. Larger than expected values of Z(nS) are observed in genetic samples from the yellow-ac-scute and Adh regions of Drosophila melanogaster.     

The joint effects of background selection and genetic recombination on local gene genealogies

Background selection, the effects of the continual removal of deleterious mutations by natural selection on variability at linked sites, is potentially a major determinant of DNA sequence variability. However, the joint effects of background selection and genetic recombination on the shape of the neutral gene genealogy have proved hard to study analytically. The only existing formula concerns the mean coalescent time for a pair of alleles, making it difficult to assess the importance of background selection from genome-wide data on sequence polymorphism. Here we develop a structured coalescent model of background selection with recombination and implement it in a computer program that efficiently generates neutral gene genealogies for an arbitrary sample size. We check the validity of the structured coalescent model against forward-in-time simulations and show that it accurately captures the effects of background selection. The model produces more accurate predictions of the mean coalescent time than the existing formula and supports the conclusion that the effect of background selection is greater in the interior of a deleterious region than at its boundaries. The level of linkage disequilibrium between sites is elevated by background selection, to an extent that is well summarized by a change in effective population size. The structured coalescent model is readily extendable to more realistic situations and should prove useful for analyzing genome-wide polymorphism data.     

The Coalescent Process in Models with Selection

Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the ancestral frequency process can be approximated by a diffusion, then the mean and the variance of the number of segregating sites due to selectively neutral mutations in random samples can be numerically calculated. The calculations are greatly simplified if the frequencies of the alleles are tightly regulated. If the mutation rates between alleles maintained by balancing selection are low, then the number of selectively neutral segregating sites in a random sample of genes is expected to substantially exceed the number predicted under a neutral model.     

The Sampling Distribution of Linkage Disequilibrium under an Infinite Allele Model without Selection

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.     

COMPUTER PROGRAM FOR THREE-DIMENSIONAL RECONSTRUCTIONS AND NUMERICAL ANALYSES OF PLANT ORGANS FROM SERIAL SECTIONS

A computer program (SECTION) is presented which allows for the three-dimensional reconstruction of serial cross sections through biological materials. The program provides a numerical analysis of perimeter length and transverse area of each anatomical feature designated in a cross section, as well as surface area and volume computations for features that pass from one section to another. In addition to rotating and tilting the 3-D reconstruction in any desired orientation, the program has editing capabilities which allow different combinations of anatomical features to be shown in neutral gray outline or interconnected by colored lines.     

Effects of nutrient addition on phytoplankton in Lake Nakanuma,Japan I. Changes in biochemical components

Effects of nutrient conditions on biochemical components (sugars and amino acids) of phytoplankton were examined in Lake Nakanuma in Japan. Phosphate, ammonium and silicate were added to water samples collected at 0 m, which were incubated for 15 days in situ. Chlorophyll a in phosphate-added samples increased much more than that in other samples. Total amino acids and total neutral sugars in phosphate-added samples also increased more than those in other samples. The increase of total amino acids and chlorophyll began faster than that of total neutral sugars during the first 5 days of incubation. Total neutral sugars in the phosphate-added samples increased rapidly after 8 days. The composition of amino acids did not change so much. However, the composition of neutral sugars changed according to the different nutrient addition. Phosphate-added samples changed greatly during the incubation. These changes were explained at least partly by changes in nutrient conditions. Addition of limiting nutrients decreased glucose content, whereas depletion of nutrients increased the content. This study indicates that measurements of the biochemical components contribute to the analysis of effects of nutrients on phytoplankton in natural waters.     

A strategy to discover genes that carry multi-allelic or mono-allelic risk for common diseases: a cohort allelic sums test (CAST)

A method is described to discover if a gene carries one or more allelic mutations that confer risk for any specified common disease. The method does not depend upon genetic linkage of risk-conferring mutations to high frequency genetic markers such as single nucleotide polymorphisms. Instead, the sums of allelic mutation frequencies in case and control cohorts are determined and a statistical test is applied to discover if the difference in these sums is greater than would be expected by chance. A statistical model is presented that defines the ability of such tests to detect significant gene-disease relationships as a function of case and control cohort sizes and key confounding variables: zygosity and genicity, environmental risk factors, errors in diagnosis, limits to mutant detection, linkage of neutral and risk-conferring mutations, ethnic diversity in the general population and the expectation that among all exonic mutants in the human genome greater than 90% will be neutral with regard to any effect on disease risk. Means to test the null hypothesis for, and determine the statistical power of, each test are provided. For this "cohort allelic sums test" or "CAST", the statistical model and test are provided as an Excel program, CASTAT(c) at . Based on genetics, technology and statistics, a strategy of enumerating the mutant alleles carried in the exons and splice sites of the estimated approximately 25,000 human genes in case cohort samples of 10,000 persons for each of 100 common diseases is proposed and evaluated: A wide range of possible conditions of multi-allelic or mono-allelic and monogenic, multigenic or polygenic (including epistatic) risk are found to be detectable using the statistical criteria of 1 or 10 "false positive" gene associations approximately 25,000 gene-disease pair-wise trials and a statistical power of >0.8. Using estimates of the distribution of both neutral and gene-inactivating nondeleterious mutations in humans and the sensitivity of the test to multigenic or multicausal risk, it is estimated that about 80% of nullizygous, heterozygous and functionally dominant gene-common disease associations may be discovered. Limitations include relative insensitivity of CAST to about 60% of possible associations given homozygous (wild type) risk and, more rarely, other stochastic limits when the frequency of mutations in the case cohort approaches that of the control cohort and biases such as absence of genetic risk masked by risk derived from a shared cultural environment.     

Nemo: an evolutionary and population genetics programming framework

Nemo is an individual-based, genetically explicit and stochastic population computer program for the simulation of population genetics and life-history trait evolution in a metapopulation context. It comes as both a C++ programming framework and an executable program file. Its object-oriented programming design gives it the flexibility and extensibility needed to implement a large variety of forward-time evolutionary models. It provides developers with abstract models allowing them to implement their own life-history traits and life-cycle events. Nemo offers a large panel of population models, from the Island model to lattice models with demographic or environmental stochasticity and a variety of already implemented traits (deleterious mutations, neutral markers and more), life-cycle events (mating, dispersal, aging, selection, etc.) and output operators for saving data and statistics. It runs on all major computer platforms including parallel computing environments. AVAILABILITY: The source code, binaries and documentation are available under the GNU General Public License at http://nemo2.sourceforge.net.     

Estimating Genetic Variability with Restriction Endonucleases

The estimation of the amount of sequence variation in samples of homologous DNA segments is considered. The data are assumed to have been obtained by restriction endonuclease digestion of the segments, from which the numbers and frequencies of the cleavage sites in the sample are determined. An estimator, p, of the proportion of sites that are polymorphic in the sample is derived without assuming any particular population genetic model for the evolution of the population. The estimator is very close to the EWENS, SPIELMAN and HARRIS (1981) estimator that was derived with the symmetric WRIGHT-FISHER neutral mode. ENGELS (1981) has also recently proposed an estimator of the same quantity, and he arrived at his estimator without assuming a particular population genetic model. The sampling variance of p and ENGELS' estimator are derived. It is found that the sampling variance of p is lower than the sampling variance of ENGELS' estimator. Also, the sampling variance of theta, an estimate of theta (=4Nu) is obtained for the symmetric WRIGHT-FISHER neutral model with free recombination and with no recombination.