A discussion of simulation results for various aspects of the neutral alleles model

In this paper a number of simulation results relating to the theory of neutral alleles are discussed. In particular, results derived from the distribution of Karlin, McGregor, and Ewens for the number and configuration of alleles in a sample of genes from a selectively neutral locus are considered. The problems discussed concern efficiencies of estimation, an approximation to the distribution of a test-statistic for neutrality, and the effect of changes in population size on an index of neutrality.     

Simulation results with stepwise mutation model and their interpretations

Summary Monte Carlo simulations are performed to compare the predictions based on the two presently used theoretical models for studying genetic variations in natural populations, the infinite allele model and the stepwise mutation model. Distribution of heterozygosity is noticed to be similar under these models until the product of population size and mutation rate is large. It is seen that electromorphs with high population frequency usually contain older alleles (at the codon level) than an electromorph of low population frequency. The interpretations of these results in explaining the allelic variations at electrophoretic level is also discussed.Research supported by U.S. Public Health Service General Research Support Grant 5 SO 5 RR 07148 from the University of Texas Health Science Center, Graduate School of Biomedical Sciences, Houston, Texas     

Analytical results on the neutral non-equilibrium allele frequency spectrum based on diffusion theory

The allele frequency spectrum has attracted considerable interest for the simultaneous inference of the demographic and adaptive history of populations. In a recent study, Evans et al. (2007) developed a forward diffusion equation describing the allele frequency spectrum, when the population is subject to size changes, selection and mutation. From the diffusion equation, the authors derived a system of ordinary differential equations (ODEs) for the moments in a Wright–Fisher diffusion with varying population size and constant selection. Here, we present an explicit solution for this system of ODEs with variable population size, but without selection, and apply this result to derive the expected spectrum of a sample for time-varying population size. We use this forward-in-time-solution of the allele frequency spectrum to obtain the backward-in-time-solution previously derived via coalescent theory by Griffiths and Tavaré (1998). Finally, we discuss the applicability of the theoretical results to the analysis of nucleotide polymorphism data.     

Some new observations and interpretations on the vital staining of leaf epidermal tissue by neutral red

Summary The lower leaf epidermis from 5 plant species was stained with neutral red at 2 pH's (7.1 and 5.6) in the light and dark when the stomata were open or closed. At pH 5.6 no globule (= droplet) formation was observed in the guard cells whether the stomata were open or closed and cell walls possessed a high affinity for the stain. At pH 7.1 globules appeared in guard cells of open stomata, but not closed stomata, within 15 minutes. Anaerobic conditions prevented this globule formation. InZea mays, globules also appeared in subsidiary cells when the stomata were closed and in certain epidermal cells. Where globule formation did not occur increased diffuse staining of certain epidermal cells was considered to be the indication of cell integrity. In old leaf material very large numbers of dark blue globules appeared in epidermal cells ofCommelina diffusa, C. communis andSenecio odoris and this was associated with cell senescence.The staining characteristics were discussed in terms of cellular K⁺, Cl^–, tannin and flavonoid content and vacuolar pH.     

MHC allele frequency distributions under parasite-driven selection: A simulation model

Background  

The extreme polymorphism that is observed in major histocompatibility complex (MHC) genes, which code for proteins involved in recognition of non-self oligopeptides, is thought to result from a pressure exerted by parasites because parasite antigens are more likely to be recognized by MHC heterozygotes (heterozygote advantage) and/or by rare MHC alleles (negative frequency-dependent selection). The Ewens-Watterson test (EW) is often used to detect selection acting on MHC genes over the recent history of a population. EW is based on the expectation that allele frequencies under balancing selection should be more even than under neutrality. We used computer simulations to investigate whether this expectation holds for selection exerted by parasites on host MHC genes under conditions of heterozygote advantage and negative frequency-dependent selection acting either simultaneously or separately.     

Reversibility and the age of an allele. I. Moran's infinitely many neutral alleles model

A population of constant size is subjected to mutation, such that each mutant is of a new allelic type. For the particular population model studied in this paper, the age of an allele, whose present frequency is known, is a random variable with distribution independent of the frequencies of other alleles. As a consequence of reversibility of the population process, the age of an allele, from the past to the present, has the same distribution as its time to extinction, from the present into the future. This verifies, and re-interprets, certain diffusion approximations found by Kimura and Ohta [Genetics 75, 199–212 (1973)] and Maruyama [Genet. Res. Cambridge 23, 137–143 (1974)].     

Some further results from a stochastic fertility model for women

Any realistic model of human fertility should encompass the distributions and interactions of three time intervals a fecund married woman may experience repeatedly in her childbearing period: (1) waiting time for a conception, (2) gestation period, and (3) period of postpartum amenorrhea. Perrin & Sheps (1964) presented a model in which human reproduction is viewed as a Markov renewal process with a finite number of states. Das Gupta (1973b) presented a general probability model of fertility along the lines suggested by Perrin & Sheps which removes two limitations of their model. First, it does not assume that the distributions of durations of stay in the fertility states are independent of each other. Second, it allows us to study the effect of breast-feeding on demographic characteristics, such as interval between live births or birth rate. Results derived in Das Gupta (1973b) include the distributions of time intervals and the exact probabilities of different states at a particular time. The present paper includes additional results pertaining to the same general model, such as the distribution of number of conceptions in a fixed period of time, the distribution of time needed for a fixed number of conceptions, pregnancy rate and fertility rate, and the distribution of the time elapsed since last live birth. The general results are applied to specific models to obtain some known results.     

The onion model, a simple neutral model for the evolution of diversity in bacterial biofilms

Bacterial biofilms are particularly resistant to a wide variety of antimicrobial compounds. Their persistence in the face of antibiotic therapies causes significant problems in the treatment of infectious diseases. Seldom have evolutionary processes like genetic drift and mutation been invoked to explain how resistance to antibiotics emerges in biofilms, and we lack a simple and tractable model for the genetic and phenotypic diversification that occurs in bacterial biofilms. Here, we introduce the 'onion model', a simple neutral evolutionary model for phenotypic diversification in biofilms. We explore its properties and show that the model produces patterns of diversity that are qualitatively similar to observed patterns of phenotypic diversity in biofilms. We suggest that models like our onion model, which explicitly invoke evolutionary process, are key to understanding biofilm resistance to bactericidal and bacteriostatic agents. Elevated phenotypic variance provides an insurance effect that increases the likelihood that some proportion of the population will be resistant to imposed selective agents and may thus enhance persistence of the biofilm. Accounting for evolutionary change in biofilms will improve our ability to understand and counter diseases that are caused by biofilm persistence.     

Eigenanalysis for the Kolmogorov backward equation for the neutral multi-allelic model

In a previous paper [9], we have given an algorithm for obtaining the time dependent solution of all polynomial moments of gene frequencies in neutral models. The recurrence formula for the moment generating functions obtained in [9] gives information about the eigenvalues and the eigenfunctions in neutral models. In this article, we solve the eigenvalue problem for the Kolmogorov backward equation for the case of neutral alleles under mutation pressure.     

A coalescent model of ancestry for a rare allele

In disequilibrium mapping from data on a rare allele, interest may focus on the ancestry of a random sample of current descendants of a mutation. The mutation is assumed to have been introduced into the population as a single copy a known time ago and to have reached a given copy number within the population. Theory has been developed to describe the ancestral distribution under arbitrary patterns of population expansion. Further results permit convenient realization of the ancestry for a random sample of copies of a rare allele within populations of constant size or within populations growing or shrinking at constant exponential rate. In this article, we present an efficient approximate method for realizing coalescence times under more general patterns of population growth. We also apply diagnostics, checking the age of the mutation. In the course of the derivation, some additional insight is gained into the dynamics of the descendants of the mutation.     

HapSim: a simulation tool for generating haplotype data with pre-specified allele frequencies and LD coefficients

We have developed a simulation tool HapSim for the generation of haplotype data. The simulated haplotypes are such that their allele frequencies and linkage disequilibrium coefficients match exactly those estimated in a real sample. AVAILABILITY: The program is available as an R package and can be downloaded from http://cran.r-project.org/.     

Specific interactions of isoguanine with the neutral and deprotonated carboxylic group of amino acids: results of model quantum chemical calculations

The MNDO/H quantum chemical calculations performed in order to estimate energetic features of the isoguanine (isoGua) prototropic tautomers complexes with acetic acid and its carboxylate-ion (models of neutral and deprotonated forms of amino acid carboxylic group) demonstrate ability of the latter to induce the N9H-->N7H tautomeric transition in the base, being characteristic to other purine bases as well. By contrast, the neutral carboxylic group forms the most stable complex with the ground-state isoGua tautomer N3HN9H.     

Ecologists should not use statistical significance tests to interpret simulation model results

Simulation models are widely used to represent the dynamics of ecological systems. A common question with such models is how changes to a parameter value or functional form in the model alter the results. Some authors have chosen to answer that question using frequentist statistical hypothesis tests (e.g. ANOVA). This is inappropriate for two reasons. First, p‐values are determined by statistical power (i.e. replication), which can be arbitrarily high in a simulation context, producing minuscule p‐values regardless of the effect size. Second, the null hypothesis of no difference between treatments (e.g. parameter values) is known a priori to be false, invalidating the premise of the test. Use of p‐values is troublesome (rather than simply irrelevant) because small p‐values lend a false sense of importance to observed differences. We argue that modelers should abandon this practice and focus on evaluating the magnitude of differences between simulations. Synthesis Researchers analyzing field or lab data often test ecological hypotheses using frequentist statistics (t‐tests, ANOVA, etc.) that focus on p‐values. Field and lab data usually have limited sample sizes, and p‐values are valuable for quantifying the probability of making incorrect inferences in that situation. However, modern ecologists increasingly rely on simulation models to address complex questions, and those who were trained in frequentist statistics often apply the hypothesis‐testing approach inappropriately to their simulation results. Our paper explains why p‐values are not informative for interpreting simulation models, and suggests better ways to evaluate the ecological significance of model results.