Estimating relative fitness in asexually reproducing plant pathogen populations

Summary A mathematical model is presented and analysed to find the conditions under which changes in gene frequencies can be used in asexually reproducing populations for estimating fitness of single genes, for example, for estimating the fitnesses of unnecessary virulence genes relative to their corresponding avirulence genes. It is concluded that the underlying distribution of relative fitness of clones (genotypes) has to be unimodal and that many populations consisting of a mixture of distinguishable clones then provide the best experimental data for estimating relative fitness of single genes. An improved statistical test procedure, i.e. generalized logistic regression, is suggested for analysing changes in gene frequencies in population experiments with a mixture of distinguishable clones. A population study of Erysiphe graminis f.sp. hordei (Klug-Andersen 1980) provides data to illustrate the procedure in the case where the population consists of a large number of genotypes. A bimodal distribution of genotypes possessing the virulence gene is indicated here.     

Absolute fitness, relative fitness, and utility

It is well known that (1) natural selection typically favors an allele with both a large mean fitness and a small variance in fitness; and (2) investors typically prefer a portfolio with both a large mean return and a small variance in returns. In the case of investors, this mean-variance trade-off reflects risk aversion; in the case of evolution, the mathematics is straightforward but the result is harder to intuit. In particular, it is harder to understand where, in the mathematics of natural selection, risk aversion arises. Here I present a result that suggests a simple answer to this question. Although my answer is essentially identical to one offered previously, my path to it differs somewhat from previous approaches. Some may find this new approach easier to intuit.     

Evaluation of dissociation constants from competition binding experiments based on the relative binding ratio

Methods probing protein–DNA associations include direct binding titrations and competition binding experiments. For the latter, we present here a simple procedure allowing the quantitative evaluation of dissociation constants. We show that the ratio between the fraction of a DNA probe bound to protein in the absence of competitor and that in the presence of competitor is, at large competitor concentrations, a linear function of the competitor concentration, and we derive equations allowing the dissociation constant for the protein–competitor complex to be evaluated from the slope. We show further that a self-competition experiment, where the DNA probe and competitor are chemically the same species, can be used as a complement to a direct titration to determine the fraction of protein that is correctly folded for specific DNA binding. Thus, such a combination of direct and self-competition titration can be used as a check of the conformational purity of DNA binding proteins.     

Diploid Amazon mollies (Poecilia formosa) show a higher fitness than triploids in clonal competition experiments

The gynogenetic livebearing Amazon molly (Poecilia formosa) is a sexual parasite that exploits males of closely related species for sperm. This is needed as physiological stimulus for embryo development; however, none of the male’s genes are normally incorporated into the genome of the gynogenetic offspring. Mostly diploid individuals were reported from the natural habitats in North-Eastern Mexico and South-Eastern Texas but stable populations of triploids have been reported from the Río Soto la Marina drainage and in the Río Guayalejo in North-Eastern Mexico. Triploidy is the result of defects in the mechanisms that normally clear the host sperm from the ameiotic diploid egg. Triploids also reproduce gynogenetically and their frequencies fluctuate markedly between years, seasons, and localities. To understand the dynamics of this mating system, it is important to understand the relative reproductive success of triploids and diploids. We hypothesize that triploids should have a selective advantage over diploids due to heterosis and/or gene redundancy based on the additional genetic material from the sexual host. However, clonal competition experiments revealed a clear reproductive advantage of diploids competing with triploids. This result contradicts not only our hypothesis but also the stable co-existence of diploids and triploids in natural habitats. Frequency dependent selection, niche partitioning and environmental heterogeneity are discussed as possible explanations.     

Estimating fitness by competition assays between drug susceptible and resistant Mycobacterium tuberculosis of predominant lineages in Mumbai, India

Background

Multi Drug Resistant Tuberculosis (MDR TB) is a threat to global tuberculosis control. A significant fitness cost has been associated with DR strains from specific lineages. Evaluation of the influence of the competing drug susceptible strains on fitness of drug resistant strains may have an important bearing on understanding the spread of MDR TB. The aim of this study was to evaluate the fitness of MDR TB strains, from a TB endemic region of western India: Mumbai, belonging to 3 predominant lineages namely CAS, Beijing and MANU in the presence of drug susceptible strains from the same lineages.

Methodology

Drug susceptible strains from a single lineage were mixed with drug resistant strain, bearing particular non synonymous mutation (rpoB D516V; inhA, A16G; katG, S315T1/T2) from the same or different lineages. Fitness of M.tuberculosis (M.tb) strains was evaluated using the difference in growth rates obtained by using the CFU assay system.

Conclusion/Significance

While MANU were most fit amongst the drug susceptible strains of the 3 lineages, only Beijing MDR strains were found to grow in the presence of any of the competing drug susceptible strains. A disproportionate increase in Beijing MDR could be an alarm for an impending epidemic in this locale. In addition to particular non synonymous substitutions, the competing strains in an environment may impact the fitness of circulating drug resistant strains.     

Estimating viral titres in solutions with low viral loads

An important consideration in the manufacture of products derived from animal or human sources is the virus reduction capacity of the manufacturing process as estimated using validated bench-scale models of relevant manufacturing steps. In these studies, manufacturing process intermediates are spiked with virus and processed using the bench-scale model and the resulting viral titres of input and output samples are typically determined using cell-based infectivity assays. In these assays, the Spearman-Kärber (SK) method is commonly used to estimate titres when there is one or more positive observation (i.e., the presence of any viral cytopathic effect). The SK method is most accurate when the proportion of positive observations ranges from <0.1 to >0.9 across dilutions but can be biased otherwise. Maximum likelihood (ML) based on a single-hit Poisson model is an alternative widely used estimation method. We compared SK with ML and found the methods to have similar properties except for situations in which the concentration of virus is low but measurable. In this case, the SK method produces upwardly biased estimates of titres. Based on our results, we recommend the use of either ML or SK at most virus concentrations; however, at low virus concentrations ML is preferred.     

Estimating mutation rates in low-replication experiments

Since mutation rate is a key biological parameter, its proper estimation has received great attention for decades. However, instead of the mutation rate, many authors opt for reporting the average mutant frequency, a less meaningful quantity. This is because the standard methods to estimate the mutation rate, derived from the Luria and Delbrück's fluctuation analysis, ideally require high-replication experiments to be applied; a requirement often unattainable due to constraints of time, budget or sample availability. But the main problem with mutant frequency, apart from being less informative, is its poor reproducibility; an especially marked defect when the chosen average is the arithmetic mean. Several authors tried to avoid this by employing other averages (such as the median or the geometric mean) or discarding outliers, though as far as we know nobody has evaluated which method performs best under low-replication settings. Here we use computer simulations to compare the performance of different methods used in low-replication experiments (≤4 cultures). Besides the customary averages of mutant frequency, we also tested two well-known fluctuation methods. Contrary to common practice, our results support that fluctuation methods should be applied in such circumstances, as they perform as well as or better than any average of mutant frequency. In particular, experimentalists will benefit from using MSS maximum likelihood in low-replication experiments because it: (i) provides more reproducible results, (ii) allows for direct estimation of mutation rate and (iii) allows for the application of conventional statistics.     

Estimating p-values in small microarray experiments

MOTIVATION: Microarray data typically have small numbers of observations per gene, which can result in low power for statistical tests. Test statistics that borrow information from data across all of the genes can improve power, but these statistics have non-standard distributions, and their significance must be assessed using permutation analysis. When sample sizes are small, the number of distinct permutations can be severely limited, and pooling the permutation-derived test statistics across all genes has been proposed. However, the null distribution of the test statistics under permutation is not the same for equally and differentially expressed genes. This can have a negative impact on both p-value estimation and the power of information borrowing statistics. RESULTS: We investigate permutation based methods for estimating p-values. One of methods that uses pooling from a selected subset of the data are shown to have the correct type I error rate and to provide accurate estimates of the false discovery rate (FDR). We provide guidelines to select an appropriate subset. We also demonstrate that information borrowing statistics have substantially increased power compared to the t-test in small experiments.     

Estimating the relative fitness of local adaptive peaks: the aerodynamic costs of flight in mimetic passion-vine butterflies Heliconius

In a related paper, we demonstrated that mimetic Heliconius butterflies have converged in wing-beat frequency and degree of asymmetry in the wing motion, whereas sister species are dissimilar in these same traits. Warning signals of sympatric, distasteful species converge in evolutionary models in order to educate their predators more efficiently that the signal is associated with unprofitable prey. Barring other constraints, the behaviours of the different co-mimetic pairs should ultimately converge on that behaviour which minimizes the energetic cost of flight. We estimated the energetic cost of each mimic''s flight behaviour in order to predict the difference in height of each fitness peak and the direction of convergent selection qualitatively. Following adjustments for body mass, mimetic Heliconius melpomene and Heliconius erato required more aerodynamic power than Heliconius cydno and Heliconius sapho. This difference was attributed to the slower flight speeds and higher wing-beat frequencies of H. melpomene and H. erato. Consequently, H. melpomene and H. erato expended more energy per unit distance per unit body mass than H. cydno and H. sapho. However, differences in body mass may equalize energy budgets and stabilize the sympatric coexistence of the two pairs of co-mimics.     

Replacement interaction diagrams in interspecific competition experiments

Replacement interaction diagrams offer a new approach in displaying results of interspecific competition experiments. They allow visual assessment of both actual and relative responses of two species in a replacement series to treatments arranged in a factorial array. Yield data are plotted on a semi-logarithmic scale along the vertical axis. Treatments are arranged on the horizontal axis. The degree of interspecific interference or competition in mixed populations is best assessed by comparing the species response in a mixture with that in the monoculture. In competition experiments involving a number of treatment variables, replacement interaction diagrams highlight trends in treatment responses and allow some comparisions of responses between plant frequences.     

Slow fitness recovery in a codon-modified viral genome

Extensive synonymous codon modification of viral genomes appears to be an effective way of attenuating strains for use as live vaccines. An assumption of this method is that codon changes have individually small effects, such that codon-attenuated viruses will be slow to evolve back to high fitness (and thus to high virulence). The major capsid gene of the bacterial virus T7 was modified to have varying levels of suboptimal synonymous codons in different constructs, and fitnesses declined linearly with the number of changes. Adaptation of the most extreme design, with 182 codon changes, resulted in a slow fitness recovery by standards of previous experimental evolution with this virus, although fitness effects of substitutions were higher than expected from the average effect of an engineered codon modification. Molecular evolution during recovery was modest, and changes evolved both within the modified gene and outside it. Some changes within the modified gene evolved in parallel across replicates, but with no obvious explanation. Overall, the study supports the premise that codon-modified viruses recover fitness slowly, although the evolution is substantially more rapid than expected from the design principle.     

Differential equation modeling of HIV viral fitness experiments: model identification, model selection, and multimodel inference

Summary .  Many biological processes and systems can be described by a set of differential equation (DE) models. However, literature in statistical inference for DE models is very sparse. We propose statistical estimation, model selection, and multimodel averaging methods for HIV viral fitness experiments in vitro that can be described by a set of nonlinear ordinary differential equations (ODE). The parameter identifiability of the ODE models is also addressed. We apply the proposed methods and techniques to experimental data of viral fitness for HIV-1 mutant 103N. We expect that the proposed modeling and inference approaches for the DE models can be widely used for a variety of biomedical studies.     

Modeling and estimation of replication fitness of human immunodeficiency virus type 1 in vitro experiments by using a growth competition assay

Growth competition assays have been developed to quantify the relative fitnesses of human immunodeficiency virus (HIV-1) mutants. In this article we develop mathematical models to describe viral/cellular dynamic interactions in the assay experiment, from which new competitive fitness indices or parameters are defined. These indices include the log fitness ratio (LFR), the log relative fitness (LRF), and the production rate ratio (PRR). From the population genetics perspective, we clarify the confusion and correct the inconsistency in the definition of relative fitness in the literature of HIV-1 viral fitness. The LFR and LRF are easier to estimate from the experimental data than the PRR, which was misleadingly defined as the relative fitness in recent HIV-1 research literature. Calculation and estimation methods based on two data points and multiple data points were proposed and were carefully studied. In particular, we suggest using both standard linear regression (method of least squares) and a measurement error model approach for more-accurate estimates of competitive fitness parameters from multiple data points. The developed methodologies are generally applicable to any growth competition assays. A user-friendly computational tool also has been developed and is publicly available on the World Wide Web at http://www.urmc.rochester.edu/bstools/vfitness/virusfitness.htm.     

Reproductive interference in laboratory experiments of interspecific competition

Many studies that have researched interspecific competition in Callosobruchus (bean beetles), Drosophila (fruit flies), and Tribolium (flour beetles) have considered the major drivers of interspecific competition to be interspecific resource competition and intraguild cannibalism. These competition drivers have a density-dependent effect on the population dynamics. However, some studies have also detected a relative-frequency-dependent effect in the observed population dynamics. The most likely causal mechanism of this relative frequency dependence is reproductive interference, defined as any interspecific sexual interaction that damages female reproductive success. Reproductive interference has been overlooked by most laboratory studies in spite of the critical effect on the competition outcome. In this paper, I review laboratory studies of these insect genera from the perspective of reproductive interference and show that the reported results can be more reasonably interpreted by the joint action of reproductive interference and resource competition, including intraguild cannibalism. In addition, on the basis of results reported by a small number of related studies, I discuss the behavioral and evolutionary changes induced in those genera by reproductive interference.     

Estimating relative parental investment in sons versus daughters

Fisher proposed that natural selection would adjust the population sex ratio so that parental expenditure on sons equals expenditure on daughters. Thus if two daughters can be produced for every son, the Fisherian equilibrium is ? sons and ? daughters. The relative cost of a son versus a daughter is necessarily manifested in the trade-off between family size and sex ratio, and we offer a method to estimate this trade-off from data on family compositions. Simulation studies indicate that the method works well in some cases but not others. Application of the method to data on a polychaete suggests that sons are much costlier than daughters; the observed sex ratio in fact significantly favored daughters, but not to the extreme predicted by our measure of differential cost.     

Estimating tumor incidence rates in animal carcinogenicity experiments

Tumor incidence is the primary measure of carcinogenesis. This article focuses on estimating time-dependent incidence rates in animal experiments with few sacrifices. When the context of observation is known for none or all of the animals dying with the tumor of interest, previous results are obtained under relaxed assumptions. The link with existing semiparametric and nonparametric procedures based on latent failure times is exploited by using these methods to compute maximum likelihood estimates of the incidence rates without introducing latent random variables. Nonparametric estimators that are appropriate when all contexts of observation are known are generalized to the case in which the contexts of observation are unknown for a subset of the tumor-bearing animals.     

Estimating the fitness effect of an insertion sequence

Since its discovery, mobile DNA has fascinated researchers. In particular, many researchers have debated why insertion sequences persist in prokaryote genomes and populations. While some authors think that insertion sequences persist only because of occasional beneficial effects they have on their hosts, others argue that horizontal gene transfer is strong enough to overcome their generally detrimental effects. In this study, we model the long-term fate of a prokaryote cell population, of which a small proportion of cells has been infected with one insertion sequence per cell. Based on our model and the distribution of IS5, an insertion sequence for which sufficient data is available in 525 fully sequenced proteobacterial genomes, we show that the fitness cost of insertion sequences is so small that they are effectively neutral or only slightly detrimental. We also show that an insertion sequence infection can persist and reach the empirically observed distribution if the rate of horizontal gene transfer is at least as large as the fitness cost, and that this rate is well within the rates of horizontal gene transfer observed in nature. In addition, we show that the time needed to reach the observed prevalence of IS5 is unrealistically long for the fitness cost and horizontal gene transfer rate that we computed. Occasional beneficial effects may thus have played an important role in the fast spreading of insertion sequences like IS5.     

Inclusive fitness,asymmetric competition and kin selection in plants

The findings that some plants alter their competitive phenotype in response to genetic relatedness of its conspecific neighbour (and presumed competitor) has spurred an increasing interest in plant kin‐interactions. This phenotypic response suggests the ability to assess the genetic relatedness of conspecific competitors, proposing kin selection as a process that can influence plant competitive interactions. Kin selection can favour restrained competitive growth towards kin, if the fitness loss from reducing own growth is compensated by increased fitness in the related neighbour. This may lead to positive frequency dependency among related conspecifics with important ecological consequences for species assemblage and coexistence. However, kin selection in plants is still controversial. First, many studies documenting a plastic response to neighbour relatedness do not estimate fitness consequences of the individual that responds, and when estimated, fitness of individuals grown in competition with kin did not necessarily exceed that of individuals grown in non‐kin groups. Although higher fitness in kin groups could be consistent with kin selection, this could also arise from mechanisms like asymmetric competition in the non‐kin groups. Here we outline the main challenges for studying kin selection in plants taking genetic variation for competitive ability into account. We emphasize the need to measure inclusive fitness in order to assess whether kin selection occurs, and show under which circumstances kin selected responses can be expected. We also illustrate why direct fitness estimates of a focal plant, and group fitness estimates are not suitable for documenting kin selection. Importantly, natural selection occurs at the individual level and it is the inclusive fitness of an individual plant – not the mean fitness of the group – that can capture if a differential response to neighbour relatedness is favoured by kin selection.