Simulation Studies on Electrophoretically Detectable Genetic Variability in a Finite Population

Using a new model of isoalleles, extensive Monte Carlo experiments were performed to examine the pattern of allelic distribution in a finite population. In this model it was assumed that the set of allelic states is represented by discrete points on a one-dimensional lattice and that change of state by mutation occurs in such a way that an allele moves either one step in the positive direction or one step in the negative direction on the lattice. Such a model was considered to be appropriate for estimating theoretically the number of electrophoretically detectable alleles within a population. The evenness of allelic distribution was measured by the ratio of the effective to the actual number of alleles (n(e)/n(a)). The results of the Monte Carlo experiments have shown that this ratio is generally larger under the new model of isoalleles than under the conventional Kimura-Crow model of neutral isoalleles. In other words, the distribution of allelic frequencies within a population is expected to be more uniform in the new model. By comparing the Monte Carlo results with actual observations, it was concluded that the observed deviation from what is predicted under the new model with selective neutrality is not in the direction of conforming to the overdominance hypothesis but is, in fact, in the opposite direction.     

A Novel Statistical Model to Estimate Host Genetic Effects Affecting Disease Transmission

There is increasing recognition that genetic diversity can affect the spread of diseases, potentially affecting plant and livestock disease control as well as the emergence of human disease outbreaks. Nevertheless, even though computational tools can guide the control of infectious diseases, few epidemiological models can simultaneously accommodate the inherent individual heterogeneity in multiple infectious disease traits influencing disease transmission, such as the frequently modeled propensity to become infected and infectivity, which describes the host ability to transmit the infection to susceptible individuals. Furthermore, current quantitative genetic models fail to fully capture the heritable variation in host infectivity, mainly because they cannot accommodate the nonlinear infection dynamics underlying epidemiological data. We present in this article a novel statistical model and an inference method to estimate genetic parameters associated with both host susceptibility and infectivity. Our methodology combines quantitative genetic models of social interactions with stochastic processes to model the random, nonlinear, and dynamic nature of infections and uses adaptive Bayesian computational techniques to estimate the model parameters. Results using simulated epidemic data show that our model can accurately estimate heritabilities and genetic risks not only of susceptibility but also of infectivity, therefore exploring a trait whose heritable variation is currently ignored in disease genetics and can greatly influence the spread of infectious diseases. Our proposed methodology offers potential impacts in areas such as livestock disease control through selective breeding and also in predicting and controlling the emergence of disease outbreaks in human populations.     

On Models of Quantitative Genetic Variability: A Stabilizing Selection-Balance Model

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.     

Genetic Variability and Distribution of Mating Type Alleles in Field Populations of Leptosphaeria maculans from France

Leptosphaeria maculans is the most ubiquitous fungal pathogen of Brassica crops and causes the devastating stem canker disease of oilseed rape worldwide. We used minisatellite markers to determine the genetic structure of L. maculans in four field populations from France. Isolates were collected at three different spatial scales (leaf, 2-m² field plot, and field) enabling the evaluation of spatial distribution of the mating type alleles and of genetic variability within and among field populations. Within each field population, no gametic disequilibrium between the minisatellite loci was detected and the mating type alleles were present at equal frequencies. Both sexual and asexual reproduction occur in the field, but the genetic structure of these populations is consistent with annual cycles of randomly mating sexual reproduction. All L. maculans field populations had a high level of gene diversity (H = 0.68 to 0.75) and genotypic diversity. Within each field population, the number of genotypes often was very close to the number of isolates. Analysis of molecular variance indicated that >99.5% of the total genetic variability was distributed at a small spatial scale, i.e., within 2-m² field plots. Population differentiation among the four field populations was low (G_ST < 0.02), suggesting a high degree of gene exchange between these populations. The high gene flow evidenced here in French populations of L. maculans suggests a rapid countrywide diffusion of novel virulence alleles whenever novel resistance sources are used.     

Maintenance of Genetic Variability under Strong Stabilizing Selection: A Two-Locus Model

We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which ``hides' additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability.     

Nonelectrophoretic Genetic Variability in Mosquitoes: Polymorphism for Temperature-Resistant and Temperature-Sensitive Phosphoglucomutase Alleles in CULEX PIPIENS

Homogenates of single individuals of two natural populations and five laboratory populations of Culex pipiens were examined by combining electrophoresis and heat denaturation studies on phosphoglucomutase (PGM). All populations showed a high degree of polymorphism for isoelectrophoretic temperature-resistant (tr) and temperature-sensitive (ts) alleles. Formal genetic data on the heat stability differences of the PGM are given. If both electrophoretic and isoelectrophoretic alleles are taken into account, the mean increase in the degree of heterozygosity is quite remarkable, i.e., about 65%.--The data are considered in relation to the biological significance that this new type of variability of structural genes could have in natural populations.     

A Proprioception Based Regulation Model to Estimate the Trunk Muscle Forces

Evaluation of loads acting on the spine requires the knowledge of the muscular forces acting on it, but muscles redundancy necessitates developing a muscle forces attribution strategy. Optimisation, EMG, or hybrid models allow evaluating muscle force patterns, yielding a unique muscular arrangement or/and requiring EMG data collection. This paper presents a regulation model of the trunk muscles based on a proprioception hypothesis, which searches to avoid the spinal joint overloading. The model is also compared to other existing models for evaluation. Compared to an optimisation model, the proposed alternative muscle pattern yielded a significant spine postero-anterior shear decrease. Compared to a model based on combination of optimisation criteria, present model better fits muscle activation observed using EMG (38% improvement). Such results suggest that the proposed model, based on regulation of all spinal components, may be more relevant from a physiologic point of view.     

Genetic Analyses of the Polarity Alleles in Recombinants from Mitochondrial Genetic Crosses

A number of minority recombinant and parental types from a heterosexual cross were analyzed for the omega allele they carry. It was found that recombinant progeny can be omega(-), that minority parental types among the progeny can be omega(+) rather than omega(-), and, finally, that certain of the results suggest that the omega locus may not be at the proximal end of the mitochondrial genetic map (Bolotin et al., 1971; Grivell et al., 1973) but rather may lie between the [cap1-r/cap-s] and [ery1-r/ery-s] loci.     

Cryptosporidium,Giardia, Cryptococcus,Pneumocystis Genetic Variability: Cryptic Biological Species or Clonal Near-Clades?

An abundant literature dealing with the population genetics and taxonomy of Giardia duodenalis, Cryptosporidium spp., Pneumocystis spp., and Cryptococcus spp., pathogens of high medical and veterinary relevance, has been produced in recent years. We have analyzed these data in the light of new population genetic concepts dealing with predominant clonal evolution (PCE) recently proposed by us. In spite of the considerable phylogenetic diversity that exists among these pathogens, we have found striking similarities among them. The two main PCE features described by us, namely highly significant linkage disequilibrium and near-clading (stable phylogenetic clustering clouded by occasional recombination), are clearly observed in Cryptococcus and Giardia, and more limited indication of them is also present in Cryptosporidium and Pneumocystis. Moreover, in several cases, these features still obtain when the near-clades that subdivide the species are analyzed separately (“Russian doll pattern”). Lastly, several sets of data undermine the notion that certain microbes form clonal lineages simply owing to a lack of opportunity to outcross due to low transmission rates leading to lack of multiclonal infections (“starving sex hypothesis”). We propose that the divergent taxonomic and population genetic inferences advanced by various authors about these pathogens may not correspond to true evolutionary differences and could be, rather, the reflection of idiosyncratic practices among compartmentalized scientific communities. The PCE model provides an opportunity to revise the taxonomy and applied research dealing with these pathogens and others, such as viruses, bacteria, parasitic protozoa, and fungi.     

A Model Allowing Continuous Variation in Electrophoretic Mobility of Neutral Alleles

The infinite-sites model with no recombination is extended to include mutations that affect electrophoretic mobility. The model allows the effect of a single-site mutation to have a continuous effect on mobility. Formulae are obtained for the variance of electrophoretic mobility of alleles after an arbitrary lenght of time. A special case of the general model is the case of stepwise production of neutral alleles with an arbitrary number of steps.     

Genetic Variability Under the Seedbank Coalescent

We analyze patterns of genetic variability of populations in the presence of a large seedbank with the help of a new coalescent structure called the seedbank coalescent. This ancestral process appears naturally as a scaling limit of the genealogy of large populations that sustain seedbanks, if the seedbank size and individual dormancy times are of the same order as those of the active population. Mutations appear as Poisson processes on the active lineages and potentially at reduced rate also on the dormant lineages. The presence of “dormant” lineages leads to qualitatively altered times to the most recent common ancestor and nonclassical patterns of genetic diversity. To illustrate this we provide a Wright–Fisher model with a seedbank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seedbank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seedbank, are compared. The effect of a seedbank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seedbank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect from genetic data the presence of a large seedbank in natural populations.     

A Mathematical Model of Cell Cycle Dysregulation Due to Human Papillomavirus Infection

Human papillomaviruses (HPVs) that infect mucosal epithelium can be classified as high risk or low risk based on their propensity to cause lesions that can undergo malignant progression. HPVs produce the E7 protein that binds to cell cycle regulatory proteins including the retinoblastoma tumor suppressor protein (RB) to modulate cell cycle control. Generally, high-risk HPV E7 proteins bind to RB with a higher affinity than low-risk HPV E7s, but both are able to deactivate RB and trigger S phase progression. In uninfected cells, RB inactivation is a tightly controlled process that must coincide with growth factor stimulation to commit cells to division. High-risk HPV E7 proteins short-circuit this control by decreasing growth factor requirement for cell division. We develop a mathematical model to examine the role that RB binding affinity, growth factor concentration, and E7 concentration have on cell cycle progression. Our model predicts that high RB binding affinity and E7 concentration accelerate the \(\mathrm {G_{1}}\) to S phase transition and weaken the dependence on growth factor. This model thus captures a key step in high-risk HPV oncogenesis.