The infinitesimal model with dominance

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and a non-genetic (environmental) component and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the trait values of the parents. In previous work, Barton et al.(2017), we showed that when trait values are determined by the sum of a large number of Mendelian factors, each of small effect, one can justify the infinitesimal model as limit of Mendelian inheritance. In this paper, we show that the robustness of the infinitesimal model extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and identities determined by the pedigree. In this setting, it is natural to decompose trait values, not just into the additive and dominance components, but into a component that is shared by all individuals within the family and an independent `residual' for each offspring, which captures the randomness of Mendelian inheritance. We show that, even if we condition on parental trait values, both the shared component and the residuals within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/\sqrt{M}. We illustrate our results with some numerical examples.Comment: 62 pages, 8 figure

Serological proteome analysis reveals new specific biases in the IgM and IgG autoantibody repertoires in autoimmune polyendocrine syndrome type 1

Objective: Autoimmune polyendocrine syndrome type 1 (APS 1) is caused by mutations in the AIRE gene that induce intrathymic T-cell tolerance breakdown, which results in tissue-specific autoimmune diseases. Design: To evaluate the effect of a well-defined T-cell repertoire impairment on humoral self-reactive fingerprints, comparative serum self-IgG and self-IgM reactivities were analyzed using both one- and two-dimensional western blotting approaches against a broad spectrum of peripheral tissue antigens. Methods: Autoantibody patterns of APS 1 patients were compared with those of subjects affected by other autoimmune endocrinopathies (OAE) and healthy controls. Results: Using a Chi-square test, significant changes in the Ab repertoire were found when intergroup patterns were compared. A singular distortion of both serum self-IgG and self-IgM repertoires was noted in APS 1 patients. The molecular characterization of these antigenic targets was conducted using a proteomic approach. In this context, autoantibodies recognized more significantly either tissue-specific antigens, such as pancreatic amylase, pancreatic triacylglycerol lipase and pancreatic regenerating protein 1α, or widely distributed antigens, such as peroxiredoxin-2, heat shock cognate 71-kDa protein and aldose reductase. As expected, a well-defined self-reactive T-cell repertoire impairment, as described in APS 1 patients, affected the tissue-specific self-IgG repertoire. Interestingly, discriminant IgM reactivities targeting both tissue-specific and more widely expressed antigens were also specifically observed in APS 1 patients. Using recombinant targets, we observed that post translational modifications of these specific antigens impacted upon their recognition. Conclusions: The data suggest that T-cell-dependent but also T-cell-independent mechanisms are involved in the dynamic evolution of autoimmunity in APS 1

Hyphal network whole field imaging allows for accurate estimation of anastomosis rates and branching dynamics of the filamentous fungus Podospora anserina

The success of filamentous fungi in colonizing most natural environments can be largely attributed to their ability to form an expanding interconnected network, the mycelium, or thallus, constituted by a collection of hyphal apexes in motion producing hyphae and subject to branching and fusion. In this work, we characterize the hyphal network expansion and the structure of the fungus Podospora anserina under controlled culture conditions. To this end, temporal series of pictures of the network dynamics are produced, starting from germinating ascospores and ending when the network reaches a few centimeters width, with a typical image resolution of several micrometers. The completely automated image reconstruction steps allow an easy post-processing and a quantitative analysis of the dynamics. The main features of the evolution of the hyphal network, such as the total length L of the mycelium, the number of "nodes" (or crossing points) N and the number of apexes A, can then be precisely quantified. Beyond these main features, the determination of the distribution of the intra-thallus surfaces (S; i; ) and the statistical analysis of some local measures of N, A and L give new insights on the dynamics of expanding fungal networks. Based on these results, we now aim at developing robust and versatile discrete/continuous mathematical models to further understand the key mechanisms driving the development of the fungus thallus

Inference in two dimensions: Allele frequencies versus lengths of shared sequence blocks

We outline two approaches to inference of neighbourhood size, N, and dispersal rate, σ2, based on either allele frequencies or on the lengths of sequence blocks that are shared between genomes. Over intermediate timescales (10-100 generations, say), populations that live in two dimensions approach a quasi-equilibrium that is independent of both their local structure and their deeper history. Over such scales, the standardised covariance of allele frequencies (i.e. pairwise F S T) falls with the logarithm of distance, and depends only on neighbourhood size, N, and a 'local scale', κ; the rate of gene flow, σ2, cannot be inferred. We show how spatial correlations can be accounted for, assuming a Gaussian distribution of allele frequencies, giving maximum likelihood estimates of N and κ. Alternatively, inferences can be based on the distribution of the lengths of sequence that are identical between blocks of genomes: long blocks (>0.1cM, say) tell us about intermediate timescales, over which we assume a quasi-equilibrium. For large neighbourhood size, the distribution of long blocks is given directly by the classical Wright-Malécot formula; this relationship can be used to infer both N and σ2. With small neighbourhood size, there is an appreciable chance that recombinant lineages will coalesce back before escaping into the distant past. For this case, we show that if genomes are sampled from some distance apart, then the distribution of lengths of blocks that are identical in state is geometric, with a mean that depends on N and σ2. © 2013 Elsevier Inc

Genetic hitchhiking in spatially extended populations

When a mutation with selective advantage s spreads through a panmictic population, it may cause two lineages at a linked locus to coalesce; the probability of coalescence is exp ( - 2. r T) , where T ~ log (2. N s) / s is the time to fixation, N is the number of haploid individuals, and r is the recombination rate. Population structure delays fixation, and so weakens the effect of a selective sweep. However, favourable alleles spread through a spatially continuous population behind a narrow wavefront; ancestral lineages are confined at the tip of this front, and so coalesce rapidly. In extremely dense populations, coalescence is dominated by rare fluctuations ahead of the front. However, we show that for moderate densities, a simple quasi-deterministic approximation applies: the rate of coalescence within the front is λ ~ 2. g (η) / (ρℓ) , where ρ is the population density and ℓ=σ2/s is the characteristic scale of the wavefront; g (η) depends only on the strength of random drift, η=ρσs/2. The net effect of a sweep on coalescence also depends crucially on whether two lineages are ever both within the wavefront at the same time: even in the extreme case when coalescence within the front is instantaneous, the net rate of coalescence may be lower than in a single panmictic population. Sweeps can also have a substantial impact on the rate of gene flow. A single lineage will jump to a new location when it is hit by a sweep, with mean square displacement σeff2/σ2=(8/3)(L/ℓ)(Λ/R); this can be substantial if the species' range, L, is large, even if the species-wide rate of sweeps per map length, Λ / R, is small. This effect is half as strong in two dimensions. In contrast, the rate of coalescence between lineages, at random locations in space and on the genetic map, is proportional to (c / L) (Λ / R) , where c is the wavespeed: thus, on average, one-dimensional structure is likely to reduce coalescence due to sweeps, relative to panmixis. In two dimensions, genes must move along the front before they can coalesce; this process is rapid, being dominated by rare fluctuations. This leads to a dramatically higher rate of coalescence within the wavefront than if lineages simply diffused along the front. Nevertheless, the net rate of coalescence due to a sweep through a two-dimensional population is likely to be lower than it would be with panmixis. © 2012 Elsevier Inc