The infinitesimal model: Definition, derivation, and implications.

Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, …. We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Simulations suggest that in some cases the convergence may be as fast as 1∕M.

Spread of pedigree versus genetic ancestry in spatially distributed populations.

Ancestral processes are fundamental to modern population genetics and spatial structure has been the subject of intense interest for many years. Despite this interest, almost nothing is known about the distribution of the locations of pedigree or genetic ancestors. Using both spatially continuous and stepping-stone models, we show that the distribution of pedigree ancestors approaches a travelling wave, for which we develop two alternative approximations. The speed and width of the wave are sensitive to the local details of the model. After a short time, genetic ancestors spread far more slowly than pedigree ancestors, ultimately diffusing out with radius ∼ t rather than spreading at constant speed. In contrast to the wave of pedigree ancestors, the spread of genetic ancestry is insensitive to the local details of the models.

Ancestries of a recombining diploid population.

We derive the exact one-step transition probabilities of the number of lineages that are ancestral to a random sample from the current generation of a bi-parental population that is evolving under the discrete Wright-Fisher model with n diploid individuals. Our model allows for a per-generation recombination probability of r . When r = 1, our model is equivalent to Chang's (Adv Appl Probab 31:1002-1038, 1999) model for the karyotic pedigree. When r = 0, our model is equivalent to Kingman's (Stoch Process Appl 13:235-248, 1982) discrete coalescent model for the cytoplasmic tree or sub-karyotic tree containing a DNA locus that is free of intra-locus recombination. When 0 < r < 1 our model can be thought to track a sub-karyotic ancestral graph containing a DNA sequence from an autosomal chromosome that has an intra-locus recombination probability r . Thus, our family of models indexed by r ∈ [0, 1] connects Kingman's discrete coalescent to Chang's pedigree in a continuous way as r goes from 0 to 1. For large populations, we also study three properties of the ancestral process corresponding to a given r ∈ (0, 1): the time Tn to a most recent common ancestor (MRCA) of the population, the time Un at which all individuals are either common ancestors of all present day individuals or ancestral to none of them, and the fraction of individuals that are common ancestors at time Un. These results generalize the three main results of Chang's (Adv Appl Probab 31:1002-1038, 1999). When we appropriately rescale time and recombination probability by the population size, our model leads to the continuous time Markov chain called the ancestral recombination graph of Hudson (Theor Popul Biol 23:183-201, 1983) and Griffiths (The two-locus ancestral graph, Institute of Mathematical Statistics 100-117, 1991).

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, σ(2), 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 FST) falls with the logarithm of distance, and depends only on neighbourhood size, N, and a 'local scale', κ; the rate of gene flow, σ(2), 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 (>0.1 cM, 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 σ(2). 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 σ(2).

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(-2rT), where T∼log(2Ns)/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∼2g(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 σeff(2)/σ(2)=(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.

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 (Si) 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.

Novel WWOX deleterious variants cause early infantile epileptic encephalopathy, severe developmental delay and dysmorphism among Yemenite Jews.

The human WW Domain Containing Oxidoreductase (WWOX) gene was originally described as a tumor suppressor gene. However, recent reports have demonstrated its cardinal role in the pathogenesis of central nervous systems disorders such as epileptic encephalopathy, intellectual disability, and spinocerebellar ataxia. We report on six patients from three unrelated families of full or partial Yemenite Jewish ancestry exhibiting early infantile epileptic encephalopathy and profound developmental delay. Importantly, four patients demonstrated facial dysmorphism. Exome sequencing revealed that four of the patients were homozygous for a novel WWOX c.517-2A > G splice-site variant and two were compound heterozygous for this variant and a novel c.689A > C, p.Gln230Pro missense variant. Complementary DNA sequencing demonstrated that the WWOX c.517-2A > G splice-site variant causes skipping of exon six. A carrier rate of 1:177 was found among Yemenite Jews. We provide the first detailed description of patients harboring a splice-site variant in the WWOX gene and propose that the clinical synopsis of WWOX related epileptic encephalopathy should be broadened to include facial dysmorphism. The increased frequency of the c.517-2A > G splice-site variant among Yemenite Jews coupled with the severity of the phenotype makes it a candidate for inclusion in expanded preconception screening programs.

Combined Differential scanning calorimetry, Raman and Brillouin spectroscopies: A multiscale approach for materials investigation.

A new experimental setup combining DSC, Raman and Brillouin spectroscopies was developed. In order to estimate its accuracy and stability a study of silicon and the alpha-beta quartz phase transition were performed. The data obtained demonstrated good agreement with previous studies using these three different techniques. For quartz, the temperature behavior of its 147 cm-1 Raman mode was studied in detail. Using a two-phonon coupling treatment of the Raman band, we show for the first time that its behavior can be well described by Landau theory of first-order phase transitions. The combined DSC-Raman-Brillouin technique is a powerful tool for material science capable of studying thermal, structural and elastic properties simultaneously.

The genotoxicity of iron and chromium in electroplating effluents.

Electroplating effluents were tested for their genotoxicity with the micronucleus test on newt larvae. The metallic content of the tested samples was responsible for the induction of micronuclei in red blood cells (RBC). Then, iron (Fe3+), chromium (Cr3+, Cr6+) and zinc (Zn2+) which were identified in these samples, were tested either separately or combined, at their concentrations in the electroplating effluents. Fe3+ induced a high level of micronuclei at 12.5 and 25 mg/l (nominal concentrations). Both soluble and non-soluble forms of iron were responsible for these genotoxic effects. At lower concentrations (0.6 and 4.5 mg/l) Fe3+ was not systematically genotoxic. Zinc could not be considered genotoxic on newt. Cr3+ gave negative responses, but exposure to Cr6+ (1 mg/l) could result in a significant number of micronucleated RBC in some cases. The most dramatic genotoxic effects were registered when Fe3+ and Cr6+ were combined. This study demonstrates that interactions between pollutants and the effects of non-soluble chemicals on aquatic vertebrates and invertebrates can no longer be neglected.

Ecotoxicity of a polycyclic aromatic hydrocarbon (PAH)-contaminated soil.

Soil samples from a former cokery site polluted with polycyclic aromatic hydrocarbons (PAHs) were assessed for their toxicity to terrestrial and aquatic organisms and for their mutagenicity. The total concentration of the 16 PAHs listed as priority pollutants by the US Environmental Protection Agency (US-EPA) was 2634+/-241 mg/kgdw in soil samples. The toxicity of water-extractable pollutants from the contaminated soil samples was evaluated using acute (Vibrio fischeri; Microtox test, Daphnia magna) and chronic (Pseudokirchneriella subcapitata, Ceriodaphnia dubia) bioassays and the EC values were expressed as percentage water extract in the test media (v/v). Algal growth (EC50-3d=2.4+/-0.2% of the water extracts) and reproduction of C. dubia (EC50-7d=4.3+/-0.6%) were the most severely affected, compared to bacterial luminescence (EC50-30 min=12+/-3%) and daphnid viability (EC50-48 h=30+/-3%). The Ames and Mutatox tests indicated mutagenicity of water extracts, while no response was found with the umu test. The toxicity of the soil samples was assessed on the survival and reproduction of earthworms (Eisenia fetida) and collembolae (Folsomia candida), and on the germination and growth of higher plants (Lactuca sativa L.: lettuce and Brassica chinensis J.: Chinese cabbage). The EC50 values were expressed as percentage contaminated soil in ISO soil test medium (weight per weight-w/w) and indicated severe effects on reproduction of the collembola F. candida (EC50-28 d=5.7%) and the earthworm E. fetida (EC50-28 d=18% and EC50-56 d=8%, based on cocoon and juvenile production, respectively). Survival of collembolae was already affected at a low concentration of the contaminated soil (EC50-28 d=11%). The viability of juvenile earthworms was inhibited at much lower concentrations of the cokery soil (EC50-14 d=28%) than the viability of adults (EC50-14 d=74%). Only plant growth was inhibited (EC50-17d=26%) while germination was not. Chemical analyses of water extracts allowed us to identify inorganic water-extractable pollutants as responsible for toxicity on aquatic species, especially copper for effects on D. magna and C. dubia. The soil toxicity on collembolae and earthworms could be explained by 4 PAH congeners-fluorene, phenanthrene, pyrene, and fluoranthene. Yet, toxicity of the cokery soil as a whole was much lower than toxicity that could be deduced from the concentration of each congener in spiked soils, indicating that pollutants in the soil became less bioavailable with ageing.