Product Of Population Size Research Articles

Clonal Dynamics of Normal Haematopoiesis with Human Ageing

The haematopoietic system manifests several age-associated phenotypes including anaemia; loss of regenerative capacity, especially in the face of insults such as infection, chemotherapy or blood loss; and increased risk of clonal haematopoiesis and blood cancers. The cellular alterations that underpin these age-related phenotypes, which typically manifest in individuals aged over 70, remain elusive. We aimed to investigate whether changes in HSC population structure with age might underlie any aspects of haematopoietic system ageing.We sequenced 3579 genomes from single-cell-derived colonies of haematopoietic stem cell/multipotent progenitors (HSC/MPPs) from 10 haematologically normal subjects aged 0-81 years. HSC/MPPs accumulated 17 somatic mutations/year after birth with no increased rate of mutation accumulation in the elderly. HSC/MPP telomere length declined by 30 bp/yr. In cord blood and adults aged <65, a small proportion of HSC/MPPs had unexpectedly long telomeres, as assessed using several criteria for outliers. The proportion of cells with unexpectedly long telomeres reduced in frequency with age. Given that telomeres shorten at cell division, these outlier cells have presumably undergone fewer historic cell divisions, supporting the existence of a rare population of dormant HSCs in humans that declines in frequency with age.To interrogate changes in HSC population structure with age, we used the pattern of unique and shared mutations between the sampled cells from each individual to reconstruct their phylogenetic relationships. The frequency of branch-points (known as coalescences) in phylogenetic trees in a neutrally evolving, well-mixed population of somatic cells is primarily determined by the product of population size and time between symmetric self-renewal cell divisions (Nt). Smaller populations and more frequent symmetric divisions both increase the density of coalescences. Specific clones can come to dominate either through neutral drift or positive selection.We found that haematopoiesis in adults aged <65 was polyclonal, with high indices of clonal diversity. The number and pattern of coalescent events in the phylogenies showed that a stable population of 20,000 to 200,000 HSC/MPPs was contributing evenly to blood production in young adult life. In contrast, haematopoiesis in individuals aged >75 showed profoundly decreased clonal diversity. In each elderly subject, 30-60% of haematopoiesis was accounted for by 12-18 independent clones, each contributing 1-34% of blood production. Most clones had begun their expansion before age 40, but only 22% had known driver mutations.We used the ratio of non-synonymous to synonymous mutations (dN/dS) to identify any excess of non-synonymous (driver) mutations in the dataset. This genome-wide selection analysis estimated that 1/34 to 1/12 non-synonymous mutations were drivers, occurring at a constant rate throughout life, such that the set of 300 - 400 HSC/MPPs sampled from each adult individual harboured around 100 driver mutations, over 10-fold higher than the number of known drivers we could identify. Novel drivers affected a wider pool of genes than identified in blood cancers. The genes DNMT3A, ZNF318 and HIST2H3D were identified as being under significant positive selection in HSC/MPPs, despite ZNF318 and HIST2H3D not being enriched in the setting of myeloid malignancies. Loss of Y chromosome conferred selective benefits on HSC/MPPs in males.Simulations from a simple model of haematopoiesis, with constant HSC population size and constant acquisition of driver mutations conferring moderate fitness benefits, entirely explained the abrupt change in clonal structure observed in the elderly, which could not be explained by neutral models incorporating drift alone. Our data supports the view that dramatically decreased clonal diversity is a universal feature of haematopoiesis in aged humans, underpinned by pervasive positive selection acting on many more genes than currently known. By old age the majority of HSCs harbour at least one driver mutation. With such ubiquity of driver mutations, selected purely for their competitive advantage within the stem cell compartment, and with the wholesale rewiring of cellular pathways they induce, it is feasible that they may contribute to age-related phenotypes beyond the increased risk of blood cancer. DisclosuresSpencer: Wugen, Inc.: Consultancy, Other: Stock Options. Vassiliou: Kymab Ltd: Divested equity in a private or publicly-traded company in the past 24 months; STRM.BIO: Consultancy; Astrazeneca: Consultancy. Kent: STRM.bio: Research Funding. Campbell: Mu Genomics: Current holder of individual stocks in a privately-held company, Membership on an entity's Board of Directors or advisory committees.

Are there species smaller than 1 mm?

The rapid advance in genetic sequencing technologies has provided an unprecedented amount of data on the biodiversity of meiofauna. It was hoped that these data would allow the identification and counting of species, distinguished as tight clusters of similar genomes. Surprisingly, this appears not to be the case. Here, we begin a theoretical discussion of this phenomenon, drawing on an individual-based ecological model to inform our arguments. The determining factor in the emergence (or not) of distinguishable genetic clusters in the model is the product of population size with mutation rate—a measure of the adaptability of the population as a whole. This result suggests that indeed one should not expect to observe clearly distinguishable species groupings in data gathered from ultrasequencing of meiofauna.

The weight of nations: an estimation of adult human biomass

BackgroundThe energy requirement of species at each trophic level in an ecological pyramid is a function of the number of organisms and their average mass. Regarding human populations, although considerable attention is given to estimating the number of people, much less is given to estimating average mass, despite evidence that average body mass is increasing. We estimate global human biomass, its distribution by region and the proportion of biomass due to overweight and obesity.MethodsFor each country we used data on body mass index (BMI) and height distribution to estimate average adult body mass. We calculated total biomass as the product of population size and average body mass. We estimated the percentage of the population that is overweight (BMI > 25) and obese (BMI > 30) and the biomass due to overweight and obesity.ResultsIn 2005, global adult human biomass was approximately 287 million tonnes, of which 15 million tonnes were due to overweight (BMI > 25), a mass equivalent to that of 242 million people of average body mass (5% of global human biomass). Biomass due to obesity was 3.5 million tonnes, the mass equivalent of 56 million people of average body mass (1.2% of human biomass). North America has 6% of the world population but 34% of biomass due to obesity. Asia has 61% of the world population but 13% of biomass due to obesity. One tonne of human biomass corresponds to approximately 12 adults in North America and 17 adults in Asia. If all countries had the BMI distribution of the USA, the increase in human biomass of 58 million tonnes would be equivalent in mass to an extra 935 million people of average body mass, and have energy requirements equivalent to that of 473 million adults.ConclusionsIncreasing population fatness could have the same implications for world food energy demands as an extra half a billion people living on the earth.

Evolutionary dynamics in finite populations can explain the full range of cooperative behaviors observed in the centipede game

Classical economic models make behavioral predictions based on the assumption that people are fully rational and care only about maximizing their own payoffs. Although this approach successfully explains human behavior in many situations, there is a wealth of experimental evidence demonstrating conditions where people deviate from the predictions of these models. One setting that has received particular attention is fixed length repeated games. Iterating a social dilemma can promote cooperation through direct reciprocity, even if it is common knowledge that all players are rational and self-interested. However, this is not the case if the length of the game is known to the players. In the final round, a rational player will defect, because there is no future to be concerned with. But if you know the other player will defect in the last round, then you should defect in the second to last round, and so on. This logic of backwards induction leads to immediate defection as the only rational (sub-game perfect Nash equilibrium) strategy. When people actually play such games, however, immediate defection is rare. Here we use evolutionary dynamics in finite populations to study the centipede game, which is designed to explore this issue of backwards induction. We make the following observation: since full cooperation can risk-dominate immediate defection in the centipede game, stochastic evolutionary dynamics can favor both delayed defection and even full cooperation. Furthermore, our evolutionary model can quantitatively reproduce human behavior from two experiments by fitting a single free parameter, which is the product of population size and selection intensity. Thus we provide evidence that people’s cooperative behavior in fixed length games, which is often called ‘irrational’, may in fact be the favored outcome of natural selection.

Selection for mutational robustness in finite populations

We investigate the evolutionary dynamics of a finite population of RNA sequences replicating on a neutral network. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated-equilibrium transitions, after initial mutation–selection balance has been reached. We find that a product of population size and mutation rate of approximately 30 or larger is sufficient to generate selection pressure for mutational robustness, even if the population size is orders of magnitude smaller than the neutral network on which the population resides. Our results show that quasispecies effects and neutral drift can occur concurrently, and that the relative importance of each is determined by the product of population size and mutation rate.

The effect of selection on genealogies.

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.

The Effect of Selection on Genealogies

Abstract The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price’s equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns &amp;gt; 3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.

On the use of star-shaped genealogies in inference of coalescence times.

Genealogies from rapidly growing populations have approximate "star" shapes. We study the degree to which this approximation holds in the context of estimating the time to the most recent common ancestor (T(MRCA)) of a set of lineages. In an exponential growth scenario, we find that unless the product of population size (N) and growth rate (r) is at least approximately 10(5), the "pairwise comparison estimator" of T(MRCA) that derives from the star genealogy assumption has bias of 10-50%. Thus, the estimator is appropriate only for large populations that have grown very rapidly. The "tree-length estimator" of T(MRCA) is more biased than the pairwise comparison estimator, having low bias only for extremely large values of Nr.

Oscillatory Dynamics of Smallpox and the Impact of Vaccination

The evolution of smallpox epidemics in London, 1647-1893, was studied by time series analysis of deaths from the disease in the Bills of Mortality. The interepidemic interval ( T) evolved progressively from 4 years to 2 years at 1800. The dynamics of epidemics during 1647-1800 are explicable in terms of the transmission of viral diseases which shows that (i) Tis determined by the product of population size ( N) and susceptibility (β), (ii) Tdetermines the mean age of catching the disease, (iii) the system will settle at its steady-state, endemic level unless the epidemics are driven. It is suggested that (i) the progressive change in Twas initially caused by a rise in Nand later by an increased β related to malnutrition and (ii) the epidemics were driven by an oscillation in δβ associated with seasonal dry conditions. the effects of variolation and vaccination became apparent after 1800: the endemic level fell progressively, the epidemics were reduced in amplitude and they were not driven. The dynamics of the disease can now be described by an SEIR model: severe outbreaks of smallpox are followed by decaying epidemics. Endemic smallpox mortality also interacts with the dynamics of the population so that a long wavelength oscillation (associated with recovery after the plague) and a 5/6 year (associated with immigration) oscillation are generated.

Vegetative Incompatibility in Ascomycetes: Highly Polymorphic but Selectively Neutral?

Vegetative incompatibility, the prevention of somatic fusion between individuals, occurs frequently in ascomycetes. In all species studied, a large number of Vegetative Compatibility Groups (VCGs) is found. In this study the role of mutation rate, random genetic drift and selection for the evolution of these large numbers of VCGs are investigated, both analytically and by computer simulation. We find that, irrespective of selection, the product of population size and mutation rate for new VCGs has to be larger than one to get realistic numbers of VCGs in asexual populations. If the number of VCGs is large, selection does not lead to a significant increase in the number of VCGs. Sexual reproduction, however, may enlarge the number of VCGs, due to recombination of incompatiblity genes. Here strong selective pressure does give an extra increase in VCG numbers. These results suggest that vegetative incompatibility may be a selectively neutral trait, although that does not explain it s ubiquity. Finally, it can be crucial that fungi can live in extremely large populations. An extremely large population size may offer an alternative explanation for a high degree of polymorphism. This explanation does not apply for incompatibility systems of higher organisms.

The divergence of a polygenic system subject to stabilizing selection, mutation and drift.

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.

Simulation results with stepwise mutation model and their interpretations.

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 allels (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.

The effects of population size and selection intesnity in selection for a quantitative character in Drosophila. II. Long-term response to selection.

1. An experimental evaluation of Robertson's (1960) theory of limits in artificial selection was attempted. A number of lines from the Canberra base population were selected for abdominal bristle number over 50 generations with population sizes of 10, 20, and 40 pairs of parents and selection intensities of 10, 20 and 40% as well as unselected controls.2. In general, the total response obtained increased with an increase inNī(product of population size and standardized selection differential).3. Thus, total response increased with increase in the number of individuals scored, or, for a fixed number of parents, increase in selection intensity increased both rates of response per generation and total response.4. But for the same total number scored, the response increased as selection intensity decreased. However, the proportion selected had only a small effect as compared with that of the total number scored.5. Sublines in which the population size was reduced after 16 generations of selection but with the selection intensity kept constant, immediately fell behind their parent lines and gave much less response.6. Agreement between replicate lines was generally poor, particularly for the 10- and 20-pair lines.7. Patterns of response in individual lines were frequently irregular and ‘waves of response’ were not uncommon.8. The results are discussed in terms of several theoretical models of selection limits. In general, agreement with these models was poor, as much of the response appeared to be due to a few genes (or gene combinations) with large effects on bristle number.

The effect of initial reverse selection upon total selection response

A computer has been used to investigate the effect of an initial period of reverse selection on the subsequent response of a population to renewed forward selection with the same population size and selection intensity. As the computer was used to derive gene frequency distributions, there was no random element in the results obtained. A theoretical solution to the problem was obtained for genes with small effects.The process can be adequately described by the duration of the reverse selection (expressed in terms of the population sizeN), the product of population size and gene effect,Ns, and the initial gene frequency. If the duration of reverse selection,t, is less thanN/2, the loss in selection advance due to the reverse selection is roughlyt/N, though slightly greater than this for genes with low frequency. The ‘point of no return’ after which it is impossible, with the same population size and selection intensity, to return even to the starting frequency is 1·4Ngenerations for genes with small effect and this declines as the gene effect increases.Some extension of results to recessive genes is also given.