The infinite alleles model revisited: a Gibbs sampling approach

Mapping Intimacies ◽

10.1101/2021.07.21.452479 ◽

2021 ◽

Author(s):

Marc Manceau

Keyword(s):

Viral Sequence ◽

Mutation Process ◽

Effective Population ◽

Viral Genomes ◽

Joint Reconstruction ◽

The Past ◽

Simplifying Assumptions ◽

Population Sizes ◽

New Perspective ◽

Infinite Alleles Model

The SARS-CoV-2 outbreak started in late 2019 in the Hubei province in China and the first viral sequence was made available to the scientific community on early January 2020. From there, viral genomes from all over the world have followed at an outstanding rate, reaching already more than 10^5 on early May 2020, and more than 10^6 by early March 2021. Phylodynamics methods have been designed in recent years to process such datasets and infer population dynamics and sampling intensities in the past. However, the unprecedented scale of the SARS-CoV-2 dataset now calls for new methodological developments, relying e.g. on simplifying assumptions of the mutation process. In this article, I build on the infinite alleles model stemming from the field of population genetics to develop a new Bayesian statistical method allowing the joint reconstruction of the outbreak's effective population sizes and sampling intensities through time. This relies on prior conjugacy properties that prove useful both to develop a Gibbs sampler and to gain intuition on the way different parameters of the model are linked and inferred. I finally illustrate the use of this method on SARS-CoV-2 genomes sequenced during the first wave of the outbreak in four distinct European countries, thus offering a new perspective on the evolution of the sampling intensity through time in these countries from genetic data only.

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Estimating required ‘lockdown’ cycles before immunity to SARS-CoV-2: Model-based analyses of susceptible population sizes, ‘S0’, in seven European countries including the UK and Ireland

10.1101/2020.04.10.20060426 ◽

2020 ◽

Cited By ~ 4

Author(s):

Rosalyn J. Moran ◽

Erik D. Fagerholm ◽

Maell Cullen ◽

Jean Daunizeau ◽

Mark P. Richardson ◽

...

Keyword(s):

Continuous Time ◽

Total Population ◽

European Countries ◽

Effective Population ◽

Susceptible Population ◽

Death Rates ◽

Seir Model ◽

The Past ◽

Population Sizes ◽

The Uk

AbstractBackgroundFollowing stringent social distancing measures, some European countries are beginning to report a slowed or negative rate of growth of daily case numbers testing positive for the novel coronavirus. The notion that the first wave of infection is close to its peak begs the question of whether future peaks or ‘second waves’ are likely. We sought to determine the current size of the effective (i.e. susceptible) population for seven European countries—to estimate immunity levels following this first wave. We compare these numbers to the total population sizes of these countries, in order to investigate the potential for future peaks.MethodsWe used Bayesian model inversion to estimate epidemic parameters from the reported case and death rates from seven countries using data from late January 2020 to April 5th 2020. Two distinct generative model types were employed: first a continuous time dynamical-systems implementation of a Susceptible-Exposed-Infectious-Recovered (SEIR) model and second: a partially observable Markov Decision Process (MDP) or hidden Markov model (HMM) implementation of an SEIR model. Both models parameterise the size of the initial susceptible population (‘S0’), as well as epidemic parameters. Parameter estimation (‘data fitting’) was performed using a standard Bayesian scheme (variational Laplace) designed to allow for latent unobservable states and uncertainty in model parameters.ResultsBoth models recapitulated the dynamics of transmissions and disease as given by case and death rates. The peaks of the current waves were predicted to be in the past for four countries (Italy, Spain, Germany and Switzerland) and to emerge in 0.5 – 2 weeks in Ireland and 1-3 weeks in the UK. For France one model estimated the peak within the past week and the other in the future in two weeks. Crucially, Maximum a posteriori (MAP) estimates of S0 for each country indicated effective population sizes of below 20% (of total population size), under both the continuous time and HMM models. Using for all countries—with a Bayesian weighted average across all seven countries and both models, we estimated that 6.4% of the total population would be immune. From the two models the maximum percentage of the effective population was estimated at 19.6% of the total population for the UK, 16.7% for Ireland, 11.4% for Italy, 12.8% for Spain, 18.8% for France, 4.7% for Germany and 12.9% for Switzerland.ConclusionOur results indicate that after the current wave, a large proportion of the total population will remain without immunity. This suggests that in the absence of strong seasonal effects, new medications or more comprehensive contact tracing, a further set of epidemic waves in different geographic centres are likely. These findings may have implications for ‘exit strategies’ from any lockdown stage.

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Estimation of effective population sizes from data on genetic markers

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2005.1682 ◽

2005 ◽

Vol 360 (1459) ◽

pp. 1395-1409 ◽

Cited By ~ 245

Author(s):

Jinliang Wang

Keyword(s):

Genetic Markers ◽

Evolutionary Biology ◽

Genetic Model ◽

Spatial Scales ◽

Effective Population ◽

Future Developments ◽

The Past ◽

Heterozygosity Excess ◽

Population Sizes ◽

The Many

The effective population size ( N e ) is an important parameter in ecology, evolutionary biology and conservation biology. It is, however, notoriously difficult to estimate, mainly because of the highly stochastic nature of the processes of inbreeding and genetic drift for which N e is usually defined and measured, and because of the many factors (such as time and spatial scales, systematic forces) confounding such processes. Many methods have been developed in the past three decades to estimate the current, past and ancient effective population sizes using different information extracted from some genetic markers in a sample of individuals. This paper reviews the methodologies proposed for estimating N e from genetic data using information on heterozygosity excess, linkage disequilibrium, temporal changes in allele frequency, and pattern and amount of genetic variation within and between populations. For each methodology, I describe mainly the logic and genetic model on which it is based, the data required and information used, the interpretation of the estimate obtained, some results from applications to simulated or empirical datasets and future developments that are needed.

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Population inter-connectivity over the past 120,000 years explains distribution and diversity of Central African hunter-gatherers

10.1101/2021.06.21.449204 ◽

2021 ◽

Author(s):

Cecilia Padilla-Iglesias ◽

Lane Atmore ◽

Jesus Olivero ◽

Karen Lupo ◽

Andrea Manica ◽

...

Keyword(s):

Homo Sapiens ◽

Central Africa ◽

Modern Human ◽

Archaeological Sites ◽

Effective Population ◽

Hunter Gatherers ◽

The Past ◽

Population Sizes ◽

History Of ◽

Local Differentiation

The evolutionary history of African hunter-gatherers holds key insights into modern human diversity. Here we combine ethnographic and genetic data on Central African hunter-gatherers (CAHG) to show that their current distribution and density is explained by ecology rather than by a displacement to marginal habitats due to recent farming expansions, as commonly assumed. We also predicted hunter-gatherer presence across Central Africa over the past 120,000 years using paleoclimatic reconstructions, which were statistically validated by dated archaeological sites. Finally, we show that genomic estimates of separation times between CAHG groups match our ecological estimates of periods favouring population splits, and that recoveries of connectivity would have facilitated subsequent gene-flow. Our results reveal that CAHG stem from a deep history of partially connected populations. This form of sociality allowed the coexistence of relatively large effective population sizes and local differentiation, with important implications for the evolution of genetic and cultural diversity in Homo sapiens.

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MUTATION RATES, POPULATION SIZES AND AMOUNTS OF ELECTROPHORETIC VARIATION OF ENZYME LOCI IN NATURAL POPULATIONS

Genetics ◽

10.1093/genetics/92.2.623 ◽

1979 ◽

Vol 92 (2) ◽

pp. 623-646

Author(s):

E Zouros

Keyword(s):

Allelic Variation ◽

Natural Populations ◽

Purifying Selection ◽

Mutation Rates ◽

Electrophoretic Variation ◽

Effective Population ◽

Molecular Weights ◽

Enzyme Subunits ◽

Population Sizes ◽

Infinite Alleles Model

ABSTRACT A method is presented for estimating relative mutation rates or relative effective population sizes, under the hypothesis of adaptively neutral allelic variation. This method was applied to seven surveys of electrophoretic variation. It was observed that electrophoretic mutation rates so obtained follow the gamma distribution and, in Drosophila, are positively correlated with the molecular weights of the enzyme subunits. The variance in mutation rate is larger under the step-wise model of electrophoretic mutation than under the infinite-alleles model. Rates for the most variable loci may exceed rates for less variable loci by a factor of 500. For completely invariant loci, this factor may be as high as 4 × 104, an observation suggesting that these loci are subject to purifying selection. In contrast to mutation rates, effective population sizes may vary at the most by a factor of ten. These results support the hypothesis that differences in the amount of electrophoretic variability among polymorphic loci may reflect differences in the rate by which electrophoretically detectable variation is generated in populations.

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Response of an Afro-Palearctic bird migrant to glaciation cycles

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2023836118 ◽

2021 ◽

Vol 118 (52) ◽

pp. e2023836118

Author(s):

Kasper Thorup ◽

Lykke Pedersen ◽

Rute R. da Fonseca ◽

Babak Naimi ◽

David Nogués-Bravo ◽

...

Keyword(s):

Global Scale ◽

Seasonal Migration ◽

Migratory Species ◽

Effective Population ◽

Long Distance ◽

Climate Conditions ◽

The Past ◽

The North ◽

Population Sizes ◽

Glacial Periods

Migration allows animals to exploit spatially separated and seasonally available resources at a continental to global scale. However, responding to global climatic changes might prove challenging, especially for long-distance intercontinental migrants. During glacial periods, when conditions became too harsh for breeding in the north, avian migrants have been hypothesized to retract their distribution to reside within small refugial areas. Here, we present data showing that an Afro-Palearctic migrant continued seasonal migration, largely within Africa, during previous glacial–interglacial cycles with no obvious impact on population size. Using individual migratory track data to hindcast monthly bioclimatic habitat availability maps through the last 120,000 y, we show altered seasonal use of suitable areas through time. Independently derived effective population sizes indicate a growing population through the last 40,000 y. We conclude that the migratory lifestyle enabled adaptation to shifting climate conditions. This indicates that populations of resource-tracking, long-distance migratory species could expand successfully during warming periods in the past, which could also be the case under future climate scenarios.

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Faculty Opinions recommendation of Fitness decline in spontaneous mutation accumulation lines of Caenorhabditis elegans with varying effective population sizes.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.723874420.793504625 ◽

2015 ◽

Author(s):

Charles Baer

Keyword(s):

Caenorhabditis Elegans ◽

Spontaneous Mutation ◽

Mutation Accumulation ◽

Effective Population ◽

Population Sizes

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EFFECTS OF POPULATION SIZE AND SELECTION INTENSITY ON SHORT-TERM RESPONSE TO SELECTION FOR POSTWEANING GAIN IN MICE

Genetics ◽

10.1093/genetics/73.3.513 ◽

1973 ◽

Vol 73 (3) ◽

pp. 513-530

Author(s):

J P Hanrahan ◽

E J Eisen ◽

J E Legates

Keyword(s):

Population Size ◽

Selection Response ◽

Selection Intensity ◽

Realized Heritability ◽

Family Selection ◽

Effective Population ◽

Population Sizes ◽

Selection For ◽

Selection Intensities ◽

Term Response

ABSTRACT The effects of population size and selection intensity on the mean response was examined after 14 generations of within full-sib family selection for postweaning gain in mice. Population sizes of 1, 2, 4, 8 and 16 pair matings were each evaluated at selection intensities of 100% (control), 50% and 25% in a replicated experiment. Selection response per generation increased as selection intensity increased. Selection response and realized heritability tended to increase with increasing population size. Replicate variability in realized heritability was large at population sizes of 1, 2 and 4 pairs. Genetic drift was implicated as the primary factor causing the reduced response and lowered repeatability at the smaller population sizes. Lines with intended effective population sizes of 62 yielded larger selection responses per unit selection differential than lines with effective population sizes of 30 or less.

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A detailed analysis of the hybrid lattice-reduction and meet-in-the-middle attack

Journal of Mathematical Cryptology ◽

10.1515/jmc-2016-0044 ◽

2019 ◽

Vol 13 (1) ◽

pp. 1-26 ◽

Cited By ~ 3

Author(s):

Thomas Wunderer

Keyword(s):

Detailed Analysis ◽

Runtime Analysis ◽

Lattice Reduction ◽

Signature Schemes ◽

The Past ◽

Encryption Schemes ◽

Simplifying Assumptions ◽

Security Levels

Abstract Over the past decade, the hybrid lattice-reduction and meet-in-the middle attack (called hybrid attack) has been used to evaluate the security of many lattice-based cryptographic schemes such as NTRU, NTRU Prime, BLISS and more. However, unfortunately, none of the previous analyses of the hybrid attack is entirely satisfactory: They are based on simplifying assumptions that may distort the security estimates. Such simplifying assumptions include setting probabilities equal to 1, which, for the parameter sets we analyze in this work, are in fact as small as 2^{-80} . Many of these assumptions lead to underestimating the scheme’s security. However, some lead to security overestimates, and without further analysis, it is not clear which is the case. Therefore, the current security estimates against the hybrid attack are not reliable, and the actual security levels of many lattice-based schemes are unclear. In this work, we present an improved runtime analysis of the hybrid attack that is based on more reasonable assumptions. In addition, we reevaluate the security against the hybrid attack for the NTRU, NTRU Prime and R-BinLWEEnc encryption schemes as well as for the BLISS and GLP signature schemes. Our results show that there exist both security over- and underestimates in the literature.

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The effect of life-history and mode of inheritance on neutral genetic variability

Genetics Research ◽

10.1017/s0016672301004979 ◽

2001 ◽

Vol 77 (2) ◽

pp. 153-166 ◽

Cited By ~ 114

Author(s):

BRIAN CHARLESWORTH

Keyword(s):

Sequence Variation ◽

Adult Mortality ◽

Structured Populations ◽

Human Populations ◽

Effective Population ◽

Transmission Modes ◽

Population Sizes ◽

Age Structured ◽

Infinite Sites Model ◽

Site Diversity

Formulae for the effective population sizes of autosomal, X-linked, Y-linked and maternally transmitted loci in age-structured populations are developed. The approximations used here predict both asymptotic rates of increase in probabilities of identity, and equilibrium levels of neutral nucleotide site diversity under the infinite-sites model. The applications of the results to the interpretation of data on DNA sequence variation in Drosophila, plant, and human populations are discussed. It is concluded that sex differences in demographic parameters such as adult mortality rates generally have small effects on the relative effective population sizes of loci with different modes of inheritance, whereas differences between the sexes in variance in reproductive success can have major effects, either increasing or reducing the effective population size for X-linked loci relative to autosomal or Y-linked loci. These effects need to be accounted for when trying to understand data on patterns of sequence variation for genes with different transmission modes.

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