scholarly journals The ancestral population size conditioned on the reconstructed phylogenetic tree with occurrence data

2019 ◽  
Author(s):  
Marc Manceau ◽  
Ankit Gupta ◽  
Timothy Vaughan ◽  
Tanja Stadler
Keyword(s):  
Phylogenetic Tree ◽  
Population Size ◽  
Death Process ◽  
Ancestral Population ◽  
Conditional Probability Distribution ◽  
Sampling Schemes ◽  
Occurrence Data ◽  
Fixed Probability ◽  
Case Count ◽  
Joint Examination

AbstractWe consider a homogeneous birth-death process with three different sampling schemes. First, individuals can be sampled through time and included in a reconstructed tree. Second, they can be sampled through time and only recorded as a point ‘occurrence’ along a timeline. Third, extant individuals are sampled and included in the reconstructed tree with a fixed probability. We further consider that sampled individuals can be removed or not from the process, upon sampling, with fixed probability.Given an outcome of the process, composed of the joint observation of a reconstructed phylogenetic tree and a record of occurrences not included in the tree, we derive the conditional probability distribution of the population size any time in the past. We additionally provide an algorithm to simulate ancestral population size trajectories given the observation of a reconstructed tree and occurrences.This distribution can readily be used to perform inferences of the ancestral population size in the field of epidemiology and macroevolution. In epidemiology, these results will pave the way towards jointly considering data from case count studies and reconstructed transmission trees. In macroevolution, it will foster the joint examination of the fossil record and extant taxa to reconstruct past biodiversity.

scholarly journals The probability distribution of the reconstructed phylogenetic tree with occurrence data

2019 ◽  
Author(s):  
Ankit Gupta ◽  
Marc Manceau ◽  
Timothy Vaughan ◽  
Mustafa Khammash ◽  
Tanja Stadler
Keyword(s):  
Probability Density ◽  
Phylogenetic Trees ◽  
Joint Probability ◽  
Death Process ◽  
Joint Analysis ◽  
Successive Sampling ◽  
Sampling Schemes ◽  
Extinction Rates ◽  
Case Count ◽  
Extant Species

AbstractWe consider a homogeneous birth-death process with incomplete sampling. Three successive sampling schemes are considered. First, individuals can be sampled through time and included in the tree. Second, they can be occurrences which are sampled through time and not included in the tree. Third, individuals reaching present day can be sampled and included in the tree. Upon sampling, individuals are removed (i.e. die).The outcome of the process is thus composed of the reconstructed evolutionary tree spanning all individuals sampled and included in the tree, and a timeline of occurrence events which are not placed along the tree. We derive a formula allowing one to compute the joint probability density of these, which can readily be used to perform maximum likelihood or Bayesian estimation of the parameters of the model.In the context of epidemiology, our probability density allows us to estimate transmission rates through a joint analysis of epidemiological case count data and phylogenetic trees reconstructed from pathogen sequences. Within macroevolution, our equations are the basis for taking into account fossil occurrences from paleontological databases together with extant species phylogenies for estimating speciation and extinction rates. Thus, we provide the theoretical framework for bridging not only the gap between phylogenetics and epidemiology, but also the gap between phylogenetics and paleontology.

scholarly journals On the Number of Ancestors to a DNA Sequence

Genetics ◽  
1997 ◽  
Vol 147 (3) ◽  
pp. 1459-1468 ◽  
Author(s):  
Carsten Wiuf ◽  
Jotun Hein
Keyword(s):  
Population Size ◽  
Dna Sequence ◽  
Ancestral Sequence ◽  
Ancestral Population ◽  
Homologous Sequences ◽  
Actual Size

If homologous sequences in a population are not subject to recombination, they can all be traced back to one ancestral sequence. However, the rest of our genome is subject to recombination and will be spread out on a series of individuals. The distribution of ancestral material to an extant chromosome is here investigated by the coalescent with recombination, and the results are discussed relative to humans. In an ancestral population of actual size 1.3 million a minority of <6.4% will carry material ancestral to any present human. The estimated actual population size can be even higher, 5 million, reducing the percentage to 1.7%.

scholarly journals Stochastic Models for a Chemostat and Long-Time Behavior

2013 ◽  
Vol 45 (03) ◽  
pp. 822-836 ◽  
Author(s):  
Pierre Collet ◽  
Servet Martínez ◽  
Sylvie Méléard ◽  
Jaime San Martín
Keyword(s):  
Population Size ◽  
Nutrient Concentration ◽  
Bacterial Population ◽  
Fixed Number ◽  
Death Process ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Nutrient Distribution ◽  
Long Time ◽  
Number Of Individuals

We introduce two stochastic chemostat models consisting of a coupled population-nutrient process reflecting the interaction between the nutrient and the bacteria in the chemostat with finite volume. The nutrient concentration evolves continuously but depends on the population size, while the population size is a birth-and-death process with coefficients depending on time through the nutrient concentration. The nutrient is shared by the bacteria and creates a regulation of the bacterial population size. The latter and the fluctuations due to the random births and deaths of individuals make the population go almost surely to extinction. Therefore, we are interested in the long-time behavior of the bacterial population conditioned to nonextinction. We prove the global existence of the process and its almost-sure extinction. The existence of quasistationary distributions is obtained based on a general fixed-point argument. Moreover, we prove the absolute continuity of the nutrient distribution when conditioned to a fixed number of individuals and the smoothness of the corresponding densities.

scholarly journals Nuclear pseudogenes of mtDNA (NUMTS) suggest repeated distant inter-species hybridization among direct human ancestors

2017 ◽  
Author(s):  
Konstantin Gunbin ◽  
Konstantin Popadin ◽  
Leonid Peshkin ◽  
Sofia Annis ◽  
Zoe Fleischmann ◽  
...  
Keyword(s):  
Mitochondrial Genome ◽  
Population Size ◽  
Genetic Exchange ◽  
Ancestral Population ◽  
Functional Genes ◽  
Human Lineage ◽  
Present Evidence ◽  
Znf230 Gene ◽  
Species Hybridization ◽  
Human Chromosome 5

Introduction: Increasingly, the emergence and evolution of our species is being tied to genetic exchange between divergent lineages within ~1Ma (e.g., Neanderthals, Denisovans). However, little is known about genetic exchange during earlier (pre-1Ma) human evolution and between more divergent lineages. Results: We present evidence of hybridization within human lineage, show that it likely happened between highly divergent (~4.5My) lineages, more than once. We use analysis of nuclear pseudogenes of mtDNA (“NUMTs”). NUMTs are considered “mtDNA fossils”, as they preserve sequences of ancient mtDNA because mutational rate in the nucleus is much lower than in mtDNA. We demonstrate that a NUMT on human chromosome 5, which is shared by chimpanzee and gorilla, had descended from a mitochondrial genome that had been divergent from our ancestor’s mtDNA by ~4.5% at the time of pseudogene insertion. This implies that this pseudogene should have been inserted in a hominid that at that time had been diverged by about 4.5My of evolution from the hominid that at that time carried our mtDNA lineage. In order for this pseudogene and our mtDNA to end up in the same body, these two hominids should have mated with each other. The large divergence implies a distant interspecies (or even inter-generic) hybridization. Additionally, analysis of two other NUMTs (on Chr11 and Chr7) suggests that hybridization events occurred repeatedly. To exclude the large ancestral population size effect we show that mtDNA divergence in extant ape populations does not depend on population size. Discussion: It is thought that within mammals, it takes ~2-4My to establish reproductive isolation. However, fertile inter-generic hybrids have been documented among several primates, separated by ca. 4My. Very recently, hybridization between Colobine genera separated by ~5 My was reported to involve a NUMT scenario similar to what we had proposed human ancestors. Interestingly, phylogenic analysis consistently places the chr5 NUMT insertion around the time of the Homo/Pan split. Intriguingly, certain hominin fossils of that epoch have been interpreted alternately as more human-like or more ape-like. Such morphological mosaicisity could potentially be explained by hybridization. Fixation of NUMTs in question within population should have been rather efficient, since these pseudogenes appear to have been fixed in more than one population. Thus their spread across populations might have been driven by selection. Indeed, NUMTs on chr5 and chr11 are located in 3’ regions of functional genes. Most intriguingly, Ps11 is located 3’ to the RNF141/ZNF230 gene, essential for spermatogenesis. NUMT might have served as an expression modifier for RNF141, resulting in reproductive advantage. Indeed, RNF141 demonstrates selectively driven expression shift in testis of the ancestor of hominines.

Extinction times for a general birth, death and catastrophe process

2004 ◽  
Vol 41 (4) ◽  
pp. 1211-1218 ◽  
Author(s):  
Ben Cairns ◽  
P. K. Pollett
Keyword(s):  
Population Size ◽  
Rate Coefficients ◽  
Death Process ◽  
Transition Rates ◽  
Linear Rate ◽  
Expected Time ◽  
Current Population ◽  
Time To Extinction ◽  
Limited Class ◽  
Birth Death

The birth, death and catastrophe process is an extension of the birth–death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.

scholarly journals On the estimation of ancestral population sizes of modern humans

1997 ◽  
Vol 69 (2) ◽  
pp. 111-116 ◽  
Author(s):  
ZIHENG YANG
Keyword(s):  
Population Size ◽  
Sequence Data ◽  
Divergence Time ◽  
Ancestral Population ◽  
Rate Variation ◽  
Effective Population ◽  
Modern Humans ◽  
Extant Species ◽  
Population Sizes ◽  
Highly Correlated

The theory developed by Takahata and colleagues for estimating the effective population size of ancestral species using homologous sequences from closely related extant species was extended to take account of variation of evolutionary rates among loci. Nuclear sequence data related to the evolution of modern humans were reanalysed and computer simulations were performed to examine the effect of rate variation on estimation of ancestral population sizes. It is found that the among-locus rate variation does not have a significant effect on estimation of the current population size when sequences from multiple loci are sampled from the same species, but does have a significant effect on estimation of the ancestral population size using sequences from different species. The effects of ancestral population size, species divergence time and among-locus rate variation are found to be highly correlated, and to achieve reliable estimates of the ancestral population size, effects of the other two factors should be estimated independently.

The extinction time of a birth, death and catastrophe process and of a related diffusion model

1985 ◽  
Vol 17 (01) ◽  
pp. 42-52 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Population Size ◽  
Diffusion Processes ◽  
Death Process ◽  
Arbitrary Distribution ◽  
Initial Population ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Expected Time ◽  
Time To Extinction ◽  
Initial Population Size

The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined. The catastrophes occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·). The asymptotic behaviour (for large initial population size) of the expected time to extinction is found under the assumption that d(.) has radius of convergence greater than 1. Corresponding results are derived for a related class of diffusion processes interrupted by catastrophes with sizes having an arbitrary distribution function.

scholarly journals Stochastic Models for a Chemostat and Long-Time Behavior

2013 ◽  
Vol 45 (3) ◽  
pp. 822-836 ◽  
Author(s):  
Pierre Collet ◽  
Servet Martínez ◽  
Sylvie Méléard ◽  
Jaime San Martín
Keyword(s):  
Population Size ◽  
Nutrient Concentration ◽  
Bacterial Population ◽  
Fixed Number ◽  
Death Process ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Nutrient Distribution ◽  
Long Time ◽  
Number Of Individuals

We introduce two stochastic chemostat models consisting of a coupled population-nutrient process reflecting the interaction between the nutrient and the bacteria in the chemostat with finite volume. The nutrient concentration evolves continuously but depends on the population size, while the population size is a birth-and-death process with coefficients depending on time through the nutrient concentration. The nutrient is shared by the bacteria and creates a regulation of the bacterial population size. The latter and the fluctuations due to the random births and deaths of individuals make the population go almost surely to extinction. Therefore, we are interested in the long-time behavior of the bacterial population conditioned to nonextinction. We prove the global existence of the process and its almost-sure extinction. The existence of quasistationary distributions is obtained based on a general fixed-point argument. Moreover, we prove the absolute continuity of the nutrient distribution when conditioned to a fixed number of individuals and the smoothness of the corresponding densities.

scholarly journals Ghosts of a Structured Past: Impacts of Ancestral Patterns of Isolation-by-Distance on Divergence-Time Estimation

2020 ◽  
Vol 111 (6) ◽  
pp. 573-582
Author(s):  
Zachary B Hancock ◽  
Heath Blackmon
Keyword(s):  
Population Size ◽  
Isolation By Distance ◽  
Divergence Time ◽  
Time Estimation ◽  
Ancestral Population ◽  
Recent Common Ancestor ◽  
Divergence Times ◽  
Population Divergence ◽  
Divergence Time Estimation ◽  
Coalescent Time

Abstract Isolation-by-distance is a widespread pattern in nature that describes the reduction of genetic correlation between subpopulations with increased geographic distance. In the population ancestral to modern sister species, this pattern may hypothetically inflate population divergence time estimation due to allele frequency differences in subpopulations at the ends of the ancestral population. In this study, we analyze the relationship between the time to the most recent common ancestor and the population divergence time when the ancestral population model is a linear stepping-stone. Using coalescent simulations, we compare the coalescent time to the population divergence time for various ratios of the divergence time over the population size. Next, we simulate whole genomes to obtain single nucleotide polymorphisms (SNPs), and use the Bayesian coalescent program SNAPP to estimate divergence times. We find that as the rate of migration between neighboring demes decreases, the coalescent time becomes significantly greater than the population divergence time when sampled from end demes. Divergence-time overestimation in SNAPP becomes severe when the divergence-to-population size ratio < 10 and migration is low. Finally, we demonstrate the impact of ancestral isolation-by-distance on divergence-time estimation using an empirical dataset of squamates (Tropidurus) endemic to Brazil. We conclude that studies estimating divergence times should be cognizant of the potential ancestral population structure in an explicitly spatial context or risk dramatically overestimating the timing of population splits.

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