Estimating ancestral distributions of lineages with uncertain sister groups： a statistical approach to Dispersal-Vicariance Analysis and a case using Aesculus L. （Sapindaceae） including fossils

We propose a simple statistical approach for using Dispersal-Vicariance Analysis （DIVA） software to infer biogeographic histories without fully bifurcating trees. In this approach, ancestral ranges are first optimized for a sample of Bayesian trees. The probability P of an ancestral range r at a node is then calculated as P（rY） = ∑t^n=1 F（rY）t Pt where Y is a node, and F（rY） is the frequency of range r among all the optimal solutions resulting from DIVA optimization at node Y, t is one of n topologies optimized, and Pt is the probability of topology t. Node Y is a hypothesized ancestor shared by a specific crown lineage and the sister of that lineage ＂x＂, where x may vary due to phylogenetic uncertainty （polytomies and nodes with posterior probability 〈 100%）. Using this method, the ancestral distribution at Y can be estimated to provide inference of the geographic origins of the specific crown group of interest. This approach takes into account phylogenetic uncertainty as well as uncertainty from DIVA optimization. It is an extension of the previously described method called Bayes-DIVA, which pairs Bayesian phylogenetic analysis with biogeographic analysis using DIVA. Further, we show that the probability P of an ancestral range at Y calculated using this method does not equate to pp＊F（rY） on the Bayesian consensus tree when both variables are 〈 100%, where pp is the posterior probability and F（rY） is the frequency of range r for the node containing the specific crown group. We tested our DIVA-Bayes approach using Aesculus L., which has major lineages unresolved as a polytomy. We inferred the most probable geographic origins of the five traditional sections of Aesculus and ofAesculus californica Nutt. and examined range subdivisions at parental nodes of these lineages. Additionally, we used the DIVA-Bayes data from Aesculus to quantify the effects on biogeographic inference of including two wildcard fossil taxa in phylogenetic analysis. Our analysis resolved the geographic     

INFERRING THE RATES OF BRANCHING AND EXTINCTION FROM MOLECULAR PHYLOGENIES

Molecular techniques provide ancestral phylogenies of extant taxa with estimated branching times. Here we studied the pattern of ancestral phylogeny of extant taxa produced by branching (or cladogenesis) and extinction of taxa, assuming branching processes with time-dependent rates. (1) If the branching rate b and extinction rate c are constant, the semilog plot of the number of ancestral lineages over time is not a straight line but is curvilinear, with increasing slope toward the end, implying that ancestral phylogeny shows apparent increase in the branching rate near the present. The estimate of b and c based on nonlinear fitting is examined by computer simulation. The estimate of branching rate can be usable for a large phylogeny if b is greater than c, but the estimate of extinction rate c is unreliable because of large bias and variance. (2) Gradual decrease in the slope of the semilog plot of the number of ancestral lineages over time, as was observed in a phylogeny of bird families based on DNA hybridization data, can be explained equally well by either the decreasing branching rate or the increasing extinction rate. Infinitely many pairs of branching and extinction rates as functions of time can produce the same ancestral phylogeny. (3) An explosive branching event in the past would appear as a quick increase in the number of ancestral lineages. In contrast, mass extinction occurring in a brief period, if not accompanied by an increase in branching rate, does not produce any rapid change in the number of ancestral lineages at the time. (4) The condition in which the number of ancestral lineages of extant species changes in parallel with the actual number of species in the past is derived.     

Investigating age‐dependency of species extinction rates using dynamic survivorship analysis

Survivorship curves with taxon lifespans normalised to variations in the real‐time extinction rate (the ‘Corrected Survivorship Score’ technique) are plotted for various fossil groups. Of five groups tested at the ‘species level’ (strictly speaking, Linnean morphospecies), only the calcareous nannoplankton are found to have had a constant extinction probability with respect to morphospecies age. The planktonic foraminifer, trilobite, conodont and graptolite data all show a significant age‐dependent effect (convexity of survivorship curves), which reveals in each case a progressively increasing extinction probability as morphospecies became older. This effect is found to be much reduced for trilobite genera and absent for ammonoid families, suggesting that age‐dependency of extinction probability is primarily a characteristic of the species level in some, but not all groups. However, the pattern may be partly an artefact of taxonomic methodology. Morphospecies range data, which are gathered primarily for biostratigraphic purposes, are far from ideal for the purpose of survivorship analysis. Therefore, survivorship curves for a specially‐developed lineage phylogeny of Palaeogene planktonic foraminifera are also presented. These do not indicate a similar age‐dependency to the extinction probability with respect to either the terminal or non‐terminal lineages.     

The probability of preservation of a newly arisen gene duplicate.

Newly emerging data from genome sequencing projects suggest that gene duplication, often accompanied by genetic map changes, is a common and ongoing feature of all genomes. This raises the possibility that differential expansion/contraction of various genomic sequences may be just as important a mechanism of phenotypic evolution as changes at the nucleotide level. However, the population-genetic mechanisms responsible for the success vs. failure of newly arisen gene duplicates are poorly understood. We examine the influence of various aspects of gene structure, mutation rates, degree of linkage, and population size (N) on the joint fate of a newly arisen duplicate gene and its ancestral locus. Unless there is active selection against duplicate genes, the probability of permanent establishment of such genes is usually no less than 1/(4N) (half of the neutral expectation), and it can be orders of magnitude greater if neofunctionalizing mutations are common. The probability of a map change (reassignment of a key function of an ancestral locus to a new chromosomal location) induced by a newly arisen duplicate is also generally >1/(4N) for unlinked duplicates, suggesting that recurrent gene duplication and alternative silencing may be a common mechanism for generating microchromosomal rearrangements responsible for postreproductive isolating barriers among species. Relative to subfunctionalization, neofunctionalization is expected to become a progressively more important mechanism of duplicate-gene preservation in populations with increasing size. However, even in large populations, the probability of neofunctionalization scales only with the square of the selective advantage. Tight linkage also influences the probability of duplicate-gene preservation, increasing the probability of subfunctionalization but decreasing the probability of neofunctionalization.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.      

Conditional ancestral times and related properties of an extant mutant at a locus A given the number of segregating sites observed at a linked locus B

 It is shown how the mean ancestral times at one locus are affected in a two- locus model with recombination when information is given regarding the number of segregating sites at another locus. For samples of n genes, recursive equations are derived that describe precisely the evolution of the time-depth of such a linked genealogy. Exact numerical solutions and Markov chain Monte Carlo simulations are discussed and compared. The dependence of some properties of a singleton mutation on waiting times between events in the two-locus genealogy is quantified and illustrates the effect of recombination on these properties. The following cases are presented: (1) the distribution of the number of mutant genes in a sample arising from a singleton mutation; (2) the probability that an allele observed in a genes of a sample of size n is the ancestral type (the oldest); (3) the expectation and variance of the age of a mutant having b copies in a sample of n genes. Received: 1 September 2000 / Revised version: 1 October 2001 / Published online: 8 May 2002     

Temporal dynamics and nestedness of an oceanic island bird fauna

Aim To examine temporal variation in nestedness and whether nestedness patterns predict colonization, extinction and turnover across islands and species. Location Dahlak Archipelago, Red Sea. Method The distributions of land birds on 17 islands were recorded in two periods 30 years apart. Species and islands were reordered in the Nestedness Temperature Calculator, software for assessing degrees of nestedness in communities. The occupancy probability of each cell, i.e. species–island combinations, was calculated in the nested matrix and an extinction curve (boundary line) was specified. We tested whether historical and current nested ranks of species and islands were correlated, whether there was a relationship between occupancy probability (based on the historical data) and number of extinctions or colonizations (regression analyses) and whether the boundary line could predict extinctions and colonizations (chi‐square analyses). Results Historical and current nested ranks of islands and species were correlated but changes in occupancy patterns were common, particularly among bird species with intermediate incidence. Extinction and turnover of species were higher for small than large islands, and colonization was negatively related to isolation. As expected, colonizations were more frequent above than below the boundary line. Probability of extinction was highest at intermediate occupancy probability, giving a quadratic relationship between extinction and occupancy probability. Species turnover was related to the historical nested ranks of islands. Colonization was related negatively while extinction and occupancy turnover were related quadratically to historical nested ranks of species. Main conclusions Some patterns of the temporal dynamics agreed with expectations from nested patterns. However, the accuracy of the predictions may be confounded by regional dynamics and distributions of idiosyncratic, resource‐limited species. It is therefore necessary to combine nestedness analysis with adequate knowledge of the causal factors and ecology of targeted species to gain insight into the temporal dynamics of assemblages and for nestedness analyses to be helpful in conservation planning.     

Minimisation of extinction probabilities in reproducing populations

In an attempt to explain variability in clutch size among laying birds of the same species, models are considered in which birds have to choose a randomised strategy for clutch size in the face of random environments in order to minimise a probability of extinction. Three models emerge, depending upon whether this is the probability of extinction of the whole species or that of an individual line of descent, and whether change of strategy from one generation to the next is allowed. In two of these models an asymptotically optimal strategy, which typically is randomised, is predicted for large populations.     

Ancestral Processes with Selection

In this paper, we show how to construct the genealogy of a sample of genes for a large class of models with selection and mutation. Each gene corresponds to a single locus at which there is no recombination. The genealogy of the sample is embedded in a graph which we call theancestral selection graph. This graph contains all the information about the ancestry; it is the analogue of Kingman's coalescent process which arises in the case with no selection. The ancestral selection graph can be easily simulated and we outline an algorithm for simulating samples. The main goal is to analyze the ancestral selection graph and to compare it to Kingman's coalescent process. In the case of no mutation, we find that the distribution of the time to the most recent common ancestor does not depend on the selection coefficient and hence is the same as in the neutral case. When the mutation rate is positive, we give a procedure for computing the probability that two individuals in a sample are identical by descent and the Laplace transform of the time to the most recent common ancestor of a sample of two individuals; we evaluate the first two terms of their respective power series in terms of the selection coefficient. The probability of identity by descent depends on both the selection coefficient and the mutation rate and is different from the analogous expression in the neutral case. The Laplace transform does not have a linear correction term in the selection coefficient. We also provide a recursion formula that can be used to approximate the probability of a given sample by simulating backwards along the sample paths of the ancestral selection graph, a technique developed by Griffiths and Tavaré (1994).     

The distribution of the ancestral haplotype in finite stepping-stone models with population expansion

Recent extensive analyses of human DNA polymorphism reveal that the ancestral haplotype at various genetic loci occurs almost exclusively in African samples. We develop a coalescence-based simulation method in stepping-stone models with population expansion and examine the probability (P(A)) that the ancestral haplotype is found in African samples and the probability (Q(A)) that the most recent common ancestor of sampled genes occurs in Africa. These probabilities and other summary statistics are used to infer the human demographic history. It is shown that the high observed P(A) value cannot be explained simply by sampling bias. Rather, it suggests that the African population has been more strongly subdivided and isolated from each other than the non-African population and that there must have been some African populations which were not directly involved in the Out-of-Africa expansion in the late Pleistocene.     

Cladogenesis, coalescence and the evolution of the three domains of life

In this article, we explore the large-scale structure of the tree of life by using a simple model with a constant number of species and rates of speciation that equal the rates of extinction. In addition, we discuss the consequences of horizontal gene transfer for the concept of a most recent common ancestor of all living organisms (cenancestor). A simple null hypothesis based on coalescence theory explains some features of the observed topologies of the tree of life. Simulations of genes and organismal lineages suggest that there was no single common ancestor that contained all the genes ancestral to those shared among the three domains of life. Each contemporary molecule has its own history that traces back to an individual molecular cenancestor. However, these molecular ancestors were likely to be present in different organisms and at different times.     

Gene extinction and allelic origins in complex genealogies

With the increasing emphasis on data analysis in mathematical genetics, problems of parametrizing genealogical structure become of practical importance. A complete specification of the genetic effects of genealogical structure is provided by the probabilities of genetically distinct states of gene identity by descent. Although this provides a direct parametrization for the joint distribution of traits on a set of related individuals, it is an unwieldy tool in the analysis of large and complex genealogies. Probabilities of joint descent of founder genes and likely ancestries of alleles provide alternative characterizations of relationship and have direct application in practical problems. Joint extinction probabilities of founder genes can also be derived as ancestral likelihoods: evolutionarily, the most significant characteristic of a genealogical structure must be its effect on the survival and extinction of genes.     

Complete nucleotide and encoded amino acid sequence of a mammalian myosin heavy chain gene. Evidence against intron-dependent evolution of the rod

The complete nucleotide sequence and exon/intron structure of the rat embryonic skeletal muscle myosin heavy chain (MHC) gene has been determined. This gene comprises 24 X 10(3) bases of DNA and is split into 41 exons. The exons encode a 6035 nucleotide (nt) long mRNA consisting of 90 nt of 5' untranslated, 5820 nt of protein coding and 125 nt of 3' untranslated sequence. The rat embryonic MHC polypeptide is encoded by exons 3 to 41 and contains 1939 amino acid residues with a calculated Mr of 223,900. Its amino acid sequence displays the structural features typical for all sarcomeric MHCs, i.e. an amino-terminal "globular" head region and a carboxy-terminal alpha-helical rod portion that shows the characteristics of a coiled coil with a superimposed 28-residue repeat pattern interrupted at only four positions by "skip" residues. The complex structure of the rat embryonic MHC gene and the conservation of intron locations in this and other MHC genes are indicative of a highly split ancestral sarcomeric MHC gene. Introns in the rat embryonic gene interrupt the coding sequence at the boundaries separating the proteolytic subfragments of the head, but not at the head/rod junction or between the 28-residue repeats present within the rod. Therefore, there is little evidence for exon shuffling and intron-dependent evolution by gene duplication as a mechanism for the generation of the ancestral MHC gene. Rather, intron insertion into a previously non-split ancestral MHC rod gene consisting of multiple tandemly arranged 28-residue-encoding repeats, or convergent evolution of an originally non-repetitive ancestral MHC rod gene must account for the observed structure of the rod-encoding portion of present-day MHC genes.     

Estimates of natural selection due to protein tertiary structure inform the ancestry of biallelic loci

We consider the inference of which of two alleles is ancestral when the alleles have a single nonsynonymous difference and when natural selection acts via protein tertiary structure. Whereas the probability that an allele is ancestral under neutrality is equal to its frequency, under selection this probability depends on allele frequency and on the magnitude and direction of selection pressure. Although allele frequencies can be well estimated from intraspecific data, small fitness differences have a large evolutionary impact but can be difficult to estimate with only intraspecific data. Methods for predicting aspects of phenotype from genotype can supplement intraspecific sequence data. Recently developed statistical techniques can assess effects of phenotypes, such as protein tertiary structure on molecular evolution. While these techniques were initially designed for comparing protein-coding genes from different species, the resulting interspecific inferences can be assigned population genetic interpretations to assess the effect of selection pressure, and we use them here along with intraspecific allele frequency data to estimate the probability that an allele is ancestral. We focus on 140 nonsynonymous single nucleotide polymorphisms of humans that are in proteins with known tertiary structures. We find that our technique for employing protein tertiary structure information yields some biologically plausible results but that it does not substantially improve the inference of ancestral human allele types.     

Genetic sex determination and extinction

Genetic factors can affect the probability of extinction either by increasing the effect of detrimental variants or by decreasing the potential for future adaptive responses. In a recent paper, Zayed and Packer demonstrate that low variation at a specific locus, the complementary sex determination (csd) locus in Hymenoptera (ants, bees and wasps), can result in a sharply increased probability of extinction. Their findings illustrate situations in which there is a feedback process between decreased genetic variation at the csd locus owing to genetic drift and decreased population growth, resulting in an extreme type of extinction vortex for these ecologically important organisms.     

Extinction time and age of an allele in a large finite population

For a single locus with two alleles we study the expected extinction and fixation times of the alleles under the influence of selection and genetic drift. Using a diffusion model we derive asymptotic approximations for these expected exit times for large populations. We consider the case where the fitness of the heterozygote is in between the fitnesses of the homozygotes (incomplete dominance). The asymptotic analysis not only yields new quantitative results but also reveals interesting features that remain hidden in the exact solution. Some of the outcomes are extensions of results known in the literature. The asymptotic approximations also apply to the expected first arrival time of an allele at a specified frequency and to the expected age of an allele.     

On the survival probabilities of mutant genes and the evolution of dominance.

Intrinsic biological resemblance between two types is measured in terms of a correlation between their fitnesses under various possible environmental conditions. A tendency toward dominance is defined as the intrinsic biological resemblance between homozygote and heterozygote. The effect of a tendency toward dominance on the à priori survival probability of a mutant gene is studied when the fitnesses of the mutated forms are given only by their distributions. Close intrinsic resemblance between homozygous and heterozygous forms of a new mutant gene is shown to substantially increase the à priori survival probability of this gene. A probabilistic effect of selection is, thus, shown to statistically favor dominant or near dominant mutant genes to start with.This probabilistic effect is suggested as complementary to the Fisherian process of selection on the heterozygote modifiers, taking place at further stages of the progress of a mutant gene.     

Toward localization of the Werner syndrome gene by linkage disequilibrium and ancestral haplotyping: lessons learned from analysis of 35 chromosome 8p11.1-21.1 markers.

Werner syndrome (WS) is an autosomal recessive disorder characterized by premature onset of a number of age-related diseases. The gene for WS, WRN, has been mapped to the 8p 11.1-21.1 region with further localization through linkage disequilibrium mapping. Here we present the results of linkage disequilibrium and ancestral haplotype analyses of 35 markers to further refine the location of WRN. We identified an interval in this region in which 14 of 18 markers tested show significant evidence of linkage disequilibrium in at least one of the two populations tested. Analysis of extended and partial haplotypes covering 21 of the markers studied supports the existence of both obligate and probable ancestral recombinant events which localize WRN almost certainly to the interval between D8S2196 and D8S2186, and most likely to the narrower interval between D8S2168 and D8S2186. These haplotype analyses also suggest that there are multiple WRN mutations in each of the two populations under study. We also present a comparison of approaches to performing disequilibrium tests with multiallelic markers, and show that some commonly used approximations for such tests perform poorly in comparison to exact probability tests. Finally, we discuss some of the difficulties introduced by the high mutation rate at microsatellite markers which influence our ability to use ancestral haplotype analysis to localize disease genes.     

The ancestral graph and gene genealogy under frequency-dependent selection.

Minority-advantage frequency-dependent selection has been proposed as the cause for the high level of observed polymorphism in some self/nonself-recognition systems. We present a mathematically rigorous derivation of the ancestral graph for a sample of genes that evolved according to a haploid infinite-alleles model of minority-advantage frequency-dependent selection. In the case of sufficiently weak selection, the gene genealogy can be extracted from the ancestral graph. We demonstrate that the gene genealogy under this model is identical to that obtained for a diploid model with heterozygote advantage. The case of strong selection is exemplified by a one-locus haploid self-incompatibility system; in this context, we investigate the number of alleles that can be maintained in a spatial versus a non-spatial habitat. Finally, we compare gametophytic self-incompatibility to the haploid self-incompatibility model.     

Epidemiological modeling in a branching population. Particular case of a general SIS model with two age classes

This paper covers the elaboration of a general class of multitype branching processes for modeling in a branching population, the evolution of a disease with horizontal and vertical transmissions. When the size of the population may tend to infinity, normalization must be carried out. As the initial size tends to infinity, the normalized model converges a.s. to a dynamical system the solution of which is the probability law of the state of health for an individual ancestors line. The focal point of this study concerns the transient and asymptotical behaviors of a SIS model with two age classes in a branching population. We will compare the asymptotical probability of extinction on the scale of a finite population and on the scale of an individual in an infinite population: when the rates of transmission are small compared to the rate of renewing the population of susceptibles, the two models lead to a.s. extinction, giving consistent results, which no longer applies to the opposite situation of important transmissions. In that case the size of the population plays a crucial role in the spreading of the disease.