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.     

Parentage and sibship exclusions: higher statistical power with more family members

Parentage exclusion probabilities are now routinely calculated in genetic marker-assisted parentage analyses to indicate the statistical power of the analyses achievable for a given set of markers, and to measure the informativeness of a set of markers for parentage inference. Previous formulas invariably assume that parentage is to be sought for a single offspring, while in practice multiple full siblings might be sampled (for example, seeds, eggs or young from a pair of monogamous parents) and their father, mother or both are to be assigned among a number of candidates. In this study, I derive formulas for parentage exclusion probabilities for an arbitrary number (n) of fullsibs, which reduce to previous equations for the special case of n=1. I also derive sibship exclusion probabilities, and investigate the power of differentiating half-sib, avuncular and grandparent-grandoffspring relationships using unlinked autosomal markers among different numbers of tested individuals. Applications of the formulas are demonstrated using both theoretical and empirical data sets of allele frequencies. The results from the study highlight the conclusion that the power of genealogical relationship inferences can be enhanced enormously by analysing multiple individuals for a given set of markers. The equations derived in this study allow more accurate determination of marker information and of the power of a parentage/sibship analysis. In addition, they can be used to guide experimental designs of parentage analyses in selecting markers and determining the number of offspring to be sampled and genotyped.     

Functional morphology and phylogenetic testing within the framework of symecomorphosis

On the basis of the contrasting evolutionary patterns of the Teleostei and the "Chondrostei" the merit of phylogenetic testing is summarized as a non-arbitrary method for assessing the possible role of various designs in producing differential morphological diversity in different lineages. Arguments are presented for the recognition of a genealogical (reproductive, informational) and an ecological hierarchy. Various levels are proposed within hierarchies, because there are processes intrinsic to each level that are not reducible to those of lower levels or subsumed by higher levels. Mutual influences exist between successive levels within a hierarchy and possible interhierarchical mutual influences are hypothesized between organisms, demes, and avatars, and from the germ line to functional units. The term symecomorphosis is proposed to denote the balanced symmetry of the co-existing and mutually interdependent ecological and genealogical hierarchies. Symecomorphosis predicts that a disturbance in environmental systems can destroy this balance with profound effects on the genealogical hierarchy. Using the evolutionary differentiation of four lineages of air breathing teleosts as an example, it is demonstrated how the principle of symecomorphosis can be included in tests establishing a causal relationship between design and differential diversity among lineages.     

The politics of genealogical incorporation: ethnic difference,genetic relatedness and national belonging*

This paper explores the relationship between genomic accounts of ethnic origins and distinctiveness and genealogical models of ethnic and national similarity and difference. It does so by focusing on genetic investigations of Irish Traveller origins in the context of ongoing campaigns for state recognition of Irish Travellers as an ethnic group, and in relation to the politics of national belonging. The ostensibly ethical practice of liberal genomics is entangled with the fraught politics of the Irish state’s commitments to addressing ethnic minority rights, insistence on differentiating between Travellers and other ethnic groups on the basis of genealogical difference, and the genealogical incorporation of Travellers within the national community of shared descent. Though ideas of ancestral relatedness across social or cultural boundaries are often figured as politically progressive, locating groups within a national family tree on the basis of genealogical relatedness can simultaneously deny ethnic difference and naturalize exclusive models of nationhood.     

Genetic Divergence in Mandible Form in Relation to Molecular Divergence in Inbred Mouse Strains

Genetic divergence in the form of the mandible is examined in ten inbred strains of mice. Several univariate and multivariate genetic distance estimates are given for the morphological data and these estimates are compared to measures of genealogical and molecular divergence. Highly significant divergence occurs among the ten strains in all 11 mandible traits considered individually and simultaneously. Genealogical relationship among strains is highly correlated with genetic divergence in single locus molecular traits. However, the concordance between genealogical relationship and multivariate genetic divergence in morphology is much more complex. Whether there is a significant correlation between morphological divergence and genealogy depends upon the method of analysis and the particular genetic distance statistic being employed.     

Equilibrium Values of Measures of Population Subdivision for Stepwise Mutation Processes

Expected values of WRIGHT's F-statistics are functions of probabilities of identity in state. These values may be quite different under an infinite allele model and under stepwise mutation processes such as those occurring at microsatellite loci. However, a relationship between the probability of identity in state in stepwise mutation models and the distribution of coalescence times can be deduced from the relationship between probabilities of identity by descent and the distribution of coalescence times. The values of F(IS) and F(ST) can be computed using this property. Examination of the conditional probability of identity in state given some coalescence time and of the distribution of coalescence times are also useful for explaining the properties of F(IS) and F(ST) at high mutation rate loci, as shown here in an island model of population structure.     

Revisiting Robustness and Evolvability: Evolution in Weighted Genotype Spaces

Robustness and evolvability are highly intertwined properties of biological systems. The relationship between these properties determines how biological systems are able to withstand mutations and show variation in response to them. Computational studies have explored the relationship between these two properties using neutral networks of RNA sequences (genotype) and their secondary structures (phenotype) as a model system. However, these studies have assumed every mutation to a sequence to be equally likely; the differences in the likelihood of the occurrence of various mutations, and the consequence of probabilistic nature of the mutations in such a system have previously been ignored. Associating probabilities to mutations essentially results in the weighting of genotype space. We here perform a comparative analysis of weighted and unweighted neutral networks of RNA sequences, and subsequently explore the relationship between robustness and evolvability. We show that assuming an equal likelihood for all mutations (as in an unweighted network), underestimates robustness and overestimates evolvability of a system. In spite of discarding this assumption, we observe that a negative correlation between sequence (genotype) robustness and sequence evolvability persists, and also that structure (phenotype) robustness promotes structure evolvability, as observed in earlier studies using unweighted networks. We also study the effects of base composition bias on robustness and evolvability. Particularly, we explore the association between robustness and evolvability in a sequence space that is AU-rich – sequences with an AU content of 80% or higher, compared to a normal (unbiased) sequence space. We find that evolvability of both sequences and structures in an AU-rich space is lesser compared to the normal space, and robustness higher. We also observe that AU-rich populations evolving on neutral networks of phenotypes, can access less phenotypic variation compared to normal populations evolving on neutral networks.     

Stochasticity overrules the "three-times rule": genetic drift,genetic draft,and coalescence times for nuclear loci versus mitochondrial DNA

Abstract.— Palumbi et al. (2001) proposed a "three-times rule" that uses mitochondrial DNA (mtDNA) sequences to predict probabilities of monophyly for nuclear loci (i.e., whether the alleles within a taxon coalesce with one another before they coalesce with alleles from a sister taxon). They use neutral coalescent theory to infer these probabilities from the ratio of interspecific divergence to intraspecific variation of mtDNA. We show that the estimated probabilities have very wide confidence intervals because of the inherent stochasticity of the mtDNA coalescent process. Under neutrality, the true probability of monophyly can be much higher, or much lower, than predicted by the three-times rule. We also review recent empirical and theoretical studies that refute neutrality-based predictions concerning mtDNA variation and divergence. We conclude that the three-times rule is neither a useful test for neutral molecular evolution nor a reliable guide to genealogical species.     

Relationship type affects the reliability of dispersal distance estimated using pedigree inferences in partially sampled populations: A case study involving invasive American mink in Scotland

Estimating dispersal—a key parameter for population ecology and management—is notoriously difficult. The use of pedigree assignments, aided by likelihood‐based software, has become popular to estimate dispersal rate and distance. However, the partial sampling of populations may produce false assignments. Further, it is unknown how the accuracy of assignment is affected by the genealogical relationships of individuals and is reflected by software‐derived assignment probabilities. Inspired by a project managing invasive American mink (Neovison vison), we estimated individual dispersal distances using inferred pairwise relationships of culled individuals. Additionally, we simulated scenarios to investigate the accuracy of pairwise inferences. Estimates of dispersal distance varied greatly when derived from different inferred pairwise relationships, with mother–offspring relationship being the shortest (average = 21 km) and the most accurate. Pairs assigned as maternal half‐siblings were inaccurate, with 64%–97% falsely assigned, implying that estimates for these relationships in the wild population were unreliable. The false assignment rate was unrelated to the software‐derived assignment probabilities at high dispersal rates. Assignments were more accurate when the inferred parents were older and immigrants and when dispersal rates between subpopulations were low (1% and 2%). Using 30 instead of 15 loci increased pairwise reliability, but half‐sibling assignments were still inaccurate (>59% falsely assigned). The most reliable approach when using inferred pairwise relationships in polygamous species would be not to use half‐sibling relationship types. Our simulation approach provides guidance for the application of pedigree inferences under partial sampling and is applicable to other systems where pedigree assignments are used for ecological inference.     

The identity by descent process along the chromosome

The probabilities of the various possible identity by descent (IBD) states at a locus captures all the genealogical information for that locus for the set of individuals under consideration. Here we study the stochastic process of the IBD state as one moves across the genome of a set of individuals. In general it is no longer sufficient to specify the IBD state, one needs to increase the state space if one is to maintain the Markov property, as has been discussed by for instance McPeak and Sun [Am J Hum Genet 2000;66:1076-1094] and Browning and Browning [Theor Popul Biol 2002;62:1-8]. This paper discusses a general method of deriving the transition matrix for that Markov chain iteratively from one time point to a subsequent one. This method allows a considerable reduction in the size of the state space needed. The basic recursion is set out here and the application is illustrated by two specific examples.     

On the probabilities of identity states in permutable populations.

Génin and Clerget-Darpoux recently discussed the derivation of the probabilities of identity states for populations in which there was some degree of kinship, primarily to allow the extension of the classical affected-sib-pair method to such populations. It is argued here that their derivation makes certain assumptions that are valid only for some very restricted population models and that are not needed for an appropriate treatment. Here the probabilities of the identity states of two individuals with a given genealogical relationship are specified in terms of the kinship parameters of the underlying population, from which the founders of the individuals'' genealogy have been randomly selected. It is argued that an appropriate representation for a permutable population, one in which gene identity does not depend on the pattern of genes across individuals, requires three parameters. This representation is related to that of Génin and Clerget-Darpoux and to that of Weir.     

Genome-Wide Estimates of Coancestry and Inbreeding in a Closed Herd of Ancient Iberian Pigs

Maintaining genetic variation and controlling the increase in inbreeding are crucial requirements in animal conservation programs. The most widely accepted strategy for achieving these objectives is to maximize the effective population size by minimizing the global coancestry obtained from a particular pedigree. However, for most natural or captive populations genealogical information is absent. In this situation, microsatellites have been traditionally the markers of choice to characterize genetic variation, and several estimators of genealogical coefficients have been developed using marker data, with unsatisfactory results. The development of high-throughput genotyping techniques states the necessity of reviewing the paradigm that genealogical coancestry is the best parameter for measuring genetic diversity. In this study, the Illumina PorcineSNP60 BeadChip was used to obtain genome-wide estimates of rates of coancestry and inbreeding and effective population size for an ancient strain of Iberian pigs that is now in serious danger of extinction and for which very accurate genealogical information is available (the Guadyerbas strain). Genome-wide estimates were compared with those obtained from microsatellite and from pedigree data. Estimates of coancestry and inbreeding computed from the SNP chip were strongly correlated with genealogical estimates and these correlations were substantially higher than those between microsatellite and genealogical coefficients. Also, molecular coancestry computed from SNP information was a better predictor of genealogical coancestry than coancestry computed from microsatellites. Rates of change in coancestry and inbreeding and effective population size estimated from molecular data were very similar to those estimated from genealogical data. However, estimates of effective population size obtained from changes in coancestry or inbreeding differed. Our results indicate that genome-wide information represents a useful alternative to genealogical information for measuring and maintaining genetic diversity.     

Entropy and information in evolving biological systems

Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state to another in a manner that generates structures which allows the system to continue to persist. Two classes of energetic transformations allow this; heat-generating transformations, resulting in a net loss of energy from the system, and conservative transformations, changing unusable energy into states that can be stored and used subsequently. All conservative transformations in biological systems are coupled with heat-generating transformations; hence, inherent biological production, or genealogical proesses, is positively entropic. There is a self-organizing phenomenology common to genealogical phenomena, which imparts an arrow of time to biological systems. Natural selection, which by itself is time-reversible, contributes to the organization of the self-organized genealogical trajectories. The interplay of genealogical (diversity-promoting) and selective (diversity-limiting) processes produces biological order to which the primary contribution is genealogical history. Dynamic changes occuring on times scales shorter than speciation rates are microevolutionary; those occuring on time scales longer than speciation rates are macroevolutionary. Macroevolutionary processes are neither redicible to, nor autonomous from, microevolutionary processes.Authorship alphabetical     

ARE GREENBEARDS INTRAGENOMIC OUTLAWS?

Greenbeard genes identify copies of themselves in other individuals and cause their bearer to behave nepotistically toward those individuals. Hence, they can be favored by kin selection, irrespective of the degree of genealogical relationship between social partners. Although greenbeards were initially developed as a thought experiment, a number of recent discoveries of greenbeard alleles in real populations have led to a resurgence of interest in their evolutionary dynamics and consequences. One issue over which there has been disagreement is whether greenbeards lead to intragenomic conflict. Here, to clarify the "outlaw" status of greenbeards, we develop population genetic models that formally examine selection of greenbeard phenotypes under the control of different loci. We find that, in many cases, greenbeards are not outlaws because selection for or against the greenbeard phenotype is the same across all loci. In contrast, when social interactions are between genealogical kin, we find that greenbeards can be outlaws because different genes can be selected in different directions. Hence, the outlaw status of greenbeard genes crucially depends upon the particular biological details. We also clarify whether greenbeards are favored due to direct or indirect fitness effects and address the relationship of the greenbeard effect to sexual antagonism and reciprocity.     

Estimation of population divergence times from non-overlapping genomic sequences: examples from dogs and wolves

Despite recent technological advances in DNA sequencing, incomplete coverage remains to be an issue in population genomics, in particular for studies that include ancient samples. Here, we describe an approach to estimate population divergence times for non-overlapping sequence data that is based on probabilities of different genealogical topologies under a structured coalescent model. We show that the approach can be adapted to accommodate common problems such as sequencing errors and postmortem nucleotide misincorporations, and we use simulations to investigate biases involved with estimating genealogical topologies from empirical data. The approach relies on three reference genomes and should be particularly useful for future analysis of genomic data that comprise of nonoverlapping sets of sequences, potentially from different points in time. We applied the method to shotgun sequence data from an ancient wolf together with extant dogs and wolves and found striking resemblance to previously described fine-scale population structure among dog breeds. When comparing modern dogs to four geographically distinct wolves, we find that the divergence time between dogs and an Indian wolf is smallest, followed by the divergence times to a Chinese wolf and a Spanish wolf, and a relatively long divergence time to an Alaskan wolf, suggesting that the origin of modern dogs is somewhere in Eurasia, potentially southern Asia. We find that less than two-thirds of all loci in the boxer and poodle genomes are more similar to each other than to a modern gray wolf and that--assuming complete isolation without gene flow--the divergence time between gray wolves and modern European dogs extends to 3,500 generations before the present, corresponding to approximately 10,000 years ago (95% confidence interval [CI]: 9,000-13,000). We explicitly study the effect of gene flow between dogs and wolves on our estimates and show that a low rate of gene flow is compatible with an even earlier domestication date ～30,000 years ago (95% CI: 15,000-90,000). This observation is in agreement with recent archaeological findings and indicates that human behavior necessary for domestication of wild animals could have appeared much earlier than the development of agriculture.     

The shapes of neutral gene genealogies in two species: probabilities of monophyly,paraphyly, and polyphyly in a coalescent model

Abstract.— The genealogies of samples of orthologous regions from multiple species can be classified by their shapes. Using a neutral coalescent model of two species, I give exact probabilities of each of four possible genealogical shapes: reciprocal monophyly, two types of paraphyly, and polyphyly. After the divergence that forms two species, each of which has population size N , polyphyly is the most likely genealogical shape for the lineages of the two species. At ∼ 1.300 N generations after divergence, paraphyly becomes most likely, and reciprocal monophyly becomes most likely at ∼1.665 N generations. For a given species, the time at which 99% of its loci acquire monophyletic genealogies is ∼5.298 N generations, assuming all loci in its sister species are monophyletic. The probability that all lineages of two species are reciprocally monophyletic given that a sample from the two species has a reciprocally monophyletic genealogy increases rapidly with sample size, as does the probability that the most recent common ancestor (MRCA) for a sample is also the MRCA for all lineages from the two species. The results have potential applications for the testing of evolutionary hypotheses.     

A graphical approach to multi-locus match probability computation: revisiting the product rule

The genealogical relationships of individuals in a finite population can create statistical non-independence of alleles at unlinked loci. In this paper, we introduce a flexible graphical method for computing the probabilities that two individuals in a finite, randomly mating population have the same haplotype or genotype at several loci. This method allows us to generalize the analysis of Laurie and Weir [2003. Dependency effects in multi-locus match probabilities. Theor. Popul. Biol. 63, 207-219] to cases with more loci and other models of mating. We show that monogamy increases the probabilities of genotypic matches at unlinked loci and that the effect of monogamy increases with the number L of loci. We conjecture a sharp upper bound on the effect of monogamy for a given L.     

The Mutation Process in Colored Coalescent Theory

The mutation process is introduced into the colored coalescent theory. The mutation process can be viewed as an independent Poisson process running on the colored genealogical random tree generated by the colored coalescent process, with the edge lengths of the random tree serving as the time scale for the mutation process. Moving backward along the colored genealogical tree, the color of vertices may change in two ways, when two vertices coalesce, or when a mutation happens. The rule that governs the coalescent change of color involves a parameter x; the rule that governs the mutation involves a parameter μ. Explicit computations of the expectation of the coalescent time (the first hitting time), and the coalescent probabilities (the first hitting probabilities) are carried out. For example, our calculation shows that when x=1/2, for a sample of n colored individuals, the expected time for the colored coalescent process with the mutation process superimposed to first reach a black MRCA or a white MRCA, respectively, is 3−2/n with probability 1/2 for any value of the parameter μ. On the other hand, the expected time for the colored coalescent process with mutation to first reach a MRCA, either black or white, is 2−2/n for any values of the parameters μ and x, which is the same as that for the standard Kingman coalescent process.     

A general noninteractive multiple toxicity model including probit, logit, and Weibull transformations

A multiple toxicity model for the quantal response of organisms is constructed based on an existing bivariate theory. The main assumption is that the tolerances follow a multivariate normal distribution function. However, any monotone tolerance distribution can be applied by mapping the integration region in the n-dimensional space of transforms on the n-dimensional space of normal equivalent deviates. General requirements to noninteractive bivariate tolerance distributions are discussed, and it is shown that bivariate logit and Weibull distributions, constructed according to the mapping procedure, meet these criteria. The univariate Weibull dose-response model is given a novel interpretation in terms of reactions between toxicant molecules and a hypothetical key receptor of the organism. The application of the multiple toxicity model is demonstrated using literature data for the action of gamma-benzene hexachloride and pyrethrins on flour beetles (Tribolium castaneum). Nonnormal tolerance distributions are needed when the mortality data include extreme response probabilities.     

transition priors for protein hidden Markov models: an empirical study towards maximum discrimination.

Insertions and deletions in a profile hidden Markov model (HMM) are modeled by transition probabilities between insert, delete and match states. These are estimated by combining observed data and prior probabilities. The transition prior probabilities can be defined either ad hoc or by maximum likelihood (ML) estimation. We show that the choice of transition prior greatly affects the HMM's ability to discriminate between true and false hits. HMM discrimination was measured using the HMMER 2.2 package applied to 373 families from Pfam. We measured the discrimination between true members and noise sequences employing various ML transition priors and also systematically scanned the parameter space of ad hoc transition priors. Our results indicate that ML priors produce far from optimal discrimination, and we present an empirically derived prior that considerably decreases the number of misclassifications compared to ML. Most of the difference stems from the probabilities for exiting a delete state. The ML prior, which is unaware of noise sequences, estimates a delete-to-delete probability that is relatively high and does not penalize noise sequences enough for optimal discrimination.