Can the theory of evolution be falsified?

In this paper we discuss the epistemological positions of evolution theories. A sharp distinction is made between the theory that species evolved from common ancestors along specified lines of descent (here called the theory of common descent), and the theories intended as causal explanations of evolution (e.g. Lamarck's and Darwin's theory). The theory of common descent permits a large number of predictions of new results that would be improbable without evolution. For instance, (a) phylogenetic trees have been validated now; (b) the observed order in fossils of new species discovered since Darwin's time could be predicted from the theory of common descent; (c) owing to the theory of common descent, the degrees of similarity and difference in newly discovered properties of more or less related species could be predicted. Such observations can be regarded as attempts to falsify the theory of common descent. We conclude that the theory of common descent is an easily-falsifiable & often-tested & still-not-falsified theory, which is the strongest predicate a theory in an empirical science can obtain. Theories intended as causal explanations of evolution can be falsified essentially, and Lamarck's theory has been falsified actually. Several elements of Darwin's theory have been modified or falsified: new versions of a theory of evolution by natural selection are now the leading scientific theories on evolution. We have argued that the theory of common descent and Darwinism are ordinary, falsifiable scientific theories.     

Descent measures for two loci with some applications

For any four genes, two at each of two loci, in a population, a 15 component descent measure has been introduced. These components are the probabilities of the 15 possible arrangements on a set of initial gametes of those genes of which the four of interest are copies. Since identity by descent of genes is equivalent to their being copies of a single gene on an initial gamete, descent measures have inbreeding coefficients as special cases. The individual descent measure, defined for four genes on two uniting gametes can be evaluated for any pedigree by means of an algorithm developed here. If initial gametic frequencies are specified, descent measures allow genotypic frequencies and disequilibria functions at one and two loci to be found. The procedures are illustrated for selfing and for sib mating. Several applications of the descent measures are discussed.     

Estimation of effective population size and migration rate from one- and two-locus identity measures

Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.     

Investigating the Interactions of Yeast Prions: [SWI+], [PSI+], and [PIN+]

The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ∼16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed.     

Evolutionary games and two species population dynamics

Competition between species has long been modeled by population dynamics based on total numbers of each species. Recently, the evolution of strategy frequencies has been used successfully for competition models between individuals. In this paper, we illustrate that these two views of competition are compatible. It is shown that the rate of intra and interspecific competitions between individuals largely determines the population dynamics. Competition models over a single common resource and predator-prey models are developed from this individual competition approach. In particular, the equilibrium strategies in a co-evolving predator-prey system are shown to be more stable than the predicted strategy cycling of standard evolutionary game theory.     

Two-locus inbreeding measures for recurrent selection

Summary For a population undergoing recurrent selection, a method is presented for determining the average inbreeding coefficients at the end of each breeding cycle. The coefficients are derived in terms of probability measures that genes are identical by descent. For the one-locus case, two digametic measures are defined and employed in the derivation of a recurrence formula for the inbreeding coefficient. Two further classes of measures, trigametic and quadrigametic, are required for transition from one cycle to the previous one to allow the calculation of the inbreeding function for the two-locus case. Numerical values of the average probability of double identity by descent for populations with various imposed assumptions are listed to illustrate the effects of linkage and population size on the accrual of inbreeding and hence of homozygosity.Paper number 5018 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, North Carolina. This investigation was supported in part by NIH research grant number GM 11546 from the National Institute of General Medical Sciences.     

Linkage disequilibria in finite populations

Four-locus recombination frequencies are summarized into two-locus pair frequencies and three-locus frequencies, and further, into two-locus frequencies such that higher-order frequencies are linear functions of lower-order frequencies. Frequencies of gene combinations are defined according to their position on the same or distinct gametes, and linear functions of these provide the measures of linkage disequilibria. These concepts are utilized to derive the transitional behavior of the gene combinations frequencies and the linkage disequilibria in a finite monoecious population with random union of gametes for up to four loci. The transitions of lower-order disequilibria in a higher-order (more loci) setting involve the higher-order disequilibria which must be taken into account in arriving at the final (fixation) frequencies. The methods allow different initial conditions. Since corresponding data functions of the gene combination frequencies provide unbiased estimates of the parameters, estimators follow naturally.     

Current versus historical population sizes in vertebrate species with high gene flow: a comparison based on mitochondrial DNA lineages and inbreeding theory for neutral mutations

Using inbreeding theory as applied to neutral alleles inherited maternally, we generate expected probability distributions of times to identity by descent for random pairs of mitochondrial genotypes within a population or within an entire species characterized by high gene flow. For comparisons with these expectations, empirical distributions of times to most recent common ancestry were calculated (by conventional mtDNA clock calibrations) from mtDNA haplotype distances observed within each of three vertebrate species--American eels, hardhead catfish, and redwinged blackbirds. These species were chosen for analysis because census population size in each is currently large and because both genetic and life-history data are consistent with the postulate that historical gene flow within these species has been high. The observed molecular distances among mtDNA lineages were two to three orders of magnitude lower than predicted from census sizes of breeding females, suggesting that rate of mtDNA evolution is decelerated in these species and/or that long-term effective population size is vastly smaller than present-day population size. Several considerations point to the latter possibility as most likely. The genetic structure of any species is greatly influenced by historical demography; even for species that are currently abundant, mtDNA gene lineages appear to have been channeled through fairly small numbers of ancestors.      

Lines of descent in the diffusion approximation of neutral Wright-Fisher models

This paper studies lines of descent in the diffusion approximation of neutral Wright-Fisher models where the mutation rate away from each gene per generation is the same. Here a line of descent begins with a single gene and has branches at each generation where genes are reproduced from a parent in the line. New mutations are not included in a line of descent but are considered to begin a new line. The joint distribution of the number of lines of descent surviving in a population from time 0 to time t and the frequencies in these lines is derived. Expected times between loss of lines of descent are found. The distribution of the number of lines of descent in a sample from the population is derived. This leads to the distribution of the number of types in a sample from a nonstationary infinite alleles population.     

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.     

Predicting the frequencies of transgressive segregants for yield and yield components in wheat

Summary Genetical analysis of the F₂ triple test cross design combined with conventional early generations was used to elucidate the genetical control of yield and yield components in two crosses of winter wheat. From estimates of the additive, {d}, and additive X additive, {i}, components of means, together with the additive genetical variance, D, predicted frequencies of recombinant inbred lines that would transgress the parental range were calculated for each cross. The accuracy of predictions was evaluated by comparing expected frequencies with observed numbers in populations of F₆ lines previously developed by single seed descent.For both crosses and all characters where an adequate genetical model was found to explain the observed variation between the early generations, good agreement between predicted and observed frequencies of transgressive segregants was obtained. Furthermore, for characters exhibiting significant epistasis, allowance for additive X additive {i} epistasis in the prediction equations was sufficient to allow for skewness of the recombinant inbred population.These results demonstrate that cross performance in wheat can be predicted from genetical analysis of early generations, and the value of this approach in breeding new varieties is discussed.     

A competitive selection model

A multi-locus model for complete positive assortative mating is discussed. For a two-locus model, if the gene frequencies for the two loci are different, as they are likely to be, it is shown that in equilibrium the population is not composed of only two homozygous types, as is usually thought. The limiting distribution will have three homozygous genotypes depending upon the initial gene frequencies. If there are m-loci such that gene frequencies at all loci are different, there will be (m+1) such homozygous genotypes present in the equilibrium population, one in each phenotypic group.     

Additive by Additive Variance with Inbreeding and Linkage

Two-locus coancestries, which provide the coefficients of the additive by additive component in the variance and covariance of relatives for a quantitative trait, were formulated generally in terms of two-locus probabilities of identity by descent for combinations of parental and recombinant gametes. Explicit expressions, with linkage, were developed for all relatives of self-fertilization, for selfed and outbred relatives and for full and half sibs from unrelated inbred parents. The relative effect of linkage on the two-locus coancestry decreases rapidly as inbreeding and relatedness of the relatives increase. It was concluded that the error caused by ignoring linkage would probably be small in the estimation of genetic variances or in the projection of selection response with self-fertilization.     

Partial selfing and linkage: the effect of a heterotic locus on a neutral locus

Equilibria are determined for the two-locus model in a partially selfing population when one locus is neutral and the other locus is heterotic. At an equilibrium point, the frequency of heterozygotes at the neutral locus is greater than that expected from one-locus theory, even if the heterotic locus is on a different chromosome. Thus, the neutral locus also appears to be heterotic. The magnitude of this effect is determined for several different proportions of selfing and amounts of recombination.     

Simulating allele frequencies in a population and the genetic differentiation of populations under mutation pressure

A method is developed for simulating the allele frequencies in an equilibrium or transient population under the effects of neutral mutation and random drift. The method is based on diffusion theory and is fast so that it can be used to study in detail the distribution of heterozygosity or any quantity that can be expressed as a function of allele frequencies. It has been applied to study the distribution of heterozygosity and the distributions of the frequencies of the first three most frequent alleles in a population. It also has been applied to study the distribution of the number of alleles shared by two populations that were derived from a common stock.     

Stabilizing selection and linkage disequilibrium

An approach to the investigation of the evolution of quantitative traits on the basis of analysis of two-locus marginal systems dynamics has been developed. It has been shown that under stabilizing selection the "quasi-stationary" state is quickly reached and maintained continuously. The "quasi-stationary" state is characterized by small changes in allele frequencies and by linkage disequilibrium that significantly decreases genotypic variance. Equations defining the role of linkage disequilibrium in the stationary state of mutation-selection balance are derived.     

The mutation G298A-->Ala100Thr on the coding sequence of the Duffy antigen/chemokine receptor gene in non-caucasian Brazilians

Ala100Thr has been suggested to be a Caucasian genetic marker on the FY*B allele. As the Brazilian population has arisen from miscegenation among Portuguese, Africans, and Indians, this mutation could possibly be found in Euro- and Afro-Brazilians, or in Brazilian Indians. Fifty-three related individuals and a random sample of 100 subjects from the Brazilian population were investigated using the polymerase chain reaction and four restriction fragment length polymorphisms. Confirming the working hypothesis, among the related individuals three Afro-Brazilians (two of them a mother and daughter) and a woman of Amerindian descent had the Ala100Thr mutation on the FY*B allele. Five non-related Euro-Brazilians also carried the mutation. All nine individuals presented the Fy(a-b+) phenotype. We conclude that the Ala100Thr mutation can occur in populations other than Caucasians and that this mutation does not affect Duffy expression on red blood cells. Gene frequencies for this allele in the non-related individuals were in agreement with those of other populations. The Duffy frequencies of two Amerindian tribes were also investigated.     

Genetic variability of the marine mussel Mytilus galloprovincialis assessed using two-dimensional electrophoresis

Two-dimensional electrophoresis (2-DE) has been used to measure the degree of genetic variability of the marine mussel Mytilus galloprovincialis. Genetic polymorphisms were detected in 33 of a total of 86 polypeptides scored among the most abundant proteins from foot samples in 38 individuals. Estimates of average heterozygosity were 0.101+/-0.018 and 0.114+/-0.021 in a natural and a cultured population, respectively, from the NW of the Iberian Peninsula. These are the highest estimates of average heterozygosity reported by 2-DE in an animal species to date. We consider that these data throw open the question of the level of genetic variability detectable by two-dimensional electrophoresis. Multilocus genotype data were used to infer haplotypic frequencies by means of the EM algorithm in order to detect linkage disequilibrium between loci coding abundant proteins. Significant associations were found in 22.7% of the 406 two-locus pairs analysed. Also, clusters of loci in which all pairwise combinations exhibit statistically significant associations were detected and physical linkage between some of these loci is postulated from the linkage disequilibrium data.     

Mapping genes underlying ethnic differences in disease risk by linkage disequilibrium in recently admixed populations.

Where recent admixture has occurred between two populations that have different disease rates for genetic reasons, family-based association studies can be used to map the genes underlying these differences, if the ancestry of the alleles at each locus examined can be assigned to one of the two founding populations. This article explores the statistical power and design requirements of this approach. Markers suitable for assigning the ancestry of genomic regions could be defined by grouping alleles at closely spaced microsatellite loci into haplotypes, or generated by representational difference analysis. For a given relative risk between populations, the sample size required to detect a disease locus that accounts for this relative risk by linkage-disequilibrium mapping in an admixed population is not critically dependent on assumptions about genotype penetrances or allele frequencies. Using the transmission-disequilibrium test to search the genome for a locus that accounts for a relative risk of between 2 and 3 in a high-risk population, compared with a low-risk population, generally requires between 150 and 800 case-parent pairs of mixed descent. The optimal strategy is to conduct an initial study using markers spaced at < or = 10 cM with cases from the second and third generations of mixed descent, and then to map the disease loci more accurately in a subsequent study of a population with a longer history of admixture. This approach has greater statistical power than allele-sharing designs and has obvious applications to the genetics of hypertension, non-insulin-dependent diabetes, and obesity.     

Genetic dissection of intermated recombinant inbred lines using a new genetic map of maize

A new genetic map of maize, ISU-IBM Map4, that integrates 2029 existing markers with 1329 new indel polymorphism (IDP) markers has been developed using intermated recombinant inbred lines (IRILs) from the intermated B73xMo17 (IBM) population. The website http://magi.plantgenomics.iastate.edu provides access to IDP primer sequences, sequences from which IDP primers were designed, optimized marker-specific PCR conditions, and polymorphism data for all IDP markers. This new gene-based genetic map will facilitate a wide variety of genetic and genomic research projects, including map-based genome sequencing and gene cloning. The mosaic structures of the genomes of 91 IRILs, an important resource for identifying and mapping QTL and eQTL, were defined. Analyses of segregation data associated with markers genotyped in three B73/Mo17-derived mapping populations (F2, Syn5, and IBM) demonstrate that allele frequencies were significantly altered during the development of the IBM IRILs. The observations that two segregation distortion regions overlap with maize flowering-time QTL suggest that the altered allele frequencies were a consequence of inadvertent selection. Detection of two-locus gamete disequilibrium provides another means to extract functional genomic data from well-characterized plant RILs.