Resolving the paradox of sex and recombination

Sexual reproduction and recombination are ubiquitous. However, a large body of theoretical work has shown that these processes should only evolve under a restricted set of conditions. New studies indicate that this discrepancy might result from the fact that previous models have ignored important complexities that face natural populations, such as genetic drift and the spatial structure of populations.     

Quantitative genetic models for the balance between migration and stabilizing selection

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.     

Bayesian selection of continuous-time Markov chain evolutionary models

We develop a reversible jump Markov chain Monte Carlo approach to estimating the posterior distribution of phylogenies based on aligned DNA/RNA sequences under several hierarchical evolutionary models. Using a proper, yet nontruncated and uninformative prior, we demonstrate the advantages of the Bayesian approach to hypothesis testing and estimation in phylogenetics by comparing different models for the infinitesimal rates of change among nucleotides, for the number of rate classes, and for the relationships among branch lengths. We compare the relative probabilities of these models and the appropriateness of a molecular clock using Bayes factors. Our most general model, first proposed by Tamura and Nei, parameterizes the infinitesimal change probabilities among nucleotides (A, G, C, T/U) into six parameters, consisting of three parameters for the nucleotide stationary distribution, two rate parameters for nucleotide transitions, and another parameter for nucleotide transversions. Nested models include the Hasegawa, Kishino, and Yano model with equal transition rates and the Kimura model with a uniform stationary distribution and equal transition rates. To illustrate our methods, we examine simulated data, 16S rRNA sequences from 15 contemporary eubacteria, halobacteria, eocytes, and eukaryotes, 9 primates, and the entire HIV genome of 11 isolates. We find that the Kimura model is too restrictive, that the Hasegawa, Kishino, and Yano model can be rejected for some data sets, that there is evidence for more than one rate class and a molecular clock among similar taxa, and that a molecular clock can be rejected for more distantly related taxa.     

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.     

Calibrating the Tree of Life: fossils, molecules and evolutionary timescales

Background

Molecular dating has gained ever-increasing interest since the molecular clock hypothesis was proposed in the 1960s. Molecular dating provides detailed temporal frameworks for divergence events in phylogenetic trees, allowing diverse evolutionary questions to be addressed. The key aspect of the molecular clock hypothesis, namely that differences in DNA or protein sequence between two species are proportional to the time elapsed since they diverged, was soon shown to be untenable. Other approaches were proposed to take into account rate heterogeneity among lineages, but the calibration process, by which relative times are transformed into absolute ages, has received little attention until recently. New methods have now been proposed to resolve potential sources of error associated with the calibration of phylogenetic trees, particularly those involving use of the fossil record.

Scope and Conclusions

The use of the fossil record as a source of independent information in the calibration process is the main focus of this paper; other sources of calibration information are also discussed. Particularly error-prone aspects of fossil calibration are identified, such as fossil dating, the phylogenetic placement of the fossil and the incompleteness of the fossil record. Methods proposed to tackle one or more of these potential error sources are discussed (e.g. fossil cross-validation, prior distribution of calibration points and confidence intervals on the fossil record). In conclusion, the fossil record remains the most reliable source of information for the calibration of phylogenetic trees, although associated assumptions and potential bias must be taken into account.     

Population genetics of polymorphism and divergence for diploid selection models with arbitrary dominance

We develop a Poisson random-field model of polymorphism and divergence that allows arbitrary dominance relations in a diploid context. This model provides a maximum-likelihood framework for estimating both selection and dominance parameters of new mutations using information on the frequency spectrum of sequence polymorphisms. This is the first DNA sequence-based estimator of the dominance parameter. Our model also leads to a likelihood-ratio test for distinguishing nongenic from genic selection; simulations indicate that this test is quite powerful when a large number of segregating sites are available. We also use simulations to explore the bias in selection parameter estimates caused by unacknowledged dominance relations. When inference is based on the frequency spectrum of polymorphisms, genic selection estimates of the selection parameter can be very strongly biased even for minor deviations from the genic selection model. Surprisingly, however, when inference is based on polymorphism and divergence (McDonald-Kreitman) data, genic selection estimates of the selection parameter are nearly unbiased, even for completely dominant or recessive mutations. Further, we find that weak overdominant selection can increase, rather than decrease, the substitution rate relative to levels of polymorphism. This nonintuitive result has major implications for the interpretation of several popular tests of neutrality.     

Developmental canalization with no part of stabilizing selection

Referring the developmental canalization to stabilizing selection may be a bias that results from the ignorance of developmental mechanisms. Considering the morphological evolution of one-cell trichomes in Draba plants makes it clear that the transition from continuous variation in morphological traits to developmental creods occurs in the evolution of remote lineages of the genus irrespective of contribution to the net fitness. Morphological diversification of trichome branching is not under selection control, being a physical consequence of the trichome cell volume growth equilibrated by complication of the cell surface shape. At the start of evolution, the trichome development refers not to an individual trichome, but rather to repetitive trichome modules (branches), whose spatiotemporal order is arbitrary, except that some variants of branching depend on events that occur at earlier developmental stages more than others. Under selection fluctuating at random, or with no selection at all, fixing of these variants leads to the formation of trichome ontogeny, in which earlier developmental stages correspond to later stages of developmental evolution.     

A statistical model of evolution with stabilizing selection

We consider a population of fixed size and reproducing asexually, evolving in a rugged fitness landscape. Selection takes place only via the elimination of individuals with unfit genomes. Unfit genotypes are distributed at random in genotypic space. The genetic structure of the population and the speed of genetic drift are explicitly computed in the infinite genome limit.     

DNA and the theory of stabilizing selection

A comparison of structural-functional features of genomic DNAs allowed to estimate the role of internal and external factors in evolution of different groups of organisms. The basic difference between higher and lower organisms has been demonstrated. It is reflected in the difference of their reaction on to external factors in accordance with two adaptation types, the openness and autonomization. There is a correlation between structural-functional organization of genomic DNAs of higher and lower organisms and the above mentioned types of adaptation. DNA of lower organisms has been proposed to be characterized as "labile", and that of higher organisms, as "stable". The "DNA lability" means high mutation ability, which characterizes the existence of and evolution of lower organisms (genetic inconstancy of the lower organisms). On the contrary, "DNA stability" means the creation of stable genetic apparatus, reduction of variability in higher organisms (genetic constancy of higher organisms). This suggests the existence of the two principal ways of evolution.     

Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection.

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination.     

Two-locus epistasis with sexually antagonistic selection: a genetic Parrondo's paradox

An example is provided where, with antagonistic selection and epistatic interaction of alleles at two loci, an autosomal allele can rise in frequency, persist in the population, and even continue to fixation, despite having an apparently lower average fitness than the alternative allele, in a process similar to Parrondo's paradox.     

Dependence of expected heterozygosity on locus number with stabilizing selection and drift

I determine expected levels of heterozygosity in two allele multilocus models with mutation, stabilizing selection and drift. In the range 2 to 32 loci, the per locus heterozygosity can depend on the locus number. The per locus heterozygosity for ten loci can be as low as three fourths of the per locus heterozygosity in the limit, as the number of loci gets large. Simulations indicate that this dependence on locus number is not due to the population approaching equilibria at which the mean differs from the optimum, but is due to changes in the substitution rate as a function of the number of loci.     

Some additional results about polymorphisms in models of an additive quantitative trait under stabilizing selection

 The existence of two stable, symmetric (allelic frequency 0.5 in each locus) polymorphic states is demonstrated for a two-locus model of an additive quantitative trait under strong Gaussian selection. Linkage disequilibrium at one of the states is negative whereas it is positive at the other state. For a three-locus model, it is shown that in order to maintain a stable polymorphism in all three loci, selection must be sufficiently but not exces- sively strong relative to recombination. Also, positive linkage disequilibrium can be maintained in a three-locus model under stabilizing selection that is not very strong. Received 15 July 1995     

The effect of Wolbachia on genetic divergence between populations: models with two-way migration

Wolbachia are intracellular bacteria that cause various reproduction alterations in their hosts, including cytoplasmic incompatibility (CI), an incompatibility between sperm and egg that typically results in embryonic death. We investigate theoretically the effects of Wolbachia-induced bidirectional CI on levels of divergence between two populations, where there is migration in both directions and differential selection at a single locus. The main findings are as follows: Wolbachia differences in the two populations are maintained up to a threshold migration rate, above which the system collapses to a single Wolbachia type; differential selection at a nuclear locus increases the threshold migration rate below which Wolbachia polymorphisms are maintained; Wolbachia differences between the populations enhance their genetic divergence at the selected locus by reducing the "effective migration rate," and even moderate levels of CI can cause large population differences in allele frequencies; and asymmetric CI can induce strong asymmetries in effective migration rate and dramatically alter the pattern of genetic divergence compared with the No Wolbachia situation. We derive an analytical approximation for the effective migration rate, which matches the simulation results for most parameter values. These results generally support the view that CI Wolbachia can contribute to genetic divergence between populations.     

Floral symmetry: pollinator-mediated stabilizing selection on flower size in bilateral species

Pollinator-mediated stabilizing selection (PMSS) has been proposed as the driver of the evolutionary shift from radial to bilateral symmetry of flowers. Studies have shown that variation in flower size is lower in bilateral than in radial species, but whether bilateral flowers experience more stabilizing selection pressures by employing fewer, more specialized pollinators than radial flowers remains unclear. To test the PMSS hypothesis, we investigate plant–pollinator interactions from a whole community in an alpine meadow in Hengduan Mountains, China, to examine: (i) variance in flower size and level of ecological generalization (pollinator diversity calculated using functional groups) in 14 bilateral and 13 radial species and (ii) the role pollinator diversity played in explaining the difference of variance in flower size between bilateral and radial species. Our data showed that bilateral species had less variance in flower size and were visited by fewer pollinator groups. Pollinator diversity accounted for up to 40 per cent of the difference in variance in flower size between bilateral and radial species. The mediator effect of pollinator diversity on the relationship between floral symmetry and variance in flower size in the community is consistent with the PMSS hypothesis.     

Conformational exchange divergence along the evolutionary pathway of eosinophil-associated ribonucleases

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Osmunda (Osmundaceae) from the Triassic of Antarctica: an example of evolutionary stasis

Compressed specimens of the fern Osmunda are described from the Triassic of the Allan Hills, Antarctica. The specimens consist of a once pinnate, deeply pinnatifid fertile frond as well as several sterile specimens. Six pinnae are present on the partial fertile rachis, with two sterile pinnae above four fertile pinnae. Both sterile and fertile specimens are virtually identical to the modern species Osmunda claytoniana. Entire fronds are fragmentary; the longest is 21 cm in length. Sterile pinnae are alternate and deeply pinnatifid, with slightly toothed pinnules and dichotomous venation. Fertile pinnae are 1-1.3 cm long, once pinnate, and lack vegetative lamina. Sporangia are clustered, each 300-375 um in diameter, and possess a transverse annulus 6-8 cells long; dehiscence is by a vertical slit. Fronds arise from a rhizome 4 cm long by 1 cm wide; two croziers are present on the rhizome. Two frond segments up to 6 cm long and three deeply pinnatifid pinnae are present on the uppermost part of one rachis. Pinnules are ~4 mm long and 2-3 mm wide. The presence of this Osmunda species in the Triassic demonstrates stasis of frond morphology, both fertile and vegetative, for the genus.     

Not all drift feeders are trout: a short review of fitness-based habitat selection models for fishes

Currently, there are few mechanistic fitness-based habitat selection models for stream fishes and most models used by management agencies focus on physical habitat alone. In this review, I describe the historical development and the status of mechanistic, fitness-based, habitat selection models for both water column (i.e., drift-feeding) and benthic stream fishes focusing on North America. Although the majority of drift feeders are not salmonids, most mechanistic habitat selection models have been developed and tested only in this group of fishes, likely due to their substantial economic importance. I review the fitness-based microhabitat selection model of Grossman et al. (Ecol Fresh Fish 11:2–10, 2002), which has been tested in both a salmonid and multiple cyprinid species. The model predicts optimal focal point velocities for drift feeders based on prey capture success–velocity relationships and does not include physiological costs, which are logistically difficult to quantify. In addition, I discuss mechanistic, fitness-based models used to predict microhabitat (i.e., patch) selection in benthic fishes. For both basic scientific and management/conservation perspectives, it is important to quantify habitat choice in fishes using mechanistic, fitness-based criteria.     

The size of scalable brain components in the human evolutionary lineage: with a comment on the paradox of Homo floresiensis.

The discovery of a diminutive, small-brained hominin skeleton (LB1) from the Pleistocene of Flores, Indonesia, seems to present a paradox concerning the interpretation of overall brain size in an evolutionary context. This specimen forms the holotype of a purportedly new hominin species, Homo floresiensis. As inferred from the archaeological record, it has been suggested that this species of Homo, existing as recently as 12,000 years ago, engaged in sophisticated cultural behaviors with an adult brain size equivalent to that seen in modern chimpanzees and one that in modern humans would be defined as "high degree microcephaly" and "always associated with idiocy". The alternative explanation for these behaviors at the observed brain size would require that H. floresiensis deviate from existing patterns of primate brain scaling at either a macroscopic or microscopic level. Here we develop predictive equations and confidence intervals for estimating the size of various brain components in the human evolutionary lineage by calculating scaling relationships among overall brain size and 11 components of the primate brain using phylogenetically independent contrasts (PIC) methods. Using these equations, paleoanthropologists can: (a) estimate brain component size (and confidence intervals) for any primate in the fossil record if overall brain size is known; and (b) calculate some reasonable outside limits as to how far species-specific departures from allometric constraints (i.e., brain "reorganization") can be taken in assessing human brain evolution. We conclude that if the original assessment of LB1 is correct, i.e., that it samples a population from a new species of Homo, H. floresiensis, that was capable of Homo sapiens-like cultural attributes (fire, blade manufacturing, etc.), while having a chimpanzee-sized brain, then we are faced with the paradox that 1 cm(3) of H. floresiensis brain could not be functionally equivalent to 1cm(3) of a modern human or modern chimpanzee brain.