Substitution Processes in Molecular Evolution. III. Deleterious Alleles

The substitution processes for various models of deleterious alleles are examined using computer simulations and mathematical analyses. Most of the work focuses on the house-of-cards model, which is a popular model of deleterious allele evolution. The rate of substitution is shown to be a concave function of the strength of selection as measured by α = 2Nσ, where N is the population size and σ is the standard deviation of fitness. For α<1, the house-of-cards model is essentially a neutral model; for α>4, the model ceases to evolve. The stagnation for large α may be understood by appealing to the theory of records. The house-of-cards model evolves to a state where the vast majority of all mutations are deleterious, but precisely one-half of those mutations that fix are deleterious (the other half are advantageous). Thus, the model is not a model of exclusively deleterious evolution as is frequently claimed. It is argued that there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious. Other models examined include the exponential and gamma shift models, the Hartl-Dykhuizen-Dean (HDD) model, and the optimum model. Of all those examined, only the optimum and HDD models appear to be reasonable candidates for silent evolution. None of the models are viewed as good candidates for protein evolution, as none are both biologically reasonable and exhibit the variability in substitutions commonly observed in protein sequence data.     

Counting Alleles with Rarefaction: Private Alleles and Hierarchical Sampling Designs

The number of alleles (allelic richness) in a population is a fundamental measure of genetic variation, and a useful statistic for identifying populations for conservation. Estimating allelic richness is complicated by the effects of sample size: large samples are expected to have more alleles. Rarefaction solves this problem. This communication extends the rarefaction procedure to count private alleles and to accommodate hierarchical sampling designs.     

Estimating Relatedness in the Presence of Null Alleles

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial loss of statistical power. Here, we show how loci with null alleles can be incorporated into six estimators of relatedness (two novel). We evaluate the performance of various estimators before and after correction for null alleles. If the frequency of a null allele is <0.1, some estimators can be used directly without adjustment; if it is >0.5, the potency of estimation is too low and such a locus should be excluded. We make available a software package entitled PolyRelatedness v1.6, which enables researchers to optimize these estimators to best fit a particular data set.     

Evolutionary Dynamics of Sporophytic Self-Incompatibility Alleles in Plants

The stationary frequency distribution and allelic dynamics in finite populations are analyzed through stochastic simulations in three models of single-locus, multi-allelic sporophytic self-incompatibility. The models differ in the dominance relationships among alleles. In one model, alleles act codominantly in both pollen and style (SSIcod), in the second, alleles form a dominance hierarchy in pollen and style (SSIdom). In the third model, alleles interact codominantly in the style and form a dominance hierarchy in the pollen (SSIdomcod). The SSIcod model behaves similarly to the model of gametophytic self-incompatibility, but the selection intensity is stronger. With dominance, dominant alleles invade the population more easily than recessive alleles and have a lower frequency at equilibrium. In the SSIdom model, recessive alleles have both a higher allele frequency and higher expected life span. In the SSIdomcod model, however, loss due to drift occurs more easily for pollen-recessive than for pollen-dominant alleles, and therefore, dominant alleles have a higher expected life span than the more recessive alleles. The process of allelic turnover in the SSIdomcod and SSIdom models is closely approximated by a random walk on a dominance ladder. Implications of the results for experimental studies of sporophytic self-incompatibility in natural populations are discussed.     

Rapid Screening for Temperature-Sensitive Alleles in Plants

We developed a simple and fast method to identify temperature-sensitive alleles of essential plant genes. We used primary and tertiary structure information to identify residues in the core of the protein of interest. These residues were mutated and tested for temperature sensitivity, taking advantage of the exceptionally rapid 1-week complementation assay in the moss Physcomitrella patens. As test molecules, we selected the actin-binding proteins profilin and actin-depolymerizing factor, because they are essential and their loss-of-function phenotype can be fully rescued. Screening a small number of candidate mutants, we successfully identified temperature-sensitive alleles of both profilin and actin-depolymerizing factor. Plants harboring these alleles grew well at the permissive temperature of 20°C to 25°C but showed a complete loss of function at the restrictive temperature of 32°C. Notably, the profilin mutation identified in the moss gene can be transferred to profilins from other plant species, also rendering them temperature sensitive. The ability to routinely generate temperature-sensitive alleles of essential plant proteins provides a powerful tool for the study of gene function in plants.Conditional mutants are powerful genetic tools. In yeast, temperature-sensitive mutations have yielded a wealth of information regarding gene function and have aided immensely in the discovery and elucidation of many molecular pathways (Hartwell, 1967; Bonatti et al., 1972; Pringle, 1975; Novick and Botstein, 1985; Johnston et al., 1991; Balasubramanian et al., 1994; Chang et al., 1996, 1997; Iida and Yahara, 1999). In plants, a number of studies have generated temperature-sensitive alleles to study processes ranging from plant morphology to signal transduction (Lane et al., 2001; Whittington et al., 2001; Wiedemeier et al., 2002; Quint et al., 2005; Bannigan et al., 2006, 2007).In addition to temperature-dependent function, conditional expression can be generated in a variety of ways. A common strategy in mouse cells is to incorporate lox-p sites flanking the gene of interest (Sauer and Henderson, 1988; Orban et al., 1992; Vidali et al., 2006). Gene function is conditionally lost by the expression of cre recombinase that fuses the lox-p sites, deleting the intervening sequences. This method and others, such as inducible RNA interference (RNAi; Ketelaar et al., 2004), require long incubation times needed for gene expression and protein depletion. Due to the long time course for these studies, loss-of-function effects can be complicated with the development of the organism. In contrast, temperature-sensitive mutants are potentially fast acting, losing their function in some cases within minutes of exposure to the restrictive conditions (Novick and Botstein, 1985; Pruyne et al., 1998).In most cases, temperature-sensitive mutants are generated randomly and the elucidation of the gene harboring the mutation is uncovered by cloning the mutagenized gene. In plants, this is done by performing a chromosome walk to the mutagenized allele. In yeast, due to the ease of performing complementation, it is also possible to start with a gene of interest, mutagenize that gene, and screen for temperature-sensitive alleles (Shortle et al., 1984; Budd and Campbell, 1987; Mann et al., 1987). In plants, however, this process has not been widely used, presumably due to the time-consuming nature of performing complementation studies in planta.Here, we show that the moss Physcomitrella patens is an ideal plant suited for screening potential temperature-sensitive alleles of a gene of interest. To screen for a temperature-sensitive mutation, loss of the gene of interest must produce a measurable phenotype that can be rescued by reintroduction of the wild-type allele of the gene. We chose two proteins, profilin and actin-depolymerizing factor (ADF)/cofilin, as test molecules. Profilin and ADF are well-characterized actin-binding proteins that are important for cellular growth in plants (Staiger et al., 1994; Ramachandran et al., 2000; Dong et al., 2001; Vidali et al., 2001, 2007; Chen et al., 2002, 2003; McKenna et al., 2004; Augustine et al., 2008). In the moss P. patens, both profilin and ADF are essential for protonemal filament growth. Loss of profilin or ADF results in severely stunted plants, composed of morphologically abnormal cells (Vidali et al., 2007; Augustine et al., 2008). These phenotypes are fully rescued by expression of wild-type profilin or ADF, respectively.Moss has emerged as a facile plant system due to its ability to integrate exogenous DNA molecules by homologous recombination at frequencies enabling gene-targeting studies (Cove et al., 2006). In addition, moss is amenable to transient RNAi (Bezanilla et al., 2003, 2005), which enables the study of terminal phenotypes due to loss of essential genes, something that would not be possible if performing only gene knockout experiments. We have previously demonstrated the ability to knock down essential gene families and obtain quantitative rescue of the knockdown phenotypes (Vidali et al., 2007, 2009; Augustine et al., 2008). We have performed these studies using a rapid transient assay, which enables knock down and complementation studies to be performed within 1 week of transformation (Vidali et al., 2007). This is an extremely rapid assay that is unparalleled in other plant systems. Here, we use this complementation assay to screen for temperature-sensitive alleles of both profilin and ADF. Importantly, we show that the residue that confers temperature sensitivity in moss profilin can also render both Arabidopsis (Arabidopsis thaliana) and lily (Lilium longiflorum) profilins temperature sensitive, demonstrating a wider applicability to this rapid in planta complementation system.     

The Maintenance of Single-Locus Polymorphism. IV. Models with Mutation from Existing Alleles

The ability of viability selection to maintain allelic polymorphism is investigated using a constructionist approach. In extensions to the models we have previously proposed, a population is bombarded with a series of mutations whose fitnesses in conjunction with other alleles are functions of the corresponding fitnesses with a particular allele, the parent allele, already in the population. Allele frequencies are iterated simultaneously, thus allowing alleles to be driven to extinction by selection. Such models allow very high levels of polymorphism to evolve: up to 38 alleles in one case. Alleles that are lethal as homozygotes can evolve to surprisingly high frequencies. The joint evolution of allele frequencies and viabilities highlights the necessity to consider more than the current morphology of a population. Comparisons are made with the neutral theory of evolution and it is suggested that failure to reject neutrality using the Ewens-Watterson test cannot be regarded as evidence for the neutral theory.     

The Sampling Distribution of Disease-Associated Alleles

A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.     

The Deterministic Behavior of Self-Incompatibility Alleles

For a system of n self-incompatibility alleles, neglecting mutation and random drift, it is shown that the completely symmetric equilibrium is locally stable, and any allelic frequency less than q = 1+a-(see PDF), where a = [2(n - 1)]^-1, will increase. For all n, q > (2n)^-1, but if n > > 1, q ≈ (2n)^-1.     

Historical Shifts in Brazilian P. falciparum Population Structure and Drug Resistance Alleles

Previous work suggests that Brazilian Plasmodium falciparum has limited genetic diversity and a history of bottlenecks, multiple reintroductions due to human migration, and clonal expansions. We hypothesized that Brazilian P. falciparum would exhibit clonal structure. We examined isolates collected across two decades from Amapá, Rondônia, and Pará state (n = 190). By examining more microsatellites markers on more chromosomes than previous studies, we hoped to define the extent of low diversity, linkage disequilibrium, bottlenecks, population structure, and parasite migration within Brazil. We used retrospective genotyping of samples from the 1980s and 1990s to explore the population genetics of SP resistant dhfr and dhps alleles. We tested an existing hypothesis that the triple mutant dhfr mutations 50R/51I/108N and 51I/108N/164L developed in southern Amazon from a single origin of common or similar parasites. We found that Brazilian P. falciparum had limited genetic diversity and isolation by distance was rejected, which suggests it underwent bottlenecks followed by migration between sites. Unlike Peru, there appeared to be gene flow across the Brazilian Amazon basin. We were unable to divide parasite populations by clonal lineages and pairwise FST were common. Most parasite diversity was found within sites in the Brazilian Amazon, according to AMOVA. Our results challenge the hypothesis that triple mutant alleles arose from a single lineage in the Southern Amazon. SP resistance, at both the double and triple mutant stages, developed twice and potentially in different regions of the Brazilian Amazon. We would have required samples from before the 1980s to describe how SP resistance spread across the basin or describe the complex internal migration of Brazilian parasites after the colonization efforts of past decades. The Brazilian Amazon basin may have sufficient internal migration for drug resistance reported in any particular region to rapidly spread to other parts of basin under similar drug pressure.