Revisiting the number of self-incompatibility alleles in finite populations: From old models to new results.

Under gametophytic self-incompatibility (GSI), plants are heterozygous at the self-incompatibility locus (S-locus) and can only be fertilized by pollen with a different allele at that locus. The last century has seen a heated debate about the correct way of modelling the allele diversity in a GSI population that was never formally resolved. Starting from an individual-based model, we derive the deterministic dynamics as proposed by Fisher (The genetical theory of natural selection - A complete, Variorum edition, Oxford University Press, 1958) and compute the stationary S-allele frequency distribution. We find that the stationary distribution proposed by Wright (Evolution, 18, 609, 1964) is close to our theoretical prediction, in line with earlier numerical confirmation. Additionally, we approximate the invasion probability of a new S-allele, which scales inversely with the number of resident S-alleles. Lastly, we use the stationary allele frequency distribution to estimate the population size of a plant population from an empirically obtained allele frequency spectrum, which complements the existing estimator of the number of S-alleles. Our expression of the stationary distribution resolves the long-standing debate about the correct approximation of the number of S-alleles and paves the way for new statistical developments for the estimation of the plant population size based on S-allele frequencies.

Fisher's historic 1922 paper On the dominance ratio.

R.A. Fisher's 1922 paper On the dominance ratio has a strong claim to be the foundation paper for modern population genetics. It greatly influenced subsequent work by Haldane and Wright, and contributed 3 major innovations to the study of evolution at the genetic level. First, the introduction of a general model of selection at a single locus, which showed how variability could be maintained by heterozygote advantage. Second, the use of the branching process approach to show that a beneficial mutation has a substantial chance of loss from the population, even when the population size is extremely large. Third, the invention of the concept of a probability distribution of allele frequency, caused by random sampling of allele frequencies due to finite population size, and the first use of a diffusion equation to investigate the properties of such a distribution. Although Fisher was motivated by an inference that later turned out to lack strong empirical support (a substantial contribution of dominance to quantitative trait variability), and his use of a diffusion equation was marred by a technical mistake, the paper introduced concepts and methods that pervade much subsequent work in population genetics.

Random fluctuation of selection coefficients and the extent of nucleotide variation in human populations.

It is well known that the selection coefficient of a mutant allele varies from generation to generation, and the effect of this factor on genetic variation has been studied by many theoreticians. However, no consensus has been reached. One group of investigators believes that fluctuating selection has an effect of enhancing genetic variation, whereas the other group contends that it has a diversity-reducing effect. In recent years, it has become possible to study this problem by using single nucleotide polymorphisms (SNPs) as well as exome sequence data. In this article we present the theoretical distributions of mutant nucleotide frequencies for the two models of fluctuating selection and then compare the distributions with the empirical distributions obtained from SNP and exome sequence data in human populations. Interestingly, both SNP and exome sequence data showed that the neutral mutation model fits the empirical distribution quite well. Furthermore, the mathematical models with diversity-enhancing and diversity-reducing effects also fit the empirical distribution reasonably well. This result implies that there is no need of distinguishing between the diversity-enhancing and diversity-reducing models of fluctuating selection and the nucleotide polymorphism in human populations can be explained largely by neutral mutations when long-term evolution is considered.

Positive diversifying selection on the Plasmodium falciparum surf4.1 gene in Thailand.

Plasmodium falciparum SURFIN(4.1) is a type I transmembrane protein thought to locate on the merozoite surface and to be responsible for a reversible adherence to the erythrocyte before invasion. In this study, we evaluated surf(4.1) gene segment encoding extracellular region for polymorphism, the signature of positive selection, the degree of linkage disequilibrium, and temporal change in allele frequency distribution in P. falciparum isolates from Thailand in 1988-89, 2003, and 2005. We found that SURFIN(4.1) is highly polymorphic, particularly at the C-terminal side of the variable region located just before a predicted transmembrane region. A signature of positive diversifying selection on the variable region was detected by multiple tests and, to a lesser extent, on conserved N-terminally located cysteine-rich domain by Tajima's D test. Linkage disequilibrium between sites over a long distance (> 1.5 kb) was detected, and multiple SURFIN(4.1) haplotype sequences detected in 1988/89 still circulated in 2003. Few of the single amino acid polymorphism allele frequency distributions were significantly different between the 1988/89 and 2003 groups, suggesting that the frequency distribution of SURFIN(4.1) extracellular region remained stable over 14 years.

Positive Diversifying Selection on the <i>Plasmodium falciparum</i> <i>surf_4.1</i> Gene in Thailand

<i>Plasmodium falciparum</i> SURFIN_4.1 is a type I transmembrane protein thought to locate on the merozoite surface and to be responsible for a reversible adherence to the erythrocyte before invasion. In this study, we evaluated <i>surf_4.1</i> gene segment encoding extracellular region for polymorphism, the signature of positive selection, the degree of linkage disequilibrium, and temporal change in allele frequency distribution in <i>P. falciparum</i> isolates from Thailand in 1988–89, 2003, and 2005. We found that SURFIN_4.1 is highly polymorphic, particularly at the C-terminal side of the variable region located just before a predicted transmembrane region. A signature of positive diversifying selection on the variable region was detected by multiple tests and, to a lesser extent, on conserved N-terminally located cysteine-rich domain by Tajima’s <i>D</i> test. Linkage disequilibrium between sites over a long distance (> 1.5 kb) was detected, and multiple SURFIN_4.1 haplotype sequences detected in 1988/89 still circulated in 2003. Few of the single amino acid polymorphism allele frequency distributions were significantly different between the 1988/89 and 2003 groups, suggesting that the frequency distribution of SURFIN_4.1 extracellular region remained stable over 14 years.<br>

Positive Diversifying Selection on the <i>Plasmodium falciparum</i> <i>surf_4.1</i> Gene in Thailand

<i>Plasmodium falciparum</i> SURFIN_4.1 is a type I transmembrane protein thought to locate on the merozoite surface and to be responsible for a reversible adherence to the erythrocyte before invasion. In this study, we evaluated <i>surf_4.1</i> gene segment encoding extracellular region for polymorphism, the signature of positive selection, the degree of linkage disequilibrium, and temporal change in allele frequency distribution in <i>P. falciparum</i> isolates from Thailand in 1988–89, 2003, and 2005. We found that SURFIN_4.1 is highly polymorphic, particularly at the C-terminal side of the variable region located just before a predicted transmembrane region. A signature of positive diversifying selection on the variable region was detected by multiple tests and, to a lesser extent, on conserved N-terminally located cysteine-rich domain by Tajima’s <i>D</i> test. Linkage disequilibrium between sites over a long distance (> 1.5 kb) was detected, and multiple SURFIN_4.1 haplotype sequences detected in 1988/89 still circulated in 2003. Few of the single amino acid polymorphism allele frequency distributions were significantly different between the 1988/89 and 2003 groups, suggesting that the frequency distribution of SURFIN_4.1 extracellular region remained stable over 14 years.