The fundamental theorem of natural selection: the end of a story.

The direction of research in population genetics theory is currently, and correctly, retrospective, that is directed toward the past. What events in the past have led to the presently observed genetic constitution of a population? This direction is inspired, first, by the large volumes of genomic data now available and, second, by the success of the classical prospective theory in validating the Darwinian theory in terms of Mendelian genetics. However, the prospective theory should not be forgotten, and in that theory, perhaps the most interesting and certainly the most controversial, is Fisher's so-called "Fundamental Theorem of Natural Selection.

On the sign of the average effect of an allele.

The concept of the average effect of an allele pervades much of evolutionary population genetics. In this context the average effect of an allele is often considered as the main component of the "fitness" of that allele. It is widely believed that, if this fitness component for an allele is positive, then the frequency of this allele will increase, at least for one generation in discrete-time models.

Quantifying evolution by natural selection.

The theme of this paper is that Fisher's "Fundamental Theorem of Natural Selection" has various deficiencies as a quantification of the effect of natural selection in a Mendelian population which are not shared by a new different theorem described in this paper. The deficiencies in Fisher's theorem are listed in this paper. The new theorem focuses on the implications of changes in gene frequencies under natural selection and not, as does the Fundamental Theorem of Natural Selection, on changes in mean population fitness.

The left-hand side of the Fundamental Theorem of Natural Selection: A reply.

In a recent paper, Grafen (2018) discussed the left-hand side in the equation stating Fisher's (1930, 1958) "Fundamental Theorem of Natural Selection" (FTNS). Fisher's original statement of the FTNS is, in effect, "The rate of increase in fitness of any organism is equal to its genetic variance in fitness at that time" with the rate of increase in fitness understood as the one "due to all changes in gene ratios" (Fisher, 1930, p. 35).

On the interpretation and relevance of the Fundamental Theorem of Natural Selection.

The attempt to understand the statement, and then to find the interpretation, of Fisher's "Fundamental Theorem of Natural Selection" caused problems for generations of population geneticists. Price's (1972) paper was the first to lead to an understanding of the statement of the theorem. The theorem shows (in the discrete-time case) that the so-called "partial change" in mean fitness of a population between a parental generation and an offspring generation is the parental generation additive genetic variance in fitness divided by the parental generation mean fitness.

James F. Crow and the stochastic theory of population genetics.

Research in population genetics theory has two main strands. The first is deterministic theory, where random changes in allelic frequencies are ignored and attention focuses on the evolutionary effects of selection and mutation. The second strand, stochastic theory, takes account of these random changes and thus is more complete than deterministic theory.

Adjustment for local ancestry in genetic association analysis of admixed populations.

Motivation: Admixed populations offer a unique opportunity for mapping diseases that have large disease allele frequency differences between ancestral populations. However, association analysis in such populations is challenging because population stratification may lead to association with loci unlinked to the disease locus.

Methods And Results: We show that local ancestry at a test single nucleotide polymorphism (SNP) may confound with the association signal and ignoring it can lead to spurious association.

There's plenty of time for evolution.

Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about K log L, rather than K(L), where L is the length of the genomic "word," and K is the number of possible "letters" that can occupy any position in the word.

Sam Karlin and the stochastic theory of evolutionary population genetics.

Sam Karlin's role in the development of the stochastic theory of evolutionary population genetics is outlined, together with his work in developing BLAST theory.

A flexible two-stage procedure for identifying gene sets that are differentially expressed.

Motivation: Microarray data analysis has expanded from testing individual genes for differential expression to testing gene sets for differential expression. The tests at the gene set level may focus on multivariate expression changes or on the differential expression of at least one gene in the gene set. These tests may be powerful at detecting subtle changes in expression, but findings at the gene set level need to be examined further to understand whether they are informative and if so how.

A review of family-based tests for linkage disequilibrium between a quantitative trait and a genetic marker.

Quantitative trait transmission/disequilibrium tests (quantitative TDTs) are commonly used in family-based genetic association studies of quantitative traits. Despite the availability of various quantitative TDTs, some users are not aware of the properties of these tests and the relationships between them. This review aims at outlining the broad features of the various quantitative TDT procedures carried out in the frequently used QTDT and FBAT packages.

Disease associations and family-based tests.

This unit describes the statistical techniques necessary for performing family-based association studies (such as the TDT) for genetic polymorphisms. Such studies have become increasingly important in the identification of genes that confer an increased risk to disease, particularly for common diseases with a complex etiology. The family-based approach avoids some of the problems often encountered when applying the traditional case-control design to genetic studies.

Disease associations and family-based tests.

This unit describes the statistical techniques necessary for performing family-based association studies (e.g., the TDT) for genetic polymorphisms.

Computing the distribution of the maximum in balls-and-boxes problems with application to clusters of disease cases.

We present a rapid method for the exact calculation of the cumulative distribution function of the maximum of multinomially distributed random variables. The method runs in time O(mn), where m is the desired maximum and n is the number of variables. We apply the method to the analysis of two situations in which an apparent clustering of cases of a disease in some locality has raised epidemiological concerns, and these concerns have been discussed in the recent literature.

Common genetic variants account for differences in gene expression among ethnic groups.

Variation in DNA sequence contributes to individual differences in quantitative traits, but in humans the specific sequence variants are known for very few traits. We characterized variation in gene expression in cells from individuals belonging to three major population groups. This quantitative phenotype differs significantly between European-derived and Asian-derived populations for 1,097 of 4,197 genes tested.

Heterozygous carriers of Nijmegen Breakage Syndrome have a distinct gene expression phenotype.

Autosomal recessive diseases are those that require mutations in both alleles to exhibit the disorder. Although most recessive conditions are rare, heterozygous carriers of recessive mutations are quite common. In this study, we show that carriers of Nijmegen Breakage Syndrome (NBS) have a distinct gene expression phenotype that differs from that of noncarriers and also from that of carriers of a similar syndrome, Ataxia Telangiectasia (AT).

What is the significance of a significant TDT?

This note summarizes the development of the transmission/disequilibrium test (TDT). The initial purpose of the TDT procedure was to test for linkage between a genetic marker and a disease susceptibility locus when an association had been found between the two. An association between disease and marker had sometimes been taken to imply linkage.

Gene expression phenotype in heterozygous carriers of ataxia telangiectasia.

The defining characteristic of recessive diseases is the absence of a phenotype in the heterozygous carriers. Nonetheless, subtle manifestations may be detectable by new methods, such as expression profiling. Ataxia telangiectasia (AT) is a typical recessive disease, and individual carriers cannot be reliably identified.

Genetic risk assessment in carrier testing for spinal muscular atrophy.

As evidenced by the complete absence of a functionally critical sequence in exon 7, approximately 94% of individuals with clinically typical spinal muscular atrophy (SMA) lack both copies of the SMN1 gene at 5q13. Hence most carriers have only one copy of SMN1. Combining linkage and dosage analyses for SMN1, we observed unaffected individuals who have two copies of SMN1 on one chromosome 5 and zero copies of SMN1 on the other chromosome 5.