The fundamental theorem of natural selection with mutations.

The mutation-selection process is the most fundamental mechanism of evolution. In 1935, R. A. Fisher proved his fundamental theorem of natural selection, providing a model in which the rate of change of mean fitness is equal to the genetic variance of a species. Fisher did not include mutations in his model, but believed that mutations would provide a continual supply of variance resulting in perpetual increase in mean fitness, thus providing a foundation for neo-Darwinian theory. In this paper we re-examine Fisher's Theorem, showing that because it disregards mutations, and because it is invalid beyond one instant in time, it has limited biological relevance. We build a differential equations model from Fisher's first principles with mutations added, and prove a revised theorem showing the rate of change in mean fitness is equal to genetic variance plus a mutational effects term. We refer to our revised theorem as the fundamental theorem of natural selection with mutations. Our expanded theorem, and our associated analyses (analytic computation, numerical simulation, and visualization), provide a clearer understanding of the mutation-selection process, and allow application of biologically realistic parameters such as mutational effects. The expanded theorem has biological implications significantly different from what Fisher had envisioned.

A new look at an old virus: patterns of mutation accumulation in the human H1N1 influenza virus since 1918.

BACKGROUND: The H1N1 influenza A virus has been circulating in the human population for over 95 years, first manifesting itself in the pandemic of 1917-1918. Initial mortality was extremely high, but dropped exponentially over time. Influenza viruses have high mutation rates, and H1N1 has undergone significant genetic changes since 1918. The exact nature of H1N1 mutation accumulation over time has not been fully explored. METHODS: We have made a comprehensive historical analysis of mutational changes within H1N1 by examining over 4100 fully-sequenced H1N1 genomes. This has allowed us to examine the genetic changes arising within H1N1 from 1918 to the present. RESULTS: We document multiple extinction events, including the previously known extinction of the human H1N1 lineage in the 1950s, and an apparent second extinction of the human H1N1 lineage in 2009. These extinctions appear to be due to a continuous accumulation of mutations. At the time of its disappearance in 2009, the human H1N1 lineage had accumulated over 1400 point mutations (more than 10% of the genome), including approximately 330 non-synonymous changes (7.4% of all codons). The accumulation of both point mutations and non-synonymous amino acid changes occurred at constant rates (µ = 14.4 and 2.4 new mutations/year, respectively), and mutations accumulated uniformly across the entire influenza genome. We observed a continuous erosion over time of codon-specificity in H1N1, including a shift away from host (human, swine, and bird [duck]) codon preference patterns. CONCLUSIONS: While there have been numerous adaptations within the H1N1 genome, most of the genetic changes we document here appear to be non-adaptive, and much of the change appears to be degenerative. We suggest H1N1 has been undergoing natural genetic attenuation, and that significant attenuation may even occur during a single pandemic. This process may play a role in natural pandemic cessation and has apparently contributed to the exponential decline in mortality rates over time, as seen in all major human influenza strains. These findings may be relevant to the development of strategies for managing influenza pandemics and strain evolution.

The effects of low-impact mutations in digital organisms.

BACKGROUND: Avida is a computer program that performs evolution experiments with digital organisms. Previous work has used the program to study the evolutionary origin of complex features, namely logic operations, but has consistently used extremely large mutational fitness effects. The present study uses Avida to better understand the role of low-impact mutations in evolution. RESULTS: When mutational fitness effects were approximately 0.075 or less, no new logic operations evolved, and those that had previously evolved were lost. When fitness effects were approximately 0.2, only half of the operations evolved, reflecting a threshold for selection breakdown. In contrast, when Avida's default fitness effects were used, all operations routinely evolved to high frequencies and fitness increased by an average of 20 million in only 10,000 generations. CONCLUSIONS: Avidian organisms evolve new logic operations only when mutations producing them are assigned high-impact fitness effects. Furthermore, purifying selection cannot protect operations with low-impact benefits from mutational deterioration. These results suggest that selection breaks down for low-impact mutations below a certain fitness effect, the selection threshold. Experiments using biologically relevant parameter settings show the tendency for increasing genetic load to lead to loss of biological functionality. An understanding of such genetic deterioration is relevant to human disease, and may be applicable to the control of pathogens by use of lethal mutagenesis.

Skittle: a 2-dimensional genome visualization tool.

BACKGROUND: It is increasingly evident that there are multiple and overlapping patterns within the genome, and that these patterns contain different types of information--regarding both genome function and genome history. In order to discover additional genomic patterns which may have biological significance, novel strategies are required. To partially address this need, we introduce a new data visualization tool entitled Skittle. RESULTS: This program first creates a 2-dimensional nucleotide display by assigning four colors to the four nucleotides, and then text-wraps to a user adjustable width. This nucleotide display is accompanied by a "repeat map" which comprehensively displays all local repeating units, based upon analysis of all possible local alignments. Skittle includes a smooth-zooming interface which allows the user to analyze genomic patterns at any scale.Skittle is especially useful in identifying and analyzing tandem repeats, including repeats not normally detectable by other methods. However, Skittle is also more generally useful for analysis of any genomic data, allowing users to correlate published annotations and observable visual patterns, and allowing for sequence and construct quality control. CONCLUSIONS: Preliminary observations using Skittle reveal intriguing genomic patterns not otherwise obvious, including structured variations inside tandem repeats. The striking visual patterns revealed by Skittle appear to be useful for hypothesis development, and have already led the authors to theorize that imperfect tandem repeats could act as information carriers, and may form tertiary structures within the interphase nucleus.