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- M Shpak, G P Wagner
- Artificial life
- 2000

Evolution can be regarded as the exploration of genetic or morphological state space by populations. In traditional models of population and quantitative genetics, the state space can be formally represented as a configuration space with clearly defined concepts of neighborhood and distance, defined by the action of variational operators such as mutation… (More)

- Max Shpak, Kevin Atteson
- Bulletin of mathematical biology
- 2002

We present a model of gene duplication by means of unequal crossover (UCO) where the probability of any given pairing between homologous sequences scales as a penalty factor pz < or = 1, with z the number of mismatches due to asymmetric sequence alignment. From this general representation, we derive several limiting case models of UCO, some of which have… (More)

- N H Barton, M Shpak
- Genetical research
- 2000

Within hybrid zones that are maintained by a balance between selection and dispersal, linkage disequilibrium is generated by the mixing of divergent populations. This linkage disequilibrium causes selection on each locus to act on all other loci, thereby steepening clines, and generating a barrier to gene flow. Diffusion models predict simple relations… (More)

- Max Shpak, Alexey S Kondrashov
- Evolution; international journal of organic…
- 1999

We show that the phenotypic hypergeometric model of a quantitative trait can exactly describe both haploid and diploid populations. The condition necessary for this is equiprobability of genotypes within each phenotype. This requires equal allele frequencies across the loci, which may be the case when the population is under disruptive selection.

The topological features of genotype spaces given a genetic operator have a substantial impact on the course of evolution. We explore the structure of the recombination spaces arising from four different unequal crossover models in the context of pretopological spaces. We show that all four models are incompatible with metric distance measures due to a lack… (More)

- M Shpak, G A Churchill
- Molecular phylogenetics and evolution
- 2000

The rate of evolutionary change associated with a character determines its utility for the reconstruction of phylogenetic history. For a given age of lineage splits, we examine the information content of a character to assess the magnitude and range of an optimal rate of substitution. On the one hand an optimal transition rate must provide sufficiently many… (More)

- Max Shpak
- Genetics
- 2007

It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population; i.e., a genotype with lower variance in offspring number can be favored in finite populations even if it has a somewhat lower mean fitness than a competitor. In this article, Gillespie's results are extended to population genetic… (More)

- Max Shpak
- Theory in Biosciences
- 2005

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the… (More)

- Max Shpak, Stephen R Proulx
- Bulletin of mathematical biology
- 2007

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the… (More)

- Max Shpak, Amelia Weber Hall, +4 authors Matthew C Cowperthwaite
- Genomics
- 2014

In this paper we use eQTL mapping to identify associations between gene dysregulation and single nucleotide polymorphism (SNP) genotypes in glioblastoma multiforme (GBM). A set of 532,954 SNPs was evaluated as predictors of the expression levels of 22,279 expression probes. We identified SNPs associated with fold change in expression level rather than raw… (More)