Population Genetics and Formulae

Evolution is expected to occur when selection acts on a trait that has a heritable basis of phenotypic variation. Quantitative genetic models allow an evolutionary trajectory to be predicted from the strength of selection and the amount of genetic variance, usually expressed as the heritability, h2 [1]. However, while simple theoretical models assume a constant environment, environmental heterogeneity has long been recognised as an important factor influencing the evolutionary dynamics of fitness-related traits in the wild [2]. Specifically, selection can vary considerably from year to year within a population [3,4], and it is increasingly recognised that environmental conditions also influence the heritability on which any response to selection depends [5,6]. Although these observations generate an expectation of an environment-driven coupling of the magnitude of selection and heritability, to our knowledge, no prior study has combined estimates of trait heritability with estimates of the strength of selection across a range of environmental conditions in order to fully assess the evolutionary implications of environmental heterogeneity.
A. J. Wilson, J. M. Pemberton, J. G. Pilkington, D. W. Coltman, D. V. Mifsud, T. H. Clutton-Brock, L. E. B. Kruuk. Environmental Coupling of Selection and Heritability Limits Evolution . PLoS Biology Volume 4 Issue 7 JULY 2006

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Mendel's Laws

Mendel's First Law - the law of segregation:
During gamete formation each member of the allelic pair separates from the other member to form the genetic constitution of the gamete.

Right: punnet square showing combinations of alleles for a diploid organism with one or another variant of a single allele, 'A' or 'a' from each parent:
Statistically, hyrid offspring will possess
1 AA : 2 Aa or aA : 1 aa

If 'A' is dominant and 'a' is recessive, then statistically 1/4 of the offspring will have both dominant combinations (AA), 1/2 of the offspring will display the dominant trait yet carry the recessive trait by possessing one dominant and one recessive combination (Aa or aA), and 1/4 of offspring will have two recessive genes (aa)

Mendel's Second Law - the law of independent assortment:
During gamete formation the segregation of the alleles of one allelic pair is independent of the segregation of the alleles of another allelic pair.

Combinations of alleles for a diploid organism with one or another of two alleles from each parent produces the 9:3:3:1 ratio for the two dihybrids.
Offspring:
9/16 with both dominant traits:
A_B_ = AABB, AABb, AaBb, AaBB, AAbB, AAbB, aABb, AabB, aAbB
3/16 with dominant trait 'A' and recessive trait 'b': A_bb = AAbb, Aabb, aAbb
3/16 with dominant trait 'B' and recessive trait 'a': aaB_ = aaBb, aabB, aaBB
1/16 with both recessive traits ab: aabb

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Epistasis

Epistasis is defined as the influence of the genotype at one locus on the effect of a mutation at another locus. Thus, epistasis is the interaction between two or more genes to control a single phenotype.

Crossing dihybrids produces a modified Mendelian ratio – a 9:3:3:1 ratio for two dihybrids, in accordance with Mendel's second law, the law of independent assortment.

Epistasis plays a crucial role in a variety of evolutionary phenomena such as speciation, population bottle necks, and the evolution of genetic architecture – the evolution of dominance, canalization, and genetic correlations.

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Algorithms of Evolution: * epistasis * multilinear epistatic model

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Bottleneck

A bottleneck occurs when a disaster has killed individuals by chance and not on the basis of their adaptation. This randomly eliminates gene combinations, leaving a non-representative sampling of the parent gene pool. A bottleneck is a mechanism of genetic drift.

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Founder effect

The founder effect is a mechanism of genetic drift that operates when a small sub-group of a population, containing a random and non-representative sampling of genes, is reproductively isolated from the parent population.

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Persistence of functional gene duplicates

Fitting In: Newly Evolved Genes Adopt A Variety Of Strategies To Remain In The Gene Pool: modified: "To determine the basis for the persistence of functional gene duplicates in the genome, three scientists at the Institute of Molecular Systems Biology at the Swiss Federal Institute of Technology in Zürich have collaborated on the largest systematic analysis of duplicated gene function to date. Using an integrative combination of computational and experimental approaches, they classified duplicate pairs of genes involved in yeast metabolism into four functional categories: (1) back-up, where a duplicate gene copy has acquired the ability to compensate in the absence of the other copy, (2) subfunctionalization, where a duplicate copy has evolved a completely new, non-overlapping function, (3) regulation, where the differential regulation of duplicates fine-tunes pathway usage, and (4) gene dosage, where the increased expression provided by the duplicate gene copy augments production of the corresponding protein.Their results, which appear in the October issue of the journal Genome Research, indicate that no single role prevails but that all four of the mechanisms play a substantial role in maintaining duplicate genes in the genome."

Tables  Mechanisms of Biological Evolution :  Gene Regulation in E.coli : Cold Spring Harbor Laboratory :

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