Mendel’s law of independence has been reinterpreted regarding the independence of genes and the independence of traits. Second, the law of independent assortment is explained by the “independent” expression of different genes. The law is mainly discussed with regards to the genetic segregation of alleles, whereas segregation of phenotypes is not intensively studied. Mendel’s law concerns binary traits and consists of three laws: the law of gene segregation, the law of independent assortment, and the law of dominance.įirst, the law of segregation is explained by meiosis from a modern viewpoint. Mendelian inheritance is a keystone of genetics. Group Mendelian dominance and gene-expression pattern dominance are achieved associated with the increase in phenotypic robustness to noise. Due to this dominance, the robustness to genetic differences increases, while optimal fitness is sustained to a significant difference between the two genomes. This evolution of group Mendelian dominance and pattern dominance is associated with phenotypic robustness against meiosis-induced genome mixing, whereas sexual recombination arising from the mixing of genomes from the parents further enhances dominance and robustness. We also demonstrate that the dominance of gene expression patterns evolves concurrently. Calculating the degree of dominance shows that it increases through the evolution, correlating closely with the decrease in phenotypic fluctuations and the increase in robustness to initial noise. Our results reveal that group Mendelian dominance evolves even under complex genotype–phenotype relationship. We numerically evolve the GRN model for a diploid case, in which two GRN matrices are added to give gene expression dynamics and simulate evolution with meiosis and recombination. This dominance is defined via a pair of haplotypes that differ from each other but have a common phenotype given by the expression of target genes. We examine whether complex genotype–phenotype relationship can achieve Mendelian dominance at the expression level by a pair of haplotypes through the evolution of the GRN with interacting genes. Here, by using the numerical evolution of diploid GRNs, we discuss whether the dominance of phenotype evolves beyond the classical Mendelian case of one-to-one genotype–phenotype relationship. Whether and how Mendelian dominance is generalized to the phenotypes of gene expression determined by gene regulatory networks (GRNs) remains elusive. However, in reality, some interactions between genes can exist, resulting in deviations from Mendelian dominance. ![]() Classical Mendelian dominance is concerned with which proteins are dominant, and is usually based on simple genotype–phenotype relationship in which one gene regulates one phenotype. When we consider two genomes in a diploid cell, a heterozygote’s phenotype is dominated by a particular homozygote according to the law of dominance. Therefore, multiplying this fraction for each of the four genes, (1/4) × (1/4) × (1/4) × (1/4), we determine that 1/256 of the offspring will be quadruply homozygous recessive.Mendelian inheritance is a fundamental law of genetics. We know that for each gene the fraction of homozygous recessive offspring will be 1/4. For instance, for a tetrahybrid cross between individuals that are heterozygotes for all four genes, and in which all four genes are sorting independently in a dominant and recessive pattern, what proportion of the offspring will be expected to be homozygous recessive for all four alleles? Rather than writing out every possible genotype, we can use the probability method. ![]() To fully demonstrate the power of the probability method, however, we can consider specific genetic calculations. While the forked-line method is a diagrammatic approach to keeping track of probabilities in a cross, the probability method gives the proportions of offspring expected to exhibit each phenotype (or genotype) without the added visual assistance. Thus, the probability of F2 offspring having yellow, round, and tall traits is 3 × 3 × 3, or 27. The probability for each possible combination of traits is calculated by multiplying the probability for each individual trait. The probability for shape occupies the second row (3 round:1 wrinked), and the probability for height occupies the third row (3 tall:1 dwarf). Here, the probability for color in the F2 generation occupies the top row (3 yellow:1 green). \): Independent assortment of 3 genes: The forked-line method can be used to analyze a trihybrid cross.
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