Genetics
Discrete inheritance and Mendel's laws

At its most fundamental level, inheritance in organisms occurs by passing discrete heritable units, called genes, from parents to offspring. This property was first observed by Gregor Mendel, who studied the segregation of heritable traits in pea plants, showing for example that flowers on a single plant were either purple or white—but never an intermediate between the two colors. The discrete versions of the same gene controlling the inherited appearance (phenotypes) are called alleles.

In the case of the pea, which is a diploid species, each individual plant has two copies of each gene, one copy inherited from each parent. Many species, including humans, have this pattern of inheritance. Diploid organisms with two copies of the same allele of a given gene are called homozygous at that gene locus, while organisms with two different alleles of a given gene are called heterozygous. The set of alleles for a given organism is called its genotype, while the observable traits of the organism are called its phenotype. When organisms are heterozygous at a gene, often one allele is called dominant as its qualities dominate the phenotype of the organism, while the other allele is called recessive as its qualities recede and are not observed. Some alleles do not have complete dominance and instead have incomplete dominance by expressing an intermediate phenotype, or codominance by expressing both alleles at once.

When a pair of organisms reproduce sexually, their offspring randomly inherit one of the two alleles from each parent. These observations of discrete inheritance and the segregation of alleles are collectively known as Mendel's first law or the Law of Segregation. However, the probability of getting one gene over the other can change due to dominant, recessive, homozygous, or heterozygous genes. For example, Mendel found that if you cross heterozygous organisms your odds of getting the dominant trait is 3:1. Real geneticist study and calculate probabilities by using theoretical probabilities, empirical probabilities, the product rule, the sum rule, and more.
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