Codominance is a pattern of inheritance distinct from simple dominance, where both alleles in a heterozygous individual equally and simultaneously express their traits. In simple dominance, one allele (the dominant allele) masks the expression of the other allele (the recessive allele). However, in codominance, neither allele is masked, and both are expressed fully. This results in a phenotype that displays characteristics of both alleles. A classic example of codominance is seen in human blood types, particularly the AB blood type. Individuals with this genotype have both A and B antigens on the surface of their red blood cells because the alleles for A and B blood types are codominant. This means that neither allele can mask the expression of the other, leading to a phenotype that distinctly exhibits the attributes of both alleles. Codominance thus provides a more complex and nuanced understanding of genetic inheritance, beyond the straightforward dominant-recessive relationship.

Incomplete dominance is a form of genetic inheritance where the phenotype of a heterozygote is intermediate between the phenotypes of the two homozygotes. This contrasts with Mendelian dominance, where the dominant allele completely masks the effect of the recessive allele in a heterozygote. In incomplete dominance, the heterozygous phenotype is not identical to the dominant homozygote but is a blending of the two parental phenotypes. An example is the inheritance of flower color in certain species of snapdragons: when a red-flowered plant (RR) is crossed with a white-flowered plant (rr), the offspring (Rr) have pink flowers. The pink flowers of the heterozygotes represent a mix of the red and white phenotypes, indicating that neither allele is completely dominant over the other. This phenomenon demonstrates that genetic inheritance can exhibit more variation than the simple dominant-recessive patterns initially described by Mendel.

The environment plays a significant role in the expression of genetically inherited traits, illustrating that phenotype is not determined by genotype alone. Environmental factors can influence the extent to which a genetic trait is expressed, alter the way a trait is manifested, or even cause new phenotypic characteristics to emerge. This interaction between genes and the environment is termed gene-environment interaction. For example, the color of hydrangea flowers can change depending on the soil pH, a clear environmental influence. In humans, traits like height and weight are influenced by both genetic predispositions and environmental factors like nutrition and exercise. This complexity shows that the expression of genetic traits is often the result of a dynamic interplay between inherited genetic information and a variety of environmental conditions. Understanding this interaction is crucial in fields such as medicine and ecology, where the impact of environmental factors on genetic traits can have significant implications.

Polygenic inheritance plays a crucial role in determining complex traits, which are traits influenced by multiple genes, often along with environmental factors. Unlike single-gene traits, polygenic traits are controlled by several genes, each contributing a small amount to the overall phenotype. This results in a continuous variation of phenotypes, rather than the discrete variations seen in simple Mendelian inheritance. Examples of polygenic traits include human skin color, height, and aspects of personality and behavior. The significance of polygenic inheritance lies in its ability to create a diverse range of phenotypes, contributing to the variation seen within populations. It also complicates genetic analysis because the effects of individual genes can be subtle and influenced by interactions with other genes and environmental factors. Understanding polygenic inheritance is key in fields like genetics, evolutionary biology, and medicine, particularly in the study of complex diseases like heart disease, diabetes, and mental health disorders, which do not follow simple Mendelian inheritance patterns.

The concept of linked genes challenges Mendel's principle of independent assortment, which states that alleles for different traits segregate independently during gamete formation. Linked genes do not follow this principle because they are located close together on the same chromosome and tend to be inherited together. This linkage alters the expected genetic ratios predicted by independent assortment. For instance, in dihybrid crosses involving linked genes, the offspring will more frequently exhibit parental phenotypes rather than the recombinant phenotypes expected from independent assortment. This deviation from Mendel's predictions led to the discovery of chromosomal theory of inheritance and the understanding that genes are arranged linearly on chromosomes. Genetic linkage is particularly important in genetic mapping and in understanding inheritance patterns in diseases where multiple genes are involved. It demonstrates that genetic inheritance is more complex than initially thought and involves the physical positioning and interaction of genes on chromosomes.