Incomplete dominance is a genetic scenario where neither allele is completely dominant over the other. In this case, the heterozygous phenotype is an intermediate blend of the two homozygous phenotypes. For example, in snapdragons, a cross between a red-flowered plant (RR) and a white-flowered plant (WW) will produce offspring with pink flowers (RW), demonstrating incomplete dominance. In contrast, codominance occurs when both alleles in a heterozygous organism are fully expressed without blending. A classic example is the human ABO blood group system, where individuals with the genotype I^AI^B express both A and B antigens equally. In incomplete dominance, the heterozygous phenotype is a mix or intermediate of the two homozygous phenotypes, while in codominance, both alleles are expressed independently and simultaneously.

Allele frequencies within a population are estimated using the Hardy-Weinberg equilibrium principle, which provides a mathematical framework for understanding genetic variation. This principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. To estimate allele frequencies, scientists use the formula p² + 2pq + q² = 1, where p and q represent the frequencies of the two alleles. These calculations assume random mating, no mutation, no migration, large population size, and no natural selection. Estimating allele frequencies is crucial in population genetics as it helps in understanding the genetic structure of populations, tracking how traits are passed on over generations, and predicting future genetic trends. This information is vital for fields like conservation biology, where maintaining genetic diversity is key to species survival, and in medical genetics for understanding the spread of genetic diseases.

Alleles can change over time through the process of mutation, which is a permanent alteration in the DNA sequence that makes up a gene. Mutations can be caused by errors during DNA replication or as a result of environmental factors such as UV radiation, chemicals, and viruses. These changes can create new alleles or alter existing ones. For instance, a mutation in a gene that causes a change in the amino acid sequence of a protein might result in a new trait or a change in the way an existing trait is expressed. Over generations, these mutations can lead to significant genetic diversity within a population. While many mutations are neutral or harmful, some can confer an advantage in a particular environment, contributing to the process of natural selection. Over time, these advantageous mutations can become more prevalent in the gene pool, leading to evolutionary changes.

Environmental factors can significantly influence the expression of alleles, a concept known as genotype-environment interaction. While the genotype provides the genetic potential, the environment can affect the extent to which a trait is expressed. For example, temperature can influence the colour of the fur in Siamese cats and Himalayan rabbits. In these animals, the allele responsible for fur colour is temperature-sensitive. At lower temperatures, the enzyme that produces the dark pigment becomes more active, leading to darker fur on the cooler extremities of the body. Similarly, nutrition and stress can affect height and weight in humans, even though these traits have a genetic basis. Thus, the same genotype can produce different phenotypes under different environmental conditions. This interplay between genetics and environment is crucial in understanding the complexity of phenotypic expression.

Multiple alleles increase genetic diversity by introducing more variations in the gene pool of a population. Unlike a simple scenario with just two alleles (dominant and recessive), multiple alleles provide a range of genetic possibilities for a single gene. This diversity becomes crucial in populations, influencing traits like immune responses, physical features, and susceptibility to diseases. A prime example is the human ABO blood group system, controlled by three alleles (I^A, I^B, and i). These alleles combine to form six different genotypes and four different blood types (A, B, AB, and O), each with different antigenic properties. This diversity in blood types plays a significant role in transfusions and organ transplants. In evolutionary terms, multiple alleles can offer a survival advantage by providing a broader range of traits that can adapt to changing environments, thus enhancing a species' resilience and adaptability.