was translated into several languages. Mendel's rediscovered the hypothesis of particulate inheritance was also bolstered by evidence from microscopic observations of chromosomes during cell division that led Walter Sutton to propose in 1902 that chromosomes are the physical basis of heredity, supported by results obtained independently by Theodor Boveri at around the same time (see Crow and Crow 2002).
Much of the currently used terminology was coined as the field of particulate genetics initially developed. Therefore, many of the critical terms in genetics have remained in use for long periods of time. However, the meanings and connotations of these terms have often changed as our understanding of genetics has also changed.
Unfortunately, this has led to a situation where words can sometimes mislead. A common example is equating gene and allele. For example, it is commonplace for news media to report scientific breakthroughs where a “gene” has been identified as causing a particular phenotype, often a debilitating disease. Very often what is meant in these cases is that a genotype or an allele with the phenotypic effect has been identified. Both unaffected and affected individuals all possess the gene, but they differ in their alleles and therefore in their genotype. If individuals of the same species really differed in their gene content (or loci they possessed), that would provide evidence of additions or deletions to genomes. For an interesting discussion of how terminology in genetics has changed – and some of the misunderstandings this can cause, see Judson (2001).
Gene: A unit of particulate inheritance; in contemporary usage, it usually means an exon or series of exons, or a DNA sequence that codes for an RNA or protein.
Locus (plural loci, pronounced “low‐sigh”): Literally “place” or location in the genome; in contemporary usage, it is the most general reference to any sequence or genomic region, including non‐coding regions.
Allele: A variant or alternative form of the DNA sequence at a given locus.
Genotype: The set of alleles possessed by an individual at one locus; the genetic composition of an individual at one locus or many loci.
Phenotype: The morphological, biochemical, physiological, and behavioral attributes of an individual; synonymous with character and trait.
Dominant: Where the expressed phenotype of one allele takes precedence over the expressed phenotype of another allele. The allele associated with the expressed phenotype is said to be dominant. Dominance is seen on a continuous scale that includes “complete” dominance (one allele completely masks the phenotype of another allele so that the phenotype of a heterozygote is identical to a homozygote for the dominant allele) and “partial” or “incomplete” dominance (masking effect is incomplete so that the phenotype of a heterozygote is intermediate to both homozygotes) and includes over‐ and under‐dominance (phenotype is outside the range of phenotypes seen in the homozygous genotypes). The lack of dominance (heterozygote is exactly intermediate to the phenotypes of both homozygotes) is when the effects of alleles are additive, a situation sometimes termed “codominance” or “semi‐dominance.”
Recessive: The expressed phenotype of one allele is masked by the expressed phenotype of another allele. The allele associated with the concealed phenotype is said to be recessive.
2.2 Hardy–Weinberg expected genotype frequencies
Hardy–Weinberg and its assumptions.
Each assumption is a population genetic process.
Hardy–Weinberg is a null model.
Hardy–Weinberg in haplo‐diploid systems.
Mendel's “laws” could be called the original expectations in population genetics. With the concept of particulate genetics established, it was possible to make a wide array of predictions about genotype and allele frequencies as well as the frequency of phenotypes with a one‐locus basis. Still, progress and insight into particulate genetics were gradual. Until 1914, it was generally believed that rare (infrequent) alleles would disappear from populations over time. Godfrey H. Hardy (1908) and Wilhelm Weinberg (1908) worked independently to show that the laws of Mendelian heredity did not predict such a phenomenon (see Crow 1988). In 1908, they both formulated the relationship that can be used to predict allele frequencies given genotype frequencies or predict genotype frequencies given allele frequencies. This relationship is the well‐known Hardy–Weinberg equation.
where p and q are allele frequencies for a genetic locus with two alleles.
Genotype frequencies predicted by the Hardy–Weinberg equation can be summarized graphically. Figure 2.5 shows Hardy–Weinberg expected genotype frequencies on the y axis for each genotype for any given value of the allele frequency on the x axis. Another graphical tool to depict genotype and allele frequencies simultaneously for a single locus with two alleles is the de Finetti diagram (Figure 2.6). As we will see, de Finetti diagrams are helpful when examining how population genetic processes dictate allele and genotype frequencies. In both graphs, it is apparent that heterozygotes are most frequent when the frequency of the two alleles is equal to 0.5. You can also see that when an allele is rare, the corresponding homozygote genotype is even rarer since the genotype frequency is the square of the allele frequency.
A single generation of reproduction where a set of conditions, or assumptions, is met will result in a population that meets Hardy–Weinberg expected genotype frequencies, often called Hardy–Weinberg equilibrium. The list of assumptions associated with this prediction for genotype frequencies is long. The set of assumptions includes:
Figure 2.5 Hardy–Weinberg expected genotype frequencies for AA, Aa, and aa genotypes (I‐axis) for any given value of the allele frequency (x‐axis). Note that the value of the allele frequency not graphed can be determined by q = 1 – p.
the organism is diploid,
reproduction is sexual (as opposed to clonal),
generations are discrete and non‐overlapping,
the locus under consideration has two alleles,
allele frequencies are identical among all mating types (i.e. sexes),
mating is random (as opposed to assortative),
there is random union of gametes,
population size is very large, effectively infinite,
migration is negligible (no population structure, no gene flow),
mutation does not occur or its rate is very
