Darwin expanded his principle of natural selection to explain sexually dimorphic traits (features that differ between the sexes), including why, for example, males of many species tend to have more showy traits, while females often are comparatively drab. Darwin proposed that competition for mating opportunities drives the process of sexual selection as long as the fitness benefits conferred by this selection outweigh the costs imposed by natural selection. For instance, elaborate male traits, such as the spectacular train (tail coverts) of the male peacock, are clearly important to attracting females during courtship. However, the large elongated train increases susceptibility to predators by reducing the males' flight capability. In contrast, peahens (female peacocks), for whom the males are competing, are relatively drab, and blend more successfully with their environments. Females are less vulnerable to  predators, particularly during nesting season. Darwin noted that since females and non-breeding males lack exaggerated colors or displays, these features of breeding males probably are disadvantageous. 
There are two basic forms of sexual selection: intrasexual and intersexual. Intrasexual selection is driven by direct competition among members of one sex. This can involve contests between males of a species to gain mating opportunities with females. Such male-male combat is found among deer, for example. Competition between males also may take place during reproduction. In some species, sperm from more than one male may compete to fertilize the female's eggs. In contrast, intersexual selection is driven by abilities of one sex to attract the attention of the opposite sex and be chosen as a mate. Females generally drive intersexual selection, as they choose males with which to mate based on "attractive" features, such as the showy courtship display of the peacock, or other features, such as size or vocalizations, or dominance of other males.

Early in the 20th century, the mathematician G.H. Hardy and the physician Wilhelm Weinberg, independently developed probabilistic models of genetic variation at the population level. The Hardy-Weinberg principle states that the gene pool of a population will remain constant indefinitely (i.e., it will be in equilibrium) unless a "disturbing" influence is introduced. In other words, the genetic variation introduced through the processes of meiosis and random fertilization does not affect a population's overall gene pool.

A theoretical non-evolving population is said to be in Hardy-Weinberg equilibrium. For a population to reach and maintain this equilibrium, it must meet specific criteria: it must be infinitely large, exhibit random mating patterns, have a constant, unchanging gene pool (no net mutation), have no migration into or out of the population, and have no natural or sexual selection occurring within the population.

Hardy-Weinberg calculations identify the allelic and genotypic frequencies expected from generation to generation, when a population is in Hardy-Weinberg equilibrium. For a population to reach and maintain this equilibrium, it must meet criteria (e.g. random mating patterns, no mutation, no selection) that are essentially unattainable outside of a laboratory setting. Thus, evolution occurs when natural populations deviate from Hardy-Weinberg equilibrium, causing shifts from the expected allelic and genotypic distributions. The major mechanisms that drive these shifts are selection, mutation, migration, genetic drift, and non-random mating.

Deviations from Hardy-Weinberg expectations of gene frequencies within a population also occur through non-random mating, which can lead to altered genotypic frequencies. In assortative mating, "like mates with like." In other words, individuals with similar phenotypes, and thus similar genotypes, are more likely to mate with each other than at random. Human populations are among those that exhibit assortative mating for a great number of features (genetic and non-genetic), such as height. Tall women are more likely to mate with tall men and short women are more likely to mate with short men. This kind of non-random mating violates the assumptions of Hardy-Weinberg equilibrium by creating an excess of homozygotes.

In disassortative mating, "like mates with unlike." That is, individuals with dissimilar phenotypes, and thus dissimilar genotypes, are more likely to mate with each other than at random. This kind of non-random mating violates the assumptions of Hardy-Weinberg by creating an excess of heterozygotes.

Mendelian disorders, which follow Mendel's rules of inheritance, can be inherited in an autosomal dominant, autosomal recessive, X-linked, or Y-linked manner. Humans typically carry two copies of each autosomal chromosome (chromosomes 1-22) and two copies of each autosomal gene. Individuals affected by autosomal recessive disorders carry two copies of the gene associated with the trait or disorder. The word trait is typically used by geneticists to describe genetically inherited physical characteristics or features that are not considered to be diseases or disorders. Autosomal recessive traits are inherited in a manner similar to that of autosomal recessive disorders.

Autosomal recessive inheritance is frequently observed as the appearance of a disorder in only one generation of a family as isolated cases or affected siblings and/or cousins. Autosomal recessive inheritance is sometimes described as horizontal inheritance although this term is not commonly used today. In the case of common recessive disorders or disorders that lead to non-random mating, such as deafness, which is common and frequently leads to deaf by deaf matings, a pseudo-dominant pattern of inheritance may be observed. For genetic counseling and risk assessment, it is important to recognize the possibility that pseudo-dominant inheritance might be occurring in a family.

In general, males and females affected by autosomal recessive disorders will be affected with the same frequency and severity, but there may be exceptions in cases where a disorder affects the genders differently. In general, autosomal recessive disorders do not show reduced penetrance or the considerable variability that can be associated with autosomal dominant disorders. However, there are some autosomal recessive disorders for which variability in the severity of symptoms among affected individuals is observed. Reduced penetrance is a phenomenon in which some gene carriers remain unaffected despite the fact that they carry a gene associated with a trait or disorder. One explanation for this phenomenon is that the gene is necessary but not sufficient to cause disease.

Most often, children affected by autosomal recessive disorders are born to unaffected parents. However, for certain autosomal recessive disorders, there may be very mild or atypical manifestations of the disease in a carrier parent. Frequently in autosomal recessive disorders, there is no family history of the disease and no reason to suspect an affected child could be born. Carrier couples (in which both partners are carriers of the same autosomal genetic disorder) have a 25% risk of an affected child with each pregnancy. Examples of autosomal recessive disorders include cystic fibrosis (CF), Tay-Sachs disease, and sickle cell disease.

Under what conditions widespread screening should be undertaken for the identification of unaffected carriers of autosomal recessive disorders is a topic of much debate. At present, most carrier screening programs focus on high risk groups such as screening for cystic fibrosis (CF) carriers among Caucasians and screening for CF, Tay Sachs and other genetic disease carriers among Ashkenazi Jews.

In pedigree drawings, boxes are males and circles are females. Shaded shapes are affected individuals and open shapes are unaffected individuals. The drawing in this slide illustrates an autosomal recessive disorder. In this case, the affected child is born to unaffected parents with no family history of the disease.