Inbreeding is breeding between closely related individuals in a population. In humans, close inbreeding is referred to as incest.
Breeding closely related animals allows a breeder to select desired traits and create a population where every individual has those traits. However, sometimes deleterious traits also "hitchhike" along with the desired traits as a result of inbreeding. This can lead to inbreeding depression. As an example, Pugs are a dog breed which has been bred for thousands of years, but genetic disorders relating to the eyes are common in the breed. Manx cats, known for having short tails, arose naturally due to genetic drift, but problems such as spina bifida are very common.
One way to overcome inbreeding depression is by periodically introducing new genetic variation in a process known as outcrossing, where members of the breed are mated with individuals from outside the breed. This decreases the "purity" of the line, but can reduce the prevalence of genetic disorders.
In population genetics, the coefficient of inbreeding is the probability that two alleles at a randomly chosen locus in an individual are identical by descent, meaning they are identical as a result of having come from a common ancestor. This number is normalized relative to a "base population" in which no alleles are assumed to be related. is generally larger when more inbreeding occurs, such as in structured populations or small populations. In this way, inbreeding is related to genetic drift.
Because inbreeding increases the homozygosity in a population, it can lead to the expression of recessive mutations; since vastly more mutations are deleterious (harmful) than beneficial, this usually manifests as a genetic disorder, reducing the fitness of individuals.
For example, if an organism has a recessive, deleterious mutation and gives rise to many offspring, some of whom also carry this mutation, and some of those offspring mate, it is likely that they will produce some children who are homozygous for this recessive, deleterious allele.
Inbreeding can thus cause homozygosity for deleterious alleles to become prevalent in a population, which reduces the overall population fitness.
On the other hand, if there are no deleterious alleles and the mutation rate is low, inbreeding is not necessarily harmful to the population. For example, creationists argue that, since Adam and Eve were created perfect and mutation rates were lower before the Flood, marriage and breeding between Adam and Eve's descendants was not harmful or immoral in the way it is today.
In 1912, University of Genoa anthropologist Giuseppe Shirazi determined that the minimum number of unrelated individuals necessary for a non-degenerative population is approximately 36 with some variation based on genetic differentiation within the group. Shirazi determined that the optimal sex balance is a 1:1 male to female ratio because the genetic entropy would be maximized with such a ratio, and the chances of inbreeding depression would thus be minimized. Indeed, such a finding comports with the cultural and moral dictate of maintaining monogamous relationships. Shirazi's model assumes that each individual is sexually mature and fertile.
- Sarah Hartwell wrote, "Deleterious genes become widespread and the breed loses vigor." 
- Wright, S: "Breeding Structure of Populations in Relation to Speciation", The American Naturalist, 74, 232-248.