22 Inbreeding coefficient and Inbreeding depression

Dr. Rajesh Kumar Gautam

CONTENTS:

1.Learning outcomes: At the end of the module the reader will know 

• Inbreeding
• Consanguinity
• Inbreeding co-efficient
• Inbreeding depression
• Classical examples of Inbreeding depression

Inbreeding coefficient and Inbreeding depression

Bi-parental reproduction has its own importance in natural selection and evolution. In which, a limited number of mutations, which are not too injurious, to be carried by the species furnish an almost infinite field of possible variation through which species may work its way under natural selection. But, at the same time, in bi-parental reproduction, there may have breeding or mating between closely related individuals for example: brother-sister mating and father-daughter mating. Such kind of mating practices are called Inbreeding.

In another word, Inbreeding is a mating practice among organism of common ancestry; it is contrary to out-breeding, which is the mating practice of unrelated individuals. The inbreeding has various pro and cons. In genetics, it is an important practice, for retention of desirable characteristics or the elimination of undesirable ones. For course of evolution, variation in gene pool is essential; in the same way for perpetuation and existence of any species variation in gene pool should be maintained; and to maintain variation in gene pool inbreeding should be avoided. But, at the same time; to maintain homogeneity in offsprings inbreeding is essential. Sometimes, it is the only way to perpetuate any species or group of organism in the circumstances of limited number of eligible mating population.

According to Jacquard (1975) Inbreeding’ is used to describe various related phenomena that all refer to situations in which matings occur among relatives and to an increase in homozygosity associated with such matings. However, they differ in the reference population that is used when calculating inbreeding. Inbreeding is always a relative never an absolute measure. Therefore, inbreeding estimates differ depending on the reference population to which they refer. It is this relativity that is responsible for the different meanings of the term ‘inbreeding’, and for some of the misunderstanding that have resulted. There is a historical precedence for such misunderstandings: Fisher (1965) never accepted Wright’s inbreeding coefficients because they are relative (Keller and Waller, 2002). Three of the most commonly used definitions of inbreeding are.

1. Pedigree inbreeding

An individual is considered inbred under this definition when the parents share ancestors. The extent of inbreeding is related to the amount of ancestry that is shared by the parents of an inbred individual. Pedigree information is used to determine the inbreeding coefficient. Although originally derived as a correlation by Wright (1922).

2. Inbreeding as non-random mating

This refers to the degree of relatedness between mates relative to two mates chosen at random from the population.  An individual is considered  inbred if its parents were more closely related than two randomly chosen individuals. This type of inbreeding is relative to a random mating population of the same size. Although it can be determined from pedigree data, this type of inbreeding is typically measured   by   the   deviation   of   the   observed   heterozygosity   of   an   individual   relative   to  the heterozygosity expected under random mating.

3. Inbreeding because of population sub division

When populations are subdivided into more or less isolated groups, inbreeding will also occur purely because population size is restricted and genetic drift results. This occurs even if mating is random within subpopulations (Crow and Kimura, 1970). This third definition of inbreeding corresponds to the mean inbreeding coefficient expected in subpopulations under random mating.

Inbreeding is considered a problem in humans because inbreeding increases the chances of receiving a deleterious recessive allele inherited from a common ancestor. Most studies are concerned with close inbreeding, also known as incest, which usually sets a threshold at the level of first-cousin mating (Thorn hill 1993).

Consanguinity

Two individuals are said to be consanguineous if they have at least one ancestor in common. In the breeding of domestic animals consanguineous mating are frequently made. Occasionally matings are made between very close relatives- father or sire and daughter, brother and sister etc. On the basis of the theory of evolution, all individuals of a species are to some extent consanguineous, since all are descended from a remote common ancestor. Consanguinity, and level of inbreeding, must therefore be defined as applying only to relationships established after some evolutionary time point at which, for convenience everyone is considered to be unrelated.

In practice, for human consanguinity common ancestors more remote than a great great grandfather are rarely considered. In some human societies, more distant consanguinities may have social significance, but from a genetic point of view the connection between two individuals who have one great great great grandparent in common (fourth half cousins) is very vague (Cavalli-Sforza and Bodmer 1971).

The progeny of consanguineous parents is, by definition, inbred. The inbred individuals may carry double dose of a gene that was present in a single dose in common ancestor.

A recessive gene carried in a single dose in a common ancestor may remain hidden until it comes to light for the first time in an inbred descendant. Therefore, recessive traits will occur with increased frequency in the progeny of consanguineous mates.

The occurrence of consanguinity in a population depends on various factors viz. population structure, migration, cultural practices and so on. Generally very close consanguineous mating are avoided in human population. Practically, in all human societies incest is considered to be taboo. The degree of relationship at which mating is considered incestuous may differ slightly from one society to another, but, in general, parent-offspring and brother-sister mating are forbidden in all societies. Still, incestuous union may be in most of the societies, but, they are negligible in proportion. Adam and Neel (1967) have studied such children and most of them were the result of brother-sister mating and father-daughter mating.

Marriage with a sib’s progeny (uncle-niece or aunt-nephew) is incestuous and not permissible in some societies. In others, it is permissible with certain specific dispensation. Among many of Indian tribes cross-cousin marriages are considered as preferential marriages.

By definition, an inbred individual is connected through both his father and his mother to the same recent ancestor. He can thus receive two copies of a gene that was carried by common ancestor. Two such copies are said to be identical, unless mutation has taken place in one of the line of descent, which, however, is very rare event.

An individual who is homozygous for a given gene carries at a certain locus two homologous genes that are physically identical but not necessarily identical by descent. This physical identity is what we call identity by nature. Inbreeding makes an individual homozygous for genes that are identical by descent.

Inbreeding co-efficient

Measurement of degree of inbreeding can be done by inbreeding co-efficient. The importance of having a coefficient by means of which the extent of inbreeding can be expressed was brought out by Pearl (1913). His coefficient was based on the smaller number of ancestors in each generation back of an inbred individual, as compared with the maximum possible number. A separate coefficient is obtained for each generation by the formula (Wright 1992).

This coefficient has the defect, as Pearl himself pointed out, that it may come out the same for systems of breeding which we know are radically different as far as the effects of inbreeding are concerned.

In order to overcome this objection Pearl has devised a partial inbreeding index which is intended to express the percentage of the inbreeding which is due to relationship between the father (sire) and mother (dam), inbreeding being measured as above described. A coefficient of relationship is used in this connection. There are two classes of effects which are ascribed to inbreeding: First, a decline in all elements of vigour, as weight, fertility, vitality, etc., and second, an increase in uniformity within the inbred offsprings, correlated with which is an increase in prepotency in outside crosses. Both of these kinds of effects have ample experimental support as average (not necessarily unavoidable) consequences of inbreeding. The best explanation of the decrease in vigour is dependent on the view that Mendelian factors unfavorable to vigour in any respect are more frequently recessive than dominant, a situation which is the logical consequence of the two propositions that mutations are more likely to injure than improve the complex adjustments within an organism and that injurious dominant mutations will be relatively promptly weeded out, leaving the recessive ones to accumulate, especially, if they happen to be linked with favourable dominant factors. On this view, it may readily be shown that the decrease in vigour on starting inbreeding in a previously random-bred population should be directly proportional to the increase in the percentage of homozygosis. Numerous experiments with plants and lower animals are in harmony with this view. Extensive experiments with guinea-pigs conducted by the Bureau of Animal Industry are in close quantitative agreement. As for the other effects of inbreeding, fixation of characters and increased prepotency, these are of course in direct proportion to the percentage of homozygosis. Thus, if the percentage of homozygosis can be calculated which would follow on the average from a given system of mating, a most natural coefficient of inbreeding can be formed. The Wright (1992) has pointed out a method of calculating this percentage of homozygosis which is applicable to the irregular systems of mating found in actual pedigrees as well as to regular systems, which is widely different from Pearl’s coefficient, in many cases even as regards the relative degree of inbreeding of two animals.

Taking the typical case, in which, there are an equal number of dominant and recessive genes (A and a) in the population, the random-bred population will be composed of 25 per cent AA, 50 per cent Aa and 25 per cent aa. Close inbreeding will tend to convert the proportions to 50 per cent AA, 50 per cent aa, a change from 50 per cent homozygosis, to 100 per cent, homozygosis. For a natural coefficient of inbreeding, a scale is needed which runs from 0 to 1, while the percentage of homozygosis is running from, 50 per cent, to 100 per cent. The formula 2h-1, where h is the proportion of complete homozygosis, gives the required value. This can also be written 1-2p where p is the proportion of heterozygosis. It was already shown that the coefficient of correlation between uniting egg and sperm is expressed by the same formula, f= 1-2p. In this way, the coefficient of inbreeding fb for a given individual B, can be obtained by the use of the methods outlined.

The symbol rbc, for the coefficient of the correlation between B and C, may be used as a coefficient of relationship. It has the value 0 in the case of two random individuals, 0.50 for brothers in a random population and approaches 1.00 for individuals belonging to a closely inbred subline of the general population.

In the general case in which dominants and recessives are not equally numerous, the composition of the random-bred population is of the form x2 AA , 2xy Aa, y2 aa. The percentage of homozygosis is greater than 50 per cent. The rate of increase, however, under a given system of mating, is always exactly proportional to that in the case of equality. The coefficient is thus of general application.

If an individual is inbred, his father and mother are connected in the pedigree by lines of descent from a common ancestor or ancestors. The coefficient of inbreeding is obtained by a summation of coefficients for every line by which the parents are connected, each line tracing back from the father to a common ancestor and thence forward to the mother, and passing through no individual more than once. The same ancestor may of course be involved in more than one line.

The correlation between two individuals (rbc ) is obtained by a summation of the coefficients for all connecting paths.

Thus

Where n and  ἡ are the number of generations in the paths from A to B and from A to C, respectively.

The formula for the correlation between uniting gametes, which is also the required coefficient of inbreeding, is

where is the correlation between father (sire) and mother (dam) and  and  are coefficients of

inbreeding of father (sire) and mother (dam). Substituting the value of   we obtain:

This formula gives the departure from the amount of homozygosis under random mating toward complete homozygosis. The percentage of homozygosis (assuming 50 per cent. under random mating)

is .

The inbreeding coefficient represents the probability that an offspring will receive a gene from each parent that is a copy of a single shared ancestral gene. The inbreeding coefficient is zero if the parents do not share a common ancestor, and if the inbreeding coefficient is one than the offspring has a 100% chance of receiving two copies of the ancestral gene. However, this maximum inbreeding coefficient of one cannot be achieved in human populations (Dorsten 1999).

Alternative Methods of calculating the coefficient of inbreeding

An alternative method of computing F was proposed by Falconer (1989). In this technique the ‘Co ancestries’ are used instead of working from the present back to common ancestors we work forward, keeping a running tally, generation by generation, and compute the inbreeding that will result from the mating now being made. This method is easier than path coefficients where the paths are often numerous and complex but unnecessary for normal human pedigrees.

For regular systems of inbreeding, as used in the ‘inbred-hybrid’ system for breeding of animals it is easy method for calculating F. In a a regular system of inbreeding, there is a certain type of mating such as brother-sister, is repeated indefinitely. A recurrence equation calculates the F value of the present generation from those of recent previous ones. e.g. the recurrence equation for repeated full sib mating is:

For further elucidation, the value of F is shown in the following table as per different consanguineous mating.

Table: values of F for consanguineous mating one generation, no previous inbreeding)

Inbreeding Depression

Biologically, inbreeding has many harmful effects on the offspring. They may be homozygous for certain lethal genes. In this way, reduced biological fitness in a given population as a result of inbreeding is known as Inbreeding depression. Many studies have demonstrated reduced survival and fecundity of inbred young (Wright 1977; Ralls and Ballou 1983, Sausman 1984, Templton and Read 1984). Biological fitness refers to ability to survive and reproduce. Inbreeding depression is often the result of a population bottleneck.

A population bottleneck is a sharp reduction in the size of a population due to environmental events such as earthquakes, floods, fires, disease, droughts, human genocide etc. Such events can reduce the variation in the gene pool of a population. After an incident, a smaller population with few individuals, with a correspondingly smaller genetic diversity, remains to pass on genes to future generations of offspring. Such reduction population size results in the loss of genetic variation. The robustness of the population is reduced; the ability of the population to survive is also reduced.

Figure: Population bottleneck followed for recovery and extinction.

In other words, the higher the genetic variation or gene pool within a breeding population, the less likely it is to suffer from inbreeding depression.

Mechanism responsible for inbreeding depression is the fitness advantage of heterozygous, which is known as over dominance. This can lead to reduced fitness of a population with many homozygous genotypes, even if they are not deleterious. Here, even the dominant alleles result in reduced fitness if present homozygously.

Inbreeding can increase an individual’s inclusive fitness by producing young that share more of its genome. Thus, when inbreeding has little or no genetic cost, there should be strong selective advantage for inbreeding as well as recognition and cooperation among kin (Wilson 1976, May 1979). The cost of inbreeding is therefore of theoretical importance as well.

Calculation of the total cost of inbreeding in natural population would involve considering the effects of inbreeding on several components of fitness.

For further elucidation of facts to understand the effect of inbreeding depression some characteristics of men, pig, cattle, sheep, chicken were studied by some of the investigators are being presented in the following table:

In small populations of randomly mating individuals, all may suffer from inbreeding depression because of the cumulative effects of genetic drift that decrease the fitness of all individuals in the population. Inbreeding depression may potentially be reduced, or purged, by breeding related individuals. There can be several lethal consequences of inbreeding which include mortality, morbidity and even it may lead to extinction.

Inbreeding depression in humans seems to be highly uncommon and not widely known, there have been several cases of apparent forms of inbreeding depression in human populations. Charles Darwin, through numerous experiments, was one of the first scientists to demonstrate the effects of inbreeding depression. Charles’s wife, Emma was his first cousin. He attempted to study the theory of inbreeding within his own children (Bittles 1991). Out of ten children, three died before the age of ten. Of the rest, three had child-less long-term marriages.

A study has provided the evidence for inbreeding depression on cognitive abilities among children, with high frequency of mental retardation among offspring in proportion to their increasing inbreeding coefficients (Fareed and Afzal, 2014a). The depression on growth parameters (height, weight and body mass index) due to inbreeding among children has revealed the significant increase in underweight cases with increasing inbreeding coefficients (Fareed and Afzal, 2014b).

Reasons of Inbreeding

Studies have shown that in many societies consanguineous marriages predominate. In fact, in many large populations of Asia and Africa twenty to fifty percent of all unions are that of consanguineous marriages (Bittles 1991). There are several circumstances that would give a population a reason to practice inbreeding at a large scale. Some of these reasons for practicing inbreeding include royalty, religion and culture, casteism, socioeconomic class, geographic isolation and small population size.

Religion, culture and casteism can play a large role in the amount of inbreeding that takes place in a population. In many Muslim and Hindu societies in Africa and Asia consanguious marriages, especially unions of first cousins, account for twenty to fifty-five percent of the total. These religions tend to inbreed because of religious acceptance, preference, and tradition. In many Indian tribes, the cross cousin marriages are one of the preferential marriages. Moreover, the culture of these societies also plays a large role to increased levels of inbreeding. Consanguineous marriages are thought to be an advantage when considering compatibility of the bride and her husband’s family. This is particularly important when discussing the bride’s relationship with her mother-in-law and the up-keep of the family’s property. Another incentive to close relative marriages concerns bride wealth and dowry. Consanguineous marriages can lead to greatly reduced or no payments at all in unions of this culture. This allows small landowning families to keep their property and land (Bittles 1991).

Other groups that are associated with inbreeding because of religion and culture are the small Anabaptist populations in North America. These groups include the Amish, the Mennonites, and the Hutterites. These groups settled in North America in the 18th and 19th centuries in search of religious freedom. These populations have shown increases in consanguineous marriages over time, and reached to 85% in the 1950’s. The reason for the high levels of inbreeding is not only due to religion; it can also be attributed to the small isolated farming communities in which these populations find themselves. These factors of religion and small communal societies lead to limited choices when searching for possible mates (Agarwala 2001). Studies show that inbreeding levels can depend largely on geographic, demographic, social, and economic factors (Fuster 2001). Furthermore, numerous other studies have shown that socioeconomic status can have a large impact on the level of inbreeding. In many cases the poorest and least educated members of a community tend to have the highest inbreeding levels in a population (Bittles 1991).

Inbreeding has also been seen to occur frequently in many royal families. Royal incest was commonly found in Ancient Egyptian, Incan, Hawaiian, and many European royal families. Brother-sister unions become more frequent when royalty is the major factor concerning the incidence of inbreeding. There are several factors that can explain why royalty leads to high levels of inbreeding. One factor is that the king has limitless power in many cultures, and he can do what he wants and marry who he wants. Also, in many cases inbreeding is practiced in royal families to preserve royal blood lines. Another explanation is that a royal family can keep land, material possessions and resources within the family. Moreover, brother-sister royal incest allows succession of the throne to both a male and female blood line. There are also cases in which royal incest is part of a culture and is sometimes linked to legends or myths. One of the best documented cases of this was seen in the Incan culture in the 16th century. The Incan king was to marry his full sister (Van Den Berghe 1980).

Royalty also uses inbreeding to try to maximize fitness. One of the royal strategies to maximize fitness by using inbreeding to put as close to a genetic clone as possible on the throne as the heir. Moreover, females tend to maximize fitness by picking the best possible mate, which in this case would mean marrying to a higher social class. This leads to women with the highest-status in a population to being the most inbred in this type of society (Van Den Berghe 1980).

Some classical examples of Inbreeding and its deleterious effect European Royal Families

Inbreeding was very common among the royal families of Europe, and it has been linked as the cause of the widespread number of cases of hemophilia in the families. The presence of haemophilia in the royalty of Europe started with Queen Victoria of England. Victoria is thought to be the original carrier for the recessive X-linked hemophilia gene, which lead to over twenty members of royal families inheriting the disease in just over 100 years.

No ancestor of Queen Victoria showed any evidence of hemophilia, so several theories arose on the gene’s origin. One theory is that Victoria was the victim of a mutation that could have been due to years of inbreeding in British royalty. Another interesting theory is that Victoria’s mother had an affair because of the intense pressure of producing an heir, and the Edward Duke of Kent was not Victoria’s biological father (Stevens 1991).

Study on Japanese Children after WWII

Shortly after the United States dropped two atomic bombs on Japan in World War II there was an increase in the number of consanguineous marriages in the areas surrounding Hiroshima and Nagasaki. The most common union was seen to be inbreeding at the first-cousin level. The study was set up to study some of the possible effects of inbreeding. The five effects of inbreeding looked at in this study was: the fertility of the marriages, the mortality of the offspring, the morbidity of the offspring, the reproductive performance of the offspring, and the characteristics of the offspring.

In the study, it was seen that inbreeding did not have an adverse effect on the fertility of the marriages, but there were some significant increases seen on childhood mortality in the first year of life. Inbreeding also increased morbidity in the study. There were significant increases in levels of handicapped offspring associated with inbreeding (Schull 1965).

The Hutterites

The Hutterites are a small group of Anabaptists that fled Europe and Russia and settled in what is now the Dakotas and Canada to escape from religious persecution. The Hutterites settled on communal farms, which isolated them from outside populations. Their isolation along with their beliefs leads to a highly inbred population. Moreover, the Hutterites are a good population to study because, like the Amish, they keep very detailed genealogical records. The Hutterites are also among the most fertile populations that commonly practice inbreeding (Ober 1999).

Summary

Mating practice of closely related individuals is called inbreeding or consanguinity. Consanguineous marriages are widely prevalent in human population. There are several reasons that a population would practice inbreeding that span from religion to geography to royal bloodlines. Many studies have shown that inbreeding can cause increases in mortality and morbidity. As populations become more knowledgeable to these possible effects levels of inbreeding tend to decrease. However, there are other populations that are less knowledgeable to the possible negative outcomes of inbreeding, and it is possible that the effects of inbreeding may not be detectable or visible. Therefore, if there are harmful recessive alleles present in the population, the genes and characteristics still have the possibility of surfacing and negatively affecting a population, but it is very possible that the population will never see any harmful effects due to incest. In fact, some experts believe that in some cases inbreeding can be helpful to a population by constantly exposing harmful recessive genes to selection. By frequently exposing these genes to selection, the harmful alleles can become permanently eliminated from the population. Inbreeding is a very touchy and controversial subject when it concerns humans, and there is still a lot that we do not know about the possible effects of inbreeding. By Inbreeding coefficient, it can be measured. Similarly, the inbreeding depression can be found out. Still, it is very difficult to run experiments to determine all the possible effects of inbreeding in humans, because there are too many variables to control. Moreover, ethics makes it difficult and many times impossible to perform studies on humans. However, most experts would agree that practicing out-breeding will provide a population with the best opportunity to achieve a high level of health.

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