The broad scientific definition of inbreeding is that it is the mating of individuals more closely related to each other than the average relationship within the population concerned.
This statement is really only valid for large populations, since with small populations inbreeding is inevitable, even with random mating. To be more precise, an inbred person is defined as someone whose parents are related.
In practice this means close direct relationship or, more usually, related through recent common ancestors, since all members of the same species are related to some extent.
The adverse effects of inbreeding in animals are well known. The incidence of metabolic disorders, structural abnormalities and inherited disease conditions, caused by harmful recessive genes, increases following inbreeding.
Performance in several characters, particularly those concerned with reproduction and survival, declines following the mating of close relatives. This is known as inbreeding depression.
These effects are mainly due to an increase in the frequency of homozygous genotypes (AA and aa) at the expense of heterozygotes (Aa), which is caused by inbreeding. It is only harmful, however, when the dominance is directional, which means that the undesirable member of a pair of genes is usually recessive.
When a high proportion of these harmful genes are present in the heterozygous state (Aa) the animal is protected from their debilitating effects by the dominance of the normal gene; but when some of the heterozygotes are replaced by homozygous recessives (aa), following inbreeding, their harmful effects become manifest.
Other types of gene action are sometimes responsible for inbreeding damage, but are thought to be less important. These are: overdominance, epistatic interaction and the overall level of heterozygosity.
Over-dominance occurs when the heterozygote (A1A2) is superior in performance to either of the two homozygotes (A1A1 or A2A2). In this situation, an increase in homozygosity following inbreeding also causes inbreeding depression.
Epistatic interaction between different pairs of genes occurs when one pair affects the expression of another pair at a different locus.
With one particular type, called complementary epistasis, two dominants, one from each of two separate loci, are necessary for normal development or metabolism.
Thus, AABB, AaBB, AABb and AaBb will be normal, but AAbb, aaBBAabb, aaBb and aabb will be defective. This situation arises when a metabolic pathway requires two enzymes for the essential end-product to be synthesized.
Since each enzyme requires a different dominant gene for its synthesis, the absence of one or both will result in a defective individual. Inbreeding in a population with a mixture of the above genotypes will lead to a break- up of the favorable gene combinations, with more inferior genotypes, particularly aaBB, AAbb and aabb, being produced.
Finally, Lerner (1954) found evidence that some abnormal conditions in animals were not caused by single genes but by a drop in the general level of heterozygosity throughout the whole genome.
His theory of developmental homeostasis suggests that for an animal to be able to cope with developmental accidents and environmental stress there is a minimum or obligate level of heterozygosity for normal development.
The implication being that heterozygotes in general are more versatile because they can produce a greater variety of enzymes and other proteins. This means that the heterozygosity level per se, as well as the effects of the genes themselves, may be a contributing factor.
The opposite of inbreeding depression is known as heterosis or hybrid vigour and can result from the crossing of unrelated inbred animals or lines with different genetic backgrounds.
What is lost from inbreeding is usually restored when several inbred lines are crossed randomly. Deliberate inbreeding and crossing, followed by selection between lines, is sometimes used with farm plants and animals to improve yields.
Its significance in humans is that greater mobility means that people travel further to find a spouse and are less likely to marry a person from the same locality with a similar genotype.
Thus, although most of the increase in height and improved survival is the result of better nutrition and disease control, a small part may also be due toheterosis following a change in the mating system.
Introduction
The coefficient of inbreeding (F) measures the probability that two genes at any locus in an individual are identical by descent from the common ancestor(s) of the two parents.
This means the degree to which two alleles are more likely to be homozygous (AA or aa) rather than heterozygous (Aa) in an individual, because the parents are related.
Like R,F is a relative measure, in that there will be a certain level of homozygosity within the base population; F simply estimates the increase from that initial level as a result of recent inbreeding.
The inbreeding coefficient of an individual is approximately half the relationship (R) between the two parents.
This equivalence only applies to low levels of inbreeding in an otherwise outbred population. E.g. two single first cousins normally have a relationship (R) of 1/8.
If there has been no previous inbreeding, their children will have a coefficient of inbreeding of 1/16.
With high levels of continuous inbreeding this relationship breaks down. E.g. some strains of laboratory rats and mice have reached an F value of 1.0, resulting from a long history of close inbreeding; but the coefficient of relationship (R) between any two members of the strain can never exceed 1.0.
The mathematical reason for this is that although the basic formulae for R and F are Σ(1/2)n and Σ(1/2)n+1, respectively, as inbreeding within a line progresses, the correction terms applied to R for inbreeding gradually become more important and start to reduce the value of R below Σ(1/2)n.
As F approaches 1.0, the correction terms for R also approach a maximum of (x 1/2); so that when F reaches 1.0 (complete homozygosity), R also becomes 1.0 and all members of the inbred line are identical.
The method of calculating the F coefficient of an individual is similar to that for the coefficient of relationship (R) between two collateral relatives, and involves the tracing of paths between the two parents via a common ancestor. The formula is as follows:-
Equation 1: Method of calculating the F coefficient of an individual-
Where FX is the coefficient of inbreeding of individual X, n is the number of connecting links between the two parents of X through common ancestors and FA is the coefficient of inbreeding of the common ancestor A.
Thus, if the common ancestor is inbred, a minor calculation must be performed first to determine FA, before the main calculation can take place.
In the main calculation any coefficients of paths through inbred common ancestors can then be multiplied by (1+ FA).
Example with an Inbred Common Ancestor:
The Closest Form of Inbreeding
The closest form of inbreeding is self-fertilization which normally only occurs in monoecious plants and animals which are hermaphrodites, e.g. garden peas and slugs.
The equivalent situation has been experimentally produced in turkeys where a rare form of parthenogenesis occurs. Parthenogenesis (virgin birth) is the production of viable embryos (always males in birds) from haploid infertile eggs by the artificial doubling of chromosome numbers.
The embryos are highly homozygous. If one of these parthenogenetic males is mated back to his mother this is equivalent to self- fertilization. One generation of self-fertilization produces the same coefficient of inbreeding (F) as three generations of full sib mating, i.e. 0.5.This follows from the formula for F, which is Σ(1/2)n+1 where n is the number of connecting links between the two parents via a common ancestor.
With selfing, both parents are the same individual so that the number of links (n) is 0 and, therefore Σ(1/2)n+1 = 0.5.
Sib Marriages in Humans
In some societies close consanguineous marriages have been encouraged. For example, the ancient Egyptians and the Incas favoured marriages of brothers and sisters of the reigning dynasty.
Marriages between Sibs and Half-sibs in the18th Dynasty of Egypt,c.1580–1350.
| Inbreeding Coefficients | |
| F | |
| a) Amenhotep I and Aahotep II | 25% |
| b) Aames | 37.5% |
| c) Hatsheput | 25% |
d) The rest of the individuals in the pedigree are not inbred, i.e. F = 0.
Double Grandchildren – The offspring of a full sib mating are sometimes referred to as double grandchildren because they only have two grandparents instead of the usual four.
The Special Case of Directly Related Parents
In an incestuous situation where there is a close direct relationship between the two parents, such as father-daughter, mother-son or grandparent-grandchild, they may have no common ancestors in any previous generation, even though they have a strong genetic link.
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This is because one parent is the direct ancestor of the other. In these situations, despite having no common ancestors, the correction term (1 + FA) must still be applied to the path coefficient between an inbred ancestor (A) and his/her descendant partner.
A Father-Daughter Mating
The reason is that, taking a father-daughter mating as an example; if the father (A) is inbred, his extra homozygosity will make it more likely that he will transmit to his grandson (D) further copies of the same alleles which his daughter (C) has already received from him.
Since about one half of the genes the daughter receives from her father will also be passed on to the grandson, the latter’s inbreeding coefficient (F) will rise above the normally expected level (0.25) and its value should be adjusted accordingly.
Directly Related Parents Only
find FH FE = 0.25
Common ancestors (of parents E and G
Path (1/2)n+1 (1 + FA) *
None E – G (1/2)2 x 1.25 = 0.3125 Therefore, FH= Σ[(1/2)n+1(1 + FA)] = 31.3%
However, there are cases (usually only found in animal breeding) where directly related parents do share common ancestors. If any of these common ancestors are also inbred, the correction term (1 + FA) will be required in both situations.
Find FO
Common ancestors (of parents L and
Paths (1/2)n+1
(1 + FA)
| N) | ||||||
| None | L – N | (1/2)2 | x | 1.03125 | = | 0.2578125 |
| J | L – J – M – N | (1/2)4 | x | 1.125 | = | 0.0703125 |
*
L – I – F – B – G – J – M – N
(1/2)8 x 1.0 = 0.00390625
0.33203125
Therefore FO = ∑[(1/2)n+1(1 + FA)] = 33.2%
*A refers to any relevant inbred direct ancestor or common ancestor. Alternative Methods of Calculating the coefficient of inbreeding:
An alternative method of computing F is to use the technique of ‘Coancestries’.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 matings now being made.
This method is easier than path coefficients for animal breeding programmes 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 chickens and maize, ‘recurrence equations’ are the only easy method for calculating
F. A regular system of inbreeding is where 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:
Ft = 0.25 (1 + 2Ft-1+ Ft-2)
Where Ft is the coefficient of the present generation, Ft-1 is the coefficient of the previous generation and Ft-2 is the coefficient of the generation before that. It is important to note that recurrence equations can only be used for regular systems of inbreeding. e.g. Three generations of full sib mating:-
First generation – F1 = 0.25 (1 + 0 + 0) = 0.25
Second generation – F2 = 0.25 (1 + 0.5 + 0) = 0.375
Third generation – F3 = 0.25 (1 + 0.75 + 0.25) = 0.5
Values for Consanguineous Matings (One generation, no previous inbreeding)
| Self-fertilization | 1/2 |
| Full sibs, Parent-child, Double first cousins (first degree) | 1/4 |
| Half sibs, Grandparent-grandchild, Uncle-niece, Double first cousins | 1/8 |
| First cousins | 1/16 |
| First cousins (once removed) | 1/32 |
| Second cousins | 1/64 |
| Second cousins (once removed) | 1/128 |
| Third cousins | 1/256 |
Practical Uses of F
F is a very valuable parameter in both population and quantitative genetics. From the genealogists point of view the following are perhaps the two most interesting applications:
Predicting the Effects of Inbreeding Depression
A decline in performance in certain economic characters in domestic animals is well known following inbreeding. A similar depression has also been observed in humans. e.g.
Inbreeding Depression for Every 10% Increase in F
| Animal | Characteristic | InbreedingDepression | Reference |
| Chickens | Hatchability | 4.36% | Shoffner (1948) |
| Annual egg production | 9.26 eggs | Shoffner (1948) | |
| Man | Height at age 10 | 2.0 cm | Falconer (1989) |
| I.Q. score | 4.4% | Falconer (1989) | |
| Pigs | Body weight (154 days) | 2.6 kg | Falconer (1989) |
| Litter size | 0.24 piglets | Falconer (1989) | |
| Cattle | Annual milk yield | 135 kg | Falconer (1989) |
| Sheep | Fleece weight (1 year) | 0.29 kg | Falconer (1989) |
Thus, 3 generations of full sib matings, as shown above, would lead to an expected decrease in egg production in chickens of 9.26 x 5 = 46.3 i.e 46 eggs, compared with other hens from the same population who were not inbred.
Assessing the Risk of Inheriting Genetic Defects
In a large random-mating population, where the frequency of a harmful recessive gene (a) is q, the proportions of affected individuals and ‘carriers’ can be estimated from the Hardy-Weinberg Lawas follows:
Aa (carriers) aa (affected)
2q(1 − q) q2
However, if any inbreeding has occurred, Wright’s Equilibrium Lawenables a further prediction to be made about the increased risk of inheriting any harmful conditions caused by homozygous recessive genes.
The expected frequency following inbreeding rises to: aa (affected) q2 + Fq (1 – q)
The following table shows how inbreeding increases the likelihood of inheriting three harmful recessive conditions in humans: phenylketonuria, albinism and alkaptonuria. The first and last of these three are serious metabolic disorders.
Effects of Inbreeding on the Frequency of Inherited Defects
| Conditions Caused by Homozygous Recessive Genes | Frequency of Recessive Gene (a) q | Random Mating | Proportion of Affected(aa) Following Inbreeding q2 + Fq(1 – q)2[16] | ||
| Proportion of Carriers (Aa) 2q(1 – q)3 [16] | Proportion of Affected (aa) q2 | First Cousin Marriage (F = 1/16) | Full Sib Mating (F = 1/4) | ||
| Phenylketonuria | 1/100 | 1/50 | 1/10,000 | 1/1,380 | 1/385 |
| Albinism | 1/141 | 1/70 | 1/20,000 | 1/2,000 | 1/550 |
| Alkaptonuria | 1/1,000 | 1/500 | 1/1,000,000 | 1/16,000 | 1/4,000 |
Therefore, with albinism for example, a first cousin marriage increases the risk of inheriting the condition ten-fold, and with alkaptonuria the increase following a full sib mating is 250 fold. It also comes as quite a shock to most people that, even without inbreeding, the proportion of normal people carrying phenylketonuria is as high as 1 in 50.
Inbreeding is a result of the mating of individuals which are related to one another by having one or more common ancestors. If the mated individuals are related, their offspring will to some extent be inbred.
The Coefficient of Inbreeding
The coefficient of inbreeding, is the probability that the two genes at any locus are identical by descent. i.e. that the two genes are copies of one of the genes carried by the common ancestor a few generations back.
The coefficient of inbreeding, symbolized by F, is a property of an individual, but inbreeding profoundly effects the genetic composition of a population and in appropriate circumstances can lead to the formation of inbred strains in which all individuals are virtually genetically identical.
The rate of inbreeding depends on the degree of relationship
The closest relationship is that of an individual with itself, or self- fertilisation. However, the closest relationship that is usually possible with mammals is full brother x sister (known as full-sib) mating.
Continuous mating of offspring to the younger parent (which prevents repeated backcrossing to the same individual, which would have different genetic consequences), or a single generation of parent x offspring mating is genetically equivalent to full-sib mating.
Other regular mating systems which lead to a high level of inbreeding include half- sib and cousin matings. Repeated backcrossing, say of a transgene or a new mutation, to an inbred strain increases homozygosity as rapidly as self-fertilization.
Inbreeding also arises as a result of restricted population size
In a closed colony it eventually becomes impossible to avoid the mating of related individuals. Hence even “outbred” stocks maintained as a closed colony gradually become inbred at a rate which depends on the size of the colony.
Mathematical explanations of the consequences of brother x sister mating and other regular systems of inbreeding have been shown.
Contrary to popular belief, avoiding brother x sister mating in a small closed, random-mated population may reduce the inbreeding of an individual but it does notreduce the over-all rate of inbreeding. This is because the inbreeding will be undone in a subsequent generation.
Inbreeding is always expressed relative to an arbitrary starting point at which the coefficient of inbreeding is assumed to be zero.
Therefore, the magnitude of the effects of inbreeding any specific population will depend on the previous history of the stock, and the extent to which it has already been inbred.
Figure showing inbreeding as a result of restricted population size. A strain is regarded as an “inbred strain” when the coefficient of inbreeding, F, is greater than 0.986, i.e. after 20 generations of sib-mating.
Full Sib Mating
Full sib inbreeding of a genetically heterogeneous stock doubles the total genetic variation if all the sublines are kept. However, all the genetic variation will then be due to differences betweensublines, with no genetic variation within sublines.
The phenotypic variation among sublines also increases. This is largely due to the “uncovering” of recessive genes and geneticdriftin which alleles at a particular polymorphic locus become fixed in a homozygous state with plus or minus (with respect to the character) alleles being fixed largely by chance.
The phenotypic variation among a set of inbred strains derived from an outbred stock is therefore substantially greater than the phenotypic variation within the starting population.
The converse of this is also true. If several inbred strains are mixed together, then the phenotypic variation in the combined population will be less than that of the individual inbred strains taken together.
The coefficient of inbreeding never quite reaches 100 per cent. Therefore, no strain is ever fully inbred.
Moreover, the coefficient of inbreeding is calculated on the assumption that the reproductive performance of heterozygotes is equal to that of homozygotes, and that no mutation occurs. Both of these assumptions are incorrect, and lead to a slight overestimate of the actual level of inbreeding.
On the other hand, it is assumed that the base population has a coefficient of inbreeding of zero.
In practice, many inbred strains are derived from outbred stocks which may have been maintained as closed colonies with a restricted population size for many generations, as a result of which they may already be highly inbred.
Inbreeding Depression
Inbreeding depression is a decline in reproductive performance, ability to survive and other characteristics associated with fitness as a result of inbreeding.
It occurs as a result of “uncovering” deleterious recessive genes by making them homozygous and is a consequence of the evolution of dominance of loci concerned with fitness characters.
The direction of the change is towards the value of the more recessive alleles. Inbreeding depression does not occur for those characters where the heterozygote is intermediate between the two homozygotes.
The degree of inbreeding depression depends on the previous history of the stock. A stock which has been kept as a closed population for many generations will already be partly inbred; hence, full-sib mating may not result in much inbreeding depression.
Inbreeding depression varies substantially among different lines. Anyone starting a new inbreeding project should do so on a sufficiently large scale to allow for extinction of a proportion of the lines during the first few generations.
Once an inbred strain has been established, no further inbreeding depression should occur. Any decline in breeding performance will be due either to environmental influences (particularly disease) or in some cases to new deleterious mutations becoming fixed in the strain.
Inbred Strains
The decision as to whether a strain is sufficiently inbred for any particular research project is largely arbitrary.
The Committee on Standardized Genetic Nomenclature for Mice decided in 1952 that 20 generations of full-sib mating (or its genetic equivalent), at which time F= 98.6 per cent, is the minimum level of inbreeding required before a strain of mice can be designated as an inbred strain.
However, the coefficient of inbreeding never quite reaches 100 per cent so no strain is ever fully inbred.
Moreover, the coefficient of inbreeding is calculated on the assumption that the reproductive performance of heterozygotes is equal to that of homozygotes, and that no mutation occurs.
Both of these assumptions are incorrect, and lead to a slight overestimate of the actual level of inbreeding. But it is also assumed that the base population has a coefficient of inbreeding of zero.
Many inbred strains are derived from outbred stocks which have been maintained as closed colonies with a restricted population size for many generations, as a result of which they may already be highly inbred.
Inbreeding is defined in terms of the probability of heterozygosity at a locus. However, all inbred strains used in biomedical research should also be isogenic, i.e. all individuals within an inbred strain should be genetically identical (apart from residual segregation due to the impossibility of achieving fully inbred strains).
In fact it is isogenicity rather than homozygosity that is the most useful property of inbred strains, and the two are distinct properties which should not be confused. Isogenicity is achieved by ensuring that all individuals trace back to a common ancestral full-sib breeding pair in the twentieth or a subsequent generation.
All parallel substrains should be eliminated. F1 hybrids, i.e. the first-generation cross between two inbred strains, are isogenic but not homozygous. It is unfortunate that the terms inbred and `outbred’ which describe breeding methods rather than a genetic property of a group of animals, have become so widely accepted.
In summary, Inbreeding is the mating of individuals more closely related to each other than the average relationship within the population concerned.
The incidence of metabolic disorders, structural abnormalities and inherited disease conditions caused by harmful recessive genes increases are results of inbreeding. Inbreeding can occur through self-fertilization and observed in monoecious plants and hermaphrodite animals and also when parthenogenesis takes place.
Sibling marriages in humans, where marriage between brother and sister; or in cases where there is direct relationship with parent (mating between father and daughter) and direct and collaterally related parents.
Inbreeding study is an important tool in predicting the effects of inbreeding and assessing the risk of inheritable genetic defects. The rate of inbreeding depends on the degree of relationship between the mating partners.
Inbreeding occur in both plants and animals. When they occur the results is devastating. It has predictable effects and assessable risks in the populations. The rate of which depend on how closely related the reproducing individuals are.
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