TYPES OF COLLATERAL RELATIONSHIPS

Main Categories

  1. Sib relationships
  2. Single collateral relationships (excluding sibs).

    a) Cousins

    b) Uncle/aunt - nephew/niece

  3. Double collateral relationships (excluding sibs)

    a) Conventional double cousins

    b) Double relationships from reciprocal cross-generation marriages

    c) Non - reciprocal intergeneration double relationships

    d) Removed relationships for conventional double cousins

    e) Double relationships caused by inbreeding

  4. Multiple relationships

    a) Multiple cousins

    b) Multiple half cousins

It is important to get the terminology correct for the different kinds of relationship. I have used path diagrams to demonstrate the differences and have also included the coefficient of relationship (R) between members of each type. The relevant individuals are printed in red.

Because sibs are at the heart of all other collateral relationships it was decided to keep them together and avoid fragmentation. As a group they are not amenable to being placed together in either the single or the double relationship categories, because they are split between them. Full sibs and enhanced half sibs both have a double relationship whereas normal half sibs are singly related. Furthermore, because identical twins are clones they fit into neither category.

  1. Sib Relationships

    Sib relationships are as follows:- Brother - brother, brother - sister, sister - brother and sister - sister. Identical twins develop from a single fertilised egg and are exact copies (genetically) of one another. However, although they have the same genotypes,their phenotypes do not correspond exactly because of small differences in their exposure and reaction to the environment and minor developmental aberrations. Fraternal twins are normal full sibs who happen to share a pregnancy. They are no more alike genetically than ordinary full sibs with different birth dates. However, because they share a common environment during pregnancy and early life, they may be more alike phenotypically than normal full sibs. This also applies to half sibs who can also be born as twins. The latter are usually only recognised when the fathers are from different races; although a difference in skin colour alone does not necessarily mean two fathers, since it often occurs naturally in full sibs.

    Figure 23 Sib Relationships


    Another rare type of sibship occurs when either a person marries his/her former spouse's full sib or a person marries his/her full sib's former spouse, resulting in two sets of children. Since the coefficient of relationship (R) is half way between full and half sibs, F and G should have the title:- 'Three - quarter sibs.'

    Three-quarter sibs are just one example of an enhanced half sib relationship.


    Other Enhanced Half Sibs

    a) If identical twins are substituted for the normal full sisters ( C and D) in the diagram for three-quarter sibs, RFG will be raised to 1/2. This is equivalent to normal full sib relationship, even though F and G have different mothers and are only half sibs. This is one of the few examples where the substitution of full sibs by identical twins does not double the coefficient of relationship.

    Figure 24 Identical Twin Mothers

    b) If half sibs replace the full sisters in the pedigree for three-quarter sibs, then the relationship between G and H will be slightly higher than for normal half sibs, i.e. 5/16.

    Figure 25 Half Sib Mothers

    c) Finally, if the two sisters are replaced by cousins of any degree, or even aunt and niece or mother and daughter, then a whole new range of 'fortified' half sibs will result. Although inbreeding does increase (R) between half sibs, no inbreeding is involved in any of these unusual relationships.

    The reason these half sib relationships are enhanced is because, with the exception of (a) above, where the half sib relationship is exactly doubled, there is an irregular double relationship in each case; e.g. in (b) above the two relationships are:- left side - half first cousin (R = 1/16);right side - half sib (R = 1/4). The following table lists the most important members of this class:

    Table 4 Enhanced Half Sib Relationships

    Relationship between the two spouses of the common parent R values of enhanced half sibs

    Identical Twins

    1/2

    Full Sibs

    3/8

    Half Sibs

    5/16

    Single First Cousins

    9/32

    Half Single First Cousins

    17/64

    Second Cousins

    33/128

    Half Second Cousins

    65/256

    Double First Cousins

    5/16

    Double Half First Cousins

    9/32

    Double Second Cousins

    17/64

    Father/Son or Mother/Daughter [6]

    3/8

    Uncle/Nephew or Aunt/Niece [6]

    5/16

    Half Uncle/Half Nephew or Half Aunt/Half Niece [6]

    9/32

    The 'half blood' descendants of enhanced half sibs will also have their R values increased. e.g. For half first cousins descended from 'three-quarter sibs' R will be raised from 1/16 to 3/32.

  2. Single Collateral Relationships

    a) Single Cousins

    Since single cousinships are the most common type, the word 'single' will be omitted from the titles. The 'first degree' relationship is only included for first cousins in the following diagrams, first degree second and third cousins are listed separately in Table 3.

    Figure 26 First Cousins


    Half first cousins are the children of half sibs. D and E in the first diagram are identical twins. Further subdivisions of first cousins.

    Figure 27 Second Cousins


    Second cousins are the children of first cousins and half second cousins are the children of half first cousins. In first degree second cousins (not shown), the full sibs D and E, in the second cousin diagram above, are replaced by identical twins giving RKL a value of 1/16.

    Figure 28 Third Cousins


    First degree third cousins would have a relationship of 1/64.

    Removed Cousinships

    These are relationships between cousins of different generations:

    Figure 29 Once Removed

    Figure 30 Twice Removed

    b) Uncle/Aunt - Nephew/Niece

    Figure 31 Uncle/Aunt - Nephew/Niece Relationships


    Great uncles are contemporary with grandparents not great-grandparents; this is misleading. Grand uncles and grand aunts with their corresponding grand nephews and grand nieces would be more appropriate. The Concise Oxford Dictionary does in fact use these terms; they are defined respectively: as the uncle or aunt of one's parents and the son or daughter of one's nephew or niece. Since both forms appear to be in common use, it is important to emphasise that grand uncle is the same as great uncle and great-grand uncle is equivalent to great-great uncle.

    Double half uncles can also be found later here and reciprocal half uncles here.

  3. Double Collateral Relationships

    a) Conventional Double Cousins

    Figure 32 Regular Double First Cousins


    In the first diagram, E and F are identical twin males and G and H are identical twin females. Note that the relationship between I and J in the first case is the same as that between full sibs and in the second it is equivalent to that of half sibs even though in both cases they are only cousins. This fact is used in animal breeding to produce 'full sibs' with different parents to eliminate covariance due to maternal effects. In this context, see also F and G.

    Shown below are two kinds of regular double second cousins. They are genetically equivalent in most respects: both have a double relationship and are the children of first cousins; also, both have the same coefficient of relationship (1/16) and share four of their great-grandparents (A, B, C and D in each case). An important difference, however, is that the relationship between M and N is unilineal, whereas that between Q and R is bilineal (see here).

    Figure 33 Regular Double Second Cousins

    Children of Double First Cousins

    Doubly-related Children of Two Sets of Single First Cousins

    When double second cousins (first degree) and double half second cousins are also included, (not shown), it brings the total to 6 different types. For the same reasons there are 9 possible kinds of double third cousins and 12 kinds of double fourth cousins.

    Figure 34 Irregular Double Cousins



    An irregular double cousinship results when the two parallel sets of parents have different relationships. Thus, in the first diagram above, the two parents, F and G are full sibs but H and I are only half sibs. In the second diagram, the parents, I and J are also full sibs but K and L are only single first cousins. Irregular double cousins always have two different types of relationship. In the top diagram the two relationships between J and K are: first cousins (R = 1/8) and half first cousins (R = 1/16). In the bottom diagram, M and N are: first cousins (R = 1/8) and second cousins (R = 1/32). The most common types of irregular double cousins are listed in the following table:

    Table 5 Common Types of Irregular Double Cousins

    Combinations of Parents

    R (Between Irregular Double Cousins)

    Irregular Double Cousin Relationships

    Identical Twins and Full Sibs

    3/8

    1st Cousins (1st degree) / 1st Cousins

    Identical Twins and Half Sibs

    5/16

    1st Cousins (1st degree) / Half 1st Cousins

    Identical Twins and First Cousins

    9/32

    1st Cousins (1st degree) / 2nd Cousins

    Identical Twins and Half First Cousin

    17/64

    1st Cousins (1st degree) / Half 2nd Cousins

    Identical Twins and Second Cousins

    33/128

    1st Cousins (1st degree) / 3rd Cousins

    Full Sibs and Half Sibs

    3/16

    1st Cousins / Half 1st Cousins

    Full Sibs and First Cousins

    5/32

    1st Cousins / 2nd Cousins

    Full Sibs and Half First Cousins

    9/64

    1st Cousins / Half 2nd Cousins

    Full Sibs and Second Cousins

    17/128

    1st Cousins / 3rd Cousins

    Half Sibs and First Cousins

    3/32

    Half 1st Cousins / 2nd Cousins

    Half Sibs and Half First Cousins

    5/64

    Half 1st Cousins / Half 2nd Cousins

    Half Sibs and Second Cousins

    9/128

    Half 1st Cousins / 3rd Cousins

    First cousins and Half First Cousins

    3/64

    2nd Cousins / Half 2nd Cousins

    First Cousins and Second Cousins

    5/128

    2nd Cousins / 3rd Cousins

    Half First Cousins and Second Cousins

    3/128

    Half 2nd Cousins / 3rd Cousins

    The double relationships for each category of irregular double cousins are also given in the form of coded lists.

    Other types of irregular double relationships can also be found on here. Enhanced half sibs here are further examples.

    b) Double Relationships from Reciprocal Cross - generation Marriages

    These are very rare situations, but with the present trend towards younger parents they could occur more in the future. The most weird example is when a man marries his son's wife's daughter (by a former marriage) and both he and his son have further children from their new marriages. This is perfectly legal and no inbreeding is involved.

    Figure 35 Father and Son - Daughter and Mother Reciprocal Marriages

    The double relationships between G and H in Fig. 35 are very unusual. Since G and E are half sibs and F and H are also half sibs then G is H's half uncle and H is G's half uncle. Therefore, we have a reciprocal (i.e. two-way) half uncle - half nephew relationship

    Figure 36 Uncle and Nephew - Niece and Aunt Reciprocal Marriages

    The relationship between M and N is Double (First Cousin Once Removed). The brackets are important.

    Irregular Types

    Figure 37 Father and Son - Niece and Aunt Reciprocal Marriages

    Relationships between J and K are:

    Left side - J is K's half uncle (R = 1/8)

    Right side - K is J's first cousin once removed (R = 1/16)

    Figure 38 Father and Son - Half Niece and Half Aunt Reciprocal Marriages

    Relationships between K and L are:

    Left side - K is L's half uncle (R = 1/8)

    Right side - L is K's half first cousin once removed (R = 1/32)

    Table 6 lists the most important types of these double relatives. Not included as parents are First Cousins Once Removed (+ and _ ), which would add further reciprocal combinations.

    Table 6 Different Types of Reciprocal Cross - generation Double Relatives[7]

    Parents

    R values

    Regular Doubles

    Father/Daughter - Daughter/ Father [8]

    Father/Son - Daughter /Mother

    Mother/Son - Son/Mother

    1/4

    Uncle/Niece - Niece/Uncle 8

    Uncle/Nephew - Niece/Aunt

    Aunt/Nephew - Nephew/Aunt

    1/8

    1/2 Uncle/1/2 Niece - 1/2 Niece/1/2 Uncle8

    1/2 Uncle/1/2 Nephew - 1/2 Niece/1/2 Aunt

    1/2 Aunt/1/2 Nephew - 1/2 Nephew/1/2 Aunt

    1/16

    Irregular Doubles

    Father/Daughter - Niece/Uncle8

    Father/Son - Niece/Aunt

    Mother/Daughter - Nephew/Uncle

    Mother/Son - Nephew/Aunt

    3/16

    Father/Daughter - Half Niece/Half Uncle8

    Father/Son - Half Niece/Half Aunt

    Mother/Daughter - Half Nephew/Half Uncle

    Mother/Son - Half Nephew/Half Aunt

    5/32

    Uncle/Niece - Half Niece/Half Uncle8

    Uncle/Nephew - Half Niece/Half Aunt

    Aunt/Niece - Half Nephew/Half Uncle

    Aunt/Nephew - Half Nephew/Half Aunt

    3/32


    c) Non-reciprocal Intergeneration Double Relationships

    The common feature of this class of doubles is the unusual relationships shared by four members of each group. For example, in Figure 39, F is related to both E and G but E and G are not related to each other. However, if E and G marry, their child H will be connected to F in a double between-generation relationship. F and H in Figure 39, and L and N in Figure 40, are in each case centrally placed at different levels joining two unrelated groups of relatives and consequently are related through both sides.

    Regular Examples

    The simplest and most basic form is shown in Figure 39:

    Figure 39 Double (Half Uncle/Half Aunt - Half Nephew/Half Niece)

    In the above diagram the following two sets of half sibs result from two marriages for both B and C: (E - F) and (F - G). If the unrelated members of this group (E and G) marry and have a child H, then F becomes H's double half uncle and H becomes F's double half nephew, because they are related through both of H's parents. Note that for single half uncles/half nephews R = 1/8. It is also possible to have double (half great uncles - half great nephews) where R = 1/8 (not shown).

    Similar relationships, which extend down to further generations, are shown in Figure 40, Figure 41 and Table 7 . There are difficulties with the precise nomenclature of these relationships. Since there already exists a 'double first cousin - once removed' relationship (see here), we can not refer to L and N in Figure 40 by the same name. The only way to resolve this difficulty is by the use and positioning of brackets. For example: L and N in Figure 40 can be styled 'Double (First Cousins Once Removed)', whereas K and L in Figure 51 are 'Double (First Cousins) Once Removed'. i.e. Only the double part of the relationship should be bracketed.

    Figure 40 Double (First Cousins Once Removed)

    Figure 41 Double (Half First Cousins Once Removed)

    This basic structure is continued further in Table 7 :

    Table 7 Non-reciprocal Intergeneration Doubles [9]

    Type of Relationship

    Coefficient of Relationship (R)

    Double (half uncle _ half nephew etc.)

    1/4

    Double (first cousins once removed)

    1/8

    Double (half first cousins once removed)

    1/16

    Double (second cousins once removed)

    1/32

    Double (half second cousins once removed)

    1/64


    Since the previous conventional double cousins are located entirely within the same generation, while the present intergeneration double extend between generations; suitable alternative titles could be horizontal versus vertical double relationships, respectively. (See also here and here).

    Irregular Examples of Non-reciprocal Intergeneration Doubles

    There is also a whole array of irregular forms including all the ones in the above table in different combinations of double relationships, plus others where first cousins, half first cousins, second cousins or half second cousins are also present on one side only. It should be noted that the presence of contemporary cousins (i.e. not removed, and from the same generation) on both sides, constitutes a conventional double cousin relationship (see here).

    Excluding the combinations where contemporary cousins occur on both sides, the number of combinations of two different relationships taken together from the nine referred to above, is 30. i.e.

    Below, are diagrams of six of the more important of these, (Figure 42 to Figure 47), together with details of their irregular double relationships in the titles:

    Figure 42 Half Uncle - Half Nephew (R = 1/8) and First Cousins (R = 1/8)

    Figure 43 Half Uncle - Half Nephew (R = 1/8) and First Cousins Once Removed (R = 1/16)

    Figure 44 Half Uncle - Half Nephew (R=1/8) and Half First Cousins (R=1/16)

    Figure 45 Half First Cousins Once Removed (R = 1/32) and First Cousins (R = 1/8)

    Figure 46 Half First Cousins (R = 1/16) and First Cousins Once Removed (R = 1/16)

    Figure 47 Half First Cousins Once Removed (R = 1/32) and First Cousins Once Removed (R = 1/16)

    Finally, there is a further special group of Irregular Non-reciprocal Intergeneration Doubles, first referred to here as Enhanced Half Sibs:

    Figure 48 Half Aunt - Half Niece (R = 0.125) and Half Sibs (R = 0.25)

    Figure 49 First Cousins Once Removed (R = 0.0625) and Half Sibs (R = 0.25)

    Figure 50 Half First Cousins Once Removed (R = 0.03125) and Half Sibs (R = 0.25)

    In this case, since only part of the relationship is double, only that part of the title should be enclosed by brackets.

    d) Removed Relationships for Conventional Double Cousins

    If children and other descendants of conventional double cousins occur unevenly on the two sides, the terms: once, twice, etc. removed, should be used.

    Figure 51 Conventional Double (First Cousins) Once Removed

    Figure 52 Conventional Double (First Cousins) Twice Removed

    Figure 53 Conventional Double (Second Cousins - 2nd type - see here) Once Removed

    Figure 54 Irregular Double (First Cousins/Half First Cousins) Once Removed

    Coding for these removed relationships is given here .

    e) Double (and Multiple) Relationships Caused by Inbreeding

    Although none of the other double relationships in this paper involve inbreeding, if the parents of full sibs are related, those full sibs could also be double cousins as part of a multiple relationship. e.g. If the parents of full sibs are single first cousins, those full sibs (R = 0.5) are also double second cousins (R = 0.0625). The second cousin relationship is double because full sibs are bilineally related.

    Figure 55 Full Sibs who are also Double Second Cousins

    Explanation :-Children of single first cousins are normally regarded as second cousins. If those first cousins marry each other, then their children (which are now also full sibs) are still second cousins, but because each receives his or her genes from the common great-grandparents (A and B) by two different independent routes, that relationship is doubled. The two independent routes are:

    A to I ADGI  B to I BDGI
      AEHI   BEHI
     
    A to J ADGJ B to J BDGJ
      AEHJ   BEHJ

     

    (See here for other examples of double and multiple relationships caused by inbreeding).

  4. Multiple Relationships

    As pointed out here, double first cousins are really a multiple relationship because of their four connections through two sets of full sibs. However, in conventional terminology the basic elements for double and multiple relationships are usually considered to be cousins rather than sibs.

    a) Multiple Cousins

    Figure 56 Quadruple Second Cousins (QSC) and Octuple Third Cousins (OTC)

    QSC and OTC relationships are sometimes used in animal breeding practice where planned mating systems are followed. Although double first cousins are occasionally found in humans, greater degrees of multiple cousinships are very unlikely. They can also result from very close inbreeding in animals (see here).The diagram above contains the following kinds of multiple cousins:-

    g and h; i and j; k and l; m and n: are all double first cousins (R = 1/4 )

    o and p; q and r: are quadruple second cousins (R = 1/8)

    s and t are octuple third cousins (R = 1/16)

    Complex irregular multiple cousins are also possible. (Not shown)

    b) Multiple Half Cousins

    Replacement of all the full sibs in the second generation of the previous diagram (Figure 56) by half sibs will produce quadruple half second cousins (R = 1/16) and octuple half third cousins (R = 1/32).

    Multiple half cousins can also result from half sib chains, which link several people through marriage, divorce or death of a partner, and remarriage. Like the previous examples, no inbreeding is involved

    Figure 57 Triple Half First Cousins

    B, C and D each married twice. (F and H) and (G and I) are genetically unrelated and can legally marry. Their children, J and K, will be half first cousins. This relationship is repeated three times through each of the three common grandparents: B, C and D, so that the half cousins are triply related. The sharing of grandparents is taken a stage further in Figure 58, and leads to an even closer half cousin realtionship.

    Figure 58 Quadruple Half First Cousins

    Figure 58 shows a circular half sib chain and is the result of 'wife - swapping'. After having a child in both cases, A and B change partners with C and D and the new pairs (A - D) and (B - C) each have a further child. This results in the following sets of half sibs: (E - F), (F - G), (G - H) and (H - E) where R = 1/4 in each case.

    If the two pairs of unrelated members of this group, (E - G) and (F - H), were to marry and have the children, I and J, then RIJ would also be 1/4. Unlike the double half cousins (R = 1/8), who are only related through two of their grandparents, these half first cousins are related through all four grandparents. As in previous cases no inbreeding is involved. At this stage it is interesting to summarise the full range of half first cousins:

    Table 8 Single, Double and Multiple Half First Cousins

    Relationship

    No. of Common Grandparents

    R

    Single half first cousins

    1

    1/16

    Double half first cousins

    2

    1/8

    Triple half first cousins

    3

    3/16

    Quadruple half first cousins

    4

    1/4

    Half sib chains also feature here and here. With longer half sib chains, even more complicated multiple relationships are possible, but like quadruple second cousins and octuple third cousins they only have relevance to planned animal breeding. Because none of the parents are related, it can be a short-term solution to preventing inbreeding in small, animal populations.

    The following complex diagram illustrates why it is unlikely to happen in human populations. To show all the relationships, I have traced the eight paths between U and V.

    Figure 59 Octuple Half Second Cousins

    U and V are related through all eight great-grandparents.

    Common Ancestors

    Paths

     

     

     

    A

    U_1_Q_2_I_3_A_4_J_5_R_6_V

     

     

     

    B

    U_1_Q_2_K_3_B_4_J_5_R_6_V

     

     

     

    C

    U_1_Q_2_K_3_C_4_L_5_R_6_V

     

     

     

    D

    U_1_S_2_M_3_D_4_L_5_R_6_V

     

     

     

    E

    U_1_S_2_M_3_E_4_N_5_T_6_V

     

    (1/2)6 x 8 = 1/8

    F

    U_1_S_2_O_3_F_4_N_5_T_6__V

     

     

     

    G

    U_1_S_2_O_3_G_4_P_5_T_6_V

     

     

     

    H

    U_1_Q_2_I_3_H_4_P_5_T_6_V

     

     

     

    [6] It should be pointed out that the last three entries on table 4 are also further examples of Irregular Non-Reciprocal Intergeneration Doubles. The two groups therefore are not mutually exclusive.

    [7] Other non-reciprocal combinations can be found in the next section. They include father-son and uncle/nephew pairs married to either two contemporary relatives (sibs or cousins) or to mother-daughter or aunt-niece pairs, where each marriage is not across generations, as in this section, but within the same generation.

     

    [8] These are most likely to happen in real life, i.e. the male partner is usually the most senior on both sides.

    [9] In Table 7 'once removed' double relationships can be extended to two or three times removed.