Journal of Medical Genetics, 1977, 14, 25-29
A simple non-graphic method for pedigree description and analysis TAMAR SCHAAP and MAIMON M. COHEN* From the Department of Human Genetics, Hadassah-Hebrew University Medical Center, Jerusalem, Israel
SUMMARY The graphic representation of family data for the computation of the coefficients of inbreeding [F] and relationship [r] can be replaced by an algebraic method. The organization of family data is facilitated by a data form which can be easily, thoroughly, and correctly completed, even by a layman. The computation of the coefficients is practically automatic and greatly reduces the possibility of error.
Frequently, in the course of genetic counselling, one is confronted with the task of analysing pedigrees in order to calculate the coefficients of inbreeding [F] and relationship [r]. The classic procedure entails the graphic representation of the pedigree and subsequent summation of relationship pathways [path coefficients] leading to a common ancestor. This method is straightforward when the pedigree in question is relatively simple. However, this technique becomes more complicated, cumbersome, and time consuming in complex pedigrees, containing internal and intersecting loops, where an individual may be a common ancestor by multiple
The method will be described in the computation of the inbreeding coefficient [F] of an individual named 'the propositus'. The derivation of the coefficient of relationship [r] is identical to that of F, considering the two persons in question as parents of 'the propositus'. Therefore, r between the parents is equal to twice the F of 'the propositus'.
Family data form The family data form (Table I) is constructed from the present generation ('propositus') back through parents, grandparents, etc. Each family member is represented by a number on this form. pathways. The numbers 1 and 2 designate the father and This communication describes a procedure that mother of 'the propositus' (or those persons whose will simplify the calculation of F and r in complex of relationship is to be calculated). The coefficient kindreds. The method consists of a non-graphic 1 and 2, when added to the left of an existing digits representation of family data, in which relationships number, mean 'the father of' and 'the mother of', between the members of a pedigree are expressed by 11 indicates the paternal Thus, respectively. simple numerical symbols and algebraic logic. grandfather of 'the propositus'; 2212 stands for the Such representation permits a practically automatic the of maternal maternal grandfather grandmother analysis of family trees and direct computation of For the sake of convenience, the coefficients of inbreeding and relationship. A of 'the propositus'. family data form is divided into two columns, simple computer programme can be written to make the 1 and 2. The numeral 1 indicates patriheaded these operations feasible by desk computers. Since the procedure uses only vertical relationships, lineal relationships while 2 indicates matrilineal it is suitable for the above-mentioned purposes. It relationships. is not helpful in other types of pedigree analysis, Completing the family data form e.g. determining the mode inheritance, in which information about horizontal relationships is essen- Identification symbols (letters, names, or identitytial. card numbers) for all available members of the pedigree are filled in the corresponding spaces in * Established Investigator of the Chief Scientist's Bureau, Israel the family data form, e.g.: 11-John Doe (meaning, Ministry of Health. John Doe was the paternal grandfather of 'the Received for publication 9 April 1976
25
Schaap and Cohen
26 TABLE I
TABLE II
FAMILY DATA FORM 'The propositus'
FAMILY DATA FORM COMPLETED FOR THE PEDIGREE IN Fig. 1
Column 1
Column 1
Column 2 2-
1-A
1121-
1222-
11-F 21-E
111211-
112212-
111-211--
121221-
122222-
1111211112112211-
1112211212122212-
1121212112212221-
1122212212222222-
121-I 221-G 1111-211 1-1211-2211-1121-L 2121 - M 1221 - K
11111211111211122111-
11112211121211222112-
11111-21111-12111-22111--
1121121211-
1121221212-
etc.
etc.
11211-21211-12211-22211--
1-
2221-J
11121-N 12121
21121-0 - -
propositus'). If the identity of the mother of the
22121
paternal grandmother of 'the propositus' is un-
11221-N 21221 - 0 12221 - Q 22221 - P
known, the space opposite 221 is left unfilled. In the case of common ancestry, the same identification symbol will appear in more than one space. Fig. 1 is a classic graphic representation of an imaginary pedigree, with letters used as identification symbols. Table II is the completed family data form for the same pedigree. The parents of 'the propositus', A and B in Fig. 1, appear in the spaces 1 and 2 in
- -
111111 - 211111 - 121111-221111--
112111-21211 1-12211 1-222111--
111211-211211-121211-221211--
112211-212211-122211-222211--
111121-211121--
121121-W 221121-V 112121-212121-122121 - 222121 - 111221-211221-121221-W 221221-V 112221-212221-122221-W 222221-V
Column 2 2-B
12-D 22-C 112-212-122-H 222-G 1112-2112-1212-2212--
1122-R 2122 - S 1222 - K
2222-J
11112-21112-12112-22112--
11212-21212-12212-22212--
111212-211212-121212-221212-112212-212212-122212-222212-111122-211122-121122-W 221122-V 112122-212122-122122 - 222122 - 111222-211222-121222-W 221222-V 112222-212222--
122222-W 222222-V
11122-U 21122-T 12122 - 22122 - 11222-N 21222 - 0 12222 - Q 22222 - P 111112-211112 - 121112-221112-112112-212112-122112-222112--
Table II. The parents of the individual F in Fig. 1 are unknown: individual F occupies the space 11 in Table II and spaces 111 and 211 are accordingly empty. Individual G is a common ancestor and occupies spaces 221 and 222 in Table II.
A simple non-graphic method for pedigree description and analysis TAMAR SCHAAP and MAIMON M. COHEN* From the Department of Human Genetics, Hadassah-Hebrew University Medical Center, Jerusalem, Israel
SUMMARY The graphic representation of family data for the computation of the coefficients of inbreeding [F] and relationship [r] can be replaced by an algebraic method. The organization of family data is facilitated by a data form which can be easily, thoroughly, and correctly completed, even by a layman. The computation of the coefficients is practically automatic and greatly reduces the possibility of error.
Frequently, in the course of genetic counselling, one is confronted with the task of analysing pedigrees in order to calculate the coefficients of inbreeding [F] and relationship [r]. The classic procedure entails the graphic representation of the pedigree and subsequent summation of relationship pathways [path coefficients] leading to a common ancestor. This method is straightforward when the pedigree in question is relatively simple. However, this technique becomes more complicated, cumbersome, and time consuming in complex pedigrees, containing internal and intersecting loops, where an individual may be a common ancestor by multiple
The method will be described in the computation of the inbreeding coefficient [F] of an individual named 'the propositus'. The derivation of the coefficient of relationship [r] is identical to that of F, considering the two persons in question as parents of 'the propositus'. Therefore, r between the parents is equal to twice the F of 'the propositus'.
Family data form The family data form (Table I) is constructed from the present generation ('propositus') back through parents, grandparents, etc. Each family member is represented by a number on this form. pathways. The numbers 1 and 2 designate the father and This communication describes a procedure that mother of 'the propositus' (or those persons whose will simplify the calculation of F and r in complex of relationship is to be calculated). The coefficient kindreds. The method consists of a non-graphic 1 and 2, when added to the left of an existing digits representation of family data, in which relationships number, mean 'the father of' and 'the mother of', between the members of a pedigree are expressed by 11 indicates the paternal Thus, respectively. simple numerical symbols and algebraic logic. grandfather of 'the propositus'; 2212 stands for the Such representation permits a practically automatic the of maternal maternal grandfather grandmother analysis of family trees and direct computation of For the sake of convenience, the coefficients of inbreeding and relationship. A of 'the propositus'. family data form is divided into two columns, simple computer programme can be written to make the 1 and 2. The numeral 1 indicates patriheaded these operations feasible by desk computers. Since the procedure uses only vertical relationships, lineal relationships while 2 indicates matrilineal it is suitable for the above-mentioned purposes. It relationships. is not helpful in other types of pedigree analysis, Completing the family data form e.g. determining the mode inheritance, in which information about horizontal relationships is essen- Identification symbols (letters, names, or identitytial. card numbers) for all available members of the pedigree are filled in the corresponding spaces in * Established Investigator of the Chief Scientist's Bureau, Israel the family data form, e.g.: 11-John Doe (meaning, Ministry of Health. John Doe was the paternal grandfather of 'the Received for publication 9 April 1976
25
Schaap and Cohen
26 TABLE I
TABLE II
FAMILY DATA FORM 'The propositus'
FAMILY DATA FORM COMPLETED FOR THE PEDIGREE IN Fig. 1
Column 1
Column 1
Column 2 2-
1-A
1121-
1222-
11-F 21-E
111211-
112212-
111-211--
121221-
122222-
1111211112112211-
1112211212122212-
1121212112212221-
1122212212222222-
121-I 221-G 1111-211 1-1211-2211-1121-L 2121 - M 1221 - K
11111211111211122111-
11112211121211222112-
11111-21111-12111-22111--
1121121211-
1121221212-
etc.
etc.
11211-21211-12211-22211--
1-
2221-J
11121-N 12121
21121-0 - -
propositus'). If the identity of the mother of the
22121
paternal grandmother of 'the propositus' is un-
11221-N 21221 - 0 12221 - Q 22221 - P
known, the space opposite 221 is left unfilled. In the case of common ancestry, the same identification symbol will appear in more than one space. Fig. 1 is a classic graphic representation of an imaginary pedigree, with letters used as identification symbols. Table II is the completed family data form for the same pedigree. The parents of 'the propositus', A and B in Fig. 1, appear in the spaces 1 and 2 in
- -
111111 - 211111 - 121111-221111--
112111-21211 1-12211 1-222111--
111211-211211-121211-221211--
112211-212211-122211-222211--
111121-211121--
121121-W 221121-V 112121-212121-122121 - 222121 - 111221-211221-121221-W 221221-V 112221-212221-122221-W 222221-V
Column 2 2-B
12-D 22-C 112-212-122-H 222-G 1112-2112-1212-2212--
1122-R 2122 - S 1222 - K
2222-J
11112-21112-12112-22112--
11212-21212-12212-22212--
111212-211212-121212-221212-112212-212212-122212-222212-111122-211122-121122-W 221122-V 112122-212122-122122 - 222122 - 111222-211222-121222-W 221222-V 112222-212222--
122222-W 222222-V
11122-U 21122-T 12122 - 22122 - 11222-N 21222 - 0 12222 - Q 22222 - P 111112-211112 - 121112-221112-112112-212112-122112-222112--
Table II. The parents of the individual F in Fig. 1 are unknown: individual F occupies the space 11 in Table II and spaces 111 and 211 are accordingly empty. Individual G is a common ancestor and occupies spaces 221 and 222 in Table II.
