Pure Appl. Bio., 1(1): 16-17, June- 2012.
PRINCIPLE OF BLOOD GROUP INHERITANCE AND CALCULATION OF ITS RATIO
Zhe Yin,ab Yunfei Guoa
a
b
Mathematics Department, Yanbian University, 133002, China.
Department of Information Management, Peking University, 100871, China.
*Corresponding author: [email protected]
Abstract
This paper shows the principle of blood group inheritance and gives the calculation of its ration based on the law of genetic inheritance
of paper. Besides, reason of atavism has been also provided, which is valuable for the research on genetics. Author in this paper think Principle of
blood group inheritance and calculation of its ratio improve the non- systematicness and uncertainty. Simple and feasible calculation methods of
disease rate are provided for diseases of autosomal dominant (AD), autosomal recessive (AR), X- linked dominant inheritance (XR) and Y- linked
inheritance, which is valuable for the research on the genetics in future.
Keywords: Blood group; Principle of inheritance; Ratio of inheritance
d D  D；
d d  d .
Introduction
Blood groups gain importance in the recent advance
research [1]. ABO blood type is also associated with the risk of
cancer and heart disease [2, 3]. The blood groups are genetically
transmitted and have great role in the inheritance principle [4, 5]. It
means the blood groups need attention to revisit the principle of
inheritance. The current study is aimed to reconsider the principle
of inheritance and calculate its ratio applying new approaches.
Lemma 2：When male parent and female meet recessive inheritance;
inheritance factors fit such addition principle 2:
DD  d ；
Dd  D ；
d D  D；
d d  d
Materials and Methods
Two lemmas
There is much regularity which comes from statistics
of inheritance results in the inheritance research. Will people
propose the possible results and ratio of inheritance from the
principle angle, the answer is yes. First of all, the law of genetic
inheritance will be introduced [6].
Genetic Behavior is divided into dominant inheritance and
recessive inheritance. Assume that D represents for dominant
inheritance factor in offspring, and d represents for recessive
inheritance factor in offspring. Two inheritance factors can be
dependent or independent. Dependent means there is cross effect
between D and d, that is, (Dd) is also an inheritance result.
The possible results may be D or d when inheritance factors
of male parent and female parent are independent;
The
possible
results
may
be
D, d ,( Dd ) ,( Dd ) , D( Dd ) , d ( Dd ) ，
D( Dd ) ,( Dd ) d when inheritance factors of male parent
and female parent are dependent.
n
( D  d )n   Cni Di d n i ，where Cni 
i 0
n!
。
i ! n  i !
Coefficients of the odd and even items in the expansion are
equal.
n
n
  Cni Di d n i
is just all of the
i 0
possible results of the
n  1 th generation.
Lemma 1：When male parent and female meet dominant inheritance;
inheritance factors fit such addition principle 1:
DD  D；
Dd  D；
1）
All of the possible inheritance results of the n  1 th
generation
fit
such
expansion:
n
( D  d )n   Cni Di d n i =
i 0
n 1
C D  C D d  Cn2 Dn2d 2  ...  Cnn d n
0
n
n
1
n
，
i
Where Cn

n!
；
i ! n  i !
2） Inheritance factors meet distributive law(separate
regularity );
Binomial equation formula:
Expansion ( D  d )
Gene inheritance law：
3） Inheritance factors meet associative law(law of
independent assortment);
4） Dominant inheritance meets addition principle 1;
5） Recessive inheritance meets addition principle 2;
6） When D and d are independent, possible results are D
or d;
7）When D and d are dependent, Dd will be regarded as
inheritance
factor
which
also
have
dominant
inheritance ( Dd )
(linkage

and recessive inheritance
inheritance),
and
possible
( Dd )
results
are:
D, d ,( Dd ) ,( Dd ) , D( Dd ) , d ( Dd ) ，
D( Dd ) ,( Dd ) d .
Yin & Guo, 2012
Note: when n
law.
 2 , this inheritance law is just Mendel’s
B and AB：（B+O）
Blood groups of parents:
 （A+B）=AB+BB+AO+BO=AB+2B+A→1:2:1;
O and O：（O+O）  （O+O）=4O→1;
O and AB：（O+O）  （A+B）=2AO+2BO=2A+2B→1:1;
B and O：（B+O）  （O+O）=BO+BO+OO+OO
A and A：（A+O）  （A+O）= AA+2AO+OO = 3A+O→3:1;
AB and AB：（A+B）
Principle of blood group inheritance and calculation of its ratio
In the blood groups, type A and type B are dominant inheritance,
type AB is double-dominant linked inheritance, and type O is
recessive inheritance.
=2B+2O→1:1;
 （A+B）=AA+AB+AB+BB=A+2AB+B→1:2:1.
A
and
B：（A+O）  （B+O）=AB+AO+BO+OO
=AB+A+B+O→1:1:1:1;
For details see regularity Table-I, of blood group inheritance.
A and O：（A+O）  （O+O）=AO+AO+OO+OO
=2A+2O→1:1;
In a similar way, principle of blood group inheritance and
calculation of its ratio of multi-generation can be also calculated.
A and AB：（A+O）  （A+B）=AA+AB+AO+BO
=2A+AB+B→2:1:1;
Human history is centuries-old, if linked inheritance takes
place in type AB and type A or type A and type B because of the
genetic mutation, which is the necessary and sufficient condition of
causing
particular
blood
groups.
B and B：（B+O）  （B+O）=BB+2BO+OO =3B+O→3:1;
Table-I Regularity table of blood group inheritance
Blood Groups of Parents
A and A
A and B
A and O
A and AB
B and B
B and AB
O and O
O and AB
B and O
AB and AB
Possible Blood Groups of Children
A,O
AB,A,B,O
A,O
A,AB,B
B,O
AB,B,A
O
A,B
B,O
A,AB,B
Ratios of Blood Groups
A:O=3:1
AB:A:B:O=1:1:1:1
A:O=1:1
A:AB:B=2:1:1
B:O=3:1
AB:B:A=1:2:1
O=1
A:B=1:1
B:O=1:1
A:AB:B=1:2:1
inheritance (XR) and Y- linked inheritance, which is valuable for
the research on the genetics in future.
Reason of atavism
Atavism happens in the case of recessive linked inheritance
according the inference 5 and inference 6 in paper [6], that is,
inheritance happens in even-generation , without odd-generation,
such as hemophilia, red blindness, DMD and leukocyte glucose-6phosphate dehydrogenase deficiency.
Results and Discussion
Through applying mathematical logics and approaches, the
Principle of blood group inheritance and calculation of its ratio
improve the non-systematicness and uncertainty. Roach et al. [7],
analyzed the whole-genome sequences of a family of four,
consisting of two siblings and their parents to understand the
genetic inheritance.
Furthermore, this research also solves the inheritance mechanism
in the coming generation applying the approach used here. Similar
findings were suggested by Salmon and Salmon [8], for the Blood
Groups and Genetic Markers Polymorphism and Probability of
Paternity.
Conclusions
Author in this paper think Principle of blood group
inheritance and calculation of its ratio improve the nonsystematicness and uncertainty. Simple and feasible calculation
methods of disease rate are provided for diseases of autosomal
dominant (AD), autosomal recessive (AR), X- linked dominant
Reference
1. Logdberg L, Reid ME, Zelinski T (2011). Human blood group
genes 2010: chromosomal locations and cloning strategies
revisited. Transf Med Reviews 25 (1): 36–46
2. Wolpin BM, Chan AT, Hartge P, et al. (2009). ABO blood
group and the risk of pancreatic cancer. J Natl Cancer Inst
101(6):424-431.
3. Carpeggiani C, Coceani M, Landi P, et al. (2010). ABO blood
group alleles: a risk factor for coronary artery disease. An
angiographic study. Atherosclerosis 211:461–466
4. Yamamoto F, Clausen H, White T, Marken J, Hakamori S
(1990). Molecular genetic basis of the histo blood group ABO
system. Nature 345: 229–233
5. Yip SP (2002). Sequence variation at the human ABO locus.
Ann Hum Genet 66 (1): 1–27
6. Zhe, Y (2012). The Law of Genetic Inheritance. Open J of
Genetics 2: 47-50.
7. Roach JC, Glusman G, Smit AFA, et al. (2010). Analysis of
genetic inheritance in a family quartet by whole-genome
sequencing. Sci 328: 636 (2010).
17