Poster UBI Dinamica
1
Blood Groups Gene Frequencies Carla Noronha 1 ,Ana Cunha 2 , Ulisses Azeiteiro 3 1 Universidade Aberta, MBB , Portugal, C [email protected] om 2 Universidade Aberta, MBB , Portugal, [email protected] 3 Universidade Aberta, DCeT, Portugal, [email protected] At a time of unprecedented expansion, the study of evolution transcends all areas of biology. All phenomena that are observable today in living organisms and their systems have a fantastic evolutionary component that can not be ignored! Evolution transcends mutations and natural selection of Darwin and proves to be in the first row of studying the mechanisms involved ... Life! Mathematical models have become allies in the biosciences. The probabilistic models become very useful for process analysis as it is possible to access the repetitive data, since they require a large initial sample data for forming, but the implementation of the evolutionary processes is often associated to the scarcity of data. Changes in allele frequencies over time and space are clues from which you can investigate the action of evolutionary processes. By understanding how "evolutionary forces" acting is also possible to construct mathematical models that approximate reality. These models are needed to understand the subtle interplay between "evolutionary forces" and genetic heritage, and from this knowledge, make inferences about the processes that acted in the past and which are the source of genetic diversity present. The study of gene frequencies of blood groups is one of the areas where the mathematical models and probabilistic / stochastic theories stand for the progress achieved in recent decades. In this work authors present and discuss such models. In 1908, Hardy and Weinberg concluded that if no evolutionary factor acted on a population that satisfies certain conditions, the frequencies of their alleles would remain unchanged over the generations and genotypic ratios would reach a stable equilibrium. The conditions should be fulfilled to enable the population to remain in equilibrium gene would be: 1. The population must be very large (infinite), so that they can occur all types of junctions according to the laws of probability 2. The population should have the same number of individuals of each sex 3. The population must be panmitic ,this is, all randomly marry without the existence of any type of preference genotypic or phenotypic, social stratification and inbreeding 4. All couples in the population are equally fertile and generate an equal number of children 5. There is no overlap of generations in the population 6. The genes do not mutate 7. Natural selection will not have any influence on the population as all individuals meet the same conditions for survival 8. There is no migration or admixture with neighboring populations so there is no change in gene frequencies. The Hardy-Weinberg law in fact provides a theoretical pattern for the behavior of gene populations across generations. In practice, this law allows us to understand whether or not a population is in equilibrium or whether there are evolutionary factors to act. This is a Hardy-Weinberg representation : Consider a Mendelian population, a genetic background composed by two alleles A and a and genotypes AA, Aa and aa, resulting from a pair of alleles that are distributed with the same frequency in individuals of both sexes. The frequencies of alleles A and a can be calculated easily if we take as our starting point the gametes that produced the current generation of individuals in this population. Thus, the number of gametes with the allele to be equal to twice the number of homozygous individuals generation of AA plus the number of individuals heterozygous for each individual Aa originated by two AA gametes with allele and each individual Aa was formed by a gamete in the A gene and with its other allele the. Similar reasoning enables us to say that the number of gametes that the allele produce the generation of individuals to be tested is equal to twice the number of individuals per year plus the number of heterozygous individuals Aa. Given the above, if we call the frequencies of the alleles in the population, respectively, p and q = 1-p and symbolize the frequencies of individuals with genotypes AA, Aa and aa, we can write that the p and q frequencies of alleles A and a in the generation under study are: We can summarize the frequencies of genotypes in the following table: From the observation of this table immediately follows that AA + aa+Aa= ABSTRACT INTRODUCTION Blood Group (phenoty pe) Genotyp e Genotype frequenc ie Phenotyp e frequenc ie A AA AO P 2 2pr P 2 +2pr B BB BO q 2 2qr q 2 +2qr AB AB 2pq 2pq O OO r 2 r 2 Blood is a complex, living tissue that contains many cell types and proteins. A transporter, regulator, and defender, blood courses through the body carrying out many important functions. BLOOD TYPE IS GENETIC The A and B antigen molecules on the surface of red blood cells are produced by two different enzymes. These two enzymes are encoded by different versions, or alleles, of the same gene: A and B. The A and B alleles code for enzymes that produce the type A and B antigens respectively. A third version of this gene, the O allele, codes for a protein that is not functional and does not produce surface molecules. Two copies of the gene are inherited, one from each parent. The possible combinations of alleles produce blood types in the following way: The Deterministic HARDY-WEINBERG Model Godfrey Harold Hardy (1877-1947) was an English mathematician, born in Cranley, Surrey. He wrote several essays on series and integrals. Wilhelm Weinberg (1862- 1937) was a doctor, obstetrician- gynecologist, German, half Jewish, who lived in Stuttgart. He wrote numerous articles that have been recognized in the English-speaking world for over 35 years. His studies on twins were widely favored by about 3500 deliveries which made throughout his career. UNDERSTANDING THE HARDY-WEINBERG PRINCIPLE NON APLICABILITY OF HARDY-WEINBERG THEORY The populations evolve over generations, which leads us to the obvious conclusion: the Hardy-Weinberg Law does not apply to real situations, there are always factors of evolution acting on the population. Genes do not divide in meiosis always accurately (we are talking about changing), genotypes do not transmit the uniform rates (selection), the populations are not infinitely large and the crosses are not random (genetic drift) and populations are not isolated (migration). All these factors tend to alter the balance of the people, by changing frequencies gene, are designated by factors of evolution. The model / Hardy-Weinberg theorem is a mathematical approach to a large population in which the intersection between individuals is random and where there is no migration, no mutation nor natural selection. That is, was the first successful approach between the concepts of natural selection and phenotypic traits and genotypes of Mendel. Changes in allele frequencies over time and space are clues from which you can investigate the action of evolutionary processes. By understanding how "evolutionary forces" acting is also possible to construct mathematical models that approximate reality. These models are needed to understand the subtle interplay between "evolutionary forces" and genetic heritage, and from this knowledge, make inferences about the processes that acted in the past and which are the source of genetic diversity present. The models allow to derive equations that allow us to estimate parameters of interest such as the age of an allele, the rate of migration between two populations or the rate of growth of a population. The models also allow the testing of hypotheses about what has happened in the past. The application of any model requires verification of several assumptions that may or may not be true for all species. CONCLUSIONS BIBLIOGRAPHY [1] Alvarez, Manuela, Genética das Populações Humanas,2006/2007, Universidade de Coimbra [2] Nowak, Martin A.,Evolutionary Dynamics, Exploring the Equations of Life, 2006,Cambridge, Massachusetts and London, England [3] Sene, Fábio de Melo, O teorema de Hardy Weinberg, 2008, SBG [4] Futuyama, Douglas, Evolução, Ciência e Sociedade, State University of New York, SBG [5] Silva, Pedro, Allele frequency estimation in the human ABO blood group system , 2002, Faculdade de Ciências da Universidade de Lisboa [6] Souza, Rogério F de, Noções de Genética das Populações [7] Silva, Pedro, Modelos BioMatemáticos, http://correio.fc.ul.pt/~mcg/aulas/biopop/
-
Upload
carlanoronha7812 -
Category
Documents
-
view
122 -
download
0
Transcript of Poster UBI Dinamica
Blood Groups Gene FrequenciesCarla Noronha1,Ana Cunha 2, Ulisses Azeiteiro3
1Universidade Aberta, MBB , Portugal, [email protected] Universidade Aberta, MBB , Portugal, [email protected] Aberta, DCeT, Portugal, [email protected]
At a time of unprecedented expansion, the study of evolution transcends all areas of biology. All phenomena that are observable today in living organisms and their systems have a fantastic evolutionary component that can not be ignored! Evolution transcends mutations and natural selection of Darwin and proves to be in the first row of studying the mechanisms involved ... Life! Mathematical models have become allies in the biosciences. The probabilistic models become very useful for process analysis as it is possible to access the repetitive data, since they require a large initial sample data for forming, but the implementation of the evolutionary processes is often associated to the scarcity of data. Changes in allele frequencies over time and space are clues from which you can investigate the action of evolutionary processes. By understanding how "evolutionary forces" acting is also possible to construct mathematical models that approximate reality. These models are needed to understand the subtle interplay between "evolutionary forces" and genetic heritage, and from this knowledge, make inferences about the processes that acted in the past and which are the source of genetic diversity present.The study of gene frequencies of blood groups is one of the areas where the mathematical models and probabilistic / stochastic theories stand for the progress achieved in recent decades.In this work authors present and discuss such models.
In 1908, Hardy and Weinberg concluded that if no evolutionary factor acted on a population that satisfies certain conditions, the frequencies of their alleles would remain unchanged over the generations and genotypic ratios would reach a stable equilibrium. The conditions should be fulfilled to enable the population to remain in equilibrium gene would be:1. The population must be very large
(infinite), so that they can occur all types of junctions according to the laws of probability
2. The population should have the same number of individuals of each sex
3. The population must be panmitic ,this is, all randomly marry without the existence of any type of preference genotypic or phenotypic, social stratification and inbreeding
4. All couples in the population are equally fertile and generate an equal number of children
5. There is no overlap of generations in the population
6. The genes do not mutate7. Natural selection will not have any
influence on the population as all individuals meet the same conditions for survival
8. There is no migration or admixture with neighboring populations so there is no change in gene frequencies.
The Hardy-Weinberg law in fact provides a theoretical pattern for the behavior of gene populations across generations. In practice, this law allows us to understand whether or not a population is in equilibrium or whether there are evolutionary factors to act.This is a Hardy-Weinberg representation :
Consider a Mendelian population, a genetic background composed by two alleles A and a and genotypes AA, Aa and aa, resulting from a pair of alleles that are distributed with the same frequency in individuals of both sexes.The frequencies of alleles A and a can be calculated easily if we take as our starting point the gametes that produced the current generation of individuals in this population. Thus, the number of gametes with the allele to be equal to twice the number of homozygous individuals generation of AA plus the number of individuals heterozygous for each individual Aa originated by two AA gametes with allele and each individual Aa was formed by a gamete in the A gene and with its other allele the. Similar reasoning enables us to say that the number of gametes that the allele produce the generation of individuals to be tested is equal to twice the number of individuals per year plus the number of heterozygous individuals Aa.Given the above, if we call the frequencies of the alleles in the population, respectively, p and q = 1-p and symbolize the frequencies of individuals with genotypes AA, Aa and aa, we can write that the p and q frequencies of alleles A and a in the generation under study are:
We can summarize the frequencies of genotypes in the following table:
From the observation of this table immediately follows that
AA + aa+Aa=
ABSTRACT
INTRODUCTION
Blood Group(phenotype)
Genotype Genotype frequencie
Phenotype frequencie
A AA
AO
P2
2pr
P2+2pr
B BB
BO
q2
2qr
q2+2qr
AB AB 2pq 2pq
O OO r2 r2
Blood is a complex, living tissue that contains many cell types and proteins. A transporter, regulator, and defender, blood courses through the body carrying out many important functions.
BLOOD TYPE IS GENETIC
The A and B antigen molecules on the surface of red blood cells are produced by two different enzymes. These two enzymes are encoded by different versions, or alleles, of the same gene: A and B.The A and B alleles code for enzymes that produce the type A and B antigens respectively. A third version of this gene, the O allele, codes for a protein that is not functional and does not produce surface molecules. Two copies of the gene are inherited, one from each parent. The possible combinations of alleles produce blood types in the following way:
The Deterministic HARDY-WEINBERG Model
Godfrey Harold Hardy (1877-1947) was an English mathematician, born in Cranley, Surrey. He wrote several essays on series and integrals. Wilhelm Weinberg (1862-1937) was a doctor, obstetrician-gynecologist, German, half Jewish, who lived in Stuttgart. He wrote numerous articles that have been recognized in the English-speaking world for over 35 years. His studies on twins were widely favored by about 3500 deliveries which made throughout his career.
UNDERSTANDING THE HARDY-WEINBERG PRINCIPLE
NON APLICABILITY OF HARDY-WEINBERG THEORY
The populations evolve over generations, which leads us to the obvious conclusion: the Hardy-Weinberg Law does not apply to real situations, there are always factors of evolution acting on the population. Genes do not divide in meiosis always accurately (we are talking about changing), genotypes do not transmit the uniform rates (selection), the populations are not infinitely large and the crosses are not random (genetic drift) and populations are not isolated (migration). All these factors tend to alter the balance of the people, by changing frequencies gene, are designated by factors of evolution.The model / Hardy-Weinberg theorem is a mathematical approach to a large population in which the intersection between individuals is random and where there is no migration, no mutation nor natural selection. That is, was the first successful approach between the concepts of natural selection and phenotypic traits and genotypes of Mendel.
Changes in allele frequencies over time and space are clues from which you can investigate the action of evolutionary processes.By understanding how "evolutionary forces" acting is also possible to construct mathematical models that approximate reality.These models are needed to understand the subtle interplay between "evolutionary forces" and genetic heritage, and from this knowledge, make inferences about the processes that acted in the past and which are the source of genetic diversity present.The models allow to derive equations that allow us to estimate parameters of interest such as the age of an allele, the rate of migration between two populations or the rate of growth of a population. The models also allow the testing of hypotheses about what has happened in the past. The application of any model requires verification of several assumptions that may or may not be true for all species.
CONCLUSIONS
BIB
LIO
GR
AP
HY
[1] Alvarez, Manuela, Genética das Populações Humanas,2006/2007, Universidade de Coimbra[2] Nowak, Martin A.,Evolutionary Dynamics, Exploring the Equations of Life, 2006,Cambridge, Massachusetts and London, England[3] Sene, Fábio de Melo, O teorema de Hardy Weinberg, 2008, SBG[4] Futuyama, Douglas, Evolução, Ciência e Sociedade, State University of New York, SBG[5] Silva, Pedro, Allele frequency estimation in the human ABO blood group system , 2002, Faculdade de Ciências da Universidade de Lisboa[6] Souza, Rogério F de, Noções de Genética das Populações[7] Silva, Pedro, Modelos BioMatemáticos, http://correio.fc.ul.pt/~mcg/aulas/biopop/
