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4/6/2008 Origin of Variation? Forensics and Probability Charles Darwin from, On the Origin of Species by Means of Natural Selection, 1859 "...no-one can say why the same peculiarity in different individuals....is sometimes inherited and sometimes not so: why the child often reverts in certain characters to its grandfather, or other much more remote ancestor; why a peculiarity is often transmitted from one sex to both sexes, or to one sex alone, more commonly but not exclusively to the like sex." • Genetics is the scientific study of heredity and variation • Heredity is the passing on of characteristics called “traits” traits from parent to child • Variation shows that children differ in appearance from their parents and their brothers and sisters What explains the passing of traits from parents to offspring? • The “blending” hypothesis is the idea that genetic material from the two parents blends together (like blue and yellow paint blend to make k green)) • The “particulate” hypothesis is the idea that parents pass on discrete heritable units (genes) • Mendel documented a particulate mechanism through his experiments with garden peas http://www.mendelmuseum.org/eng/1online/experiment.htm 1 4/6/2008 Mendel is as important as Darwin in 19th century science • Mendel did experiments and analyzed the results mathematically. His research required him to identify variables, isolate their effects, effects measure these variables painstakingly and then subject the data to mathematical analysis. • He was influenced by his study of physics and having an interest in meteorology. His mathematical and statistical approach was also favored by plant breeders at the time. Mendel used an Experimental, Quantitative Approach • Advantages of pea plants for genetic study: – There are many varieties with distinct heritable features, or characters (such as color); character variations are called traits – Mating of plants can be controlled – Each pea plant has sperm-producing organs (stamens) and egg-producing organs (carpels) – Cross-pollination (fertilization between different plants) can be achieved by dusting one plant with pollen from another Mendel Planned Experiments Carefully • Mendel chose to track only those characters that varied in an “either-or” manner • He also used varieties that were “truebreeding” (plants that produce offspring of the same variety when they self-pollinate) • He spent 2 years getting “true” breeding plants to study • At least three of his traits were available in seed catalogs of the day Purple flowers White flowers F1 Generation (hybrids) F2 Generation Transferred spermbearing pollen from stamens of white flower to eggbearing carpel of purple flower Parental generation (P) Carpel Stamens Pollinated carpel matured into pod Planted seeds from pod First generation offspring (F1) Examined offspring: all purple flowers Some Terminology P Generation (true-breeding parents) Removed stamens from purple flower All plants had purple flowers • In a typical experiment, Mendel mated two contrasting, true-breeding varieties, a process called hybridization • The Th ttrue-breeding b di parents t are th the P generation • The hybrid offspring of the P generation are called the F1 generation • When F1 individuals self-pollinate, the F2 generation is produced 2 4/6/2008 Mendel’s First Law: The Law of Segregation • When Mendel crossed contrasting, truebreeding white and purple flowered pea plants, all of the F1 hybrids were purple • When Mendel crossed the F1 hybrids, many of the F2 plants had purple flowers, but some had white • Mendel discovered a ratio of about three to one, purple to white flowers, in the F2 generation • Mendel reasoned that only the purple flower factor was affecting flower color in the F1 hybrids • Mendel called the purple flower color a dominant trait and white flower color a recessive trait • Mendel observed the same pattern of inheritance in six other pea plant characters, each represented by two traits • What Mendel called a “heritable factor” is what we now call a gene Mendel’s Model • Mendel developed a hypothesis to explain the 3:1 inheritance pattern he observed in F2 offspring • Four related concepts make up this model • These concepts can be related to what we now know about genes and chromosomes The First Concept Allele for purple color • Alternative versions of genes account for variations in inherited characters • For example, the gene for flower color in pea plants exists in two versions versions, one for purple flowers and the other for white flowers • These alternative versions of a gene are now called alleles • Each gene resides at a specific locus on a specific chromosome Locus for flower color gene Homologous pair of chromosomes Allele for white color 3 4/6/2008 The Second Concept The Third Concept • For each character, an organism inherits two alleles, one from each parent • Mendel made this deduction without knowing about the role of chromosomes • The two alleles at a locus on a chromosome may be identical, as in the true-breeding plants of Mendel’s P generation • Alternatively, the two alleles at a locus may differ, as in the F1 hybrids • If the two alleles at a locus differ, then one (the dominant allele) determines the organism’s appearance, and the other (the recessive allele) has no noticeable effect on appearance • In the flower-color example, the F1 plants had purple flowers because the allele for that trait is dominant The Fourth Concept Mendel’s Laws Explain the Data • Known as “the law of segregation” • Two alleles for a heritable character separate (segregate) during gamete formation and end up in different gametes g • Thus, an egg or a sperm gets only one of the two alleles that are present in the somatic cells of an organism • This segregation of alleles corresponds to the distribution of homologous chromosomes to different gametes in meiosis • Mendel’s segregation model accounts for the 3:1 ratio he observed in the F2 generation of his numerous crosses • The p possible combinations of sperm p and egg gg can be shown using a Punnett square, a diagram for predicting the results of a genetic cross between individuals of known genetic makeup • A capital letter represents a dominant allele, and a lowercase letter represents a recessive allele P Generation Appearance: Genetic makeup: Purple flowers PP White flowers pp P p Gametes F1 Generation Appearance: Genetic makeup: Purple flowers Pp 1 Gametes: 2 1 P p 2 F1 sperm P p PP Pp F2 Generation P F1 eggs p Pp 3 pp :1 Some Vocabulary Terms • Gene: sequence of DNA coding for genetic information • Allele: a variant of a single gene, inherited at a particular location on a chromosome. The variants can be written as A and a. • Genotype: The genetic constitution of an individual. The genotype consists of one complete set of genes from mother and a second complete set of genes from father. • Phenotype: An observable train in an individual. It is determined by interaction of genotype and environment. • Homozygote: individual having two copies of the same allele at a genetic location (AA or aa) 4 4/6/2008 LE 14-6 Some Vocabulary Terms • Heterozygote: individual having two different alleles at a genetic location (Aa) • Dominant: An allele A is dominant when its phenotype of the heterozygote Aa is the same as that of the homozygote AA but differs from the homozygote aa • Recessive: An allele a is recessive if the phenotype of the homozygote is different from that of the heterozygote Aa and homozygote AA, which are the same. • Codominant: An allele is codominant if both A and a contribute to the phenotype of the heterozygote Aa equally. 3 Phenotype Genotype Purple PP (homozygous Purple Pp (heterozygous Purple Pp (heterozygous White pp (homozygous Ratio 3:1 Ratio 1:2:1 1 2 1 1 LE 14-7 The Testcross • How can we tell the genotype of an individual with the dominant phenotype? • This individual must have one dominant allele, but could be either homozygous dominant or heterozygous • The answer is to carry out a testcross: breeding the mystery individual with a homozygous recessive individual • If any offspring display the recessive phenotype, the mystery parent must be heterozygous Mendel’s Second Law: The Law of Independent Assortment • Mendel derived the law of segregation by following a single character • The F1 offspring g produced in this cross were all heterozygous for that one character • A cross between such heterozygotes is called a monohybrid cross Dominant phenotype, unknown genotype: PP or Pp? Recessive phenotype, known genotype: pp If Pp, p g purple p p then 1 2 offspring and 1 2 offspring white: If PP, then all offspring purple: p p P p p Pp Pp P Pp Pp P P Pp Pp pp pp • Mendel identified his second law of inheritance by following two characters at the same time • Crossing two, true-breeding parents differing in two characters produces dihybrids in the F1 generation, heterozygous for both characters • A dihybrid cross, a cross between F1 dihybrids, can determine whether two characters are transmitted to offspring as a package or independently 5 4/6/2008 LE 14-8 P Generation YYRR yyrr Gametes YR yr YyRr F1 Generation Hypothesis of dependent assortment Hypothesis of independent assortment Sperm 1 Sperm 1 2 YR 1 2 yr 1 Eggs 1 F2 Generation (predicted offspring) 1 2 2 4 YR 1 4 Yr 1 4 yR 1 4 yr Eggs 4 YR 4 Yr 4 yR YYRR YYRr YyRR YyRr YR YYRR YyRr 1 YyRr yyrr 1 YYRr YYrr YyRr Yyrr YyRR YyRr yyRR yyRr YyRr Yyrr yr 3 4 1 4 1 Phenotypic ratio 3:1 yr 4 9 3 16 16 yyRr 3 16 yyrr 3 16 Phenotypic ratio 9:3:3:1 Probability • Ranges from 0 to 1 • Probabilities of all possible events must add up to 1 • Rule o multiplication: The probability that independent events will occur simultaneously is the product of their individual probabilities. • Rule of addition: The probability of an event that can occur in two or more independent ways is the sum of the different ways. ½ chance of P and ½ chance of p allele results in ¼ chance of each homozygous genotype. There are two ways to get the heterozygous genotype so it is ¼+¼=½ Three genotypes give the same phenotype. • The law of independent assortment states that each pair of alleles segregates independently of other pairs of alleles during gamete formation • Strictly speaking, this law applies only to genes on different, nonhomologous chromosomes • Genes located near each other on the same chromosome tend to be inherited together Multiplication and Addition Rules Applied to Monohybrid Crosses • The multiplication rule states that the probability that two or more independent events will occur together is the product of their individual probabilities p • Probability in an F1 monohybrid cross can be determined using the multiplication rule • Segregation in a heterozygous plant is like flipping a coin: Each gamete has a 1/2 chance of carrying the dominant allele and a 1/2 chance of carrying the recessive allele Solving Complex Genetics Problems with the Rules of Probability • We can apply the rules of multiplication and addition to predict the outcome of crosses involving multiple characters • A dihybrid or other multicharacter cross is equivalent i l t tto ttwo or more independent i d d t monohybrid crosses occurring simultaneously • In calculating the chances for various genotypes, each character is considered separately, and then the individual probabilities are multiplied together 6 4/6/2008 YYRR yyrr For a dihybrid cross – the chance that 2 independent events occur together is the product of their chances of occurring separately. Female Gametes YyRr ¼ YR YyRr ¼ Yr ¼ yR ¼ yr ¼ YR YyRr Male gametes 3/16 YYRr YyRR YyRr YYrR YYrr YyRr Yyrr YyRR YyRr yyRR yyRr YyRr Yyrr ¼ yR 9/16 3/16 YYRR ¼ Yr ¼ yr yyRr yyrr • • • • The chance of yellow (YY or Yy) seeds= 3/4 (the dominant trait) The chance of round (RR or Rr) seeds = 3/4 (the dominant trait) green (yy) seeds= 1/4 ((the recessive trait)) The chance of g The chance of wrinkled (rr) seeds= 1/4 (the recessive trait) Therefore: The chance of yellow and round= 3/4 x 3/4 = 9/16 The chance of yellow and wrinkled= 3/4 x 1/4 = 3/16 The chance of green and round= 1/4 x 3/4 = 3/16 The chance of green and wrinkled= 1/4 x 1/4 = 1/16 1/16 Inheritance patterns are often more complex than predicted by Mendel Extending Mendelian Genetics for a Single Gene • The relationship between genotype and phenotype is rarely as simple as in the pea plant characters Mendel studied • Many heritable characters are not determined by only one gene with two alleles • However, the basic principles of segregation and independent assortment apply even to more complex patterns of inheritance • Inheritance of characters by a single gene may deviate from simple Mendelian patterns in the following situations: The Spectrum of Dominance • Complete dominance occurs when phenotypes of the heterozygote and dominant homozygote are identical • In incomplete dominance, the phenotype of F1 hybrids h b id iis somewhere h b between t th the phenotypes of the two parental varieties • In codominance, two dominant alleles affect the phenotype in separate, distinguishable ways • Forensic Traits are codominant – When Wh alleles ll l are nott completely l t l d dominant i t or recessive – When a gene produces multiple phenotypes – When a gene has more than two alleles – The forensic characteristics usually have more than two alleles P Generation Red CRCR White CWCW CR Gametes CW Pink CRCW F1 Generation Gametes 1 1 F2 Generation 2 CR 2 CR 1 2 1 CW Sperm 2 CW Eggs 1 1 2 CR 2 CW CRCR CRCW CRCW CWCW 7 4/6/2008 The Relation Between Dominance and Phenotype • A dominant allele does not subdue a recessive allele; alleles don’t interact • Alleles are simply variations in a gene’s nucleotide sequence • For any gene, dominance/recessiveness relationships of alleles depend on the level at which we examine the phenotype • If you look directly at DNA, you can always detect codominance. Frequency of Dominant Alleles • Dominant alleles are not always more common in populations than recessive alleles • For example, one baby out of 400 in the USA iis b born with ith extra t fi fingers or ttoes • The allele for this trait is dominant to the allele for the more common trait of five digits per appendage • In this example, the recessive allele is far more prevalent than the dominant allele in the population Multiple Alleles • Most genes exist in populations in more than two allelic forms • For example, the four phenotypes of the ABO blood group in humans are determined b th by three alleles ll l ffor th the enzyme (I) th thatt attaches A or B carbohydrates to red blood cells: IA, IB, and i. LE 14-12 Polygenic Inheritance aabbcc Aabbcc AaBbcc AaBbCc AaBbCc AABbCc AABBCc AABBCC 20/64 15/64 Fraction of progeny • Quantitative characters are those that vary in the population along a continuum • Quantitative variation usually indicates polygenic inheritance, an additive effect of t two or more genes on a single i l phenotype h t • Skin color in humans is an example of polygenic inheritance AaBbCc 6/64 1/64 8 4/6/2008 Nature and Nurture: The Environmental Impact on Phenotype Relating Mendel’s Laws to Cells • Law of Segregation • Pairs of characteristics (alleles) separate during gamete formation • Each cell has two sets of chromosomes that are divided to one set per gamete. Offspring acquire genes from parents by inheriting chromosomes • Law of Independent Assortment • The inheritance of an allele of one gene does not influence the allele inherited at a second gene. • Genes on different chromosomes segregate their alleles independently. Inheritance of Genes • In a literal sense, children do not inherit particular physical traits from their parents • It is genes that are actually inherited chromosomes. • Genes are carried on chromosomes • Mendel identified 7 sets of charactersOne per each of the 7 chromosomes in peas, so his law worked out perfectly. • Two characters on the same chromosome are linked together and would have messed up his law. • Genes are the units of heredity • Genes are segments of DNA • Each gene has a specific locus on a certain chromosome • One set of chromosomes is inherited from each parent • Reproductive cells called gametes (sperm and eggs) unite, passing genes to the next generation Sexual Reproduction Chromosomes Come in Sets • Two parents give rise to offspring that have unique combinations of genes inherited from the two parents. • All humans arise from the joining of 1 egg and 1 sperm cell • 100% of a person’s DNA is the same within and throughout a human being’s body. • Whether you look at the cells of a person’s blood, skin, semen, saliva or hair, the DNA and genes will be the same. • Each human cell (except gametes) has 46 chromosomes arranged in pairs in its nucleus • The two chromosomes in each pair are called homologous g chromosomes • One of each pair came from your mother and the other came from your father. • Both chromosomes in a pair carry genes controlling the same inherited characteristics 9 4/6/2008 • The sex chromosomes are called X and Y • Human females have a homologous pair of X chromosomes (XX) • Human H males l h have one X and d one Y chromosome • The 22 pairs of chromosomes that do not determine sex are called autosomes • Each pair of homologous chromosomes includes one chromosome from each parent • The 46 chromosomes in a human somatic cell are two sets of 23: one from the mother and one from the father • The number of chromosomes in a single set is represented by n • A cell with two sets is called diploid (2n) • For humans, the diploid number is 46 (2n = 46) Meiosis reduces the number of chromosome sets from diploid to haploid Meiosis is preceded by the replication of chromosomes Meiosis takes place in two sets of cell divisions, called meiosis I and meiosis II The behavior of chromosomes during meiosis and fertilization is responsible for most of the variation that arises in each generation The two cell divisions result in four daughter cells Each daughter cell has only half as many chromosomes as the parent cell 8 Gamete Combinations Key Maternal set of chromosomes vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv Maternal set of chromosomes (n = 3) Possibility 2 Possibility 1 Paternal set of chromosomes 2n = 6 Paternal set of chromosomes (n = 3) Two equally probable arrangements of chromosomes at metaphase I Two sister chromatids of one replicated chromosomes Centromere Metaphase II Daughter cells Combination 1 Combination 2 Combination 3 Combination 4 Two nonsister chromatids in a homologous pair Pair of homologous chromosomes (one from each set) 10 4/6/2008 LE 13-5 Key Haploid gametes (n = 23) Haploid (n) Ovum (n) Diploid (2n) • Homologous pairs of chromosomes orient randomly at metaphase I of meiosis • In independent assortment, each pair of chromosomes sorts maternal and paternal g into daughter g cells independently p y of homologues the other pairs • The number of combinations possible when chromosomes assort independently into gametes is 2n, where n is the haploid number • For humans (n = 23), there are more than 8 million (223) possible combinations of chromosomes Sperm cell (n) MEIOSIS FERTILIZATION Ovary Testis Diploid zygote (2n = 46) Mitosis and development Multicellular diploid adults (2n = 46) LE 13-11 Random Fertilization Nonsister chromatids Prophase I of meiosis • Random fertilization adds to genetic variation because any sperm can fuse with any ovum (unfertilized egg) • The fusion of gametes produces a zygote with any of about 64 trillion diploid combinations • Crossing over adds even more variation • Each zygote has a unique genetic identity Tetrad Chiasma, site of crossing over Metaphase I Metaphase II Daughter cells Recombinant chromosomes Human Genome Gene Pools and Allele Frequencies 23 Pairs of Chromosomes + mtDNA Located in cell nucleus http://www.ncbi.nlm.nih h.gov/genome/guide/ Autosomes 2 copies per cell Located in mitochondria (multiple copies in cell cytoplasm) mtDNA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 X Nuclear DNA 3.2 billion bp Y Sexchromosomes 16,569 bp Mitochondrial DNA • A population is a localized group of individuals capable of interbreeding and producing fertile offspring • The gene pool is the total aggregate of genes in a population at any one time • The alleles at any particular locus can be • The gene pool consists of all gene loci in all individuals of the population 100s of copies per cell Butler, J.M. (2005) Forensic DNA Typing, 2nd Edition, Figure 2.3, ©Elsevier Science/Academic Press 11 4/6/2008 Genetic Variation in Populations • Many genes are monomorphic – They have only one common allele, i.e. with a frequency >0.01 (or 1%). • Other genes are polymorphic – They have two or more alleles with frequencies >0.01. Examples of polymorphic loci include the ABO and Rh blood groups. Mice in the Gene Pool: Calculating Genotype Frequency vs. Allele Frequency 4 + 4 + 2 = 10 8 +4 =12 B 4/10=0.4 BB 4/10=0.4 Bb 4 BB 4Bb 2/10=0.2 bb 2bb 4 + 4 =8 b 12 + 8 =20 12/20=0.6 B 8/20=0.4 b Calculating the HW Law The Hardy-Weinberg Theorem • Chance combinations of alleles of a gene in a population can be expressed by the binomial expansion. • For a two-allele locus, let p = frequency of allele G1 and q = frequency of allele G2. • Since there are no other alleles, p + q = 1.0. • The distribution of genotypes would be (p + q)2 = p2 + 2pq + q2 = 1, • where p2 and q2 are the frequencies of the two homozygotes and 2pq is the frequency of the heterozygote. • The Hardy-Weinberg theorem describes a population that is not evolving • It states that frequencies of alleles and genotypes in a population’s gene pool remain i constant t t from f generation ti to t generation, provided that only Mendelian segregation and recombination of alleles are at work • Mendelian inheritance preserves genetic variation in a population 12 4/6/2008 Population Genetics and Human Health • We can use the Hardy-Weinberg equation to estimate the percentage of the human population carrying the allele for an inherited disease • Take the square root of the recessive to solve for its allele frequency or q. • Subtract that frequency from 1 to get the other frequency, p. • The frequency of being a carrier is 2pq. • The odds of two carriers mating is (2pq)2 LE 23-5 Gametes for each generation are drawn at random from the gene pool of the previous generation: 80% CR (p = 0.8) 20% CW (q = 0.2) • The Hardy-Weinberg theorem describes a hypothetical population • In real p populations, p , allele and g genotype yp frequencies do change over time Sperm CW (20%) p2 pq 64% CR CR 16% CR CW CR (80%) CW (20%) Eggs CR (80%) Conditions for Hardy-Weinberg Equilibrium qp 4% CWCW 16% CR CW q2 Modeling Genetics with Candy • The five conditions for non-evolving populations are rarely met in nature: – Extremely large population size – No gene flow – No N mutations t ti – Random mating – No natural selection • Each type of candy is like a gene • Each Flavor is like an Allele • We can only have two pieces of each type off candyd one from f Mom, M One O From F Dad D d • Doesn’t matter how many flavors are possible, you just get two, although they can be the same flavor (homozygous) or different flavors (heterozygous) 13 4/6/2008 Modeling Genetics with Candy • Some candy has only one flavor- likewise most genes DO NOT vary. They have essential functions. • Each type of candy was independently inherited and 14