PRODUCTION OF INDIVIDUAL VARIATION By and large the physical sciences dismiss individual variation and in so doing can produce very generalized, mathematically precise results. Physics, for example, deals with the behavior of ideal bodies so that the color, shape and composition of a falling body according to the law of gravity can be dismissed as irrelevant. In the life sciences such variation cannot be dismissed; in fact it is often the phenomenon which must be explained. Living individuals differ in genetics, environmental influences and history. Hence, to explain the behavior of a living individual, its unique characteristics must be taken into account. Individual variation, as we have already seen, is a critical component of Darwin's theory of natural selection: without individual variation there is simply nothing to select! Differences between individuals can be heritable or nongenetic consequences of environmental influences, e.g., brown eyes which are inherited vs. black eyes which are acquired through some trauma. In this discussion we will focus on the production of heritable variation, but keep in mind that not all examples of individual variation are under genetic control. We owe much of our understanding of the genetic basis of individual variation to Gregor Mendel and so will start by examining his important contribution to biology. Mendelian Genetics Gregor Mendel (1822-1884) was an Augustinian monk whose experiments with plant breeding conducted at the monastery of St. Thomas in Brunn, Austria between 1854 and 1869 formed the basis of modern genetics. Unfortunately, Mendel's results, published in 1865 and 1869 in the Proceedings of the Society of Natural History of Brunn, went unnoticed until 1900 when three independent investigators, Carl Correns (Germany), Hugo De Vries (Holland) and Erich Von Tschermak (Austria), conducted similar experiments and reached the same conclusions as had Mendel. All three found in researching the literature on the subject that Mendel was the first to describe rules for the transmission of genetically controlled traits and so gave him all the credit. This rediscovery and confirm- ation of Mendel's work started the field of genetics. Mendel was not the first to conduct breeding experiments, but he was the first to discover rules governing heredity. His success was due to his choice of experimental plant (the garden pea, Pisum sativum) and his knowledge of mathematics, especially statistics. The garden pea reproduces by self-fertilization and so inbreeding over many generations can detect genetically pure lines. Furthermore, this species possesses several discontinuous traits, i.e., aspects of the organism's outward appearance (phenotype) which exist in only two character states with no intermediates between them. Each organism possesses one of the two character states. Mendel chose seven discontinuous traits to study: seed shape (either round or wrinkled), seed color (yellow or green), pod shape (smooth or wrinkled), pod color (green or yellow), flower color (red or white), flower position (axial or terminal) and vine length (tall or short). By crossbreeding genetically pure line individuals with contrasting character states for each trait and observing the phenotypes of their offspring, he could determine the pattern of inheritance . Since these character states are discontinuous (either-or expressions) with no inter- mediates, he could quantify his results by simply counting the two different phenotypes among the offspring of each experimental cross. His knowledge of statistics enabled him to recognize that his results followed exact proportions or ratios, even though small sample size caused variations in observed ratios from the theoretical or expected ratios he was able to recognize. Mendel's study provides an excellent example of the inducto-deductive method used in science and we will now examine how he handled each of this method's components. Induction Mendel started his work by allowing individuals with contrasting character states to self-fertilize through many generations until he was convinced that their traits were pure. He then selected two of these (one with each character state) for crossbreeding. These two individuals constituted the parental or P generation. Crossbreeding was effected by removing the pollen producing stamens from both plants and then using the pollen of one to fertilize the ovules of the other. The offspring produced by this cross constituted the first filial (or F1) generation. He then crossbred these individuals or simply let them self-fertilize to produce the second filial (F2) generation. Mendel's results can be illustrated by the phenotypic expression of seed shape when he crossed individuals from a pure line of plants with round seeds with individuals from a pure line of plants with wrinkled seeds. P generation: round x wrinkled F1 generation: all offspring had round seeds F2 generation: 3:1 ratio of offspring with round and wrinkled seeds (3 round : 1 wrinkled) When he performed this experiment with the six other traits, he obtained the exact same results. Thus, he recognized a pattern: a 3:1 phenotypic ratio in the F2 generation. Remember that the purpose of induction in the inducto-deductive method of science is to recognize patterns. Mendel extended his experimental results (based only on the observation of seven traits in a single plant species) through inductive reasoning to claim that all discontinuous traits no matter what animal or plant species is studied would follow the same pattern. The next step was to find a reason why this pattern obtained, i.e., to develop an hypothesis to explain this result. Hypothesis To explain this pattern Mendel hypothesized that each discontinuous phenotypic trait in an individual was controlled by two hereditary factors. The alternative hypothesis that each trait was controlled by one factor was not a viable explanation because it could not explain the presence of wrinkled seeds in the F2 generation. Since all F1 plants produced only smooth seeds, then the factor controlling the wrinkled condition would have to have been lost. But, by postulating two hereditary factors behind each trait, Mendel could explain the reappearance of wrinkled-seeded plants in the second filial generation. To account for the observation that all F1 individuals had round seeds, Mendel suggested that the factor for wrinkled seeds was masked by the factor for round seeds and so the wrinkled seed factor was recessive to the dominant round seed factor. Whereas dominant factors can influence the phenotype when only one is present, recessive factors must be paired together to produce a phenotypic effect. It must be emphasized that these hereditary factors (= genes or more precisely, alleles) cannot be observed directly; their existence is only inferred from phenotypes produced in breeding experiments. Mendel explained the hereditary make-up (genotypes = factor pairs) of his experimental plants as follows: P generation: round (RR) x wrinkled (rr) F1 generation: all round (Rr) F2 generation: 3 round (1 RR + 2 Rr) : 1 wrinkled (rr) To distinguish the three different genotypes in a monohybrid cross (a cross involving one phenotypic trait expressed in two character states) the following terminology is used: R= dominant allele, r= recessive allele, RR= homozygous dominant genotype, Rr= heterozygous genotype, and rr= homozygous recessive genotype. If, as Mendel hypothesized, each discontinuous phenotype is controlled by two alleles, it follows then that only one is passed on to an offspring by each parent, otherwise the number of alleles would double with each generation. This corollary of Mendel's hypothesis is known as his law of segregation which states that members of a pair of alleles which form a genotype segregate into sister gametes when gametes are formed during reproduction. Predictions deduced from Mendel's hypothesis For an hypothesis to be a scientific hypothesis, it must generate testable predictions. Remember that a prediction is a fact, unknown at the time the prediction is made, which is deduced from the hypothesis and must be true if the hypothesis is true. The fact that only phenotypes can be observed provided Mendel with the opportunity to make two predictions about the unseen genotypes in the F2 generation. The two predictions which follow from Mendel's hypothesis are: 1. Underlying the dominant phenotypes in the F2 generation are two different genotypes: RR and Rr. 2. The ratio of these two predicted genotypes is 1 RR to 2Rr. Thus, the 3:1 phenotypic ratio is accompanied by a 1:2:1 genotypic ratio. According to his law of segregation, the two different factors (R and r) in the F1 heterozygotes segregated into sister gametes with the result that males produced two types of pollen grains and females produced two types of eggs in their ovules. Since fertilization is a random process, each type of pollen grain has an equal chance of fertilizing each of the two types of eggs (here again is an example of how Mendel's knowledge of mathematics helped him interpret results). Consequently, the F2 generation should contain three genotypes in the following ratio: one RR; two Rr; one rr. This expected result is illustrated below with a Punnett Square. MALE GAMETES (POLLEN) R r | | | FEMALE R | RR (round) | Rr (round) | GAMETES | | | (EGGS) r | Rr (round) | rr (wrinkled) | Hypothesis testing through experimentation Mendel's two predictions could be tested in either of two ways. He could allow all F2 individuals to self-fertilize, or he could backcross each one with a homozygous recessive plant (test cross). The phenotypic results of the test cross would reveal the presence of the three different genotypes even though the genotypes could not themselves be observed. Each genotype would produce a different set of offspring that would be phenotypically recognizable. The test cross results are presented below: RR x rr = all around (Rr) Rr x rr = both round and wrinkled offspring (50% Rr; 50% rr) rr x rr = all wrinkled (rr) By allowing the F2 plants to self-fertilize Mendel could also have distinguished the three different genotypes. Show how this can be done by depicting both genotypes and phenotypes. Do the results differ in any way from those of the test cross shown above? Mendel's law of independent assortment After following the inheritance of one phenotypic trait through two generations and developing the law of segregation, Mendel then followed the pattern of two phenotypic traits possessed by a single individual. His methodology was the same as that described before and his results led to the following conclusion: members of different pairs of factors segregate independently of one another when gametes are formed. This conclusion is his law of independent assortment. To illustrate this law we will follow the phenotypic expression of two traits in the same individual: seed shape (round or wrinkled) and seed color (yellow or green). For the parental generation Mendel chose a pure bred plant with both dominant traits and crossed it with a pure bred plant with both recessive traits. The result of this cross is shown below. P generation: phenotypes - round, yellow x wrinkled, green genotypes - RR YY rr yy F1 generation: all round and yellow (RrYy) When each plant produces gametes, each gamete receives one factor controlling each trait. The pure line parental generation plant with round and yellow seeds can only produce one type of gamete (RY) and the pure line parent with wrinkled and green seeds can only produce (ry) gametes. Thus, the offspring of this cross must all be heterozygous for both traits (RrYy). According to the law of independent assortment, however, these heterozygotes can produce four different types of gametes in equal numbers. If the pairs of factors segregate independently of one another, R could find itself in a gamete with either Y or y to produce two of the four different gametes, i.e. RY and Ry. Likewise, r could find itself in the same gamete with either Y or y to yield the other two gamete types, rY and ry. Consequently, the random fusion of these four possible gametes in a cross between two heterozygotes should produce four different phenotypes in a 9:3:3:1 ratio and a total of nine different genotypes. This expectation can be illustrated by a Punnett Square. MALE GAMETES RY Ry rY ry RY RRYY RRYy RrYY RrYy round round round round yellow yellow yellow yellow FEMALE Ry RRYy RRyy RrYy Rryy round round round round yellow green yellow green GAMETES rY RrYY RrYy rrYY rrYy round round wrinkled wrinkled yellow yellow yellow yellow ry RrYy Rryy rrYy rryy round round wrinkled wrinkled yellow green yellow green The 9:3:3:1 ratio is a statistical expectation based on a large number of offspring produced by a dihybrid cross, i.e., a cross between individuals which possess factors for two different phenotypic traits. If both individuals are heterozygous for both traits this law predicts that the independent segregation of each factor will yield four possible gametes in equal numbers and four different phenotypes in a 9:3:3:1 ratio. In the example given this ratio is 9 round- yellow: 3 round-green: 3 wrinkled-yellow: 1 wrinkled-green. Find the 9 different genotypes that yield these traits. Particulate vs blending inheritance Mendel hypothesized a form of particulate inheritance with the hereditary units consisting of free-floating particles. This is in stark contrast to the prevailing idea of his day that inheritance followed a blending pattern, i.e., the parental traits blended together to form the offspring traits. An example of blending inheritance would be the production of pink- flowered offspring from a cross between a red-flowered plant and a white-flowered one. Mendel's concept of dominance enabled the particles (alleles) to retain their integrity and be passed on intact to offspring. A particulate inheritance theory was essential for Darwin's theory of natural selection, otherwise any selectively favored phenotype would be blended away as soon as the selected individual reproduced with one of a different phenotype. Thus, Mendel's theory of inheritance provided the essential requirement for Darwin's theory of evolution, even though that was not recognized at the time. Qualitative vs quantitative inheritance Mendel was successful because he chose discontinuous traits for his analysis and these traits are qualitatively different, i.e., either/or traits with no intermediate conditions. Many traits, however, are quantitative rather than qualitative and vary continuously within a population. Such traits, e.g., height and weight, tend to follow a bell-shaped curve when the number of individuals is plotted against the range of the variable trait. With continuous or quantitative variation there will always be a phenotype in between any two chosen for comparison. Can Mendel's theory of particulate inheritance explain quantitatve variation, or is it limited to discontinuous variation? The answer is that Mendel's theory explains both qualitative (discontinuous) and quantitative (continuous) patterns of individual variation. Wiot just one as Mendel proposed. Hence, crossing individuals with different character states of a continuously varying phenotype will not produce the discrete ratios which enabled Mendel to discover his laws of segregation and independent assortment. The genetics of continuous variation is not different from that of discontinuous variation - it is just far more complex. The Chromosome Theory of Inheritance Mendel's explanation of heredity was indeed remarkable since it was based solely on interpretation of breeding experiments long before the dynamics of cell division were discovered. During the early part of the 20th century, the processes of mitosis and meiosis were discovered by microscopic examination of cells. Cytologists also found that genes, or Mendel's hereditary factors, were not free-floating particles but rather were located on chromosomes in the nucleus. The model used by classical geneticists viewed the chromosome as a string of beads with each bead representing a Mendelian gene. Mendelian genes differ because they influence different aspects of the phenotype. There are two classes of Mendelian genes: those found on the same chromosome are called linked genes and those found on different chromosomes are called unlinked genes. Linked genes occupy different positions (called loci) on the same chromosome in addition to controlling different aspects of the phenotype. Study the diagram below. Chromosome 1. OOOO0OOOOOOOOO0OOOOOOOO A B Chromosome 2. OOOOOOOO0OOOOOOOOOO0OOO C D Each O represents a locus on each chromosome which appears as a string of loci. Genes A ndhromosome 2. Genes A and C, B and D, C and B, and A and D are all unlinked because they are located on different chromosomes. This distinction between linked and unlinked genes is important because the chromosome theory of inheritance states that it is the chromosomes and not individual genes which follow Mendel's law of segregation. So that you will appreciate this fact and understand the mechanistic basis for Mendel's two laws, we will examine the cellular basis of gamete formation (meiosis). To assist your understanding of the details of meiosis, I will contrast this form of cell division with another (mitosis). Each individual has a characteristic number of chromosomes found in the nucleus of each of its cells. This number can vary widely between species but is fixed for each species. Our species typically has 46 chromosomes per nucleus. It is important to note, however, that only half that number of chromosomes possesses different combinations of genes. Hence, humans only have 23 chromosomes which bear completely different genes. This means that each different chromosome type is represented twice in the nucleus and such pairs are called homologous chromosomes. Homologous chromosomes contain the same loci. Nonhomologous chromosomes contain different loci. In the example given above Chromosomes 1 and 2 are nonhomologous chromosomes. Remember that the chromosome theory of inheritance simply replaces Mendel's genes with chromosomes. Since Mendel hypothesized two genes for each trait, then the chromosome theory of inheritance hypothesizes two homologous chromosomes housing these two genes. This being the case, what would the nucleus of a dihybrid (AaBb) look like if the two genes A and B were linked? The answer appears below. OOOOOOOO0OOOOOOOOO0OOOOOO A B OOOOOOOO0OOOOOOOOO0OOOOOO a b The chromosome housing genes A and B is homologous with that containing genes a and b. This leads us to another important distinction: that of the difference between locus and allele. A, a, B, b are all different genes because they have different effects on the phenotype in the homozygous condition. But there is a big difference between A and a compared with the difference between A and b. Genes A and B (as well as genes a and B, a and b, and A and b) are called different loci because they occupy different points on the chromosome. Different loci not only have separate locations on the same chromosome (if linked) or different (nonhomologous) chromosomes (if unlinked), they also control different phenotypic traits. Genes A and a (as well as B and b) are different alleles because they occupy the same locus on their respective homologous chromosomes. In addition to occupying the same locus, different alleles control the same phenotypic trait, but produce in homozygous condition different character states of that trait, e.g., both A and a might control flower color, but the genotype AA might produce red flowers while genotype aa produces white flowers. By way of contrast, different loci influence different traits entirely, e.g., A producing flower color and B producing seed color. Be very careful of the word "gene" because it can refer to two different entities: a locus or an allele. Two genes are different if they influence different expressions of the phenotype. Thus, different alleles are different genes as well as are different loci. This brings us to a more precise definition of "alleles". Alleles are different expressions of the same locus. Therefore they are always found on homologous chromosomes and a single chromosome will contain just one allele. Different loci can be found on homologous (if linked) or nonhomologous (if unlinked) chromosomes and a single chromosome can contain many loci. Failure to appreciate this distinction will cause confusion later on in this discussion and course. Reproduction and Cell Division Although we usually think of reproduction as a process involving adult organisms, it is best understood as a process of cell division. There are two different types of cell division: mitosis which occurs in all cells of a multicellular organism and meiosis which is restricted to reproductive cells. Asexual reproduction, which results in offspring genetically identical to the parent, is the result of mitosis; sexual reproduction produces offspring which are genetically variable due to the process of meiosis. In the nucleus of the cell are molecules of DNA which contain the genes or hereditary material. The DNA is complexed with protein to form chromosomes. Each cell in a multicellular organism contains the same number of chromosomes and the same number of genes as all of the other cells in the organism and this number is characteristic of the entire species to which that organism belongs. The number of different chromosomes, i.e., those containing different sets of genes, is called the haploid number, designated by the letter "n". In our species, Homo sapiens, n = 23 which means that each cell in our body contains 23 different or nonhomologous chromosomes. In many species, including ourselves, each chromosome is represented twice so that the total number of chromosomes in each cell is 2n (the diploid number). The two representatives of the same chromosome are called homologous chromosomes and homologous chromosomes contain the same genes. Other species may have more than two sets of chromosomes per cell and this phenomenon is called polyploidy. Species with three homologous chromosomes are called triploids (3n), those with four homologues are tetraploids (4n), etc. We will confine our discussion to diploid species which have only two homologous chromosomes. The process of mitosis The cell cycle describes the events which occur in the life history of a eukaryotic cell and consists of two major phases: a long interphase followed by a relatively short division phase. The product of division is two daughter cells which then enter the interphase of their life cycle. The interphase appears to be a period of no activity since the choromosomes are not visible, but each of the three parts or stages of interphase are characterized by cell activity. The G1 stage is the first stage of interphase and is a period of growth. Next is the S stage during which the DNA is replicated. The chromosomes are not visible because they unwind from their coiled appearance during the division cycle and when spread out they are metabolically active both in RNA synthesis during the G1 or growth phase and in DNA synthesis during the S stage. After the DNA has been replicated, the cell enters the last stage of interphase during which the cell prepares for division. This last stage is called the G2 stage and it differs form the G1 stage in that the nucleus now contains twice the amount of DNA it had in the G1 stage. The division part of the cell cycle has four distinct phases: prophase, metaphase, anaphase and telophase. During prophase the chromosomes coil and so become visible again. Since the DNA has already replicated, each chromosome consists of two DNA molecules in the form of two sister chromatids held together by a structure called the centromere. These chromosomes then line up in random order in the center of the nucleus (metaphase). The sister chromatids then separate and migrate to separate halves of the cell (anaphase). The cell then divides into two equal halves, each of which has the same number of chromosomes and DNA molecules as the original parent cell when it was in its G1 stage. This final stage of the division cycle wherein the cytoplasm divides to produce two genetically identical daughter cells is called the telophase. Note that when the sister chromatids separate, they are called chromosomes; so the term chromosome can refer to a nucleoprotein complex with one DNA molecule, or to a duplicated complex in the form of sister chromatids (each chromatid consisting of one DNA molecule complexed with protein). The process of meiosis The process of cell division wherein gametes (haploid sex cells) are produced from a diploid reproductive cell is called meiosis. Meiosis only occurs in reproductive cells, i.e., in oocytes located in the female ovary which give rise to eggs (ova) and in spermatocytes located in the male testis which give rise to sperm or spermatozoa. This process is more complicated than mitosis because it involves two division cycles which give rise to four gametes rather than the two daughter cells produced by mitosis. (In spermatogenesis or the production of sperm, the cytoplasm divides equally so that four equal sized spermatozoa are produced; in oogenesis the cytoplasm divides unequally so that most of the cytoplasm ends up in one egg - the other three products are called polar bodies because they consist of inviable haploid nuclei with very little cytoplasm.) The differences between meiosis and mitosis can be summarized as follows: l. Meiosis involves two consecutive division cycles so that four haploid gametes are produced; mitosis involves a single division cycle which gives rise to only two diploid daughter cells. 2. The interphase, including DNA replication, is the same for the first cycle of meiosis as was described for mitosis, but unlike the equational division of mitosis the first division in meiosis is a reductional division in which the two daughter cells are haploid, not diploid. This reductional division occurs because before metaphase the homologous chromosomes pair up in a process called synapsis so that at metaphase the homologous pairs line up rather than the individual chromosomes as happens in mitosis. Consequently, during anaphase of the first meiotic division, the homologous chromosomes separate rather than the sister chromatids of individual chromosomes. The key event that must be understood is synapsis; if you understand synapsis you understand meiosis! 3. The interphase between the first and second divisions of meiosis is short and does not involve the replication of DNA. Since DNA is replicated during the S phase of the interphase before the first division, each chromosome has already been duplicated and is in the form of sister chromatids. Note that each of the two daughter cells resulting from the first or reductional division of meiosis has the same number of DNA molecules as the parent reproductive cell but only half the number of chromosomes. Read the last sentence again and be sure you understand it! The reason the cell has only half the number of chromosomes is because the homologous pairs separated and went to different daughter cells. The reason the number of DNA molecules is the same is because each chromosome is in the form of two sister chromatids. The second meiotic division is an equational division like mitosis and like mitosis results in the separation of the sister chromatids. The gametes produced after the second division of meiosis have half the number of chromosomes and half the number of DNA molecules as the original parent reproductive cell. In asexual reproduction offspring are produced by mitosis and so they are genetically identical to the parents, but in sexual reproduction the offspring is the product of gamete fusion (syngamy) from two genetically different parents. Each parent contributes one haploid gamete and so syngamy restores the diploid number of chromosomes. Consequently, the diploid offspring differs genetically from both of its parents. Although syngamy may involve the fusion of gametes of equal size (isogametes), for the most part sexual reproduction is characterized by the fusion of one large gamete (egg) and one small gamete (sperm). Individuals which produce many, small gametes are called males and those producing few, large gametes are females. The fusion of an egg and a sperm (fertilization) produces a diploid, one-celled organism called a zygote. The zygote then divides by mitosis to produce a multicellular organism. Meiosis, Mendel's Laws and Gametic Variation By producing variable gametes, the process of meiosis is responsible for the tremendous amount of genetically controlled individual variation due to sexual reproduction. Although Mendel was unaware of the mechanics of cell division, the process of meiosis can explain how his laws operate. Meiosis and the law of segregation The law of segregation, which states that members of a pair of factors separate into sister gametes when gametes are formed, can be explained by the reductional division in meiosis due to synapsis. In a heterozygote, e.g., Ss, the dominant allele (S) occupies locus S on one of the homologous chromosomes, while the recessive allele (s) occupies the same locus on the other homologous chromosome. When the sex cell undergoes its reductional division, the homologous pairs separate and move to different daughter cells. Each of these daughter cells then divides by separating the identical sister chromatids to produce gametes. Meiosis and the law of independent assortment The law of independent assortment, which states that members of different pairs of factors segregate independently of one another when gametes are formed, is a statistical law based on the behavior of many sex cells undergoing meiosis at the same time. This law is best illustrated by a dihybrid which is heterozygous for two unlinked loci (RrYy). At synapsis there are two possible ways in which the nonhomologous pairs can align themselves relative to one another. Although a single sex cell will exhibit only one alignment, in a large population of sex cells the two different alignments should occur with equal frequency. Consequently, a dihybrid individual should produce four different types of gametes in equal frequency. Study the follow diagram illustrating the two possible alignments of nonhomologous pairs during synapsis. Alignment #1: Alignment #2: |R |r |R |r |Y |y |y |Y Alignment #1 will eventually produce two different gametes (RY and ry) as will alignment #2 (Ry and rY). Thus, the organism will produce all four different gametes because a number of gamete-producing cells are undergoing meiosis at the same time and which aligment occurs in a cell undergoing meiosis is due simply to chance. Any one cell, however will follow only one alignment and so produce only two different gametes. Even though chromosomes rather than individual genes segregate independently of one another, Mendel's law of independent assortment will hold provided the two genes in question are located on nonhomologous chromosomes. The only constraint imposed on this process of generating gametic variation (and ultimately genotypic variation) is the number of nonhomologous chromosomes. The greater the number of nonhomologous chromosomes, the greater is the number of different gametes which can be produced. Mendel's second law is now called the law of independent assortment of chromosomes due to the chromosome theory of inheritance, and this modification results in less gametic variation than would occur if genes were free-floating units as Mendel supposed. Independent Assortment and Genotypic Variation The power of sexual reproduction in generating genotypic (as opposed to gametic) variation can be illustrated by the following formula which is based on Mendel's law of independent assortment. The number of different genotypes (g) that can be produced from the independent assortment of unlinked genes is: r(r + 1) g = 2 where r = the number of different alleles. For a single locus with two alleles, r = 2 and g = 3, i.e., there are three possible genotypic combinations of the two alleles - a1a1, a2a2, and a1a2. With three alleles the number of genotypes would be six - a1a1, a2a2, a3a3, a1a2, a1a3, and a2a3. If we now consider the number of genotypes possible due to sexual reproduction involving two unlinked loci each of which has two alleles, the formula becomes: n r(r + 1) g = 2 where n = the number of unlinked loci For this example g = 32 = 9 (see the result of a dihybrid cross). This formula can only be used if all the loci possess the same number of alleles (r). If r varies among the different loci, then the original formula must be used to calculate the number of genotypes possible for each locus and then the g values for each locus must be multiplied. For example, how many genotypes can be produced during sexual reproduction in a population with three unlinked loci in which locus A has two alleles (r=2), locus B has three alleles (r=3) and locus C has four alleles (r=4)? The answer is 180 since gA = 3, gB = 6, and gC = 10; and 3x6x10 = 180. Gametic variation and linked genes According to the chromosome theory of inheritance, genes are located on chromosomes and it is the chromosomes and not the genes which segregate during meiosis. Unlinked genes can segregate independently of one another because they are located on nonhomologous chromosomes, but linked genes cannot because they reside on the same chromosome and are inherited as a unit. Hence, linkage reduces gametic variability. Had Mendel chosen two phenotypic traits controlled by two tightly linked loci for his dihybrid cross,, his results would have been quite different. With linked loci he would have obtained only two different gametes rather than the four described in the Punnett Square illustrated in our discussion of the law of independent assortment. Consider the following: Assume that the locus for seed shape is linked to that for seed color. The dihybrid heterozygote RrYy would only be able to produce the gametes RY and ry rather than the four gametes which would result if the loci were unlinked. This result is due to the fact that it is the chromosomes and not the individual genes which segregate during meiosis. Study the homologous chromosomes depicted below to see why only two P generation: x (genotypes) R Y r y F1 generation: R Y (genotypes) F1 generation: (gametes) R Y + r y Recombination and Gametic Variation in Linked Genes So far we have only considered possible gametic variation which arises from a shuffling of allelic variation among unlinked loci, but linked loci can also generate variable gametes in a process known as recombination. Recombination produces gamete variability by swapping genetic material between homologous chromosomes during synapsis. When synapsis occurs, the two homologous chromosomes become tightly intertwined and if a section on both chromosomes should be broken off, the broken section could the original chromosome. This swapping of chromosome sections is called crossing over and it generates gametic variability because the maternal and paternal homologues exchange alleles rather than being passed on to gametes as they appear in the original zygote. Assue from its mother contained all dominant alleles and that from its father contained all recessive alleles. Without recombination the only gametes that could be produced would be AB (the maternal chromosome) and ab (the paternal chromosome). If during synapsis both chromosomes break at a point between locus A and locus B, and the broken sections recombine with the opposite homologue, then the following crossover gametes would be formed: Ab and aB. Study the following diagram. A B A B A b --> --> a b a b a B Original Crossing New, crossover gametes over gametes Recombination can be detected by breeding experiments. Suppose, as we did before, that homologous chromosome. We would expect that a heterozygote for both genes would produce only two different gametes (see diagram above under the discussion of gametic variation limited with linked genes). Thus, if we backcrossed a dihybrid heterozygote with an individual homozygous for the recessive alleles for both loci, we would expect to find two different phenotypes among the offspring in equal number: 50% of the offspring would have round-yellow seeds and 50% would have wrinkled-green seeds. Show the genotypes of this cros! different phenotypes would be observed but in rare frequency. The new crossover gametes produced by the heterozygote (Ry and rY) would yield in this backcross a few individuals which had round-green seeds (Rryy) and wrinkled-yellow seeds (rrYy). The following diagram illustrates this effect. Dihybrid echromosomes Chromosomes Chromosomes R Y R y r y x --> r y r Y r y Crossover Genotype #1 Crossover Genotype #2 (Rryy) (rrYy) R y r Y r y r y During crossing over, the maternal and paternal homologues are recombined to produce new chromosomes. How frequently recombination occurs to produce these new chromosomes depends upon how far apart the two loci are on the same chromosome. Breaks during synapsis occur at random, hence, the farther apart two loci are, the greater the probability that they will recombine. Tightly linked loci will rarely produce crossover gametes, but the overall frequency of crossing over is so high during meiosis that few, if any, of the entire homologous chromosomes received by an individual from its parents will be passed on intact in that individual's gametes. Independent Assortment vs Recombination It would appear at first glance that both independent assortment of unlinked genes and recombination of linked genes have the same effect on the production of gametic variability. In the example we used with the dihybrid (RrYy), both processes produced four different gametes: RY, Ry, rY and ry. There are, however, two critical differences between the two processes. The first difference involves the production of different gametes by the dihybrid organism. With independent assortment the four gametes will be produced in equal frequency by the organism since in a population of cells undergoing meiosis half the cells should follow alignment #1 and half alignment #2. With recombination the frequency of crossover gamete production depends upon the distance separating the two linked loci. If they are widely separated, then the frequency of crossing over would be high enough to produce the four different gametes in equal frequency, thereby mimicking the effect of independent assortment of unlinked loci. If they are tightly linked, then the parental linkage will appear in far more of the organism's gametes than the crossover linkage. The second difference involves the production of gamete variability by individual dihybrid cells undergoing meiosis. As mentioned above, with independent assortment a single cell will follow just one chromsome alignment and so can only produce two different gametes. With recombination the cell will produce all four different gametes. The reason for this is that crossing over occurs between nonsister chromatids and will affect only two. The other pair of nonsister chromatids will be unaffected. Study the following diagram to see this point. A. Synapsis in a dihybrid before recombination R Y maternal chromosome in the form of R Y sister chromatids r y paternal chromosome in the form of r y sister chromatids B. Crossing over between nonsister chromatids R Y maternal chromatid R Y (nonsister chromatids) r y r y paternal chromatid C. Final gamete chromosomes R Y unaffected maternal (RY) R y newly recombined (Ry) r Y newly recombined (rY) r y unaffected paternal (ry) Summary of differences between Mendel's law of independent assortment (of chromosomes) and recombination as sources of gametic variation in a dihybrid. A. Independent Assortment: 1. involves unlinked loci 2. occurs between nonhomologous 3. each cell produces only two different gametes 4. each organism produces four different gametes in equal frequency 5. chromosomes are not restructured B. Recombination: 1. involves linked loci 2. occurs between nonsister chromatids of a homologous chromosome pair 3. each cell undergoing recombination produces four different gametes; those which do not recombine only produce two sm produces four different gametes but the noncrossover maternal and paternal chromosomes will be more numerous than the crossovers; the extent of this difference depends upon the distance between the loci 5. new chromosomes (the crossovers) are formed as a mosaic of maternal and paternal chromatid alleles. Due to the various ways in which alleles of both linked and unlinked loci can be assorted in gamete formation it is almost impossible for any gamete to contain a complete set of an individual's maternal or paternal alleles. Since sexual reproduction also involves gametic contributions from two individuals, it is no wonder that no two individuals in a population are identical genetically. The possible gametic combinations vastly exceeds the number of offspring produced, so each individual is unique! Sexual reproduction produces a wealth of individual variation, but by itself will not cause evolution. Individual genetically-controlled variation, however, is important to the process of microevolution and so for our next topic we will examine the consequences of such variation on the population, the unit of microevolution.