Mendelian Genetics Casual observation of a population of organisms (e.g. cats) will show variation in many visible characteristics (e.g. color of fur). While members of a species will have the same number of chromosomes (i.e. humans have 6 chromosomes) each organism s genetic makeup or DNA is unique (unless it is a clone). The chromosomes within each cell contain specific regions, called genes, which code for a myriad of characteristics from cell metabolism to eye color. Such genes are responsible for the visible expression of these traits. The preservation of such variation can be important when organisms are competing for survival. However, to be of value to a species, such beneficial variations must be transmitted from one generation to the next. This prompts several questions: What mechanisms exist for the transmission of these characteristics? How do variations arise in the first place? The exercise that follows will help to answer such questions. In addition, you should review the sections about cell division and mendelian genetics in your textbook. A Monohybrid Cross The simplest study of the mechanism of transmission from one generation to the next, involves the mating (or crossing) of two pure breeding individuals, each of which exhibits one of a pair of contrasting characteristics, e.g. color. In plant s (Nasco experimental plant SB0731), albino seedlings often arise from normal green parents. In this species we can consider this as a pair of contrasting characters (i.e. alleles) for the presence or absence of chlorophyll. Plant seeds were harvested from parents that were green in color. We will assume here that the grandparents crossed were green and albino (Is this a likely possibility?). The seeds were planted on paper towels in a Petri dish and are now 10-1 days old. Obtain a plate of plant seedlings and note the two color variations. Count the number of each type (#green; #albino) on the plate and record the information below. You will pool the class data as well. Demonstrations of other monohybrid crosses (e.g. corn) may also be available. Examine these as well. Model of an F 1 and F 2 generation In attempting to explain the results of an experiment, such as the plant cross, it is helpful to devise a simple model. Everyday experience tells us that in sexually reproducing organisms, characteristics are derived from both parents (i.e. from the gametes). Therefore, a zygote must contain a contribution of genetic material for a character, such as body color, from both the egg and the pollen (or egg and sperm). In the case of the plant, let s denote a normal allele by capital letter G and an albino allele by a lower case letter g. Alternate forms of a gene (such as G and g) which are responsible for controlling contrasting characters are called alleles. If both gametes combine to produce a pure breeding, normal (green) colored plant plant, then both gametes must carry the G allele. Hence, the zygote produced has the constitution GG. (Note that in this example we are dealing with an organism that is diploid, or has 2 copies of each chromosome, and therefore has only 2 alleles for a gene). The combination GG is known as a homozygote; a zygote with the combination is called a heterozygote. A zygote with the combination gg is also a homozygote. The genetic constitution of an organism (with one or more pairs of characteristics) is known as its genotype and it is simply represented by letters. Thus the genotype of a pure breeding albino is gg, that of a pure breeding green type is GG, and that of a heterozygote is. The physical appearance of the organism (with respect to the characteristic) is referred to as its phenotype; thus the phenotype of the lab plant with the genotype gg, is white. The phenotype of a plant with a genotype of either or GG, is green. In terms of generations, the letter P represents the parents. Offspring of the first generation are designated F 1, those of the second generation as F 2. These abbreviations will become clear as you read through the following examples. Applying this terminology, we can construct a diagrammatic model of our F 1 and F 2 generations.
GG gg G g G G g g GG gg Note that in the second cross, two sorts of gametes (one type bearing G and one bearing g) will be formed in equal numbers. Hence, in the F 2, the two types of gametes will combine at random to form the three genotypes as shown. As the gametes are numerous and combine at random, the proportions of the different allele combinations that arise will depend on chance. To express this we can use a 2 x 2 table, also called a Punnett square, as a diagrammatic model of breeding. The following Punnett square depicts the possible outcomes of a cross between two heterozygous plant plants ( x ). gametes G g 1 1 G GG gametes Note that there are 3 possible combinations of alleles (GG,, or gg). Thus the probability of each combination arising is ( 1 = 0.25). The probability of the heterozygous combination () occurring is ( 1 + 1 = 1 2 = 0.5). g 1 1 gg Consider the effects of the various allele combinations in the heterozygote () on the phenotype of the plant. You might expect the heterozygous F 1 plant plants to be green, white, or an intermediate color between white and green. If the heterozygous plants are either white or green, then one of the alleles is masking the effect of the other allele. Such an allele is called the dominant allele. The dominant allele is usually indicated with a capital letter. So, if the heterozygous plants () were green, G represents the dominant green allele. The other allele is referred to as the recessive allele. The recessive allele is usually indicated with a lower case letter. So, in this case g represents the recessive white (albino) allele. Recessive alleles will only be expressed when they are homozygous. In our example only plants with the genotype gg
would be white. In light of this dominant/recessive relationship among alleles, how would you interpret the results of the plant cross demonstration? In systems where one allele is dominant over another, and heterozygotes are crossed, only two phenotypes are produced, in the proportion of 3:1.
Analysis of the results of a monohybrid cross Referring back to the model, we can now see that the distribution of phenotypes in the F 2 depends entirely upon the laws of chance. The larger the numbers involved, the nearer the ratio will approach 3:1 (expectation). In order to interpret the results of a cross it is necessary to compare laboratory data (i.e. observation) with an expectation, based on a hypothesis such as the one above. To measure how far observation deviates from expectation we use a statistic known as the chi-square (pronounced ki-square and written χ 2 ). The value of this statistic is given by the equation: k (O E) 2 χ2 = i =1 E where: k = the number of categories (phenotypes) under investigation O = the observed value (number of individuals of each phenotype observed) E = the expected value (number of individuals of each phenotype expected. In this first example of a monohybrid cross we expect a 3:1 ratio of green to white plants. 2 ( O E) Σ = indicates that the value of must be calculated separately for each E category (phenotype) and then these values must be added together to obtain the value of χ 2. An example of the calculation of the χ 2 value is given below. This uses data from the famous work of Gregor Mendel (published in 1866) on the genetics of the garden pea for a cross of tall and short pea plants. Character of plants tall short Total Observed 787 277 106 Expected 798 266 106 O-E -11 +11 -- (O-E) 2 121 121 --
2 ( O E) 0.152 0.55 E 0.607 = χ 2 The chance of obtaining perfect agreement between the observed and expected values in any breeding experiment is exceedingly remote. The value of χ 2 can be used to estimate the probability that any differences between the observed values and the expected values are not due to chance. In order to complete the calculation we must know the number of degrees of freedom involved. If the number of phenotypes (or columns in our table) is n, the number of degrees of freedom is n-1, which for our example is 2-1 =1. Referring now to the table of χ 2 values below, we see that for 1 degree of freedom and a χ 2 value of 0.607, the probability (P) lies between 0.5 and 0.3. Thus, we could expect a chance deviation of this size in 30-50% of the cases (convert 0.5 and 0.3 to percent). Ordinarily statisticians attribute deviations to chance alone (as in this example) if they have a greater than 5% probability of occurring. The reason statisticians accept deviations with such a low probability of being due to chance alone is so that valid hypotheses are not rejected. It is more desirable to accept (and thus perhaps retest?) an invalid hypothesis than to reject a valid hypothesis. Therefore, we could accept Mendel's results in this experiment as a valid 3:1 ratio because the calculated deviation (0.607) has a greater than 5% chance of being due simply to chance alone. If the value of χ 2 had been, 6.02, we would have easily concluded that there was a significant departure from the predicted values. Hence, you would have rejected this as a case of a monohybrid cross. Of course it would be advisable to carry out a further cross in order to make sure this divergence was not merely due to an error arising from faulty techniques, etc.
Now perform a χ 2 test on the class data for results of the albino and normal plant seedlings. A table for you data is on the next page. Answer the following questions: 1. What is the probability that the resulting χ 2 values could have occurred simply by chance? 2. Should you reject your hypothesis or not? Character of plant seedlings Total Green Albino # Observed (O) #Expected (E) O E --- (O E) 2 --- (O E) 2 χ 2 = E Works cited information for this source: Mendelian Genetics. University of Conneticut Biology 108. March 15, 200. <www.eeb.ucon.edu/courses/bio108/lab%20sp%20 02/