Laboratory III Quantitative Genetics Genetics Biology 303 Spring 2007 Dr. Wadsworth Introduction Mendel's experimental approach depended on the fact that he chose phenotypes that varied in simple and discrete patterns. For example his peas were either smooth or wrinkled or the flowers were either white or purple. A single gene with two alleles controlled each trait. This resulted in a simple relationship between genotype and phenotype and generated simple phenotypic ratios in his breeding experiments. These simple ratios allowed him to develop his concepts of the gene, alleles, random segregation and independent assortment. However many phenotypes don't vary in the simple patterns like those Mendel observed in peas. Traits like height, skin color, or the number of ridges on a finger print don't vary in simple patterns or have a limited number of discrete classes. Phenotypes that show these more complex patterns of variation are referred to as quantitative traits. And the study of the inheritance of these traits is referred to as quantitative genetics. Quantitative traits are also called multifactorial traits. This is because they are under the control of multiple genes and are also influenced by the environment. An example of a quantitative trait might be the number of kernels on an ear of corn. Different strains of corn are known to vary in kernel number from just a few kernels to hundreds of kernels. Because the strains differ in their kernel number there must be a genetic component controlling kernel number. In the F2 generation of a cross between a high kernel and a low kernel strain will likely generate a population of corn plants with a wide range of kernel numbers. Much of the variation in the F2 generation is due to the fact that kernel number is controlled by dozens of genes. However some of the variation is due to the influence of the environment. In this laboratory experiment you will investigate a trait that shows quantitative inheritance, the number of hairs on the leaves of the Fast Plant variety of Brassica rapa. There are two varieties of Fast Plants with different numbers of hairs on the leaves; Hir(0-2) is a hairless variety with none or few hairs on each leaf and Hir (5-8) which have as many as 50 hairs on each leaf. The hairy plants were crossed with the hairless plants to generate an F1 and F2 population. Two weeks ago, we planted the parental, F1 and F2 populations. Specific Goals 1. Analyze variation in leaf hair number in the two parental, the F1 and the F2 generations. 2. Prepare descriptive statistics describing variation for each population 3. Estimate the number of genes controlling variation in leaf hair number in these populations. 4. Conduct an artificial selection experiment for the hairy leaf trait using the F2 population of Fast Plants. Descriptive Statistics In Mendel's experiments phenotypes fell into a few distinct classes. Therefore it was possible to express the variation observed in the F1 and F2 generations as simple ratios. However with quantitative traits the variation is more complex and often continuous. Therefore it is impossible to describe it with simple ratios. In this experiment you will collect data on leaf hair number on several populations of Fast Plants. You will calculate two statistics, the mean and the variance, which together describe the distribution of the trait in each population. The mean is a measure of the central tendency of a population. It is simply the arithmetic average of the set of data. The second statistic you will calculate is variance, s 2. Variance is a measure
of the range and distribution of values around the mean. Variance is calculated as: s 2 = Number of Polygenes One goal of quantitative genetics is to determine how many genes control a specific trait in a population. This can be quite complex because not all genes have an additive effect and there can be epistatic interactions which obscure the expression of some genes in particular genetic backgrounds. To simplify the analysis for this lab, however, we will assume that all the genes controlling leaf hair have an additive affect. With that assumption we can use the following relationship to estimate polygene number: N = 8(s Heritability Σ X i 2 - nx 2 n - 1 D 2 2 F2 -s 2 F1) where N is the number of genes that affect the trait in these population and D represents the difference between the means of the two parental populations. For quantitative traits the variation in a population can be due to both genetic and environmental effects. Quantitative geneticists are interested in determining the relative importance of genetics and environment in this variation. Heritability is a measure of the genetic contribution to the variation. Heritability is an estimate of how much of the phenotypic variation in a population is due to genetic factors. If heritability is high, then almost all of the variation in a population is due to genetics. If heritability is low then most of the variation is due to environment. For example consider seed production in a pine forest. In almost any forest some of the trees may produce large cones with numerous seeds while other trees may have smaller cones with few seeds. Seed production represents a quantitative trait demonstrating a complex pattern of variation. It is easy to consider a high or low heritability scenario which could account for the variation. In the high heritability scenario genetic differences among the trees would account for most of the variation. The trees with high seed production would have alleles at the polygenes which promote high seed production while the trees with low seed production would have low production alleles. In the low heritability scenario, the trees would be genetically similar for the genes that control seed production. Instead environmental effects would cause the variation. For example trees at the edge of a stream would have plenty of water and light and therefore have high seed production, while seeds on a rocky hill side would have poor nutrients and would be shaded by higher trees and therefore have lower seed production. The variation in seed production would be due to environmental differences among the trees not genetic differences. It is important to know heritability of a trait if you are to predict how the population would respond to selection. For selection to influence a population the variation in the population must be due to genetic differences. Only under those circumstances would the genetic composition of a population change in response to selection. If all the variation in phenotype is due to environmental differences that selection for a particular phenotype will not result in genetic change in the population. Narrow Sense Heritability Two types of indices of heritability can be estimated. Broad-Sense Heritability (H 2 ) is the degree to which phenotypic variation of a population is due to genetic differences. It takes into account all types of genetic interactions including additive, dominance and epistatic. H 2 is a useful index if you are interested in the relative contribution of genetic versus the environment to the phenotypic variation in a population. However, because of the complexity of these interactions, it may not be the most useful index for predicting how a population may respond to selection. Narrow-Sense Heritability (h 2 ) is a measure of the genetic factors that contribute to variation which respond to selection. This is a much more useful index if
you are a breeder and are trying to improve a particular trait in a species by selection. If h 2 were low, then the trait would respond very slowly to selection. Alternatively, if h 2 were high then the trait would respond strongly and quickly to selection. Estimating Narrow-Sense Heritability One way to estimate h 2 is to conduct a selection experiment. Phenotypes of a population are measured and the mean phenotypic value is calculated (M o ). Then individuals at the extreme range of a phenotype (top or bottom 10%) are selected. The mean of this sub population (M S ) is calculated. This subpopulation is interbred and phenotypic variation in the progeny is analyzed including the mean (M P ). Narrowsense heritability is estimated as: h 2 = Procedure M P - M o M S - M o Important: Do not destroy or injure any of the plants during the counting. Gene Number 2. Interbreed the selected plants. When flowers emerge begin to cross-pollinate these plants using bee sticks. Repeat crosspollinations using these same individuals for three-four consecutive days. 3. For next three weeks check plants daily to observe pod development and remove any new flowers. 20 days after last pollination remove plants from watering system and allow to dry for five days. 4. Harvest seeds by gently rolling dry seedpods between your hands and collecting seeds over collecting pan. Plant seeds as directed in Fast Plants Lab Handout. 5. 12-14 days after planting count leaf hairs of all the progeny. Determine mean and variance for the progeny of the selection. 6. Estimate narrow sense heritability. Short Report: Quantitative Genetics Results and Analysis of this experiment are due next week. Please include the following for full credit. 1. Count the hairs at the margin of the first true leaf for all of the parental, F1 and F2 plants and record the data on the data sheet. (Hint: groups can share data for this portion of the lab) 1. Raw data sets in excel spread sheet 2. A table reporting sample size, mean and standard deviation (s, the square root of s 2 ) for all 4 populations, the two parentals, F1, and F2. 2. Calculate the mean and variance for each population. 3. Report the estimated number of genes 3. Estimate the number of genes contributing to this trait. Next Week: Artificial Selection controlling variation of leaf hair number in these populations and the narrow sense heritability of the trait in this population. Show your calculations. 1. Selected and mark Fast Plants that represent the top 10% most hairy leaves. Calculate mean and variance for hair number in the selected plant population. Report on Heritability will be due latter in the semester.
Hairy Parentals HY-1 HY-2 HY-3 HY-4 HY-5 HY-6 HY-7 HY-8 HY-9 HY-10 HY-11 HY-12 HY-13 HY-14 HY-15 HY-16 HY-17 HY-18 HY-19 HY-20 HY-21 HY-22 HY-23 HY-24 HY-25 HY-26 HY-27 HY-28 HY-29 HY-30 HY-31 HY-32 HY-3 HY-34 HY-35 HY-36 HY-37 HY-38 HY-39 HY-40 HY-41 HY-42 HY-43 HY-44 HY-45 HY-46 HY-47 HY-48 HY-49 HY-50 Hairless Parental HL-1 HL-2 HL-3 HL-4 HL-5 HL-6 HL-7 HL-8 HL-9 HL-10 HL-11 HL-12 HL-13 HL-14 HL-15 HL-16 HL-17 HL-18 HL-19 HL-20 HL-21 HL-22 HL-23 HL-24 HL-25 HL-26 HL-27 HL-28 HL-29 HL-30 HL-31 HL-32 HL-33 HL-34 HL-35 HL-36 HL-37 HL-38 HL-39 HL-40 HL-41 HL-42 HL-43 HL-44 HL-45 HL-46 HL-47 HL-48 HL-49 HL-50 F1 Plants F1-1 F1-2 F1-3 F1-4 F1-5 F1-6 F1-7 F1-8 F1-9 F1-10 F1-11 F1-12 F1-13 F1-14 F1-15 F1-16 F1-17 F1-18 F1-19 F1-20 F1-21 F1-22 F1-23 F1-24 F1-25 F1-26 F1-27 F1-28 F1-29 F1-30 F1-31 F1-32 F1-33 F1-34 F1-35 F1-36 F1-37 F1-38 F1-39 F1-40 F1-41 F1-42 F1-43 F1-44 F1-45 F1-46 F1-47 F1-48 F1-49 F1-50 F1-51 F1-52 F1-53 F1-54 F1-55 F1-56 F1-57 F1-58 F1-59 F1-60 F1-61 F1-62 F1-63 F1-64 F1-65 F1-66 F1-67 F1-68 F1-69 F1-70 F1-71 F1-72 F1-73 F1-74 F1-75 F1-76 F1-77 F1-78 F1-79 F1-80 F1-81 F1-82 F1-83 F1-84 F1-85 F1-86 F1-87 F1-88 F1-89 F1-90 F1-91 F1-92 F1-93 F1-94 F1-95 F1-96 F1-97 F1-98 F1-99 F1-100 F2 Plants F2-1 F2-2 F2-3 F2-4 F2-5 F2-6 F2-7 F2-8 F2-9 F2-10 F2-11 F2-12 F2-13 F2-14 F2-15 F2-16 F2-17 F2-18 F2-19 F2-20 F2-21 F2-22 F2-23 F2-24 LEAF HAIR DATA F2-25 F2-26 F2-27 F2-28 F2-29 F2-30 F2-31 F2-32 F2-33 F2-34 F2-35 F2-36 F2-37 F2-38 F2-39 F2-40 F2-41 F2-42 F2-43 F2-44 F2-45 F2-46 F2-47 F2-48 F2-49 F2-50 F2-51 F2-52 F2-53 F2-54 F2-55 F2-56 F2-57 F2-58 F2-59 F2-60 F2-61 F2-62 F2-63 F2-64 F2-65 F2-66 F2-67 F2-68 F2-69 F2-70 F2-71 F2-72 F2-73 F2-74 F2-75 F2-76 F2-77 F2-78 F2-79 F2-80 F2-81 F2-82 F2-83 F2-84 F2-85 F2-86 F2-87 F2-88 F2-89 F2-90 F2-91 F2-92 F2-93 F2-94 F2-95 F2-96 F2-97 F2-98 F2-99 F2-100 F2-101 F2-102 F2-103 F2-104 F2-105 F2-106 F2-107 F2-108 F2-109 F2-110 F2-111 F2-112 F2-113 F2-114 F2-115 F2-116 F2-117 F2-118 F2-119 F2-120 F2-121 F2-122 F2-123 F2-124 F2-125 F2-126 F2-127 F2-128 F2-129 F2-130 F2-131 F2-132 F2-133 F2-134 F2-135 F2-136 F2-137 F2-138 F2-139 F2-140 F2-141 F2-142 F2-143 F2-144 F2-145 F2-146 F2-147 F2-148 F2-149 F2-150 F2-151 F2-152 F2-153 F2-154 F2-155 F2-156 F2-157 F2-158 F2-159 F2-160 F2-161 F2-162 F2-163 F2-164 F2-165 F2-166 F2-167 F2-168 F2-169 F2-170 F2-171 F2-172 F2-173 F2-174 F2-175 F2-176 F2-177 F2-178 F2-179 F2-180 F2-181 F2-182 F2-183 F2-184 F2-185 F2-186 F2-187 F2-188 F2-189 F2-190 F2-191 F2-192 F2-193 F2-194 F2-195 F2-196 F2-197 F2-198 F2-199 F2-200 F2-201 F2-202 F2-203 F2-204 F2-205 F2-206 F2-207 F2-208 F2-209 F2-210 F2-211 F2-212 F2-213 F2-214 F2-215 F2-216 F2-217 F2-218 F2-219 F2-220 F2-221 F2-222 F2-223 F2-224 F2-225 F2-226 F2-227 F2-228 F2-229 F2-230 F2-231 F2-232 F2-233 F2-234 F2-235 F2-236 F2-237 F2-238 F2-239 F2-230 F2-231 F2-232 F2-233 F2-234 F2-235 F2-236 F2-237 F2-238 F2-239 F2-240 F2-241 F2-242 F2-243 F2-244 F2-245
Some Example Tables