KEY CONCEPTS AND PROCESS SKILLS. 1. An allele is one of the two or more forms of a gene present in a population. MATERIALS AND ADVANCE PREPARATION

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1 Gene Squares o minue sessions ACIVIY OVERVIEW P R O B L E M S O LV I N G SUMMARY Sudens use Punne squares o predic he approximae frequencies of rais among he offspring of specific crier crosses. KEY CONCEPS AND PROCESS SKILLS 1. An allele is one of he wo or more forms of a gene presen in a populaion. 2. Geneic crosses can be analyzed by using a sandardized means of represenaion called a Punne square, when each paren s alleles for a rai are known. 3. A Punne square is a visual represenaion of he relaive probabiliies of offspring oucomes, for boh gene combinaions and visible rais. KEY VOCABULARY allele carrier dominan heerozygous Punne square recessive homozygous MAERIALS AND ADVANCE PREPARAION For each suden 1 Suden Shee 61.1, Punne Squares Sep by Sep * 1 blue pencil (opional) * 1 orange pencil (opional) *No supplied in ki eacher s Guide D-91

2 Aciviy 61 Gene Squares EACHING SUMMARY Geing Sared 1. Revisi he coin-ossing resuls from Aciviy 59, Gene Combo. Doing he Aciviy 2. Sudens read and learn how o use a Punne square. 3. Sudens do addiional pracice on Suden Shee 61.1, Punne Squares Sep by Sep. Follow Up 4. he class discusses he usefulness of Punne squares in helping hem o organize predicions of geneic crosses. BACKGROUND INFORMAION Punne Squares A Punne square is a ool for doing probabiliy calculaions; is srucure represens sexual reproducion. When he single alleles ha each paren can conribue are wrien along he op and side of he able (see Figure 1 on page D-41 in he Suden Book), he formaion of sex cells is implied. When one allele from each paren is ransferred o a box wihin he able (see Figure 2 on page D-42 in he Suden Book), ferilizaion is represened he union of genes conribued by egg and sperm. While Punne squares are no sricly necessary for solving geneics problems (see secion below), hey help sudens visualize geneic crosses. hey are also useful in analyzing he oucomes of more complex crosses involving muliple rais, bu his is ypically covered in high school biology. Mendel s Probabiliy Calculaions Mendel s daa enabled him o recognize ha he essence of inheriance is probabiliy, since alleles are inheried randomly during sexual reproducion. Punne squares organize and display he mahemaics behind he inheriance of a rai ha follows Mendelian behavior. For example, consider Problem 1 (he Ocean/Lucy cross) on Suden Shee 61.1, Punne Squares Sep by Sep. his cross is analogous o he classic Mendelian Generaion wo cross, as well as o he flowering-obacco breeding ha produced he green and yellow seedlings your sudens germinaed. he Punne square provides a visual represenaion of he muliplicaion rule for probabiliies. In his case, he rule D-92 Science and Life Issues

3 Gene Squares Aciviy 61 saes ha he probabiliy of producing an orange-ailed offspring () equals he probabiliy of geing an orange-ail allele () from he faher muliplied by he probabiliy of geing anoher orange-ail allele () from he moher. ha is, probabiliy of an offspring having an orange ail = probabiliy of () = (probabiliy of from faher) x (probabiliy of from moher) = (1/2) x (1/2) = 1/4 (his calculaion is he reciprocal of he calculaion of he oal number of boxes in he Punne square. ha is, he oal number of boxes = 2 x 2 = 4.) Since he probabiliy of having an orange ail is 1/4, he probabiliy of having a blue ail mus be 1-1/4 = 3/4. he explici calculaion of his is more complex han for orange ail, since here is more han one way o inheri a blue ail: probabiliy of homozygous offspring = (1/2) x (1/2) = 1 4 probabiliy of heerozygous offspring = 2 x (1/2) x (1/2) = 2 x 1/4 = 1/2 (Noe ha here are wo ways for he offspring o be heerozygous: eiher from he faher and from he moher, or from he moher and from he faher. In Aciviy 59, Gene Combo, hese wo ways were noaed as and.) he probabiliy of an offspring having a blue ail ( or ) is he sum of he wo probabiliies: 1/2 + 1/4 = 3/4 Noe ha he undersanding of Punne squares should be he focus here, no he use of vocabulary. However, he erms homozygous and heerozygous may help sudens assign meaning o he Punne squares. Odds vs. Probabiliies As was addressed in Aciviy 59, a 3:1 raio is exacly equivalen o he pair of fracions 3/4 and 1/4. In he raio 3:1, a par of he whole is compared o anoher par of he whole hence, (3 blue-ailed):(1 orange-ailed). A raio is ofen wrien x:y, bu can also be wrien x/y (a fracion is a raio). In conras, a rue fracion compares a par o he whole hence, 3 4 of a large se of offspring criers are blue-ailed and 1/4 are orange-ailed. Sudens ofen confuse hese wo noaions, for example wriing 4:1 when hey mean 3:1, or 2:1 when hey mean 1:1. Such confusion can obscure an oherwise sound undersanding and make classroom communicaion difficul, so i is a good idea o address his direcly. eacher s Guide D-93

4 Gene Squares Aciviy 61 EACHING SUGGESIONS GEING SARED 1. Revisi he coin-ossing resuls from Aciviy 59, Gene Combo. Review wih sudens he oucomes of he breeding experimen beween Ocean and Lucy, as simulaed in Aciviy 59. Ask for a voluneer o come o he board and explain he frequency of each ail color. Ask, Why do abou 1/4 of he offspring have orange ails? Do no be concerned if no suden can ye provide a clear, concise explanaion. Have sudens read he Inroducion and Challenge on page D-39 in he Suden Book. Sae ha a Punne square is a sandard way of displaying he prediced oucomes of a geneic cross. Have sudens begin working hrough he ineracive reading in he Procedure. hese passages explain how o se up, complee, and inerpre a Punne square, using he ail colors produced by he Skye/Poppy cross as a simple example. (Sudens will work hrough he Lucy/Ocean cross and wo more examples on Suden Shee 61.1, Punne Squares Sep by Sep. ) eacher s Noe: You may wish o have sudens complee he reading as individuals or aloud in groups of four. Alernaively, you can use he maerial as a guide o presen how o complee a Punne square. DOING HE ACIVIY 2. Sudens read and learn how o use a Punne square. Be prepared o help sudens undersand why Skye is assumed o be for ail-color alleles, and Poppy. he crier breeding experimens confirmed his assumpion, since i was demonsraed ha orange ail color is recessive and ha Skye was homozygous for blue ail. By consrucing Punne squares, sudens are showing how hose resuls could have been prediced. (Alhough he crierbreeding experimens are imaginary, Mendel s resuls using several differen pea plan rais were exacly parallel. In addiion, sudens hemselves are abou o obain a 3:1 raio among heir flowering obacco seedlings.) In consrucing a Punne square, he sep ha usually causes he mos difficuly is he placemen of parenal alleles around he able. One paren s alleles are spli apar along he op row, while he oher s are divided along he side column (his represens he formaion of sex cells). Be sure o sress ha i doesn maer which paren is on he op and which is along he side. he boxes in he square are filled in wih he alleles from he appropriae inersecing column and row, as shown in Figure 2 on page D-42 in he Suden Book (his represens ferilizaion). eacher s Noe: Be aler for he need o clarify he erm allele. here are wo differen forms, or alleles, of he crier ail-color gene: one, represened here as, is associaed wih he dominan rai of blue ail; he oher, represened as, is responsible for he recessive rai of orange ail. A single gene deermines crier ail color, bu each crier has wo alleles of ha gene which may be he same (homozygous) or differen (heerozygous). he second mos challenging sep in using Punne squares is inerpreing he resuls. he four boxes of a 2 x 2 square do no indicae he resuls for any four paricular offspring. Insead, each box represens a eacher s Guide D-95

5 Aciviy 61 Gene Squares 1/4 probabiliy for any one offspring. In he cross of Skye and Poppy, every box conains, so he chance of one of heir offspring being a heerozygous blue-ailed crier is 4 imes 1/4, or 1 (100%). Remind sudens ha in Aciviy 59, Gene Combo, hey modeled he randomness of geneic crosses by ossing coins. he reading also inroduces he erm carrier as a concep in geneics: an individual heerozygous for a recessive geneic condiion (usually a herediy disease, bu i can be any recessive rai) carries an allele for ha condiion bu does no show he rai. Noe ha Analysis Quesions 3 and 4 provide furher experience working wih geneic carriers. 3. Sudens do addiional pracice on Suden Shee 61.1, Punne Squares Sep by Sep. Suden Shee 61.1 provides sudens wih addiional guided pracice. Noe ha grids for he squares are provided. hese problems may be done in class by sudens working individually, or hey may be assigned as homework. Problem 1 includes hins for how o place he parens alleles around he square and includes a reprining of Figure 2 from he Suden Book. Assis sudens as needed. he expeced answers are as follows: Problem 1 Problem 2 Orange ail Blue ail 3/4 blue 1/4 orange 1/2 blue 1/2 orange Noe ha abou 1/4 of he offspring are homozygous for blue ail color (), and abou 1/2 are heerozygous for blue ail color (). Noe ha all of he blue-ailed offspring are heerozygous (). D-96 Science and Life Issues

6 Gene Squares Aciviy 61 Problem 3 Blue ail can be very imporan (sudens may recall some discussion of his in he film hey wached in Aciviy 56, Joe s Dilemma ). Blue ail Noe ha abou 1/2 of he offspring are homozygous for blue ail color (), and abou 1/2 are heerozygous for blue ail color (). When you observe ha mos or all of he sudens have masered how o se up and complee he squares, move on o he Analysis Quesions. FOLLOW UP 4. he class discusses he usefulness of Punne squares in helping hem o organize predicions of geneic crosses. Discuss he advanages of using a sandard forma for solving geneics problems: his organizes one s work and makes i easier o compare resuls wih ohers. Analysis Quesion 1 revisis he beginning of his aciviy where sudens were asked o explain he resuls of Gene Combo in words. Punne squares provide a visual represenaion for probable resuls. ell sudens ha soon hey will apply his kind of reasoning o human geneics. hough breeding experimens may no be performed wih humans, predicing he possible offspring of wo individuals all blue Analysis Quesion 2 encourages sudens o make heir own choices in how o represen alleles of a gene. here is no one correc way o do his; he soluions in he Suggesed Answers presen raionales for he wo mos common ways used in inroducory geneics. Quesions 3 and 4 address he concep of carrier in biology. he concep of geneic carrier ofen appears in he media in connecion wih herediary condiions and geneic counseling. Finally, emphasize ha, despie heir misleading appearance, Punne squares do no indicae specific maing resuls. Genes are no used up as organisms reproduce, so perfec offspring raios are no o be expeced alhough he larger he sample size of offspring, he closer he experimenal raio is likely o be. Refer again o he coin-ossing daa (Aciviy 59, Gene Combo ), sudens seedling resuls (if gahered already), and Mendel s daa. SUGGESED ANSWERS O ANALYSIS QUESIONS 1. Compare he resuls of your Punne square for Problem 1 on Suden Shee 61.1 wih he resuls of he Ocean/Lucy cross in Aciviy 59, Gene Combo. Why are hey similar? he Punne square allows an easy calculaion of he likelihood of each allele combinaion and rai in he offspring. In Gene Combo, random coin osses were used o model he 1/2 chance of each parenal allele being given o an offspring. eacher s Guide D-97

7 Aciviy 61 Gene Squares Sudens may noice ha in a sense here is no difference: he cross is he same and he resuls are he same. However, in his aciviy sudens have used a Punne square o display heoreical resuls, whereas Aciviy 59 was a simulaion of real experimenal resuls, which do no perfecly mach heoreical predicions. 2. Refer o he able of Mendel s resuls in Aciviy 60, Mendel, Firs Geneicis, on page D- 36. a. Wha are he rais for pea flower color? Sugges leers you migh use o represen he alleles for flower color. Flower color is eiher purple or whie. Since purple is dominan o whie, he alleles could be represened as eiher F = purple and f = whie, or P = purple and p = whie. (F/f are shor for flower color, he descripion of he characerisic. P/p are shor for purple, he dominan rai.) b. Wha are he rais for seed surface? Sugges leers you migh use o represen he alleles for seed surface. he paren homozygous for he dominan rai canno conribue a recessive allele o any offspring (barring, of course, an unlikely random muaion). As long as an allele for he dominan rai is presen, he offspring will display he dominan rai. Offspring may be carriers of he recessive allele, bu none will display he recessive rai. 4. A scienis has some purple-flowered pea plans. She wans o find ou if he pea plans are homozygous for he purple flower color. a. Wha cross will be bes o find ou if he purpleflowered peas are homozygous? Cross hem wih whie-flowered plans, so ha he whie allele, if presen, will reveal iself. his kind of breeding es, agains a second paren showing he recessive rai, is called a es cross. b. Use Punne squares o show wha will happen if he plans are crossed wih whie-flowered plans and i. he purple-flowered plans do no have an allele for he whie rai. F F Seed surface is eiher wrinkled or smooh. Since smooh is dominan o wrinkled, he alleles could be represened as S = smooh and s = f wrinkled. (S/s could be shor for eiher seed surface, he characerisic in general, or smooh, he dominan rai.) 3. Review your resuls on Suden Shee f Why is i impossible for offspring o show he recessive rai if one paren is homozygous for he dominan rai? here will be no whie-flowered offspring, as all offspring will be heerozygous for purple flowers. D-98 Science and Life Issues

8 Gene Squares Aciviy 61 ii. he purple-flowered plans do have an allele for he whie rai. F F f ff Half he offspring will have whie flowers and half will have purple flowers. Because here are whie-flowered offspring, he purple-flowered parens mus have been carrying a recessive whie allele. (Abou half he offspring will have whie flowers if he purple-flowered paren is heerozygous.) f ff eacher s Guide D-99

9 Name Dae Punne Squares Sep by Sep he cross beween he Generaion 2 () criers Ocean and Lucy is: Ocean x Lucy x = allele for blue ail color (dominan) = allele for orange ail color (recessive) Noe ha while Ocean and Lucy boh have blue ails, hey are boh heerozygous. 1. Referring o he example above from your book, complee his Punne square for he cross beween Ocean and Lucy. a. Place Ocean s and Lucy s alleles on he doed lines in he Punne square. b. Complee he Punne square by filling in each box wih he allele above i and he allele o is lef he Regens of he Universiy of California c. Use eiher a blue pencil or a regular pencil o shade in he squares for offspring ha will have blue ails in your Punne square above. d. Abou wha fracion of he offspring of Ocean and Lucy are prediced o have blue ails, according o he Punne square? e. Abou wha fracion are prediced o have orange ails? Science and Life Issues Suden Shee 61.1 D-101

10 Name Dae Punne Squares Sep by Sep Generaion 3 includes some criers wih orange ails and some wih blue ails. 2. Complee his Punne square for a cross beween an orange-ailed crier and a heerozygous blue-ailed () crier. Orange ail Blue ail a. Use pencil o shade in he squares for offspring wih blue ails. b. Abou wha fracion of he offspring are prediced o have blue ails? c. Abou wha fracion are prediced o have orange ails? 3. Complee his Punne square for a cross beween a heerozygous blue-ailed () crier and a heerozygous blue-ailed () crier Blue ail 2006 he Regens of he Universiy of California Blue ail a. Use pencil o shade in he squares for offspring wih blue ails. b. Abou wha fracion of he offspring are prediced o have blue ails? c. Abou wha fracion are prediced o have orange ails? Science and Life Issues Suden Shee 61.1 D-103

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