Completion and analysis of Punnett squares for dihybrid traits 10.2 Inheritance Understanding: Unlinked genes segregate independently as a result of meiosis Gene loci are said to be linked if on the same chromosome Variation can be discrete or continuous The phenotypes of polygenic characteristics tend to show continuous variation Chi-squared tests are used to determine whether the difference between an observed and expected frequency distribution is statistically significant Applications: Completion and analysis of Punnett squares for dihybrid traits Morgan’s discovery of non-Mendelian ratios in Drosophila Polygenic traits such as human height may also be influenced by environmental factors Nature of science: Looking for patterns, trends and discrepancies: Mendel used observations of the natural world to find and explain patterns and trends. Since then, scientists have looked for discrepancies and asked questions based on further observations to show exceptions to the rules. For example, Morgan discovered non-Mendelain ratios in his experiments with Drosophila Skills: Calculation of the predicted genotypic and phenotypic ratio of offspring of dihybrid crosses involving unlinked autosomal genes Identification of recombinants in crosses involving two linked genes Use of a chi-squared test on data from dihybrid crosses

Key words Locus: Location of a gene on a chromosome Homologous chromosome: Two chromosomes with same sequence of genes Alleles: Different forms of same gene on different chromosomes Segregation: Separation of two alleles of every gene (in meiosis – chromosomes separate) Independent Assortment: Alleles for one trait segregate independently from alleles for another trait

Linked or Unlinked? Unlinked genes Found on different chromosomes Segregate independently Linked genes On the same chromosome Do not segregate independently (unless crossed over) Autosomal linked = on a non-sex chromosome Sex linked = on an X or Y chromosome Understanding: Unlinked genes segregate independently as a result of meiosis Gene loci are said to be linked if on the same chromosome

Variation: Discrete or continuous Categories = discrete/discontinuous E.g blood types AB B A O Nothing in between Monogenic inheritance (single gene) Understanding: Variation can be discrete or continuous

Polygenic inheritance (two or more genes involved) Variation Continuous = Complete range in variation Usually creates a ‘normal’ distribution Polygenic inheritance (two or more genes involved) Understanding: Variation can be discrete or continuous

We have looked at Mendel’s tests on peas previously Morgan’s Tests We have looked at Mendel’s tests on peas previously Dihybrid cross Yellow/Green Wrinkled/Smooth Skills: Calculation of the predicted genotypic and phenotypic ratio of offspring of dihybrid crosses involving unlinked autosomal genes Understanding: Variation can be discrete or continuous

RY Ry rY ry

RY Ry rY RRYY RRYy RrYY RrYy RRyy Rryy rrYY rrYy rryy

This is the typical ratio expected in a dihybrid cross. F2 : : : 9 3 3 1 Round Yellow Round Green Wrinkled Yellow Wrinkled Green This is the typical ratio expected in a dihybrid cross.

Using fruit flies (Drosophila) he crossed red eye and white eye flies Morgan’s Tests Thomas Hunt Morgan found some examples to contradict Mendel’s results from his Dihybrid crosses. Using fruit flies (Drosophila) he crossed red eye and white eye flies What did he find out? Nature of science: Looking for patterns, trends and discrepancies: Mendel used observations of the natural world to find and explain patterns and trends. Since then, scientists have looked for discrepancies and asked questions based on further observations to show exceptions to the rules. For example, Morgan discovered non-Mendelain ratios in his experiments with Drosophila Applications: Completion and analysis of Punnett squares for dihybrid traits Morgan’s discovery of non-Mendelian ratios in Drosophila

Morgan’s Tests Some traits do not independently assort Sex-linked genes (Morgan called them ‘sex-limited’) In this case on the X chromosome Could become uncoupled by crossing over – but low frequency Nature of science: Looking for patterns, trends and discrepancies: Mendel used observations of the natural world to find and explain patterns and trends. Since then, scientists have looked for discrepancies and asked questions based on further observations to show exceptions to the rules. For example, Morgan discovered non-Mendelain ratios in his experiments with Drosophila Applications: Completion and analysis of Punnett squares for dihybrid traits Morgan’s discovery of non-Mendelian ratios in Drosophila

Complete your work sheet as we go through the example Chi Squared Determine whether the difference between an observed and expected frequency distribution is statistically significant Complete your work sheet as we go through the example Understanding: Chi-squared tests are used to determine whether the difference between an observed and expected frequency distribution is statistically significant Skills: Use of a chi-squared test on data from dihybrid crosses

No independent assortment = no variation Before we begin… Independent assortment states that when gametes are produced the segregation of one pair of alleles is independent of the segregation of another pair of alleles. When homologous chromosomes separate during meiosis I, it is random which pole each chromosome travels to, therefore random which pole the alleles go to (random orientation) You can have any combination of alleles (RRYY, RrYY, RRYy, rrYY…) therefore you would expect variation. No independent assortment = no variation Skills: Use of a chi-squared test on data from dihybrid crosses

Chi Squared White leghorn chickens with large single combs Crossed with Indian game fowl with dark feathers and small pea combs Ho = the traits are assorted independently (no association) H1 = the traits do not assort independently (is an association) Skills: Use of a chi-squared test on data from dihybrid crosses

Chi Squared All of the F1 generation were white chickens with pea combs F2 generation was different from the 9:3:3:1 ratio normally expected. Were these differences statistically significant, random or due to sampling error? Skills: Use of a chi-squared test on data from dihybrid crosses

Start with a contingency table Fill in your contingency table with the observed frequencies for F2 generation White pea White single Dark pea Dark single Total Observed 111 37 34 8 190 Expected Skills: Use of a chi-squared test on data from dihybrid crosses

Expected Values Expected values calculated using expected probability from Punnett grids, multiplied by actual total Complete the expected values using what you would expect the ratio to be (remember 9:3:3:1 when doing di-hybrid crosses) Then use the total number as already stated Expected = row total x column total grand total White pea White single Dark pea Dark single Total Observed 111 37 34 8 190 Expected (9/16) x 190 (3/16) x 190 (1/16) x 190 Skills: Use of a chi-squared test on data from dihybrid crosses

Then use the total number as already stated Expected Values Complete the expected values using what you would expect the ratio to be (remember 9:3:3:1 when doing di-hybrid crosses) Then use the total number as already stated White pea White single Dark pea Dark single Total Observed 111 37 34 8 190 Expected 106.9 35.6 11.9 Skills: Use of a chi-squared test on data from dihybrid crosses

Degrees of Freedom One less than the total number of outcomes White pea White single Dark pea Dark single Total Observed 111 37 34 8 190 Expected 106.9 35.6 11.9 Skills: Use of a chi-squared test on data from dihybrid crosses

Remember to use a significance level of 0.05 (5%) Critical Region Use the critical values table to find the critical region for your chi-squared test Remember to use a significance level of 0.05 (5%) Critical value: 7.815 Skills: Use of a chi-squared test on data from dihybrid crosses

Remember to use a significance level of 0.05 (5%) Critical Region Use the critical values table to find the critical region for your chi-squared test Remember to use a significance level of 0.05 (5%) Critical value: 7.815 Skills: Use of a chi-squared test on data from dihybrid crosses

Σ (O – E)2 E (O – E)2 E (O – E)2 E (O – E)2 E (O – E)2 E Chi Squared Test χ2 = (O – E)2 E Σ (O – E)2 E (O – E)2 E (O – E)2 E (O – E)2 E

Chi Squared Test χ2 = (O – E)2 E Σ (111-106.9)2 106.9 (37-35.6)2 35.6 χ2 = (O – E)2 E Σ (111-106.9)2 106.9 (37-35.6)2 35.6 (34-35.6)2 35.6 (8-11.9)2 11.9

Chi Squared Value Chi squared = 1.56

Which Hypothesis? Chi squared = 1.56 Critical region = 7.815 Compare calculated chi squared value to critical region Higher than critical region = reject null hypothesis (the traits do not assort independently) Equal to or lower than critical region = keep null hypothesis Ho = the traits are assorted independently There is no association between the alleles 95% sure. Results are statistically significant

Remember Independent assortment states that when gametes are produced the segregation of one pair of alleles is independent of the segregation of another pair of alleles. Due to crossing over and random orientation When homologous chromosomes separate during meiosis I, it is random which pole each chromosome travels to. (This is what you just proved in your chi squared test!) Variation = independent assortment Results are statistically significant