1	Independent Assortment First, the Chi-squared Test and then Independent Assortment
2	Reading Assignment Reread chapter 13. Pay special attention to the segregation and assortment. When does segregation occur in the life cycle? What conditions are necessary to ‘see’ segregation? When does independent assortment occur? What conditions are necessary to see whether of not assortment is independent?
3	Segregation occurs in meiosis Each haploid gamete has only one of the two alleles that are in each cell of the diploid individual that formed the gamete. The separation of the allele from the mother from the allele from the father occurs during the first division of meiosis and is called segregation.
4	Locus & Allele symbol conventions Loci and Alleles should be italicized. In class, we typically use a letter of the alphabet for a locus with alleles being designated by case or superscripts. There are many more loci than letters. Sometimes we use two letters as a symbol for a locus. VG and vg are used for the dominant and recessive alleles at the vestigial wing locus in Drosophila.
5	Expectations for each offspring
6	Expected Numbers of offspring To calculate the expected number of YELLOW F2 peas, one multiplies the probability for each pea times the total number of peas observed. Mendel observed 556 F2 peas The expected number of YELLOW is 417, =556•0.75 (GREEN must be 139 as total must be 556). The expected number of ROUND is 417, =556•0.75. while the expected number of WRINKLED is 139, =556•0.25
7	Categorical Data When there are discrete categories that collectively cover all possibilities AND one has a hypothesis that generates probabilities of being in each possible category, one can use the Chi-squared test to compare the observed outcomes (=numbers) to the expected numbers once the total, N, of observations is known.
8	The χ² TEST The χ² test is used to evaluate if the observed numbers in the categories are compatible with the predicted numbers in each category. Differences between the expected number and the observed number in each category are used to calculate a value.
9	Chi squared Formula
10	The χ² TEST – Degrees of Freedom The meaning of the calculated χ² value depends on the degrees of freedom, df. The df = # of categories – 1 – the number of variables whose value is estimated from the data. In the case just considered, df = 2 – 1 = 1.
11	Critical χ² values With 1 df the critical value is 3.84. If the calculated value is greater than 3.84 one rejects the hypothesis or model. If the calculated value is less than 3.84 one accepts the hypothesis. With 2 df the critical χ² value is 5.99 With 3 df the critical χ² value is 7.82
12	POSSIBILITIES about truth Hypothesis is TRUE TEST ACCEPTS TEST REJECTS Typically biologists are willing to accept a 5% (1/20) rate of error of rejecting the model when it is true. Hypothesis is FALSE TEST ACCEPTS TEST REJECTS Different hypotheses can lead to similar predictions. Acceptance of hypothesis does not PROVE it to be true.
13	χ² values of Mendel’s Results YELLOW-GREEN OBS EXP 416 417 140 139 χ² = 0.01 Accept the hypothesis of ¾, ¼ split. ROUND-WRINKLED OBS EXP 423 417 133 139 χ² = 0.35 Accept the hypothesis of ¾, ¼ split.
14	Categorizing each pea for both characters Category Observed Expected if independent ROUND YELLOW 315 ¾•¾•556 = 312.75 WRINKLED YELLOW 101 ¼•¾•556 = 104.25 ROUND GREEN 108 ¼•¾•556 = 104.25 WRINKLED GREEN 32 ¼•¼•556 = 34.75 Independent means the probability of being GREEN is not affected by whether or not shape is ROUND or WRINKLED.
15	INDEPENDENT ASSORTMENT ASSORTMENT refers to the distribution of alleles from different loci into the gametes at meiosis. INDEPENDENT is a general term to describe relationship of two variables. Variables are INDEPENDENT if the probability of being both A & B = pr(A)•pr(B).
16	INDEPENDENT ASSORTMENT In genetic context, we can say the seed shape is independent of seed color if pr(ROUND&YELLOW) = pr(ROUND)•pr(yellow) If 9/16^th of offspring are ROUND&YELLOW then shape and color are independent as pr(ROUND) = ¾ and pr(YELLOW) = ¾.
17	Mendel’s Laws Mendel’s 1^st law is dominance. Mendel’s 2^nd law is segregation of alleles in gamete formation. Mendel’s 3^rd law is that different loci assort independently. Neither the 1^st or 3^rd Laws have proved to be universally true, but the hypotheses of Mendel provide a framework to evaluate genetic results.
18	Symbols representing genotypes Diploid genotypes are conventionally written in two ways. The alleles can be groups by locus, i.e., AaBBcc VGvgSEse The alleles from the parents can be listed separately separated by a slash, i.e., ABc/aBc VGSE/vgse or VGse/vgSE
19	Possible GAMETE Genotypes The doubly heterozygous F1 has the genotype RrGg or more accurately for Mendel’s cross as RG/rg. There is another possible type of double heterozygote, Rg/rG. Each gamete has to have one of the shape alleles (R or r) and one of the color alleles (G or g). One of two alleles for all loci. RG, Rg, rG & rg are the only possibilities.
20	Each allele duplicates during the S phase of the cell cycle so meiosis starts with 4 alleles
21	The TEST CROSS There are two possible genotypes for an individual with the dominant phenotype, heterozygous or homozygous. The cross of the individual whose genotype is to be determined to an individual with the homozygous recessive genotype will yield two types of offspring if heterozygous, but only one if homozygous.
22	Problems How many different kinds of gametes could an individual with the following genotypes produce? A HhMm B HHMmoo C AbC/aBC D VGvgSEse
23	Vocabulary Chi squared test Degrees of freedom Segregation Summation symbol Critical value Slash notation Independent Independent assortment Test cross Mutually exclusive symbols