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©2000 Timothy G. Standish 2 Kings 6:17 17And Elisha prayed, "O LORD, open his eyes so he may see." Then the LORD opened the servant's eyes, and he looked and saw the hills full of horses and chariots of fire all around Elisha.

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©2000 Timothy G. Standish Mendelian Genetics Timothy G. Standish, Ph. D.

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©2000 Timothy G. Standish Biography - Gregor Mendel Father of classical genetics. Born 1822 to peasant family in the Czech village of Heinzendorf (now called Hyncice), northern Moravia, part of the Austro- Hungarian empire at the time 1843 - Admitted to the St. Thomas Augustinian Monastery in Brunn (Brno), southern Moravia, now in the Czech Republic Studied mathematics in Olmutz college

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©2000 Timothy G. Standish Biography - Gregor Mendel: Education Attended University of Vienna 1851 - 1853. Influenced by: –Franz Unger, a plant physiologist who believed new species could come about via hybridization. –Christian Doppler, physicist who discovered the Doppler effect. Sharpened his math skills. 1854 Returned to Brunn

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©2000 Timothy G. Standish Biography - Gregor Mendel: Research Studied peas which he grew in a garden outside of the Abbey where he lived starting 1856 (3 years prior to publication of Origin of Species). Showed that the traits he studied behaved in a precise mathematical way and disproved the theory of "blended inheritance."

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©2000 Timothy G. Standish Biography - Gregor Mendel: Publication and Death 1865 first reported results of his work Published rules of transmission of genes in 1866 (handwritten in German, not Latin!). Work was totally ignored. 1868 - Elected Abbot of the monastery and ceased investigation of inheritance 1884 - Died of kidney failure

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©2000 Timothy G. Standish Biography - Gregor Mendel: Rediscovery Mendel’s work was rediscovered in 1900 by three botanists: –Carl Correns (Germany) –Erich von Tschermak (Austria) –Hugo de Vries (Holland)

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©2000 Timothy G. Standish Why Peas? Mendel used peas to study inheritance because: True breeding commercial strains were available Peas are easy to grow Peas have many easy to observe traits including: –Seed color - Green or yellow –Seed shape - Round or wrinkled –Pod color - Green or yellow –Pod shape - Smooth or constricted –Flower color - White or purple –Flower position - Axial or terminal –Plant size - Tall or dwarf

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©2000 Timothy G. Standish Why Peas? Pea flowers are constructed in such a way that they typically self fertilize Because of this, it is relatively easy to control crosses in peas Pea flower

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©2000 Timothy G. Standish Why Peas? Pea flowers are constructed in such a way that they typically self fertilize Because of this, it is relatively easy to control crosses in peas Stigma Pea flower Anthers

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©2000 Timothy G. Standish Why Peas? By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.

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©2000 Timothy G. Standish Why Peas? By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.

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©2000 Timothy G. Standish Why Peas? By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.............

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©2000 Timothy G. Standish Why Peas? By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.............

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©2000 Timothy G. Standish Why Peas? By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.........

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©2000 Timothy G. Standish Mendel’s Results When crossing purple-flowered peas with white-flowered peas, Mendel got the following results: In the first filial (F 1 ) generation all offspring produced purple flowers In the second generation (second filial or F 2 ): –705 purple –224 white Approximately a 3:1 ratio of purple to white

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©2000 Timothy G. Standish Interpreting Mendel’s Results Because the F 1 generation did not produce light- purple flowers and because white flowers showed up in the F 2 generation, Mendel disproved blended inheritance. Mendel said that the parents had two sets of genes, thus two copies of the flower color gene Each gene has two varieties called alleles In the case of the flower color gene the two alleles are white and purple

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©2000 Timothy G. Standish Interpreting Mendel’s Results CC Cc cc In the F 1 generation, the white allele was hidden by the purple “dominant” allele In the F 2 generation, 1/4 of the offspring wound up with two copies of the white allele thus they were white Cc C c F 2 Generation Cc CC c c F 1 Generation Gametes from the P generation Heterozygous parents make gametes either one or the other allele The F1 Generation is all heterozygous Homozygous parents can only make gametes with one type of allele

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©2000 Timothy G. Standish Mendel’s Results Trait Seeds round/wrinkled yellow/green full/constricted Pods green/yellow axial/terminal Flowers violet/white Stem Tall/dwarf Trait Seeds round/wrinkled yellow/green full/constricted Pods green/yellow axial/terminal Flowers violet/white Stem Tall/dwarf F1 Results All Round All Yellow All Full All Green All Axial All Violet All Tall F1 Results All Round All Yellow All Full All Green All Axial All Violet All Tall F2 Results 5,474 Round1,850 wrinkled 6,022 Yellow2,001 green 882 Full299 constricted 428 Green152 yellow 651 Axial207 terminal 705 Violet224 white 787 Tall277 dwarf F2 Results 5,474 Round1,850 wrinkled 6,022 Yellow2,001 green 882 Full299 constricted 428 Green152 yellow 651 Axial207 terminal 705 Violet224 white 787 Tall277 dwarf Dominent traits mask recessive traits Masked recessive traits reappear

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©2000 Timothy G. Standish Mendel’s Results F2 Results Seeds 5,474 Round1,850 wrinkled 6,022 Yellow2,001 green 882 Full299 constricted Pods 428 Green152 yellow 651 Axial207 terminal Flowers 705 Violet224 white Stem 787 Tall277 dwarf F2 Results Seeds 5,474 Round1,850 wrinkled 6,022 Yellow2,001 green 882 Full299 constricted Pods 428 Green152 yellow 651 Axial207 terminal Flowers 705 Violet224 white Stem 787 Tall277 dwarf F2 Ratios Seeds 2.96:1 Round:wrinkled 3.01:1Yellow:green 2.95:1Full:constricted Pods 2.82:1Green:yellow 3.14:1Axial:terminal Flowers 3.15:1Violet:white Stem 2.84:1Tall:dwarf F2 Ratios Seeds 2.96:1 Round:wrinkled 3.01:1Yellow:green 2.95:1Full:constricted Pods 2.82:1Green:yellow 3.14:1Axial:terminal Flowers 3.15:1Violet:white Stem 2.84:1Tall:dwarf l Ratios are not exactly 3:1 l How do we decide if the ratios are close enough to 3:1 to support and not reject our theory? l The chi square statistical test provides the tool used for this purpose

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©2000 Timothy G. Standish Chi Square Statistics fall into two categories: 1 Descriptive - Summarize characteristics of a data set –Mean, standard deviation... 2 Decision making - Assist in deciding whether a set of data is consistent or inconsistent with a hypothesis called the null hypothesis –T test, f test, chi square... Called chi square after the Greek letter “ ” or “X” d 2 e (Obs. Ex.) 2 Ex Chi Square:

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©2000 Timothy G. Standish Chi Square: On Mendel’s Seed Texture Data Degrees of freedom = N - 1 = 2 - 1 = 1 0.90 > p > 0.50 that this amount of deviation is due to chance In this case we retain the hypothesis that this data represents a 3:1 ratio d 2 e (Obs. Ex.) 2 Ex Chi Square: 19 2 /1,831 = 0.20 -19 2 /5,493 = 0.066 (1,850+5,474) x 1/4 = 1,831 (1,850+5,474) x 3/4 = 5,493 1,850 5,474 0.266X 2 = (O-E) 2 /EEx.Obs. wrinkled Round O - E 1,850 - 1,831 = 19 5,474 - 5,493 =-19

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©2000 Timothy G. Standish Chi Square: On Mendel’s Flower Color Data Degrees of freedom = N - 1 = 2 - 1 = 1 0.90 > p > 0.50 that this amount of deviation is due to chance In this case we retain the hypothesis that this data represents a 3:1 ratio d 2 e (Obs. Ex.) 2 Ex Chi Square: -8 2 /232 = 0.276 8 2 /697 = 0.092 (705+224) x 1/4 = 232 (705+224) x 3/4 = 697 224 705 0.368X 2 = (O-E) 2 /EEx.Obs. white Violet O - E 224 - 232 =-8 705 - 697 = 8

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©2000 Timothy G. Standish Mendel’s Conclusions 1 Phenotypic traits are controlled by pairs of genes which act as individual units of inheritance 2 In genes that have multiple alleles (variations) the presence of some traits, called dominant traits, masks the presence of recessive traits 3 Gene pairs segregate randomly during gamete formation with either member of a pair equally likely to end up in a given gamete But do multiple genes assort independently?

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©2000 Timothy G. Standish Mendel’s Experiment: A Case Study In Good Science Gregor Mendel’s investigation of principles of inheritance is a case study in how science should be done: He asked a good question Chose an appropriate organism to work with Practiced reductionism Made good use of his data and allowed it (not prevailing theory) to drive his conclusions

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©2000 Timothy G. Standish Mendel’s Dihybrid Cross In other dihybrid crosses a 9:3:3:1 ratio was also found Mendel chose to see if the round and yellow seed genes segregated independently Ratio 9/16 3/16 1/16 P Generation Round green RRyy X wrinkled Yellow rrYY F 1 All Round Yellow RrYy F 2 315Round Yellow RrYy RRYy or RrYY 101wrinkled Yellow rrYy or rrYY 108Round green RRyy or Rryy 32wrinkled green rryy

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©2000 Timothy G. Standish 3 Reasons Mendel’s Work Was Ignored Mendel was not on the ball Biologists were idiots (at least when it came to math) Lack of independent supporting discoveries

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©2000 Timothy G. Standish Reasons Mendel’s Work Was Ignored: 1) Mendel was not on the ball Wrote in an obscure journal (Proceedings of the Natural History Society of Brunn). Wrote in German, not Latin. Mendel was not well known and did not persevere in his attempt to push his ideas.

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©2000 Timothy G. Standish Reasons Mendel’s Work Was Ignored: 2) Biologists were idiots Biologists didn’t understand math Biologists were interested in the explaining the transmission of continuous traits like height, esp. after publication of Origin of Species in 1859. Mendel suggested that inherited characteristics were discrete units (discontinuous).

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©2000 Timothy G. Standish Reasons Mendel’s Work Was Ignored: 3) Lack of independent supporting discoveries: There was no physical element in which Mendel’s inherited particles could be identified. By the turn of the century, chromosomes had been discovered (physical particles) and biologists were better at math.

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©2000 Timothy G. Standish Chromosomes: The Physical Basis of Inheritance 1866 Mendel published his work 1875 Mitosis was first described 1890s Meiosis was described 1900 Mendel's work was rediscovered 1902 Walter Sutton, Theodore Boveri and others noted parallels between behavior of chromosomes and alleles.

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©2000 Timothy G. Standish Chromosomal Theory of Inheritance Genes have specific loci on chromosomes. Chromosomes undergo segregation (meiosis) and independent assortment, Thus alleles of genes are independently assorted.

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©2000 Timothy G. Standish E n e N Chromosomal Theory of Inheritance e N E n Father Mother N e E n N E n ee n E N e n E N e n E N e N E n Telophase II Replication Telophase I Prophase I Crossing Over

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©2000 Timothy G. Standish EnEn eNeN enen ENEN Sperm e ne ne Ne NE nE nE NE N Eggs Independent Assortment n E e N e n N E n E e n e N N E EeNnEeNnEeNNEENnEENN EennEeNnEeNnEEnnEENn eeNneeNNEeNnEeNnEeNN eenneeNnEennEeNnEeNn As long as genes are on different chromosomes, they will assort independently

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©2000 Timothy G. Standish E A a e Two Genes On One Chromosome Telophase II Father Mother e a E A Telophase I A e E A E a e a E AA e E aa e Replication e a E A Prophase I E A A a e a As long as genes on the same chromosome are located a long distance apart, they will assort independently due to crossing over during Prophase I of meiosis

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©2000 Timothy G. Standish Laws Of Probability Because alleles are usually distributed randomly, the laws of probability can describe their behavior: 1 Product Law - Describes the probability of two or more independent events occurring in a defined sequence or way 2 Sum Law - Describes the probability of two or more individual mutually exclusive events 3 Conditional Probability - Probability of events in which both events share some dependent condition 4 Binomial Expansion - The probability of a set of events arranged in no specified order

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©2000 Timothy G. Standish Determination of Gamete and Zygote Variability 2 4 8 16 12341234 2 4 8 16 3 9 27 81 Number of Different Phenotypes 2 n Number of Heterozygous Pairs n Number of Different Gametes 2 n Number of Different Genotypes 3 n

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©2000 Timothy G. Standish Laws Of Probability: 1 Product Law l The “and” law l Describes the probability of two or more independent events occurring in a defined sequence or way. l Example - What is the probability of flipping a coin and getting heads and then tails? l Probability of getting heads on the first flip = 0.5 l Probability of heads on the second flip = 0.5 l Total probability = 0.5 x 0.5 = 0.25

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©2000 Timothy G. Standish Laws Of Probability: 2 Sum Law l The “or” law l Describes the probability of two or more individual mutually exclusive events l Example - What is the probability of flipping a coin and getting heads or tails? l Probability of getting heads = 0.5 l Probability of tails on the same flip = 0.5 l Total probability = 0.5 + 0.5 = 1.0

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©2000 Timothy G. Standish Laws Of Probability: 3 Conditional Probability l Probability of events in which both events share some dependent condition l Example - If one card in a deck of 52 is the queen of hearts, and hearts make up 1/4 of the deck, if you have a card with hearts on it, what are the odds that it is the queen of hearts? l Probability queen of hearts/probability of hearts = l (1/52)/(1/4) = 4/52 = 1/13

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©2000 Timothy G. Standish Laws Of Probability: 4 Binomial Expansion l The probability of a set of events arranged in no specified order: = 0.121 asbtasbt s!t! n! p = 0.5 8 x 0.5 4 8!4! 12! = = 495 x 0.00024 l Example - If James and Bertha have 12 children, what is the chance they will have 8 boys and 4 girls? l n = 12, a = prob of boy = 0.5, b = prob of girl = 0.5, s = no. boys = 8, t = no. girls asbtasbt s!t! n! p = a = probability of outcome a b = probability of outcome b p = probability n = number of events s = number of outcome a t = number of outcome b Number of possible ways Probability of any one way Number of ways to have 8 boys and 4 girls Probability of any specific order of 8 boys and 4 girls

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©2000 Timothy G. Standish

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Fundamentals of Genetics. Gregor Mendel (1822-1884) Monk from Austria He bred pea plants in monastery gardens and used math to interpret his findings.

Fundamentals of Genetics. Gregor Mendel (1822-1884) Monk from Austria He bred pea plants in monastery gardens and used math to interpret his findings.

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