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2 Kings 6:17

2 Kings 6:17 17 And 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. Mendelian Genetics. Timothy G. Standish, Ph. D. Biography - Gregor Mendel.

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2 Kings 6:17

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  1. 2 Kings 6:17 17 And 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.

  2. Mendelian Genetics Timothy G. Standish, Ph. D.

  3. 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

  4. 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

  5. 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."

  6. 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

  7. 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)

  8. 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

  9. Pea flower 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

  10. Anthers Stigma Pea flower 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

  11. Why Peas? • By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.

  12. Why Peas? • By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas. Snip

  13. . . . . . . . . . . . . Why Peas? • By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.

  14. . . . . . . . . . . . . Why Peas? • By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.

  15. . . . . . . . . Why Peas? • By removing the anthers of one flower and artificially pollinating using a brush, crosses can be easily controlled in peas.

  16. Mendel’s Results • When crossing purple-flowered peas with white-flowered peas, Mendel got the following results: • In the first filial (F1) generation all offspring produced purple flowers • In the second generation (second filial or F2): • 705 purple • 224 white • Approximately a 3:1 ratio of purple to white

  17. Interpreting Mendel’s Results • Because the F1 generation did not produce light- purple flowers and because white flowers showed up in the F2 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

  18. C C c C c C c c Heterozygous parents make gametes either one or the other allele Homozygous parents can only make gametes with one type of allele Gametes from the P generation F1 Generation F2 Generation The F1 Generation is all heterozygous Interpreting Mendel’s Results • In the F1 generation, the white allele was hidden by the purple “dominant” allele • In the F2 generation, 1/4 of the offspring wound up with two copies of the white allele thus they were white Cc Cc CC Cc Cc Cc Cc cc

  19. Dominent traits mask recessive traits Masked recessive traits reappear Mendel’s Results 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 F2 Results 5,474 Round 1,850 wrinkled 6,022 Yellow 2,001 green 882 Full 299 constricted 428 Green 152 yellow 651 Axial 207 terminal 705 Violet 224 white 787 Tall 277 dwarf

  20. Mendel’s Results F2 Results Seeds 5,474 Round 1,850 wrinkled 6,022 Yellow 2,001 green 882 Full 299 constricted Pods 428 Green 152 yellow 651 Axial 207 terminal Flowers 705 Violet 224 white Stem 787 Tall 277 dwarf F2 Ratios Seeds 2.96:1 Round:wrinkled 3.01:1 Yellow :green 2.95:1 Full:constricted Pods 2.82:1 Green:yellow 3.14:1 Axial:terminal Flowers 3.15:1 Violet:white Stem 2.84:1 Tall:dwarf • Ratios are not exactly 3:1 • How do we decide if the ratios are close enough to 3:1 to support and not reject our theory? • The chi square statistical test provides the tool used for this purpose

  21. 2 - 2 d ( Obs . Ex .) å å Chi Square: C2 = = e Ex Chi Square • Statistics fall into two categories: • Descriptive - Summarize characteristics of a data set • Mean, standard deviation . . . • 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 “c” or “X”

  22. 2 - 2 d ( Obs . Ex .) å å Chi Square: C2 = = e Ex Obs. Ex. O - E (O-E)2/E Round 5,474 (1,850+5,474) x 3/4 = 5,493 5,474 - 5,493 =-19 -192/5,493 = 0.066 wrinkled 1,850 (1,850+5,474) x 1/4 = 1,831 1,850 - 1,831 = 19 192/1,831 = 0.20 X2 = 0.266 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

  23. 2 - 2 d ( Obs . Ex .) å å Chi Square: C2 = = e Ex Obs. Ex. O - E (O-E)2/E Violet 705 (705+224) x 3/4 = 697 705 - 697 = 8 82/697 = 0.092 white 224 (705+224) x 1/4 = 232 224 - 232 =-8 -82/232 = 0.276 X2 = 0.368 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

  24. Mendel’s Conclusions • Phenotypic traits are controlled by pairs of genes which act as individual units of inheritance • In genes that have multiple alleles (variations) the presence of some traits, called dominant traits, masks the presence of recessive traits • 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?

  25. 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

  26. Mendel’s Dihybrid Cross • Mendel chose to see if the round and yellow seed genes segregated independently P Generation Round green RRyy X wrinkled Yellow rrYY F1 All Round Yellow RrYy F2 315 Round Yellow RrYy RRYy or RrYY 101 wrinkled Yellow rrYy or rrYY 108 Round green RRyy or Rryy 32 wrinkled green rryy Ratio 9/16 3/16 3/16 1/16 • In other dihybrid crosses a 9:3:3:1 ratio was also found

  27. 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

  28. 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.

  29. 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).

  30. 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.

  31. 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.

  32. Chromosomal Theory of Inheritance • Genes have specific loci on chromosomes. • Chromosomes undergo segregation (meiosis) and independent assortment, • Thus alleles of genes are independently assorted.

  33. Mother Father Telophase I e E Prophase I Crossing Over Replication e e E E e E e e E E n N N n n N n n N N e e E E N n N N n n Chromosomal Theory of Inheritance Telophase II

  34. Eggs EN En eN en Sperm EN EENN EENn EeNN EeNn E N En EENn EEnn EeNn Eenn E n eN EeNN EeNn eeNN eeNn e e e E E N N N en EeNn Eenn n eeNn eenn n e n Independent Assortment As long as genes are on different chromosomes, they will assort independently

  35. Mother Father Telophase I e e e E E E Prophase I Replication e e E E e E a a A A a a a A A A A A a a e E e E a a A A Two Genes On One Chromosome Telophase II 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

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

  37. Determination of Gamete and Zygote Variability Number of Heterozygous Pairs n Number of Different Gametes 2n Number of Different Genotypes 3n Number of Different Phenotypes 2n 1 2 3 4 2 4 8 16 3 9 27 81 2 4 8 16

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

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

  40. Laws Of Probability:3 Conditional Probability • Probability of events in which both events share some dependent condition • 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? • Probability queen of hearts/probability of hearts = • (1/52)/(1/4) = 4/52 = 1/13

  41. Probability of any one way n! Number of possible ways p = asbt s!t! Number of ways to have 8 boys and 4 girls n! 12! 0.58 x 0.54 p = asbt = s!t! 8!4! Probability of any specific order of 8 boys and 4 girls Laws Of Probability:4 Binomial Expansion p = probability n = number of events s = number of outcome a t = number of outcome b a = probability of outcome a b = probability of outcome b • The probability of a set of events arranged in no specified order: • Example - If James and Bertha have 12 children, what is the chance they will have 8 boys and 4 girls? • n = 12, a = prob of boy = 0.5, b = prob of girl = 0.5, s = no. boys = 8, t = no. girls = 495 x 0.00024 = 0.121

  42. The End

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