2 Kings 6:17
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Transcript of 2 Kings 6:17
©2000 Timothy G. Standish
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.
©2000 Timothy G. Standish
Mendelian GeneticsMendelian Genetics
Timothy G. Standish, Ph. D.
©2000 Timothy G. Standish
Biography - Gregor MendelBiography - 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
©2000 Timothy G. Standish
Biography - Gregor Mendel:Biography - Gregor Mendel:EducationEducation
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
©2000 Timothy G. Standish
Biography - Gregor Mendel:Biography - Gregor Mendel:ResearchResearch
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."
©2000 Timothy G. Standish
Biography - Gregor Mendel:Biography - Gregor Mendel:Publication and DeathPublication and Death
1865 first reported results of his workPublished 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
©2000 Timothy G. Standish
Biography - Gregor Mendel:Biography - Gregor Mendel:RediscoveryRediscovery
Mendel’s work was rediscovered in 1900 by three botanists:– Carl Correns (Germany)
– Erich von Tschermak (Austria)
– Hugo de Vries (Holland)
©2000 Timothy G. Standish
Why Peas?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
©2000 Timothy G. Standish
Why Peas?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
©2000 Timothy G. Standish
Why Peas?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
StigmaPea flower
Anthers
©2000 Timothy G. Standish
Why Peas?Why Peas? By removing the anthers of one flower and
artificially pollinating using a brush, crosses can be easily controlled in peas.
©2000 Timothy G. Standish
Why Peas?Why Peas? By removing the anthers of one flower and
artificially pollinating using a brush, crosses can be easily controlled in peas.
©2000 Timothy G. Standish
Why Peas?Why Peas? By removing the anthers of one flower and
artificially pollinating using a brush, crosses can be easily controlled in peas.
. .... .
...
...
©2000 Timothy G. Standish
Why Peas?Why Peas? By removing the anthers of one flower and
artificially pollinating using a brush, crosses can be easily controlled in peas.
. .... .
...
...
©2000 Timothy G. Standish
Why Peas?Why Peas? By removing the anthers of one flower and
artificially pollinating using a brush, crosses can be easily controlled in peas.
.... ....
©2000 Timothy G. Standish
Mendel’s ResultsMendel’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
©2000 Timothy G. Standish
Interpreting Mendel’s ResultsInterpreting 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
©2000 Timothy G. Standish
Interpreting Mendel’s ResultsInterpreting Mendel’s Results
CC
Cc
Cc
cc
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
C c
C
c
F2 GenerationF2 Generation
Cc
Cc
Cc
Cc
C C
c
c
F1 GenerationF1 GenerationGametes 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
©2000 Timothy G. Standish
Mendel’s ResultsMendel’s ResultsTraitSeeds
round/wrinkledyellow/greenfull/constricted
Podsgreen/yellowaxial/terminal
Flowersviolet/white
StemTall/dwarf
TraitSeeds
round/wrinkledyellow/greenfull/constricted
Podsgreen/yellowaxial/terminal
Flowersviolet/white
StemTall/dwarf
F1 Results All RoundAll YellowAll Full
All GreenAll Axial
All Violet
All Tall
F1 Results All RoundAll YellowAll Full
All GreenAll Axial
All Violet
All Tall
F2 Results 5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted
428 Green 152 yellow651 Axial 207 terminal
705 Violet 224 white
787 Tall 277 dwarf
F2 Results 5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted
428 Green 152 yellow651 Axial 207 terminal
705 Violet 224 white
787 Tall 277 dwarf
Dominent traits mask recessive traits
Masked recessive traits reappear
©2000 Timothy G. Standish
Mendel’s ResultsMendel’s ResultsF2 Results Seeds5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted
Pods428 Green 152 yellow651 Axial 207 terminal
Flowers705 Violet 224 white
Stem787 Tall 277 dwarf
F2 Results Seeds5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted
Pods428 Green 152 yellow651 Axial 207 terminal
Flowers705 Violet 224 white
Stem787 Tall 277 dwarf
F2 Ratios Seeds2.96:1 Round:wrinkled3.01:1 Yellow:green2.95:1 Full:constricted
Pods2.82:1 Green:yellow3.14:1 Axial:terminal
Flowers3.15:1 Violet:white
Stem2.84:1 Tall:dwarf
F2 Ratios Seeds2.96:1 Round:wrinkled3.01:1 Yellow:green2.95:1 Full:constricted
Pods2.82:1 Green:yellow3.14:1 Axial:terminal
Flowers3.15:1 Violet:white
Stem2.84:1 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
©2000 Timothy G. Standish
Chi SquareChi 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”
d2
e (Obs. Ex.)2
ExChi Square:
©2000 Timothy G. Standish
Chi Square:Chi Square:On Mendel’s Seed Texture DataOn 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
d2
e (Obs. Ex.)2
ExChi Square:
192/1,831 = 0.20
-192/5,493 = 0.066
(1,850+5,474) x 1/4 = 1,831
(1,850+5,474) x 3/4 = 5,493
1,850
5,474
0.266X2 =
(O-E)2/EEx.Obs.
wrinkled
Round
O - E
1,850 - 1,831 = 19
5,474 - 5,493 =-19
©2000 Timothy G. Standish
Chi Square:Chi Square:On Mendel’s Flower Color DataOn 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
d2
e (Obs. Ex.)2
ExChi Square:
-82/232 = 0.276
82/697 = 0.092
(705+224) x 1/4 = 232
(705+224) x 3/4 = 697
224
705
0.368X2 =
(O-E)2/EEx.Obs.
white
Violet
O - E
224 - 232 =-8
705 - 697 = 8
©2000 Timothy G. Standish
Mendel’s ConclusionsMendel’s Conclusions1 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?
©2000 Timothy G. Standish
Mendel’s Experiment:Mendel’s Experiment:A Case Study In Good ScienceA 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
©2000 Timothy G. Standish
Mendel’s Dihybrid CrossMendel’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
Ratio9/16
3/16
3/16
1/16
P GenerationRound green
RRyyX
wrinkled YellowrrYY
F1
All Round YellowRrYy
F2
315 Round YellowRrYy RRYy or RrYY
101 wrinkled YellowrrYy or rrYY
108 Round greenRRyy or Rryy
32 wrinkled greenrryy
©2000 Timothy G. Standish
3 Reasons Mendel’s Work 3 Reasons Mendel’s Work Was IgnoredWas Ignored
Mendel was not on the ballBiologists were idiots (at
least when it came to math)Lack of independent
supporting discoveries
©2000 Timothy G. Standish
Reasons Mendel’s Reasons Mendel’s Work Was Ignored:Work Was Ignored:
1) Mendel was not on the ball1) 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.
©2000 Timothy G. Standish
Reasons Mendel’s Reasons Mendel’s Work Was Ignored:Work Was Ignored:2) Biologists were idiots2) Biologists were idiots
Biologists didn’t understand mathBiologists 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).
©2000 Timothy G. Standish
Reasons Mendel’s Reasons Mendel’s Work Was Ignored:Work Was Ignored:
3) Lack of independent supporting 3) Lack of independent supporting discoveries: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.
©2000 Timothy G. Standish
Chromosomes:Chromosomes:The Physical Basis of InheritanceThe Physical Basis of Inheritance
1866 Mendel published his work1875 Mitosis was first described1890s Meiosis was described1900 Mendel's work was rediscovered1902 Walter Sutton, Theodore Boveri and
others noted parallels between behavior of chromosomes and alleles.
©2000 Timothy G. Standish
Chromosomal Theory Chromosomal Theory of Inheritanceof Inheritance
Genes have specific loci on chromosomes.
Chromosomes undergo segregation (meiosis) and independent assortment,
Thus alleles of genes are independently assorted.
©2000 Timothy G. Standish
E
n
e
N
Chromosomal Theory Chromosomal Theory of Inheritanceof Inheritance
e
N
E
n
Father
Mother
N
eE
n
N
E
n
e e
n
E
N
e
n
E
N
e
n
E
N
e
N
E
n
Telophase II
Replication
Telophase IProphase I
Crossing Over
©2000 Timothy G. Standish
En
eN
en
EN
Sperm e ne NE nE N
EggsIndependent AssortmentIndependent Assortment
n
E
e
N
e
n
N
E
n
Ee
n
e
NN
E
EeNnEeNNEENnEENN
EennEeNnEEnnEENn
eeNneeNNEeNnEeNN
eenneeNnEennEeNn
As long as genes are on different chromosomes, they will assort independently
©2000 Timothy G. Standish
E
A a
e
Two Genes On One Two Genes On One ChromosomeChromosome
Telophase II
Father
Mother
e
a
E
A
Telophase I
A
eE
A
E
a
e
a
E
A A
e E
a a
e
Replication
e
a
E
A
Prophase I
E
AA 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
©2000 Timothy G. Standish
Laws Of ProbabilityLaws 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
©2000 Timothy G. Standish
Determination of Gamete and Determination of Gamete and Zygote Variability Zygote Variability
248
16
1234
248
16
39
2781
Number of Different
Phenotypes2n
Number of Heterozygous
Pairsn
Number of Different Gametes
2n
Number of Different
Genotypes3n
©2000 Timothy G. Standish
Laws Of Probability:Laws Of Probability:1 Product Law1 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
©2000 Timothy G. Standish
Laws Of Probability:Laws Of Probability:2 Sum Law2 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
©2000 Timothy G. Standish
Laws Of Probability:Laws Of Probability:3 Conditional Probability3 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
©2000 Timothy G. Standish
Laws Of Probability:Laws Of Probability:4 Binomial Expansion4 Binomial Expansion
The probability of a set of events arranged in no specified order:
= 0.121
asbt
s!t!n!p =
0.58 x 0.54
8!4!12!= = 495 x 0.00024
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
asbt
s!t!n!p =
a = probability of outcome a
b = probability of outcome b
p = probabilityn = number of eventss = number of outcome at = 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
©2000 Timothy G. Standish