Transcript BIOL 112 – Principles of Zoology

Gregor Johann Mendel
“Father of Genetics”
Mendel’s success
• Came up with an elegant model of experimental
design
– chose a good “model” organism: Pisum sativum
– restricted his examination to one or very few pairs of
contrasting traits in each experiment
– took meticulous notes with accurate quantitative
records
Empirical approach
• Mendel did not have a hypothesis that he
was testing (hypothetico-deductive
method)… instead his experiments were
designed to determine the quantitative
relationships from which laws could be
discovered
Seven pairs of contrasting characteristics of the garden pea
-seed coat, seed color, petal color, pod shape, pod color, stem
size, axial/terminal flowers.
Monohybrid cross
• Hybridization = when
two plants of the same
species but with different
characteristics are
crossed (mated) to each
other.
• Mono = dealing with one
pair of contrasting
characteristics
Mendels results
Parental
Round x wrinkled
F1
All
round
F2
5474 round
1850 wrinkled
6022 yellow
2001 green
705 purple 224
white
882 inflated
229 pinched
428 green 152
yellow
651 axial 207
terminal
All long 787 long 277
short
F2 ratio
2.96:1
Yellow x green seeds All
yellow
Purple x white
All
purple
Inflated x pinched
All
inflated
Green x yellow pods All
green
Axial x terminal
All axial
3.01:1
Long x short
2.84:1
3.15:1
2.95:1
2.82:1
3.14:1
Mendel’s explanation
1) the existence of “factors” – particulate
theory of inheritance
2) genes are in pairs
3) the principle of segregation
4) gametic content
5) random fertilization
Mendel’s First Law
• Equal Segregation = The two members of a
gene pair segregate from each other into the
gametes; so half the gametes carry one
member of the pair and the other half of the
gametes carry the other member of the pair.
Punnent Squares & The branch
diagram method
• Used to visualize the genotypes and
phenotypes resulting from the
recombination of gametes during
fertilization
Dihybrid Cross
• Follows the inheritance of two different
traits within the same individual.
• i.e. Yellow, Round x Green, Wrinkled
Mendel’s Second Law
• Independent Assortment = two different
genets will randomly assort their alleles
during gamete formation
4 possible male
gametes
4 possible female
gametes
The testcross
• Crossing an individual of “unknown”
genotype with a fully recessive
homozygote.
Hypothesis Testing
• To determine if the data from genetic crosses are
consistent with a particular pattern of inheritance
– We can distinguish between inheritance patterns that obey
Mendel’s laws and those that do not…
• Can quantitatively analyze the offspring – testing
provides an objective, statistical method to evaluate
whether or not the observed data really agree with
the hypothesis.
• Evaluate the “Goodness of Fit”
Hypothesis testing
• Falsification is the basis for hypothesis testing
• A statement about population characteristics
through their corresponding parameters, such as
the population mean µ, or the population
proportion p.
• 1) make an initial assumption
• 2) collect data
• 3) based upon the evidence, conclude whether or
not your initial assumption is supported
If an event can easily occur, we attribute it to chance, but if the event
appears to be unusual, we conclude that the significant departure makes
it unlikely that our initial null hypothesis is true
We reject the null hypothesis when the computed statistic falls in
the tail areas
p value or critical value
• The random sample with the proper
transformation known as test statistic will provide
the evidence from the data in terms of a p-value,
to either reject or not to reject the null hypothesis
H0.
• p-values are measures of how well the evidence
from the data support the null hypothesis.
Therefore, large p-values mean the null hypothesis
should not be rejected, and small p-values mean
the null hypothesis should be rejected.
Chi Square Test
• Parametric test that can be used to analyze population
data in which the members of the population fall into
different categories.
• If we draw all possible samples of size n from a
normal population and plotted, they would form the χ2
distribution
• The χ2 test is used to compare the shape of our data
distribution to a distribution of known shape
[goodness of fit]
• Good for genetics, because crosses usually produce a
population of offspring that differ with regard to
phenotypes.
Degrees of Freedom
• Degrees of Freedom: measure of the number
of categories that are independent of each
other. [typically n – 1, where n = the total # of
categories]
• Allows us to choose the appropriate
distribution for the data
X2 = 4.72
• For example, does 787 tall to 277 short really indicate a 3:1
ratio?
tall
short
observed #
787
277
expected ratio 3/4
1/4
expected # (787 + 277)3/4 = 798 (787 + 277)1/4 = 266
(O - E)
-11
+11
(O - E)2
121
121
(O - E)2/E
0.15
0.45
• X2 = 0.15 + 0.45 = 0.60
• A true-breeding cut leaf, green stem (CC pp) tomato is
crossed with a true-breeding potato leaf, purple stem (cc PP)
tomato plant. F1 is all cut and purple tomato plants.
• F1 xF1 progeny:
• X2 = 0.15 + 0.45 = 0.60
Class
Obs Exp d
Cut, purple
189
Cut, green
67
Potato, purple
50
Potato, green
14
Total
320
d2
d2/e
• A true-breeding cut leaf, green stem (CC pp) tomato is
crossed with a true-breeding potato leaf, purple stem (cc PP)
tomato plant. F1 is all cut and purple tomato plants.
• F1 xF1 progeny:
• X2 = 4.72, df = 4-1 = 3
Class
Obs
Exp
d
d2
d2/e
Cut, purple
189
180
9
81
0.45
Cut, green
67
60
7
49
0.81
Potato, purple
50
60
-10 100
1.66
Potato, green
14
20
-6
1.80
Total
320
320
0
36
X2=4.72
Restrictions of
2
χ
• O and E values must be actual counts, ie 2
can only be used with absolute frequencies;
the test is not valid if data are converted to
relative frequencies or %.
• Categories must be independent and
complete, ie a 2 test must be carried out on
the whole sample at once, not on subsets of it
at a time