4. Standard phenotype classes numerical ratios in the segregation and deviations from it
There are some expedients (средство достижения цели) for testing genetic ratios: significant results choice, evaluation of sample size and degrees of freedom, calculation of chi-square test.
Significant results in biological experiments
All experiments involve finite numbers of observations and therefore some deviation from the expected numbers (sampling error) is to be waited. If there is no difference between the observed results and the expected results this can be accounted for only by chance. Hypothesis in most biological experiments is true when the deviation by chance is less than 5%. Such results are significant. When the deviation by chance is less than 1% such results are highly significant. When the hypothesis is rejected at the 5% level, we take 1 chance in 20 of hypothesis discarding. Statistics can never render absolute proof of the hypothesis, but sets limits to our uncertainty.
Sample Size
If experiment is based on small numbers, we might wait relatively large deviations from the expected values. As the sample size increases and tends to infinity the deviation should become proportionately less and tend to expected values.
Degrees of Freedom
We have n–1 degrees of freedom (df) in assigning numbers at random to the n classes within an experiment. For example, in an experiment involving 3 phenotypes (n = 3) we can fill 2 of the classes at random, but the number in the third class must constitute the remainder of the total number of individuals observed. Therefore we have 3 - 1 = 2 degrees of freedom.
Chi-Square Test
In order to evaluate a genetic hypothesis, we need a test that can convert deviations from expected values into the probability of such inequalities occurring by chance. This test must take into consideration the size of the sample and the number of variables (degrees of freedom). If the size of the sample is less than 16, segregation in the ratio 9:3:3:1 is impossible.
The chi-square test (pronounced ki-; symbolized x2) proposed by Karl Pearson (1857 – 1936) in 1901 includes all of these factors. It allows analyzing if the deviation of observed results from expected ones is random or consequential for any reason, statistically estimates the difference between empirical and theoretical expected results.
Using
the chi-square it may be established whether actually received
frequency of phenotypic classes corresponds to theoretically expect
one. Chi-square is the sum of squared deviations from the theoretical
of empirical frequencies, referred to the theoretical frequencies:
where
d2
is
squared deviations of each phenotype frequency from the theoretical
value,
means theoretical frequencies of phenotypes appearance.
To find the value of chi-square it is necessary
to calculate the difference between actual and calculated frequencies for each class,
to make a square of differences and divide it to the calculated frequencies for each phenotypic class,
to summarize the obtained relations.
If the chi-square is equal to 0, actually received frequency fully corresponds to the theoretical frequency. If the value is not 0, the table theoretical value of the standard chi-square test value for a given degrees of freedom and the chosen level of significance should be founded. If the experimental value is less than the standard, discrepancies between actual and theoretical expected frequencies are random and the null hypothesis (the assumption that between actually received and the calculated theoretical data is no significant difference) is retained; if more – rejected.
Thus, events probability that is neglected in the evaluation of the statistic parameter is expressed as accepted level of significance. Events probability when the hypothesis is true is called the confidence level.
Significance level 5% is assigned as P0.05, corresponding confidence level is P0.95. If P ≥ 0, 05 or P < 0, 95 the null hypothesis is retained, if P< 0, 05 or P ≥ 0, 95 – it is rejected.
Schaum's Outline of Theory and Problems of Genetics - William D. Stansfield.pdf
Example
If 705 pea plants have red flowers, and 224 – white, the resulting ratio of plants (3,15:1) approaches monohybrid splitting scheme (3:1). Chi-square test estimates whether obtained experimentally results and theoretically expected are the same.
The amount of plant is 929, 3/4 and 1/4 are 697 and 232. Deviation of experimental data from the theoretical value is +8 and –8, square deviation is 64. Square deviation divided by the theoretically expected value are 64/697 = 0,092 and 64/232 = 0,276. The sum of these values, i.e. chi-square is equal to 0.368. Degrees of freedom number is equal to 1, significance level is 0,05; then the table chi-square value is equal 3,84. The calculated value is less than a table one, so the experimental data are consistent with the scheme monohybrid segregation.
Number of hybrids classes by phenotype and genotype and the character of splitting in F2 with a different number of traits pairs (complete dominance)
Cross |
Number of sign pairs that are different in parents |
Num- ber of game- tes formed |
Number of possible gametes combi- nations |
Number of classes |
Ratio of phenotypic classes |
|
Pheno- typic |
Geno- typic |
|||||
Mono- hybrid |
1 |
21=2 |
41=4 |
21=2 |
31=3 |
3:1 |
Di- hybrid |
2 |
22=4 |
42=16 |
22=4 |
32=9 |
9:3:3:1 |
Tri- hybrid |
3 |
23=8 |
43=64 |
23=8 |
33=27 |
27:9:9:9:3:3:3::1 |
Tetra- hybrid |
4 |
24=16 |
44=256 |
24=16 |
34=81 |
81:27:27:27:27: :9:9:9:9:9:9: :3:3:3:3:1 |
Poly- hybrid |
n |
2n |
4n |
2n |
2n |
(3:1)n |
Causes of deviations from standard ratios:
statistical reasons, differential mortality (lethal genes), incomplete genes expression, genes interaction
Lecture 3 Cytological basis of heredity
Nucleus role in transmission of hereditary information
Plan
Nucleic acids - carriers of genetic information
Chromosomes brief characteristic
Central dogma of molecular biology
Cytogenetics as the science of chromosomes
General plan of prokaryotic and eukaryotic cell
The unique structure of mitochondria
The main differences of prokaryotic and eukaryotic cell structure
1. Nucleic acids - carriers of genetic information
It was known for a long time that chromosomes possess a unique molecular constituent, deoxyribonucleic acid (DNA), but there was not shown that this constituent carried genetic information. There weren’t direct evidences of gene chemical nature. In the early 1940s, research on the mold Neurospora by George W. Beadle and Edward Tatum supported the hypothesis of Archibald E. Garrod that genes work by controlling the synthesis of specific enzymes (the one gene-one enzyme hypothesis). Genetic information within genes determines the order of the 20 different amino acids within the polypeptide chains of proteins.
A complementary double helix was found in 1953 by Frances Crick and James Watson. In the double helix, the two DNA chains are held together by hydrogen bonds (a weak noncovalent chemical bond) between pairs of bases on the opposing strands. This base pairing is very specific: The purine adenine only base-pairs to the pyrimidine thymine, while the purine guanine only base-pairs to the pyrimidine cytosine. In double-helical DNA, the number of A residues must be equal to the number of T residues, while the number of G and C residues must also be equal (Chargaff's rules). As a result, the sequence of the bases of the two chains of a given double helix has a complementary relationship and the sequence of any DNA strand exactly defines that of its partner strand.
Chromosomes brief characteristic
Chromosome is a structural element of the cell nucleus, which is able to reproduce, and is composed of a large number of DNA and nuclear proteins of different types. The word ''chromosome'' comes from the Greek (''chroma'', color) and (''soma'', body) due to their property of being very strongly stained by particular dyes.
