Numeracy: formulas and ratios

Question 1

In the three point cross, how is the distance between two loci determined?

Answer 1

Map distance (cM) = (number of recombinants/total) * 100

Question 2

In the three point cross, how is the coefficient of interference determined?

Answer 2

Coef. interference = 1 - C

Where C is the coefficient of coincidence:

C = observed DR freq/expected DR frequency

Question 3

In order to calculate the coefficient of coincidence, how is the expected freq DR determined?

Answer 3

e. g if you have the loci “cv ct ve”, and cv-ct = 0.064, ct-ve=0.132 and total number of offspring = 1448,
(0. 064*0.132)*1448 = 12 DR

Question 4

What formula relates the number of loci to the number of phenotypic classes?

Answer 4

2n+1

where n is the number of loci

Question 5

What formula gives

a) number of possible P gametes
b) number of F2 genotypes
c) number of F2 phenotypes (with simple dominance)

Answer 5

a) 2ⁿ
b) 3ⁿ
c) 2ⁿ

Question 6

What is the arithmetic weighted mean?

Answer 6

w: number of individuals in each category
x: value of each category
e. g

Imagine a popula/on of twenty people, with the following heights;

One 1.4m, two 1.5m, two 1.6m, three 1.7m, five 1.8m, four 1.9m, two 2.0m, one 2.1m

Mean is

(1 x 1.4) + (2 x 1.5) + (2 x 1.6) + (3 x 1.7) + (5 x 1.8) + (4 x 1.9) + (2 x 2.0) + (1 x 2.1) /20

= 35.4/20 = 1.77m

Question 7

What is the variance?

Answer 7

sum of (squared deviations from the mean*f)/ n

n being number of individuals

f is the number of individuals for each value (n is sum of f)

Question 8

What is the standard deviation?

Answer 8

square root of the variance

Question 9

What is heritability?

Answer 9

It is the proportion of total variation in the population that is due to genetic variation. Proportion of total phenotypic variance which is due to genetic varianche:

H²= Vg/Vp

Question 10

What is the formula for broad sense heritability?

Answer 10

Note: Vp takes into account the interaction between gene and environment present in phenotypic variation, and by extension the norms of reaction (pattern of phenotypic expression of a single genotype across a range of environments, e.g Achillea)

Question 11

What is the formula for narrow sense heritability?

Answer 11

Question 12

What can Vg be subdivided into?

Answer 12

Vg = Va + Vd + Vi

Va: additive variance

Vd: dominance variance

Vi: interaction variance

Question 13

What does a high narrow sense heritability imply?

Answer 13

Rapid response to selection

Question 14

What is a good way of measuring heritability? Why?

Answer 14

Correlation between relatives. If a given character has a genetic basis, there will be closer correlations between relatives than among unrelated individuals.

In other words: since relatives have gene sin common, comparing the extent to which a phenotype is correlated to the extent to which genes are shared (corr coeff) is hence a measure of heritability.

However, this might not be definite proof that the trait is heritable! It might just be familial, like Pellagra

Question 15

What is covariance?

Answer 15

Tendency of two variables to vary together.

x: height fathers
y: height sons

Question 16

What is th formula for the correlation coefficient?

Answer 16

Question 17

What is the formula for F, the coefficient of inbreeding?

Answer 17

Question 18

What is regression to the mean?

Answer 18

In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and, paradoxically, if it is extreme on its second measurement, it will tend to have been closer to the average on its first.

In genetics: tendency of sons to be closer to the mean than parents (Galton)

Question 19

What is the formula for R, the response to selection?

Answer 19

R = h²S, where:

S = Selection differential

R = Response to selection

h2 = Narrow sense heritability

Question 20

How is R, the response to selection, calculated?

Answer 20

R = (Mean _{next generation} - Mean _population)

Question 21

How is S, the selection differential, calculated?

Answer 21

S = (Mean _{selected individuals} - Mean _population)

Question 22

What is another way of working out the number of loci involved in the expression of a phenotypic trait (other than 2n+1)?

Answer 22

(1/4)ⁿ

take proportion of individuals expressing either of the two extreme P1 phenotypes and equate it to(1/4)ⁿ, where n is equal to the total number of polygenes involved in the trait (loci)

Question 23

In a HW population, what is the freq_{next generation} for an allele q with a selective value of 0?

Answer 23

q/1+q

Question 24

What is the HW equation for genotype frequencies?

Answer 24

p² + q² + 2pq = 1

Question 25

What is the HW equation for allele frequencies?

Answer 25

p + q = 1

Question 26

What are

a) p²
b) q²
c) 2pq

Answer 26

a) freq(AA)
b) freq(aa)
c) freq(Aa)

Question 27

What are the assumptions of a HW population?

Answer 27

1. Individuals of all genotypes have equal rates of survival and equal reproductive success (no NS)
2. No new alleles are created or converted from one allele into another by mutation
3. Individuals do not migrate in or out of the population
4. The population is infinitely large, which in practical terms means that the populatio is large enough that sampling errors and other random effects are negligible
5. Individuals in the population mate at random

Question 28

What factors modify a HW equilibrium?

Answer 28

• Mutation
• Migration
• NS
• Assortative mating
• Genetic drift
• Inbreeding

Question 29

What effect does population size have on the likelihood of HW ratios being followed?

Answer 29

The larger, the more likely, as sampling errors and other random effects are reduced.

Extent of genetic drift (i.e importance of sampling erro) depends on population size:

pop variance given by pq/N

N: population size

thus, it is larger for

a) intermediate gene frequencies
b) small populations

Question 30

What is the formula for the harmonic mean and why is it useful?

Answer 30

Important because it takes into account any bottleneck, past or present, which may have had drastic effects: harmonic mean takes into account N over time, as it takes account of extreme disparities