Probability & genetic crosses

Question 1

What are ratios?

Answer 1

• a ratio is a measure of the relative size of two classes that is expressed as a proportion
• for example, any group of humans can be divided into two classes, male and females
• if in a group of 60 humans there are 40 males and 20 females, then the ratio of males to females is 40 to 20
• this is usually expressed as a ratio which is simplified to 2 to 1 is written 2:1
• if our group of 60 humans comprised 35 males and 25 females the ratio of males to females would be 7:5
• for easy comparisons, ratios are often obtained by dividing the value of the smallest group into the value of each larger group
• in which case, all ratios have their smallest value as open
• for example, our ration of 7:5 would be 7/5+1.4 which is written as 1.4:1

Question 2

Why are actual results of genetic crosses rarely the same as the predicted results?

Answer 2

• our knowledge of genetics tells us that for each cross we would expect that, in the F2 generation, there would be three offspring showing the dominant feature to every one showing the recessive feature
• however in no case did Mendel obtain an exact 3:1 ratio
• the same is true for almost any genetic cross
• these discrepancies are due to statistical error
• imagine tossing a coin 20 times
• I theory you would expect it to come down heads on 10 occasions
• in practice it rarely does
• this is because each toss of the coin is an independent event that is not affected by what we went before
• if the coin has come down heads nine times out of 19 tosses, these is still a 50% chance it will come down tails, rather than the head needed to complete the 1:1 ratio
• the coin does not know it is expected to come down heads
• the same is true of gazettes
• it is chance that determines which ones fuse with which
• in our cross between the heterozygote (Gg) and the homozygous recessive (gg), all the gazettes of the homozygous parent are recessive (g) whereas the heterozygote parent produces gazettes of which half are dominant (G) and half are recessive (g)
• if it is the dominant gamete that combines with the recessive one, plants with green pods are produced (Gg)
• if it is the recessive gamete the plants have yellow pods
• the larger the sample, the more likely the actual; results are to come near to matching the theoretical ones
• it is therefore important to use large numbers of organisms in genetic. Crosses if representative results are to be obtained
• it is no coincidence that the two ratios nearest to the theoretical value of 3:1 in Mendel’s experiments were those with the largest sample size, whereas the ratio furthest from the theoretical value had the smallest sample size