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

If you look at Table 1, you will see the results that Gregor Mendel actually obtained in his experiments. 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 of almost any genetic cross. These discrepancies are due to statistical error. Imagine tossing a coin 20 times. In theory you would expect it to come down heads on 10 occasions and tails on 10 occasions. In practice it rarely does - try it. This is because each toss of the coin is an independent event that is not affected by what went before. If the coin has come down heads nine times out of 19 tosses, there 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 gametes. It is chance that determines which ones fuse with which. In our cross between the heterozygote (Gg) and the homozygous recessive (gg), all the gametes of the homozygous parent are recessive (g), whereas the heterozygote parent produces gametes 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 (Table 1).