Experiments in Plant Hybridisation, by Gregor Mendel,
edited by J.H.Bennett,
published by Oliver & Boyd, Edinburgh, 1965.
Mendel's first series of experiments were concerned with demonstrating
the 3:1 segregation ratio when F1 hybrids are crossed. That is, he first
took two "pure lines" of plants, (e.g. one with red flowers, the other with
white). The F1 hybrid plants are all red, since red is dominant to white.
So these F1 hybrids have the heterozygous RW genotype. When they are
crossed with each other, each of the F2 offspring has probability 3/4 of
having red flowers and 1/4 of having white flowers, independently for each
offspring plant.
Mendel did seven such experiments; four are summarized here:
1. 253 F1 plants produced 7324 seeds,
5474 were round and 1850 were wrinkled (ratio 2.96:1).
2. 258 F1 plants produced 8023 seeds,
6022 were yellow and 2001 were green (ratio 3.01:1)
3. Among 929 F2 plants, 705 had red flowers and 224 had white flowers
(ratio 3.15:1)
4. Among 580 F2 plants, 428 had green pods and 152 had yellow pods
(ratio 2.82:1)
Note that, where the F2 plant has to be grown to see its characteristics, Mendel had a smaller sample (experiments 3 and 4), whereas when he could see the characteristic in the seed, he could sample as many as 8000 (experiments 1 and 2). Note that where the samples are largers, the proportion of the dominant type is closer to 3:1, as we expect (but remember also that as samples get larger we expect the difference in number from the expectation to get larger).
As shown in class, we can, in principle compute the probability for any particular count k of the dominant type, out of the total n, when each of the n has probability 3/4 of being of that type. Hence we can compute (given a good calculator, or a computer) the probability that someone doing Mendel's experiment would get as close as he got, or closer, to the expected 3:1 ratio. This summarizes the result of that:
Expt n k expected=3n/4 diff P(diff this small) [approx.] -------------------------------------------------------------- 1 7324 5474 5493 19 0.38 2 8023 6022 6017 5 0.10 3 929 705 697 8 0.46 4 580 428 435 7 0.5 ----------------------------------------------------------------None of these probabilities is VERY small, but in every case Mendel did better than 50-50 chance in getting close to the 3:1 ratio he expected. In his other experiments also, his results are a bit "too good".
Now as his second series of experiments, Mendel took the F2
plants, and tried to decide their genotype. To do this, he crossed each
plant with itself (one can do this with peas!). He grew up 10 offspring
plants from each. If all 10 had the same phenotype, he decided the
parent plant was homozygous. If not all 10 are the same, the parent
has to be heterozygous.
When he "selfed" the white F2 plants, each produced only white flowers,
and he concluded correctly that these were all WW genotype.
When he "selfed" 600 red F2 plants, 201 produced 10 offspring
all with red flowers, and 399 had some red-flowering and some white-flowering
among the 10 offspring grown.
Mendel was happy, as his theory predicted (correctly), that among the
red-flowering F2 plants, 1/3 should be RR, 2/3 should be RW.
He expected 200 would be RR. The probability of a result this good
(that is of getting 199, 200 or 201 out of 600, when the probability for
each is 1/3) is only 0.06. Again Mendel was very lucky.
Or was he?
He made a mistake here. Even if a selfed plant is RW, its first 10 offspring are all red with a non-negligible probability. Each is red with probability 3/4, and (3/4)^10 is about 0.056. So Mendel should have seen about 37% of his selfed F2's producing all 10 red offspring, not 1/3 or 33% (we'll see later exactly where this 37% comes from). So then the corrected expectation is 0.37*600 or 222, and his results differed from this by 21. A probability of a difference THIS LARGE is only about 0.075.