On Fisher's criticism of Mendel's results with the garden pea.

IT is generally agreed that the overall results from ratios that Mendel reports, as well as the rationale for experiments with the garden pea reported by Gregor those ratios, with the later, more limited results from Mendel (1866) conform more closely with the ratios runs with plant characters serving to determine whether theoretically expected (such as 3:1, 1:2:1, etc.) than one those characters behave in their transmission like the might reasonably expect to obtain on a chance basis. seed characters. It is not surprising that more than threeParticularly troubling are those two groups of experifourths of Mendel’s observations were made on the two ments in which Mendel’s results are in close agreement seed characters and fewer than one-fourth were made with ratios that Mendel may have considered approon all five plant characters combined. priate, but which were, according to Fisher (1936), The experiments under consideration here involve incorrect. Wright (1966, p. 174) states that these two the determination of the frequency of the genotypes in represent “the most serious evidence for fraud by Menthe phenotypically dominant class, i.e., the ratio of the del, presented by Fisher.” AA to Aa genotypes in the expected ratio of 1:2, as in Here I consider an alternative way of examining Menthe classic 1AA:2Aa:1aa distribution in the F2 of a simple del’s procedures and results in those experiments (9 of monohybrid cross. They will be considered in two parts: 24 total) and suggest that Fisher, in his detailed and illumithe 2:1 ratio and the trifactorial cross. nating analysis of Mendel’s results, may have erred in The 2:1 ratio: In crosses involving the seed characters assigning specific expectations to those runs and that of round vs. wrinkled and yellow vs. green, 1084 plants Mendel’s expectations in fact may have been closer to showed the dominant trait in the first generation (and the mark than Fisher’s. so could be either AA or Aa). When these seeds were The seven pairs of characters described by Mendel can planted and the resulting plants allowed to self-fertilize, be assigned to two distinct categories. In the first group 359 produced the dominant character only, indicating are five plant characters (length of stem, position of flowthat the parent was homozygous AA, and 725 plants ers, color of flowers, color of pods, and form of pods) produced both the dominant and recessive characters and in the second group two seed characters (round vs. on each plant, indicating heterozygosity (Aa) for an wrinkled and yellow vs. green). The seed characters reveal overall ratio of 2.02:1. the properties of the next generation on the parental Mendel tested the five different pairs of plant characplant, making it unnecessary to grow that subsequent ters. For these, it was necessary to rely on progeny tests, generation as individual plants. Since there are 30 and he specified the exact numbers to be reached in seeds per parental plant, each of those plants provides each case. He stated, “For each separate trial in the 30 independent observations on the next (unplanted) following experiments, 100 plants were selected which generation. Capitalizing on the unusual properties of displayed the dominant character in the first generathis second group of seed characters made it possible tion, and in order to ascertain the significance of this, for Mendel to reach large numbers in his experiments ten seeds of each were cultivated” (Mendel 1866, p. 12). on a relatively small plot of land. Further, since the The set of five experiments (six, counting one repeat) results from runs with seeds are available sooner than with plant characters was unusual because, to make the those from plant characters, the seed experiments, indistinction between AA and Aa plants, it was necessary volving larger numbers, would serve as the basis for the to grow a number of progeny after selfing to see if a homozygous recessive plant appeared. This, however, would happen in only one-fourth of the offspring of a 1Address for correspondence: 1690 E. 26th Ave., Eugene, OR 97403. E-mail: [email protected] heterozygote when selfed, so that the chance that any