Uniqueness, Diversity, Similarity,
Repeatability, and Heritability
University of Illinois at Urbana-Champaign
Since the emergence of genetics following the triple rediscovery in 1900 of Mendel's (1866) classic study, there have been attempts to calculate and estimate the number of possible genotypes for a species (Sutton, 1903, pp. 24–39, 231–251). An example of such attempts isBorel (1961), which, according toH. Pieron (1962, p. 12), Borel had made as early as 1941 (see too Corcos & Monaghan, 1993, pp. 188–189; Morgan, 1934, p. 139; Wright, 1932;Snyder, 1949). I too once contributed to this literature (Hirsch, 1963). Re-examination of this work recently has revealed a previously unappreciated complexity.
I made and published the individuality calculation in an invited lead article in Science magazine 40 years ago (Hirsch, 1963) and have always been proud that my arithmetic has withstood the test of time. It was and still is correct. Nobody has succeeded in challenging it. But now, I find that I myself must challenge the interpretation that I gave to the calculation at that time, because the calculation does not answer the question I was then asking, however mistakenly at that time we all believed that it did. It answers a different question; however, as you will see, it is a related question.
My purpose now is to explain what formerly has been assumed and what must henceforth be analyzed more carefully. Formerly the situation had been analyzed in the following way: We estimated “the probability that the second offspring born to parents will have exactly the same genotype as their firstborn” to be “less than 1 chance in over 70 trillion, ” that is C/223)2 because man, with 23 chromosome pairs, produces gametes with any of 221 = 8,388,608 alternative genomes. For the second born to be identical to the firstborn, it requires both parents to produce a gamete that