The Galton Laboratory, University College London, Wolfson House, 4 Stephenson Way, London NW1 2HE, UK
Dear Sir,
In a recent paper (James, 2000), I gave grounds for suspecting that P, the probability that a birth will be male, is simultaneously subject to two forms of variation, i.e. within (Poisson variation) and across (Lexis variation) couples. These two forms of variation have countervailing influences on the correlations between the sexes within sibships. These latter are roughly zero (Maconochie and Roman, 1997
; Jacobsen et al., 1999
). In other words, there is the appearance of binomial sampling. Nevertheless, in my paper I cited evidence that there is a substantial (but unquantified) measure of Lexis variation. If this were so, then a comparable measure of counter-balancing Poisson variation must exist (to account for the near-zero correlations between the sexes within sibships). However, I was unable to offer persuasive external evidence for this, relying lamely on the assertion that steroid hormones vary substantially `within couples (Kemper 1990
) (thus ex hypothesi causing the chaotic Poisson variation' (James, 2000
; p. 1186).
It now seems that though this argument is modestly true, it may be powerfully supplemented. In that paper, I distinguished between `systematic' and what I called `chaotic' Poisson variation. I suggested that only the latter is of substantial magnitude. A major cause of this chaotic Poisson variation would seem to be that as a woman proceeds through her reproductive life, ovulation switches randomly from one ovary to the other (Fukuda et al., 2000). These authors also reported that the right ovary is associated with higher oestrogen and testosterone concentrations than the left. And in conformity with my hypothesis (James 1996
), these are responsible for the substantially higher sex ratios reported to be associated with right-sided ovulations (Schoner, 1927
). Let Pi be the probability that woman i will have a son. Then following right-sided ovulations Pi will be high, and following left-sided ovulations, Pi will be low.
Alternatively, one may think of a woman's ovaries as two urns, the right one being associated with an excess of male zygotes, and the left one with an excess of female zygotes. Students of probability theory are often taught in terms of urns containing balls of different colours. Only occasionally (as here) does the image seem remotely life-like.
References
Fukuda, M., Fukuda, K., Andersen, C.Y., and Byskov, A.G. (2000) Right-sided ovulation favours pregnancy more than left-sided ovulation. Hum. Reprod., 15, 19211926.
Jacobsen, R., Moller, H. and Mouritsen, A. (1999) Natural variation in the human sex ratio. Hum. Reprod., 14, 31203125.
James, W.H. (1996) Evidence that mammalian sex ratios at birth are partially controlled by parental hormone levels at the time of conception. J. Theor. Biol., 180, 271286.[ISI][Medline]
James, W.H. (2000) The variation of the probability of a son within and across couples. Hum. Reprod., 15, 11841188
Kemper, T.D. (1990) Social Structure and Testosterone. Rutgers University Press, London, UK.
Maconochie, N. and Roman, E. (1997) Sex ratios: are there natural variations within the human population? Br. J. Obstet. Gynaecol., 104, 10501053.[ISI][Medline]
Schoner (No initial). (1927) Besteht eine Bezichung zwischen dem Geschlechte und der Seite des Corpus-luteum-Sitzes? Schweiz. Med. Woch., Basel, 8, 953954.