Summary. The value of Poisson distribution theory in describing and predicting the nature of sperm—egg interaction in vitro has been investigated using an interspecific in-vitro fertilization system, incorporating zona-free hamster oocytes and human spermatozoa. The frequency distribution of polyspermic oocyte penetrations in 72 experiments exhibited good agreement with the Poisson distribution at all levels of fertilization, indicating that each oocyte must be of equal penetrability and that there can be no block to polyspermy in this interspecific system. Poisson distribution theory also accurately described the relationship between oocyte penetration and sperm motility in 50 out of 54 separate experiments spread across 10 serial dilution curves. For each dilution series the shape of the fitted curve was fixed but its location along the x-axis varied from donor to donor. The fixed nature of the relationship between sperm motility and egg penetration enables the results of such in-vitro fertilization experiments to be corrected for the number of motile spermatozoa in the incubation media. On the basis of these findings a protocol is described for assessing the results of the zona-free hamster oocyte penetration assay, which involves analysis of the degree of polyspermy followed by the application of Poisson distribution theory to correct the results to a standard concentration of motile spermatozoa. Changes in the penetrating ability of human spermatozoa after vasectomy and characterization of the degree of inter-ejaculate variation in penetrating potential are two clinical examples of such analyses given in the text. The statistical methods described in this paper should also be of general relevance to the study of fertilization mechanisms, in providing a rationale by which to analyse the quantitative nature of sperm—egg interaction in vitro.
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