Application of a Poisson-gamma model to study the influence of gamete concentration on sperm-oocyte fusion in the zona-free hamster egg penetration test

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Abstract
Summary. A Poisson–gamma distribution model has been developed for studying sperm–oocyte interaction in the zona-free hamster egg penetration test. With the aid of this model we have analysed the relationship between the penetration results achieved with semen of normal fertile men and the concentration of spermatozoa and oocytes used in the assay. From this analysis we have drawn up reference tables estimating the number of spermatozoa and occytes which must be present in the assay for the result to represent a significant (P < 0·05) decline in sperm function relative to the normal fertile population. Since there is, as yet, no fixed protocol for the penetration assay, these tables have been constructed to fit a range of methodologies varying with respect to the nature of the preincubation phase and including (a) a 7-h preincubation in Medium BWW, (b) a 3-h preincubation in hyperosmotic Medium BWW or (c) a 3-h preincubation in the presence of A23187.