A mathematical model for the dynamics of spermatozoa entry into the spermathecae of instrumentally inseminated queen honeybees

Queens were inseminated instrumentally with 1, 2, 4 or 8 mm³ of semen, killed and examined at different times up to 40 h after insemination. The number of spermatozoa (S) entering a queen's spermatheca from a given dose of semen, fitted the logarithmic function, S = a + b . 1n t (t, time). At first, the rate of increase of the number of spermatozoa in the spermatheca was high, but later, the same increase required twice as long. As time progressed, larger doses resulted in both higher absolute numbers and higher relative increases of numbers of spermatozoa in the spermatheca. The rate at which spermatozoa entered the spermatheca fitted the function dS/dt = b/t. It was highest at the beginning, and decreased by half with each doubling of time. Spermatozoa from larger doses entered the spermatheca faster, but relative change of rate with time remained the same.