I understand that, but what I'm saying is that if the number of fathers dying remains constant than the naming will gradually increase for 9 months at which point it will remain constant. If there's 100000 fathers and 1000 died a week and there is also 1000 births we would only expect 1% or 10 of those babies to have dead fathers. This means that the number of babies with dead fathers is proportional to the proportion of fathers who are dead. The next week if both numbers remained constant we would expect the number to be 2% and so on. Conversely even if fathers stopped dying there would still be a large number of births with dead fathers for several months.