Where "one in three women over 35" came from
It is not from a study of modern women, and the paper usually blamed for it says the opposite.
You will have met this statistic. It is usually attributed to a 1986 paper in Science by Menken, Trussell and Larsen, and it is usually used to say that a woman who waits past 35 has a one in three chance of never conceiving.
Two things are wrong with that.
First, the number is not in that paper. What the Menken paper's own abstract says is that direct evidence cannot be obtained from modern populations, because too many couples use contraception, so historical data are exploited to yield upper bounds applicable to contemporary populations.
Upper bounds. The authors' actual conclusion reads: a woman in a monogamous union faces only moderate increases in the probability of becoming sterile (or infecund) until her late thirties.
That is close to the reverse of how the paper is used.
Second, the number that does exist comes from a computer model. A 2004 simulation reported that under natural conditions, 66% of women starting to try at age 35 would have a conception ending in a live birth within one year. The remaining 34% is where "one in three" comes from. The same model gives 84% within four years at that age.
This tool does not repeat the "one in three" figure, because the observed data are better than the modelled data and say something less frightening. But the model is real research and its four-year figures are worth knowing too. What is not defensible is presenting a simulation as though it were a count of real women, or citing Menken for a conclusion Menken did not reach.