As you may know, the Chinese policy that penalizes families with more than one child has led to a horrible gender-ratio imbalance as many families make damn sure their one child is a boy; consider the effect of a revised policy that would allow families to try for a boy as much as possible but then mandate no more children after that boy (it may be easier to look first at a variant of the policy that also sets a limit on the total number of children).
Another one to consider comes from
ARIS 2008, the American Religious Identification Survey: 41% of the 9% of respondents who had no religion at age 12 joined a religion by the time of the survey, while only 12% of the 81% of respondents who had a religion at age 12 had lost it by the time of the survey; the result is that the non-religious portion of the population has grown, as about 4% of respondents got religion between age 12 and the time of the survey, while 11% of respondents lost it, for a net gain of 7 percentage points for the non-religious crowd (this specific figure has questionable validity, however, because the respondents were of varying ages at the time of the survey, rather than being segregated into narrow age cohorts; the non-religious portion at survey time was 15%, which is within rounding error of what may be derived above as 9%+7%=16%).
Despite the lack of segregation into age cohorts, imagine that the above figures are valid for modeling the lack of religion among Americans from pre-adolescence to pre-middle-age; that is, 41% of people raised non-religious become religious, and 12% of people raised religious become non-religious. Absent some grander societal shift (like the one that made lack of religion tolerable beyond the educated elites in the first place), what would the stable religious and non-religious portions of the population be? It surely isn't the case that the non-religious portion increases by 7 percentage points every 30 years or so under this model; rather, as the non-religious portion increases, its rate of increase as a percentage of the population will decline until a stable proportion is reached.
This could be treated as a Markov process, but this can be greatly simplified, so that no matrix operations are needed.