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There is only minor evidence of low birth rates and only in the late Republic - early Empire and only among the aristocracy, before the Empire reached it's peak power

"Low" implying below replacement level

Replacement level is determined by infant and child mortality rates

Correlation between birth rates and population decline does not imply causation

Mortality due to plagues, famines and wars cause

* population decline and

* reduced birth rates due to reduced life expectancy of women of child-bearing age and

* increased infant and child mortality and

* increase the replacement level

Plagues, famines and wars also cause political instability, economic and military decline

In the modern world low birth rates are correlated with stronger economies, military power and political stability

The men of X need to think more about the Roman Empire