There is some evidence to indicate that China's one child policy has already led to such a scenario. The rationale is that Chinese people still carry the tradition that the next generation looks after the previous one, and that if you can only have one child, then have a boy because boys will be better able to care for their parents later in life.
This did not lead to biological biases per se, but rather to higher infant mortality rates among female babies. That said, the impact is the same; a much higher number of males by proportion to females of a certain age.
If you have social pressures such as this that make a culture 'prefer' a specific gender, then prospective mothers will find other ways to make sure that they have a better chance of conceiving such a gender.
There are many herbal remedies already available that are believed to assist with gender selection; pH levels in the uterus are supposed to have an impact, and of course rhythm method can improve your odds if you want to conceive a specific gender (I won't go into the science or beliefs behind any of these as they are out of scope of the question).
Ultimately, while it's possible things as simple as diet could have a material impact on birth genders, the first pressure is likely to be social in nature and such pressure, combined with human ingenuity, will lead to a material outcome as has already been demonstrated in places like China.