Does population increase when famine hits? As I understand it the main brakes on population in human history have been famine and disease. The level of population that a society can support is usually based on its agriculture resources and technology. However, historically, the population would tend towards the highest level supportable, and then years with poor food producing conditions would cause famine and the population would contract.
Over the last century or so, the cycle has changed. Now societies with a food surplus don't generally see constant population growth because of two things - food production is no longer dependant on how many humans can you put to work in the fields, so there's less need for more kids to make a family's work easier (in fact, each modern child costs more effort and expense than they produce); and we have birth control and education, which allow people to make more intentional decisions about when and if they have children.
Combining a lack of incentive with the capacity to choose means that many societies have broken the population growth and contraction (ie baby boom followed by famine) cycle. This leads to different problems such as aging populations, but that's another discussion.