Roman empire expansion dynamics from 338 BC to 116 AD

A lot of ancient civilizations has risen and fallen again, namely a few as Roman empire, Macedonia kingdom, Inca Empire, etc. To date many interesting and already available facts are known about ancient empires, but not much about their evolutionary dynamics,-for example their timeline of population or occupied area in a world. Using carefully selected information sources, in this paper I try to represent how Roman empire size has changed over time with quantitative metrics from 338 BC to 116 AD.