The tie between energy supply, population, and the economy goes back to the hunter-gatherer period. Hunter-gatherers managed to multiply their population at least 4-fold, and perhaps by as much as 25-fold, by using energy techniques which allowed them to expand their territory from central Africa to virtually the whole world, including the Americas and Australia.
The agricultural revolution starting about 7,000 or 8,000 BCE was the next big change, multiplying population more than 50-fold. The big breakthrough here was the domestication of grains, which allowed food to be stored for winter, and transported more easily.
The next major breakthrough was the industrial revolution using coal. Even before this, there were major energy advances, particularly using peat in Netherlands and early use of coal in England. These advances allowed the world’s population to grow more than four-fold between the year 1 CE and 1820 CE. Between 1820 and the present, population has grown approximately seven-fold.