A part of the question has been answered in an older thread.

I can't ping the person who answered because they deleted their account.

I'd like to take on an additional question, has the geography always been fairly barren or has there been substantial changes such as a river changing course that has resulted in the area being more barren now than in the past?

That is a pretty broad area and includes thousands of years of history. But we can pull similar themes: rivers, trade, and civilization.

Most importantly in my mind, water was available for irrigation. The Nile in Egypt and Tigris as well as Euphrates in Mesopotamia are huge rivers that could be used in irrigation of nearby lands. Given the vast length of these rivers, that produces a large amount of prime farmland - the Nile especially produces fertile soil when it floods its banks, leaving behind the nutrient-rich silt. Persia may not have a huge river in the same way, but still has rivers. Additionally, the Persians utilized underground aqueducts (qanats), which allowed them to transport water to their farms without the evaporation loss from outdoor plumbing. Furthermore, these peoples had access to a variety of foods: wheat, barely, peas, lentils, and other fruits, nuts, and vegetables, in addition to an extensive use of donkeys. It should be mentioned that these areas also are not total barren desert, but do have extensive arid zones conducive to grazing and occasional agriculture.

Water was why the civilizations could rise to any significant amounts of population, but trade is what really made them successful on the world stage (in addition to having the leadership to spend the income wisely). Egypt, Arabia, and Persia are at a huge crossroads of Eurasia. Foods, finished goods, and valuable metals were moving across Africa through Egypt, across Europe through Anatolia and Mesopotamia, across China and southeast Asia through India, Persia, Arabia, and Egypt. Trade seems to have been happening between civilizations since they began, but of course picked up as new seafaring methods were developed and civilizations built and maintained roads (which all these societies are known for doing). You've likely heard of the Silk Road, and this is a very real and serious contribution to the wealth of the nations along its routes. These series of trade links occurred in earnest (at least under the concept of the "Silk Road") for about 1500 years. This could obviously bring in profits, but also allowed the exchange of animals and foods (planting crops from far-off places that might suit certain previously underutilized regions, or simply provide a more balanced diet) as well as technology. Technologies and general knowledge could originate from either side of Eurasia and end up crossing in the middle. (Which isn't to say the Persians or anyone else were less intelligent or advanced, as they certainly invented things in their own right). But most of this only worked because of the correct leadership.

The bountiful rivers and the cross-continental trade sustained these civilizations for thousands of years, despite a large amount of "dead" or just less useful space as compared to say Europe. But it provided enough to give them a kickstart and let them stay ahead. You might also argue the limited agricultural space forced urbanity, which leads more quickly to a larger and stronger central state, but I'll leave that to an anthropologist.

There is also so much to be said why each society managed to succeed: their forms of government, ideas about taxes, technological advancements making them leaders of their time, etc. I would leave that to someone else who has that extensive historical knowledge to share, however.

Edit: Missed some poor grammar.

Is there an explanation for now such a rocky, mountainous area such as Iran was so heavily populated? They did not have any of the major rivers that were part of the fertile crescent AFAIK