User:Revanche/Population Growth and BattleTech

Note: This essay was written by CBT.com forum poster Psychopompous and re-posted to those forums on 11 Apr, 2010. Added here with his permission.

In a fairly recent discussion, I found myself bringing up a point about how the nature of population growth and how population figures significantly smaller than described in the BattleTech canon could be quite realistic. I will acknowledge that it's also quite possible for much larger populations to have developed in the same time if we assume very large inter-stellar merchant fleets (we're talking probably tens of millions of JumpShips here, though) along with a much greater number of planets colonized by humanity, or a large amount of water accessible water in space to support a tremendous number of orbital habitats.

I'd like to start this discussion with the conceptual principles of population growth. These principles are the same for all living organisms and are well known to biologists, in general - some are fairly well known in the general populace. First, the population of living organisms tends to grown exponentially. There are two ways to mathematically model this growth trend, one is based on Calculus and although I understand it, I'll stick with with the other one: Percent growth per time interval (for human populations years are convenient, as with most macroscopic organisms). It's a fairly simple model, you take 1 + (the percentage growth observed, in hundredths) and raise it to the power of the number of time intervals you are considering. If the earth is experiencing 1.133% population growth (as reported for the worldwide average in 2009 by the CIA World Factbook) over a period of, say, 25 years you would take 1.01133 and raise it to the 25th power then multiply be the population you started with to get the final population (so, starting with a population of 6.8 billion, you'd get 9 billion people after 25 years at the present rate of growth).

This model does fail to account for a few things, though. Particularly the very important concept when dealing with any population of living organisms that sets an upper limit on total population regardless of the number of time intervals considered: Carrying Capacity of the environment. Living things need air, water, and especially food to live. Every environment has limited resources, and depending on the rate that those resources can be replenished, there is a maximum number of any particular type of organism that can survive in a particular environment. The mechanism controlling population growth as you approach an environment's carrying capacity is starvation. As a result, when the total population approaches this number of total living organisms, the growth rate switches from being exponential to logarithmic and the population effectively stabilizes at a fixed number. I won't explain the math to model population growth as you approach carrying capacity, it involves calculus. But as a simple approximation, you set a number to be the carrying capacity of the environment (around 90-98% of the actual theoretical maximum, depending on the rate of growth - 95% is basically good enough for my consideration here) and treat the population growth as exponential until you hit that maximum and then assume that population growth stops completely (it will be negligible in magnitude). This concept is often overlooked when considering human population growth in science fiction, and there's a pretty good reason for that: For the majority of recorded history continuing advancements in agricultural techniques have allowed humans to squeeze ever-increasing supplies of food from our environment. Our technological progress has rarely fallen behind our population growth, and when it has it's usually been fairly briefly - although devastating famines usually ensue. If you just look at the overall trend over recorded history, it seems that human population may be able to continue growing infinitely. This fails to account for evidence of a stable human population at a fairly fixed number for thousands of years prior to horticulture which allowed slow population growth for several thousand years before we have the earliest recorded history. It also fails to account for the maximum amount of energy that can possibly be collected from the sun on earth's surface and converted to usable food. There's a theoretical limit based on the amount of sunlight that strikes the earth's surface and the energy required to sustain human life - I don't know exactly what this limit is, and it's probably not terribly important anyway, I doubt we'll ever get there. But anyway, based on the limits of food-production technology, earth can only sustain so many people and to get more we'd have to start leaving earth, or shipping food to earth from somewhere else.

So, any particular planet will have a carrying capacity - a level of population that cannot be exceeded. This has some interesting repercussions on the growth of population in any science-fiction setting where humans travel the stars and colonize other planets. It means that the rate of population growth will eventually become tied to the limits of inter-stellar transportation in one way or another.

Now, to apply these concepts to BattleTech. According to most available sources the total population of humans in the Inner Sphere is approximately 6 trillion, give or take a few hundred billion. A couple of canon sources state that the population growth trend has been 0.7%, which is reasonable to generate that level of population. If you start with a population of 7 billion, and estimate final population with 0.7% annual growth over 1015 years you wind up at 8.3 trillion. Given that BattleTech is the future of the 80s, I assume they just figured a slightly lower starting population (say, 5 billion, starting a couple decades ago) to wind up with the 6 trillion figure. But, wait, that doesn't take into account the carrying capacity of individual planets. It also doesn't explain how the people got (fairly) evenly dispersed over the entirety of the Inner Sphere, especially after a large number of colonists were concentrated on a relatively small number of densely populated "core" planets fairly early on.

First, the entire base population we are examining starts on earth and needs to be moved to the other planets in the Inner Sphere over time. Of particular note, by 3025 Terra actually has less people than are currently residing on this little planet. It's possible that Earth's population was growing very early in the diaspora and as enough JumpShips and dropshuttles became available, the excess population - slightly more than the actual growth rate was transported out to mankind's various new colonies - early on it's even fairly likely that the colonization ships may have brought back food from the colonies to keep earth going. But what sort of transportation capabilities would be required to move the colonists? Well, an average is fairly easy to establish with starting and ending population numbers but the peak would likely be much higher at some intermediate time. I'll go with the average, though because it's conservative and easy to calculate. To prevent population growth on Terra by transporting people to colonies on other planets with a growth rate of 0.7% would require moving 47.6 million people every year. Now, we don't really know too much about the transport capacity of early JumpShips but since the inter-stellar economy shifted to the modern JumpShip/DropShip paradigm, it is safe to assume that the most common early JumpShips could transport less than the most common JumpShip/DropShip combination at the time of transition so assuming modern Inner Sphere JumpShips and DropShips will most likely give us a smaller number of ships than would have actually been required. I think it’s also fair to assume that the colonists would be transported in the equivalent of steerage quarters (5 tons/person), although I’d be willing to revise my figures if you guys think that some other mass/passenger is more reasonable.

Then, you be as conservative as possible in terms of the number of ships required I’ll assume for the moment or colonization ships are Star Lords with all six collars (yes, I’m use the pre-retcon stats) packed with Behemoth-class DropShips. Each Behemoth can transport around 14,790 people so each Star Lord can transport around 88,740 people. So, you allow the total human population to growth without the population on earth growing at all would require at least 537 (rounding up) ships. On the other hand, Behemoths (or other DropShips with similar cargo capacity) were not available near the time DropShips were first introduced, nor is the Star Lord an especially common JumpShip. The Invader and Merchant are by far the most common JumpShips in the Inner Sphere. And the Mule-class DropShip, aside from being more common than the Behemoth even in 3025 is more likely to closely approximate the cargo capacity of early DropShips. A Mule can only transport 1,605 people, and an Invader can only carry 3 DropShip. With these more likely numbers we get about 9,886 JumpShips required (over the entire period of 1015 years from now to 3025) to be dedicated to the sole purpose of moving people off of Terra. Of course, remember that’s just an average over time, the peak number could be much higher, twice as many is reasonably likely. A couple notes: this is just for moving people off of Terra, not including mercantile exchange of cargo, not considering re-distribution of people between the colonies yet, and assuming a roughly 1-year round-trip average so the people can be dispersed across a large area (the Inner Sphere).

Now, getting back to the idea of planetary population carrying capacity, it’s unlikely that the initial diaspora of human colonies would evenly distribute colonists and also somewhat unlikely that the population growth rate would be exactly the same on all planets in the Inner Sphere. If any planet began to approach it’s maximum carrying capacity, you would either need to start transporting those people to other colonies, or start shipping food to that planet from off-world. Since no planet in BattleTech has a canon population of over 7 billion, I’ll just assume that there’s a tendency to disperse colonists from densely populated worlds to more sparsely populated worlds. Around the initial diaspora, this re-location of colonists from one planet to another probably wouldn’t be a terribly significant concern. But it would start to become vital late in the Age of War or early in the Star League as densely populated planets approach their carrying capacity (I suspect the real carrying capacity of Earth is probably around 10-12 billion, but I mentioned before that no planet in BattleTech has a canon population of 7 billion, so I must assume that for whatever reason population growth tends to stop around 3-7 billion depending on the habitability of the planet in question), meaning you need more transports to re-distribute people among the colonies or you need to remove the colonists on densely populated planets from the base population you’re using to calculate continuing exponential growth. Towards the end of the Star League (around 2750) the fleets required to re-distribute population to sustain the existing growth rate would take a fleet of around 264,000 JumpShips (assuming a mix of Merchants, Invaders, and Star Lords that averages 4 collars per ship and assuming the average population re-location is about 2-3 jumps) carrying mule-class DropShips. Then again, the Behemoth has been introduced at this point and starting to mix Behemoths in vastly reduces the number of ships required to move people around. If we assume that by 2750 there are only twice as many Mule-size cargo DropShips as Behemoths we could cut that number to around 71,000 JumpShips. But this is the Star League and that’s manageable. Note, this is assuming only 0.7% growth up to this point resulting in a total human population of around 1.2 trillion across the Inner Sphere.

It’s as we get into the depths of the 3rd Succession War with ongoing population growth that we start to have a problem. This problem arises for three reasons: 1) Production of new JumpShips had nearly ceased after the 2nd Succession War, 2) The proportion of planets near their carrying capacity would be substantially higher with ongoing population growth, and 3) The loss of technology and infrastructure has potentially crippled the ability of many planets to sustain as large of a population as they might have been able to during the Star League. By the year 3000 you’d need around 373,000 JumpShips (with an average of 4 docking collars each carrying a mix of 2 Mules per Behemoth) to re-distribute those people to planets that can handle them. This is significantly problematic because it’s more JumpShips than have probably ever existed in the Inner Sphere at one time, and these ships are just moving people not significant amounts of cargo.

All that considered, it would be plausible to assume that population growth in the Inner Sphere effectively stopped around the 2nd Succession War with only about 1.5 trillion people. It would be reasonable to argue for a smaller number, depending on your beliefs about the size of JumpShip fleets available to the Star League for transporting/re-locating colonists. Now, we could assume that population growth was faster than 0.7% in the ~800 years between now and the fall of the Star League and that population growth effectively stopped in the 2nd Succession War – that would be fairly consistent with the whole idea of the Successor States blasting themselves back to the stone age (among other things, a stone-age technology base can’t produce nearly as much food with the same land and water as a fully modern tech-base). A 0.9% population growth rate would get us the canon population figures by the 2nd Succession War, this just means that the 373,000 JumpShips for population re-distribution is required earlier than the late 3rd Succession War. These ships would have to exist before the fall of the Star League. Personally, I find it hard to believe that many JumpShips have ever existed in the BattleTech universe but your mileage may vary. Due to canon descriptions of inter-stellar commerce, military campaigns, and particularly the effects of conscripting a few dozen merchant ships on the civilian economy I don’t see the Inner Sphere possibly having any more than 20,000 JumpShips in 3025. If we assume that the Star League had a lot more JumpShips and many were destroyed in the Succession Wars, I still find it very hard to believe that more than 100,000 JumpShips really existed (which might constrain the total population of the Inner Sphere to only around 500-600 Billion). So knowing that (conservatively) around 373,000 JumpShips would be required to achieve canon population numbers and distribution in the BattleTech universe, I consider this a point of evidence that the Population numbers should not be what they are.

One final note, though. There’s a lot of potential wiggle room in population figures. At 0.4% growth over 1000 years, you’d only end up with 1.1 trillion people (starting from Earth’s current almost 7 billion and assuming unconstrained growth), while at 1.133% growth you’d wind up with around 630 trillion. Distributing those 630 trillion people across the Inner Sphere would take, as I mentioned above an absolute minimum of 40 million JumpShips (assuming Star Lords loaded with Behemoths), and the couple of thousand inhabited planets of the Inner Sphere might have difficulty sustaining 300 Billion people each.