Interstellar Colonization
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"New World". Artwork by Frank Frazetta
Planting a Colony
Colonization is fairly straightforwards, though things can turn nasty if the new planets already have natives.
But there are other troubling problems with the concept of colonization, at least for interplanetary non-FTL non-interstellar colonization. Rick Robinsion presents the issues in a cogent manner here on his blog. Go read it right now, I'll wait.
I'd give you some tid-bits of Rick's commentary, except I'd wind up copying his entire essay.
If your universe contains faster-than-light starships that can visit a new colony planet every afternoon (including week-ends), then establishing a colony is relatively easy. Dump your colonists on the new planet with tents, MREs, and first-aid kits. Then ship in supplies as they need it.
If your universe only has slower-than-light starships such that a new colony will be lucky to see a ship every hundred years, then of course things become much more difficult. If the colonist have forgotten some vital machine, an unstoppable alien plague pops up, or other cosmic disaster strikes, the mother planet cannot do much more than send sympathetic radio messages to the soon to be extinct colony.
What is the minimum number of colonists? For genetic reasons, if the number of colonists is too small and no new colonists arrive via starship, the colony will eventually die out due to inbreeding. This is important on a slower-than-light starship colony mission were every microgram is expensive, you do not want to waste payload mass on unnecessary colonists, and follow-up missions are unlikely. However this is a non-issue with FTL starships bringing new immigrants every week, the new colonists will quickly swell the colony size large enough to avoid genetic problems.
The minimum number of colonists also applies to a Generation starship, which is after all sort of a traveling colony.
If you do not want to fiddle with math below, the bottom line is as follows. If the colony is to survive inbreeding for up to 100 years, you'll need a minimum of 500 randomly chosen colonists or 50 hand-picked colonists all who are unrelated and of breeding age. If the colony is to have enough genetic diversity to survive for thousands of years, you'll need a minimum of 5000 randomly chosen colonists or 500 hand-picked colonists all who are unrelated and of breeding age. That's if I have not made a silly mistake in arithmetic. Now you can skip to the next section.
Most researchers use a rule of thumb invented by Franklin and Soule called the "50/500" rule. The "50" comes from Franklin (Franklin, "Evolutionary Change in Small Populations", 1980) and the 500 comes from Soule (Soule, "Thresholds for Survival: Maintaining Fitness and Evolutionary Potential", 1980). The 50 and 500 are values for a variable called Ne, the "Effective Population Number" (Kimura and Ohta, "Effective Population Number", 1977).
Ne = (4 * M * F) / (M + F)
where
- Ne = Effective Population Number
- M = number of unrelated, breeding-age (UBA) males
- F = number of unrelated, breeding-age (UBA) females
You will please note that if M and F are equal, the equation simplifies to Ne = M + F, which is kind of obvious.
If M is approximately equal to F, a rule of thumb is that both will be equal to about 10% to 20% of the total population, if the population is a random sample. If the population is nothing but hand-picked colonists, M and F could be 50% of the total population (i.e., the entire population is nothing but unrelated breeding-age males and females).
The larger Ne is, the better. The equation implies that Ne is reduced if there is a large difference between the number of UBA males and UBA females. Ne is also reduced by variations in the number of offspring per female, overlapping generations, and fluctuations in the population from generation to generation.
Franklin calculated that to avoid genetic inbreeding problems in the short term (100 years) Ne had to be a minimum of 50.
f = 1 / (2 * Ne)
where
- f = Inbreeding coefficient per generation
- Ne = Effective Population Number
Domestic animal breeders will accept f = 0.01 (inbreeding rate of 1% per generation), solving for Ne reveals Franklin's value of 50. The colony will experience significant viability problems due to inbreeding when f rises to 0.1, and the colony will probably die out when f reaches 0.5 to 0.6. The life-span of the colony before inbreeding caused extinction is (according to Soule)
t ~ 1.5 * Ne
where
- t = number of generations til extinction
- Ne = Effective Population Number
The number of years in a generation is more or less the average age of a female when she bears her first child. Probably about 25 years.
So a colony with f = 0.01 should last about 75 generations (1875 years), f = 0.1 will last 7.5 generations (190 years) and f = 0.6 will last about 0.8 generation (20 years)
In the long term Franklin figures you'll need Ne to be about 500. The idea is that you need to maintain enough overall genetic variability to evolve in step with the changing environment. Below 500 Franklin says "genetic variance for complex traits is lost at a significantly faster rate than it is renewed by mutation."
Ne can be achieved with a lower number of UBA male and females if a stockpile of frozen fertilized ova is available for host mothers. In Andre Norton's novels, such a hosted baby is called a "duty child." Breeding-age females will be obligated by the colony by-laws to bear one or two of these duty children in order to increase the genetic diversity of the colony. Soren Roberts notes that modern liberated women nowadays will be highly resistant to bearing duty children, and suggests that artificial wombs be employed instead. This will also help with the problem of couples who are infertile, non-heterosexual, or transgendered. Ne can also be effectively increased by such draconian measures as colony authorities enforcing a mandatory reduction in variations on family size, enforcing an equal number of male and female births, forbidding inbreeding, or through deliberate half-sibling or first cousin breeding (this can paradoxically increase effective Ne, but only after 16 generations). Such draconian measures can almost double Ne.
A colony has to rapidly boot-strap a technological infrastructure. While this is underway, the colony will have to use whatever primitive technology that can be supported, such as horses.
Marcin Jakubowski has a vision: an Open-sourced blueprint for civilization. He and the people at Open Source Ecology are trying to develop what they call a Global Village Construction Set (GVCS). This is a a modular, DIY, low-cost, open source, high-performance platform that will allow a small community to build a small, sustainable civilization with modern comforts. It is more or less a "civilization starter kit". It seems to me that this would also work admirably as technology seed package for an interstellar colony.
The GVCS is a set of fifty machines that support each other, allowing a a technolgy base to be grown and maintained. Each of these machines relies on other machines in order for it to exist. The various components designed to have the following properties: Open Source, Low-Cost, Modular, User-Serviceable, DIY, Closed-Loop Manufacturing, High Performance, Heirloom Design, and Flexible Fabrication. There is a list of the fifty machines here. In the links below, the interesting part of the description is the "product ecology." This is a table showing From (which of the other machines are used to build the machine in question), Uses (which of the other machines are needed to run the machine in question, and required feed stocks), Creates (the output of the machine), and Enables (the industries and other machines that are enabled by this machine).
| HABITAT | |
| CEB Press | produces Compressed Earth Blocks (CEB) from onsite soil |
| Cement Mixer | |
| Dimensional Sawmill | pattern-cuts lumber |
| AGRICULTURE | |
| Tractor | |
| Bulldozer | |
| Universal Seeder | |
| Hay Rake | |
| Backhoe | |
| Microtractor | a small, 18 hp version of the full-sized tractor |
| Rototiller and Soil Pulverizer | |
| Spader | |
| Hay Cutter | |
| Trencher | |
| Bakery Oven | cooks bread |
| Dairy Milker | |
| Microcombine | small-scale harvester-thresher |
| Baler | compresses hay and other dispersed material into bales |
| Well-Drilling Rig | a device for digging deep water wells |
| INDUSTRY | |
| CNC Precision Multimachine | for milling, lathing, drilling to make precision parts |
| Ironworker Machine | cuts steel and punches holes in metal |
| Laser Cutter | |
| Welder | |
| Plasma Cutter | |
| Induction Furnace | |
| CNC Torch/Router Table | cuts precision metal parts using a plasma torch |
| Metal Roller | shapes metal bar stock |
| Rod and Wire Mill | |
| Press Forge | |
| Universal Rotor | a tractor-mounted rotor that can be fitted with a wide array of toolheads |
| Drill Press | |
| 3d Printer | Manufactures objects by additive technology |
| 3d Scanner | Can scan an object and generate a blueprint suitable for a 3d Printer or CNC Precision Multimachine |
| CNC Circuit Mill | CNC (computer numerical control) mill produces electrical circuits by milling and drilling copper-clad circuit boards |
| Industrial Robot | a robotic arm which can perform certain human tasks — such as welding or milling |
| Chipper/Hammermill | |
| ENERGY | |
| Power Cube | a multipurpose, self-contained, hydraulic power unit that consists of an engine coupled to a hydraulic pump |
| Gasifier Burner | a clean and efficient burner that gasifies the material that is being burned prior to combustion |
| Linear Solar Concentrator | produces heat or steam from solar energy |
| Electric Motor/Generator | turns electricity into torque and vice-versa |
| Hydraulic Motors | |
| Nickel Iron Batteries | |
| Modern Steam Engine | |
| Steam Generator | |
| 50 kW Wind Turbine | Generates 50 kW of electricity from wind power |
| Pelletizer | |
| Universal Power Supply | |
| MATERIALS | |
| Aluminum Extractor from Clay | dissolves aluminum from aluminosilicate clay, then extracts it by electrolysis |
| Bioplastic Extruder | extrudes plastic stock into various forms |
| TRANSPORTATION | |
| Simplified Automobile | |
| Simplified Truck |
During the early years of a colony's development, GAILE provides the basic industrial equipment necessary to the survival of a modern society. This equipment varies from one colony to the next depending upon such factors as climate, landing sites, terrain, mineral and food sources available, and the general development plan formulated by the pioneers themselves. The following is a typical list of items GAILE might provide:
1. A gigawatt torroidal fusion core power plant
2. A computer complex including data files containing all of Human knowledge
3. Basic seed crops for up to ten years food supply
4. Cell banks containing fertilized eggs of domestic animals
5. A biolaboratory for analysis of native life, control of disease and the development of food sources better adapted to the new environment
6. Automining and refining equipment for the production of industrial materials
7. Factory equipment capable of producing, on a limited basis, all forms of mechanical and electronic equipment up to and including computer master switching centers and class one robots
8. A few antigravity vehicles for local transportation of people and goods
9. Modular sections which also can serve as temporary housing for new immigrants are carried on GAILE's starships
With this basic equipment and the knowledge stored in their central computer, pioneers have been able to construct modern industrial societies from wilderness within 100 years.
'An entirely old one, rather. The Tyranni are destroying the right of twenty billion human beings to take part in the development of the race. You've been to school. You've learned the economic cycle. A new planet is settled' - he was ticking the points off on his fingers - 'and its first care is to feed itself. It becomes an agricultural world, a herding world. It begins to dig in the ground for crude ore to export, and sends its agricultural surplus abroad to buy luxuries and machinery. That is the second step. Then, as population increases and foreign investments grow, an industrial civilization begins to bud, which is the third step. Eventually, the world becomes mechanized, importing food, exporting machinery, investing in the development of more primitive worlds, and so on. The fourth step.
'Always the mechanized worlds are the most thickly populated, the most powerful, militarily - since war is a function of machines - and they are usually surrounded by a fringe of agricultural, dependent worlds.
'But what has happened to us? We were at the third step, with a growing industry. And now? That growth has been stopped, frozen, forced to recede.
It would interfere with Tyrannian control of our industrial necessities. It is a short-term investment on their part, because eventually we'll become unprofitable as we become impoverished. But meanwhile, they skim the cream.
'Besides, if we industrialized ourselves, we might develop weapons of war. So industrialization is stopped; scientific research is forbidden. And eventually the people become so used to that, they lack the realization even that anything is missing. So that you are surprised when I tell you that I could be executed for building a visisonor.
'Of course, someday we will beat the Tyranni. It is fairly inevitable. They can't rule forever. No one can. They'll grow soft and lazy. They will intermarry and lose much of their separate traditions. They will become corrupt. But it may take centuries, because history doesn't hurry. And when those centuries have passed, we will still all be agricultural worlds with no industrial or scientific heritage to speak of, while our neighbors on all sides, those not under Tyrannian control, will be strong and urbanized. The Kingdoms will be semicolonial areas forever. They will never catch up, and we will be merely observers in the great drama of human advance.'
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When Worlds Collide -
When Worlds Collide
What's In The Neighborhood?
If you are mapping your empire, you will need to figure some sizes. If you decide upon the empire's radius and want to know how many stars and stars with Terran-type planets, use the rules of thumb:
Nstars = Rly^3 * 0.01
NhStars = Rly^3 * 0.0022
where
- Rly = empire radius in light years
- Nstars = number of stars
- NhStars = number of stars with human habitable planets
If you decide upon the number of stars in the empire and want to know it's radius:
Rly = cubeRoot(Nstars * 97)
Rly = cubeRoot(NhStars * 464)
(If your calculator does not have a cube root button, you can use the "Xy" button instead. Type in the number, hit Xy, type in 0.333333333 then hit the equal button.)
Note: the above equations are based upon the work of Jill Tarter and Margaret Turnbull. They were not trying to figure out which stars could host a human habitable planet. They were trying to figure out which stars could host a planet that was not so hideously uninhabitable that no possible form of life could live there. In other words, many of these planets could host alien life forms but would quickly kill an unprotected human being.
If my slide rule isn't lying to me, this works out to an average distance between adjacent stars of 9.2 light years, and an average distance of 15.4 light years between adjacent habitable stars.
In his Flandry of Terra novels, Poul Anderson specified that the Terran Empire was four hundred light years in diameter. How many stars will it probably have? A sphere 400 light years in diameter has a 200 light year radius. 200^3 * 0.01 = 8,000,000 * 0.01 = 80,000 stars. Anderson cites a figure of about four million stars, which means one of us is a bit off the mark (probably me).
You have decided that the NeoRoman Star Empire will contain 10,000 habitable planets. How wide is it? cubeRoot(10,000 * 464) = cubeRoot(5,643,000) = 167 light years radius = 334 light years in diameter.
Note that these rules of thumb were derived by me using an analysis of the Habcat database, and thus could be wildly inaccurate. If you can find better figures, use them, but these are better than no figures at all.
Rate of Expansion
Once you have decided that your Terran Empire is X number of light years wide or contains Y number of stars, it would help to have a realistic number for the amount of years it will take for the empire to expand to that size. Or from the other side, if you have decided how long the empire has been around, it would help to be able to figure out how many stars and how wide it is. This is a little more difficult.
The SETI scientists are always fretting about the Fermi paradox. As a result, there have been a couple of attempts to model the speed of galactic colonization by a hypothetical alien race. These can be used, keeping in mind that they always assume slower-than-light starships. Such models have inhabited planets colonizing nearby worlds. When the population of the colonies grows large enough, they send out their own colonization missions.
A comprehensive but mathematically intensive model is Burning the Cosmic Commons by Robin Hanson. Another interesting model is Computer Simulation of Cultural Drift: Limitations on Interstellar Colonisation by William Sims Bainbridge. I would like to explain how to use them, but I'm still trying to digest the models myself.
Newman & Sagan
Newman & Sagan (Galactic civilizations; population dynamics and interstellar diffusion. Icarus, 46, 293-327) attempted to apply the gas diffusion equation to interstellar migrations.
∂P/∂t = αP (1 - P/Ps) + γΔ2 ∂/∂x (P/Ps ∂P/∂x)
where
- P = population of a settlement
- Ps = the carrying capacity of a settlement
- t = time
- x = spatial coordinate
- α = local population growth rate (percentage of current population)
- γ = emigration rate (percentage of current population)
- Δ = mean separation of settlements
- ∂ = partial differential (Yes, I know. Scary Calculus. But don't panic)
The solution to the equation is:
P/Ps = 1 - exp((x - vt) / L)
where
- L = Δ sqrt(2γ / α) = gradient length scale
- v = sqrt(αγ / 2) = wave speed
However, when Newman and Sagan analyzed the problem, they came to the belated realization that the local growth rate (α) greatly exceeds the emigration rate (γ) so that L <<Δ. Translated into English, this means that the galactic colonization resembled an explosion more than it did a slow gaseous diffusion. Which means the equation is worthless for this purpose. Back to the drawing board.
Eric M. Jones
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Artwork by Wally Wood
Eric M. Jones found a more promising approach. In Discrete calculations of interstellar migration and settlement( Icarus Volume 46, Issue 3 , June 1981, Pages 328-336. Costs $15 for the article) he uses a Monte Carlo simulation (i.e., rules are established then a lot of dice are metaphorically thrown). Jones found the following equation will approximate the Monte Carlo results:
v = Δr/ [(Δ/vs) + (1/α) ln(2α/γ)]
where
- Δr = average radial distance traveled (i.e., distance as meaured from the center of the empire)
- Δ = average distance traveled
- vs = ship speed
- Δx/vs = average travel time (years)
Jones says one can usually assume that Δr = 0.7Δ and neglect the travel time, resulting in:
v = 0.7αΔ / ln(2α/γ)
Assuming the mean separation between settlements (Δ) is 7.2 light years (2.2 parsecs), local population growth rate (α) is 10-3 per year, and the emigration rate (γ) is 10-4 per year, this means the colonization wave will travel at about 2 x 10-3 light-years per year (5 x 10-4 parsecs per year). This would colonize the entire galaxy in a mere 60 million years.
The emigration rate could become much larger. In the 1840's the great Irish emigration reached a whopping 0.01/year. The population of Ireland at the time was about four million, so the emigration was an incredible 40,000 per year or about one hundred per day.
Using the upper equation, with my figure of 8.3 light years for Δ, and a slower-than-light ship speed of 10% c, I figure an expansion wave speed of 1.93 x 10-3 light-years per year. Unfortunately, upping the speed of the ships has little effect. At 50% c it's 1.97 x 10-3 ly/yr, at 100 c it's still 1.97 x 10-3 ly/yr, at ten times the speed of light it's 1.98 x 10-3 ly/yr, and at one thousand times the speed of light it is still 1.97 x 10-3 ly/yr!
At this speed, it would take about 50,000 years to expand to a 100 light year radius empire, which seems like an overly long time to me.
But maybe not. Mr. Jones is talking about a population growth of 10-3 or 0.1% per year. The United States has a growth rate closer to 0.6%, and some nations are crowding 3.0%. If our empire had a growth rate α of 0.6% and a modest emigration rate γ of 10-4 per year, it could reach 100 light years in radius in about 6900 years. And if it had a draconian γ of 10-2, it could reach that size in a mere 260 years.
Comments
Issac Kuo questions the assumptions contained in Eric M. Jones's model:
One thing I don't like about these models is that they tend to be based around "average" trip distances and speeds. However, the rate of expansion will be determined by the "pioneering" trip distances and speeds.
The sorts of interstellar propulsion I find plausible involve an incredible amount of initial investment and economic buildup, but then the marginal costs for additional colonization missions are small. This suggests that the third generation of colonization missions might as well be long range missions. The second generation of colonies will have saturated the nearby systems so the only direction to expand is into long range missions.
For example, suppose it takes 5000 years to build up from an initial colony into something that can send out missions of their own. In the meantime, the home system could be sending out colonization missions at a rate of one per decade. By the time the first generation of colonies is up for sending out colonization missions, the nearest 50 systems have already been colonized. The first generation then sends colony ships to fill out the nearest 2500 systems.
Assuming no one has yet bothered to try any long range colonization missions, the result is a compact ball of 2500 colonized systems, of which only a thin shell on the outside can expand with short range missions.
It seems to me plausible that at least some of the "core" systems will embark on long range missions. Maybe some of those long range missions will merely just barely outrun the expanding border. That's a rather short-sighted strategy. Other long range missions will daringly punch across the galaxy, starting up seeds which won't run into the "slowpoke" border for dozens of millenia.
The result is an overall frontier of expansion that is defined by sporadic long range "seed dots". They fill out eventually, but it's entirely plausible for the overall rate of expansion to be entirely defined by far reaching long range high speed missions from the home system or early generation systems.
Rick Robinson had this to say:
Just glancing though your section there, the key challenge for a lot of purposes is time scale -- and oddly, it doesn't have much to do with ship speed; an STL civilization might expand over the long haul nearly as fast as an FTL one.
The key issue - and this comes up in all sorts of contexts -- is how long does it take for a planet to go from raw young colony to major world, the kind that could and might send out colonies of its own? This is the basic problem you have to solve for settings in which anyone has a space fleet of their own but Earth.
Let me try to put a few numbers on it.
The threshold for having a space fleet is arguably lower than for colonization, because a planet of 100 million people could probably maintain starships, but probably is not feeling a big population squeeze. To be sure, on some planets the habitable area will be pretty much filled, and even on the more earthlike ones the human presence is getting pervasive, so some impulse to colonize might be developing.
Whether a planet of 10 million people - the equivalent of a single large urban region -- could realistically have a diversified enough economy to maintain and operate a fleet of starships seems a bit iffy, unless they are putting a massive effort into it, so massive that it may stunt their other prospects.
The most likely scenario for a world of 10 million people sending out a colony might be that they've decided their current home sux, and they're going to try their shot at another one.
Looking at the other end, how many people for a viable colony. I'd say 10,000 at the low end, with 100,000 seeming a lot more comfortable. That's the population of one semirural county. How many machine shops and such does it have, how much can they specialize for efficiency, and oh yeah, you need raw material, a mining sector and all that.
If you can't make it you have to import it, paying starship freight instead of truck freight, and what have you got for sale? The market for colony-world curios is going to get crowded fast, and if you really do have something to sell, you'll probably need more than a one-county economy to produce it in commercial quantities.
So I would say that you usually have to put 100,000 people onto a colony planet for it to thrive. Colonies with fewer than that can hang on, but if subsidies are cut off they may die off outright, or be stuck in a marginal existence; only lucky ones will overcome it and do okay.
For a colony to really go as a largely self-sufficient post industrial world it had better have on order of a million people -- more or less the equivalent of Bakersfield and environs. I am certain that Australia has a Bakersfield, but I do not know what it is. Maybe our Oz contingent can inform us.
But once again, if they can't make it or pay starship freight for it they do without it, and the equivalent of Bakersfield has a tough challenge producing nearly all the needs of post industrial civilization. And for exports it is good to have one sizeable airport that can double as the shuttle port and provide steady employment for a lot of the techs.
Big proviso, so hold your pitchforks. This is predicated on the 23rd century, or 28th or whatever, having about the same productive efficiencies of scale that we are used to. If you have got replicators where you shovel dirt in one end and get a washing machine or air car out the other, things are different. But you still need a wide range of human skills, very hard for small communities to provide, maintain, and keep active.
So maybe my figures could all be squeezed down by an order of magnitude, so that a colony of 10,000 is fairly viable, a colony of 100,000 can maintain a full industrial base, and one of a million people can keep its own starships in service. That helps for story settings, but you wouldn't generally expect worlds like that to be active colonizers.
Finally, and most central to time scale, how fast do colony populations grow, either from immigration or birth rate? I would call a million emigrants from Earth each year a benchmark figure for large scale colonization. That's several thousand people each day, one huge ship or several merely big ones, and it still takes a century of sustained effort to plant 100 colonies, each of a million people.
From the colony's point of view, people are another expensive import, if you have to pay them to come. If they can afford a ticket and house stake they will only go to desirable colonies. If someone is paying to ship people to you, you may want to know why, because colonies could be a good place to dump dissidents, minor troublemakers, and similar riffraff.
On the export side, I'm more dubious of shipping off refugees, because by definition you're dealing with lots of them, and shipping them all off world is horribly expensive. Much more so than just plucking the town crank and town pickpocket off the streets and getting them to volunteer for emigration.
But by and large you expect that mass colonization involves people who weren't doing so great on Earth, because the supply of nut enthusiasts like people on this board who would actually like to colonize is limited, and a million people a year is a lot.
The other side of colonial growth is reproductive growth. Doubling the population each generation is about the historical sustained maximum. That corresponds to 10x per century, so Deseret World might go from 100,000 people to 10 million people in 200 years.
But even doubling per century is a pretty robust population growth rate. That's roughly 1.2x per generation. Unless you're growing 'em in vats, about half the women are having three or four kids, and one way or another the society encourages and accommodates itself to this.
It's no given that post industrial societies will generally have this population growth rate, though colony worlds may not follow the current trend in industrialized societies toward ZPG or even less.
If colony populations do tend to grow, I suspect the driving force is not the Heinleinian trope of ranchers with half a dozen marriageable -- and "husband-high" -- daughters, but the pervasive shortage of skilled specialists of all sorts. How this is transmitted to social attitudes I'm not sure, and no doubt can vary widely.
A colony with population doubling each century will go from 100,000 people to 10 million people in about 700 years, pushing us into the second half of the millennium.
Looking at it broadly, say that the age of colonization is around 2250-2350. That is a fairly common time frame for interstellar SF with a geocentric setting; (Star) Trek is vaguely in this era, AD2300 of course, and it's implied by some of Heinlein's interstellar stories.
After a century or so colonization from Earth sputters out, because all the low-hanging fruit has been plucked, and it is increasingly costly to reach virgin planets.
Emigration from Earth to the existing colonies can continue after that, but at some point the rate will likely fall. Successful colonies will no longer want people dumped on them, unsuccessful colonies can't absorb them, so emigration falls to the level of people who can pay to go and want to go, or who the colonies are willing to pay for.
So. At some point around 2400, colonization has tapered off and emigration is tapering off. We can guess that there are at least a dozen or so full colony planets - if you can reach any you can probably reach about that many (and you need a good handful for a decent scenario).
The upward limit is about 100 or so true colony worlds, set - regardless of how many worlds are in reach of your FTL - by the postulated size of the colonization wave. A hundred million people, a hundred worlds - an average of about a million immigrants per colony, though the distribution may well be oligarchic by a power law, a handful of colonies getting a large share of total immigrants, growing to populations of up to a few tens of millions, while most have less than a million and kind of struggle along.
Beyond and between the colonies there may be planets never made into self-sustaining colonies, but remaining as outposts, and likely with some permanent populations. If someone pulls the plug on these, though, don't miss the last bus out. Same with space stations and such.
As with the chronology, I think this is a fairly classical scale for a mid-interstellar setting -- when there are already established colony worlds, that you can get to by starliner, not just outpost transport or even colonization ship.
There are enough worlds for a diverse interstellar setting, but few enough that people who deal with space, at least, will have some notion of them all as distinct places. (The way "Spain" conveys something to you, or "New Delhi," but "Florianópolis" probably does not.
A few of these colonies already in 2400 have upwards of 10 million people and some potential to colonize themselves, but these were the immigration magnets, so they probably still feel short-handed if anything, not inclined to send lots of people off.
It will take 200 or 300 years for smaller colonies with rapid population growth rates to start pushing up into the 10 million population range, and might have the impulse and capability to colonize. But it might take closer to 500 years for a substantial number of the original colonies to have much motivation to colonize.
The early goers, though, will have filled in the next layer of easy pickings. Here is where your FTL really matters - whether you can light off freely into the vastness to hunt for a suitable planet, or are constrained by a colonization sphere that is starting to grow again.
But broadly speaking, it seems that secondary colonization couldn't be expected in any serious way until sometime well after 2500, and perhaps not in a big way till sometime around 2700-3000.
Other Thoughts
An interstellar domain can have no definite borders; stars are scattered too thinly, their types too intermingled. And there are too many of them. In very crude approximation, the Terrestrial Empire was a sphere of some 400 light-years diameter, centered on Sol, and contained an estimated four million stars. But of these less than half had even been visited. A bare 100,000 were directly concerned with the Imperium, a few multiples of that number might have some shadowy contact and owe a theoretical allegiance.
Consider a single planet; realize that it is a world, as big and varied and strange as this Terra ever was, with as many conflicting elements of race and language and culture among its natives; estimate how much government even one planet requires, and see how quickly a reign over many becomes impossibly huge.
Then consider, too, how small a percentage of stars are of any use to a given species (too hot, too cold, too turbulent, too many companions) and, of those, how few will have even one planet where that species is reasonably safe. The Empire becomes tenuous indeed.
And its inconceivable extent is still the merest speck in one outlying part of one spiral arm of one galaxy; among a hundred billion or more great suns, those known to any single world are the barest, tiniest handful.