The Federal Economy
by Donovan

1. The basics
Being the backbone of your plan to take over the cluster, your economy deserves a lot of attention. Good for you the Feds are able to set up one of the strongest economies in the game, beaten only by the Borg with their many supplies and their chunnel-capability.

The need for a strong economy arises from your shiplist: a fine array of torpedoships, with the second largest torper in the game as top-of-the-line ship. But what you lack is one of those big bad carriers, and when facing one of those you'll have to sacrifice two ships so your third ship can kill that carrier. And in order to pull that off you'll have to make sure you have more ships than anyone else in the game. And with your special race-advantages it can be done.

With your 200% taxlevel money will never be a problem, unless you're playing in a game without natives (why would you ever do that?). In the early to medium game this money-advantage will enable you to take out one or two of your neighbours, simply because you have better techlevels earlier on. Less neighbours means more room, more resources and thus more ships. The 70% mining rate can be a burden on your economy, but shouldn't have to be. All it takes are a good colonisation strategy and a couple of Merlins to overcome this disadvantage. The ability to superrefit ships will make building a lot of ships much easier, and finally you have your terraformers to further aid you in setting up the best damn economy in the game.

2. Early game economy (first 15-20 turns)

2.1 Setting up your economy
Unless the homeworlds are placed at extreme close range, the first ten or so turns will completely be devoted to setting up your economy. To start off your colonization you'll send out your two initial ships, the Outrider and the Nocturne, on a clandrop trip in separate directions from your homeworld. Load them up with clans, refit the engines for transwarps unless you have a lot of planets at a close distance and have them drop one clan on each planet you send them. This will give you valuable information about the planets around you and give you and idea where exactly to send your large freighters which will follow them up. The first two or three ships you build will be large deep space freighters, used to bring clans to where they're of most use to you: planets surrounding your homeworld. Ideal mixes to fill your freighters with are 800 clans and 400 supplies, and if possible 2800 MCs. Using this you can drop off 100 clans and 100 supplies along with 700 MCs at every planet; planets with a good amount of minerals get 200 clans (200 clans can support 200 mines, while 300 clans can only support 210 mines) and planets with natives get even more clans. With a bit of luck you'll find enough planets with natives so that you won't have to bring that much money.

Now you'll find out why it was so important to drop a clan on each planet with those scouts: because you already have a clan on the planet you can dump an exact amount of money (instead of having to use the 'bdm' friendly code and dump it all on the first planet) and you can use the same turn to build your first 100 factories (for 300 MCs). You can also beam up an exact amount of fuel to make it to the next planet, and you'll know how much fuel you can get from there. The next turn your 100 factories will have given you 100 new supplies, which can then be used to build 100 mines with the 400 MCs you had left. If the planet has natives, just drop 100 supplies with either 300 MCs to build the first factories rightaway or no cash at all and wait a turn for the taxmoney to roll in (but unless the natives are Insects 100 clans won't collect 300 MCs).

After dropping the last clans and supplies pick up the minerals and earned taxes from the planets you've just colonized and head back for your homeworld; you'll need the minerals there. Don't forget to set the taxlevel the very first turn you own the planet to collect the needed initial cash. Using this method each freighter can colonise 4 planets with at least 100 clans, factories and mines, and drop more clans on good native planets. Also remember to build 21 defenseposts in the not too distant future to block your planets from enemy bioscanners and sensor sweeps and offer minor protection against probes and such.

During all this you'll be concentrating on three things: finding a suitable place for your second and third (if possible even fourth) starbase, building yourself a Merlin for each base and a couple of Neutronic Refinery Ships to overcome fuelshortages, and providing some basic protection.

2.2 Your second and third starbase (and more if possible)
To be able to outbuild your opponents you'll have to build a lot of bases, because you can still only build one ship per turn per base. A starbase will cost you 900 MCs, 402 Tritanium, 120 Duranium and 340 Molybdenum. It is possible to bring it all in one freighter from your homeworld, but an easier way is to pick it up at planets which will also supply your base once it's build, and dump all the minerals on a good site to build your base. Dedicating that much minerals to building new bases and Merlins will certainly put a burden on your shipbuilding program, but if you don't do this you'll regret it later. And for now you won't need any warships larger than Nebulas, Diplomacies and Lokis anyway.

Nice sites for starbases are easy to recognise, assuming you're lucky enough to find 'nice' sites. They are a planet within a cluster of three or more supporting planets, all within one month flying of eachother. If you've found yourself a nice cluster there are a couple of things to look at: the mineral situation is the most important one. Don't just look at amounts of minerals, have a long and hard look at the densities of the minerals. Especially with the 70% mining rate high densities are important. Temperatures are also important, you'll need to know how much clans the planets can support and if there are any growth-perspectives. This is not too important however, since terraformers are pretty often amongst the first couple of ships you'll build at new starbases. The third factor to consider are the natives: some natives provide your base with free techlevels. Ghipsoldals give your base enginetech 10 for free, Humanoids hulltech 10, Siliconoids torpedotech 10 and Amphibians beamtech 10. Which is actually the order of desirability for free tech-native races. Apart from free techlevels there are more 'special' natives: Avians are great moneymakers because you can overtax them, Insects give you double your normal taxes, Bovinoids give you one supply-unit for every 10000 natives and Amorphous worms eat your colonists. Generally speaking, I'd say a Bovinoid planet is the best location for a starbase, because then you won't have to transport all the supplies they generate, followed by the free tech-natives in the order listed above.

Apart from enginetech it isn't necessary to bring every techlevel up to 10. You can do with Mark4 torpedoes, which are techlevel 5, for a long time, and even later on I usually don't go any higher than tech 8 Mark 7 torpedoes. Same goes for beams: Disruptors are only techlevel five, and unless facing serious (web)mines even in the late game the tech 8 Heavy Disruptors are a much better -more economical- choice to put on your ships than the tech 10 Heavy Phasers. I often find myself raising the hulltech to 10 only because I need to build a Merlin; Novas are not my most common ships to build.

Be sure not to set your new bases up too close to your homeworld or eachother. I've seen people build a base on the planet next to their homeworld, and personally I'd never do that. Planets next to your homeworld should be used to supply your homeworld, and by setting up a base next to it you'll not only be dividing the resources over two bases, but also making that particular cluster very important: if your enemy launches a strike in that direction he might just take out two of your bases because they're so close.

2.3 The Merlin
The Merlin is one of the most vital ships in the Federation fleet, though apart from catching those annoying Rebel Falcons and other probes it won't ever do any fighting for you. Merlins will help you overcome your 70% mining rate by converting supplies into minerals at a rate of one mineral for every three supplies.
I usually build Merlins with lowtech engines and then tow them to where they're needed (Bovinoid planets, new bases if they can't be built at the base itself soon enough) with a LDSF. I put x-rays on them to capture wandering probes and small scouts, these beams can later be upgraded to Disruptors using the superrefit. A Merlin with warp 10 stardrive 1-engines and x-rays will cost you a grand total of 866 MCs, 635 Duranium, 308 Tritanium and 134 Moly. Especially in the case of your first Merlin it will be hard to gather these minerals, since the LDSFs you'll also be building then take a big bite out of your Duranium supply.

Now you will find out why it is so important to colonise each planet with at least 100 clans and always build the maximum number of factories on each planet. By doing this the Merlin will pay itself back very fast, and will give you the edge you need. An example: let's say you have built a base on a planet with four planets supporting it. On each planet you have 100 clans, with 100 factories and 100 mines. Let's assume you're lucky and you've found yourself some planets with nice amounts of minerals, at an average density of 50%. Following the formula of (number of mines)*(mineral density)*70% you'll mine 100*0.5*0.7=35 KT of each mineral on each planet per turn. For your five planets (base and four support planets) that's 165 KTs of each mineral per turn. And you're also producing 500 supplies per turn, which can be converted to a total of 167 minerals per turn. So 25% of your total mineral production (not counting fuel as a mineral) will actually come from your supplies! And it gets better, because with the Merlin you can decide which minerals you make using the friendly codes of 'alm' (molybdenum), 'ald' (duranium) and 'alt' (tritanium). In our example we assumed you had decent amounts and densities of each minerals, but you'll find yourself short on molybdenum quite often, or short on one of the others if that's only available in low densities at the planets you've found. At a certain point the planets will begin to run dry on minerals, and in the later stages of the game you'll actually be living off supplies alone.

2.4 Basic protection
So far we've been assuming you haven't met any of the others, though this will often be the case around turn 10 or even before then. The first contact will probably be your scout seeing one of his ships or vice versa, an enemy scout over one of your border planets or ofcourse your scouts finding 'enemy' planets. These options do not sound too terrible yet, but your first contact could very well be five of your freighters being taken out by enemy cloakers too. Since this article is mainly about your economy, I'll direct you to the main guide for parts about diplomacy and interacting with your neighbours.

3. Medium game economy (turn 15-20 to whenever the shiplimit is reached)
This is the part of the game where you continue your economical expansion, assuming you have the room for it. You might have to kick some other race out of the game to provide you with the necessary space and some other race might be trying to kick you out of the game for the same reason, so you'll have to adjust your economy to that, but basically what you'll be doing now is colonising more planets as described above, bringing even more clans to planets with good amounts of natives and building more bases. The only difference with the early game economy is that you now have to concentrate on building an armada of battleships instead of cranking out freighters to do more colonizing, and that you'll have to move large numbers of clans.

3.1 Optimising colonised planets
So far the emphasis has been on expanding, colonizing as many planets as possible. Now it is time to improve those planets. First priority is to bring more clans to planets with natives. For taxing you'll use the growth method, meaning you'll tax your natives very high for one or two turns and then not at all for a couple of turns, until their happiness reaches 100 again. What you'll typically do is tax them around 40% for one turn, which brings happiness down to 70 points, and then don't tax them for eight turns or so. So what you'll have to do now is bring out your calculator (see page 2 for formulas), Encyclopedia Galactica or VPtools and see just how much taxes you could earn, and how much clans you'd need to collect them. The following step is logical: bring those clans there.
You're still building the maximum number of factories on each planet, and you'll have to take a closer look at the mineral situations on your planets to see if it's worth it to build more mines on certain planets.

Even on planets without natives or good minerals it is wise to have more than your initial 100 or 200 clans, especially if the Lizards or Fascists are somewhere near you. Apart from building defenseposts to aid in your grounddefense against these two you could consider upgrading the number of defenseposts to 43 on each planet, so you'll have seven fighters and 4 beams against attacking ships. Not nearly sufficient against most ships, but it'll give you a chance against small armed scouts and it will improve your grounddefense to 3:1. Now is also the time to start increasing the defenses and fighters on your bases. Not too much, the main idea is still to build as many ships as possible before the shiplimit hits, but you want to be able to survive incoming attacks.

Now is also the time to colonize those Amorhpous planets. Sure, they'll eat five clans per turn even if you keep them happy (don't tax them!), but your colonists will also grow, depending on the temperature (see next page for formula) and if you drop enough of them so that they grow faster than worms can eat them it's not a big problem. In fact, anyone who leaves Amorhous planets uncolonized just because they eat clans is a rookie in my book. You do not want some planet in the middle of your territory where you can't even see if ships are orbiting it or not.

3.2 Building your armada, using Super Refit
The main goal of your economy is ofcourse to build yourself a nice big armada of battleships. Which ships you should build is discussed elsewhere, here we'll take a closer look at the economical aspects of your superrefit. While theoretically one of the advantages of this ability is that you can build a completely hightech ship using four starbases built over free tech-natives and not upgrading a single techlevel this is not a smart thing to do.

As we've seen above, a starbase will cost you a grand total of 862 minerals and 900 MCs. By building a ship using four bases without upgrading any techlevels you'll be saving some money, but let's have a look at how much money you'll be saving: For a typical ship we'll need to upgrade the hulltech ofcourse. Let's assume we're building a Nova, hulltech 10. You'll build this hull at your Humanoid base, saving 4500 MCs for the complete upgrade from hulltech 1 to 10. As we've already seen above, Humans are a good native race to build a base over. You will then put transwarps on the ship at the Ghisoldal planet. Looks like you've just saved yourself 4500 MCs for those techlevels, but you've spent 900 on the base so you've actually saved 3600 MCs. Next, you'll fly the ship to the Siliconoid base for the torpedoes. Here you've got tech 10 torpedoes, but personally I'd stick with the tech 8 Mark 7s. So you now saved the money for an upgrade to techlevel 8: 2800 MCs. But again, you spent 900 MCs on the base, so you've only saved 1900 MCs. Next stop: the Amphibian base for the beams. Depending on the amount of minefields you'll be facing, you put beams on the ship. I usually equip them with tech 5 Disruptors, but for the sake of building free tech-bases let's say you put Heavy Disruptors (tech 8) on the ship. Again, a saving of 2800-900=1900 MCs. So in conclusion you've saved a total of 7400 MCs by building four bases instead of one with all the techlevels.

Nice, sure, but let's look at what this little trick has cost you: instead of spening 862 minerals on one base you spent 2586 more minerals on three extra bases. And the nova we've just built (four transwarps, ten MK7 tubes and ten disruptors) has cost us a total of 1409 minerals. So what you just did is put almost two Novas worth of minerals into three bases, while you should have money enough to buy the needed techlevels at one base. Not to mention the fuel you've used to tow and fly the Nova around from base to base, plus the ship you've pulled away from it's normal duties to tow the Nova. Don't get me wrong here, if you can build another base and have the planets to support it go for it, and if you have two bases relatively close together and you can use your superrefit by all means do so, but don't go building free tech-bases like crazy just to make use of your superrefit.

The most common use for superrefit is to build ships in stages. If you don't have enough minerals or money on a base to build a fully equipped ship, you can always build the hull with lowtech engines and put the weapons on it as soon as the freighters with minerals and money arrive. This lets you get away with logistical mistakes, where other races are forced to build some small less useful ship if they're temporarily short on minerals. This is also a nice way of building Novas, since the drain of minerals from building a fully equipped Nova can cripple your serious shipbuilding-capability for a couple of turns. What you can do is build the hull, then in the next couple of turns a couple of smaller medium ships, when the next freighter comes in put weapons on that Nova and later on the engines. You can also take superrefit one step further, by building a bunch of 'empty hulls' throughout the game, and wait for the shiplimit to hit and refit them afterwards. You'll have to be cautios when doing this, because your enemies are well aware of this tactic and just might decide to attack those empty hulls before you get a chance to upgrade them and throw them into battle. I usually build an empty hull now and then at bases in a safe area of my empire, and then only if I already have a couple of fully armed ships to defend that base and my empty hulls with.

3.3 Moving large numbers of clans
As your empire is expanding you'll find it a burden on both your logistics and your fuelsupply to keep on flying back and forth from and to your homeworld to bring more and more clans to the edges of your ever growing empire. What you can do is find a couple of good planets at each end of your empire, terraform them to a nice 50 degrees, and use them as breeding planets. Dedicate a freighter or two to shuttle clans between your homeworld and these breeding planets. A nice 50 degree planet will give you a colonist growth of 5% (assuming you're not taxing your colonists, just like I told you), which are a nice 130 clans from a full superfreighter. If you set up a couple of these planets, you'll have enough colonist-growth to keep expansion relatively easy.

4. Late game economy (from shiplimit to end of game)
By now the shiplimit has been reached, and the time has come to upgrade your ships with the best parts your piles of money can buy you and put Novas into the buildqueue. Since you'll be building ships at a much slower rate you should now begin to develop a surplus of money, minerals and supplies. Supplies will now go in the cargoholds of your battleships to repair damage from minehits and Glory Devices. Further supplies can be converted together with minerals to fuel using a Neutronic Refinery Ship to make you the fuel you'll need for long campains into enemy territory. Since you now have an easier time supplying your bases and the number of bases you have can be of great influence on the amount of ships you'll get to build it is a good idea to build more bases. If you have properly set up your alchemy situation (a Merlin per base, minimum of 100 factories on each planet) you should now be able to build clusters of three or four bases around your existing bases, supplied solely by the minerals converted from the supplies. The new bases only get hulltechlevels as needed, all others stay one level 1. This way you can put a whole bunch of good hulls in the shipqueue, which can be towed to the 'center' base which does have all the techlevels and be refitted the turn after being built. If other races want to set up a new base they'll need to buy a lot of techlevels or concentrate on building lowtech hulls, you -the guy with cash to swim in- get to save a lot of cash. Ofcourse, this is spent on torpedoes/minefields or fighters.

Some of your native populations will now have reached the maximum size they can have, so there is now no need to keep their happiness above 70. You can tax them down to 40 happiness points, since that is the lowest happiness level at which they are still content. I usually keep them at a flat 60 or 70 happiness points. This gives me the option to overtax them for one turn when the sudden need for more money (i.e. an incoming attack needs more torpedoes or fighters to be stopped) arises. Another option would be to keep them at 40 and overtax them in case of an incoming attack, so the natives start rioting and kill the clans your enemy will land on the planet after he's conquered it. Which method you prefer depends on the situation ofcourse, but let me say the latter is not the preferable one.

After reading all that you should now be able to run a decent economy. But to truly get the best out of it, you'll need to spend a little more time on it and tax your natives in the best possible ways. The trick is to treasure your natives, yet at the same time tax them for all they have.

5. Formulas
The first step in optimising your economy is to have a clear understanding of the formulas involved, the factors influencing your economy and the consequences of your actions on it. Your economy will run by the following formulas:

The basic formula for taxing natives is as follows:

Taxes earned = (Native clans / 100) * (Taxlevel / 10) * (Native Government / 5)

The values for "Native Government" are as follows:

The earned taxes are multiplied by a factor (Player Taxrate / 100), for the Federation this results in a factor 2 added to the formula making it

Federation taxes earned = (Native clans / 100) * (Taxlevel / 10) * (Native Government / 5) * 2

Happychange = TRUNC[(1000 - SQRT(Native Clans) - Native Taxlevel*85 - (factories + mines)/2 - 50*(10-Native Government) ) / 100]

The values for "Native Government" are the same as in the table above.

If the natives are Avian, 10 happiness points are added to the happiness each turn.

The growth formulas for all native species but Siliconoids are:

Clans added = ROUND [SIN(3.14*(temperature/100)) * (native clans/25) * (5/(taxrate+5))]
"Maximum Population"  = SIN(3.14 * (temperature / 100)) * 150000

Siliconoid natives like hot planets, and have their best growth rates on those planets. The formulas for Siliconoid natives:

Clans added = ROUND [(temperature/100) * (native clans/25) * (5/(taxlevel+5)]
"Maximum Population"  = temperature * 1000

The number of native clans added is rounded (not truncated, as in many of Tim's formulas).
For all natives, the amount of clans added gets halved if before growth there are already more than 66000 clans.

The "maximum population" is not so much a hardline limit to the size of the population, but a limit above which there will be no more growth.
So a population that is just one clan smaller than the "maxiumum population" will have the full growth as derived from one of the formulas above. With that growth it will exceed "maximum population" so from there on in there will be no more growth.

6. Earning taxes
With double tax-earnings being one of your main advantages you can do without paying too much attention to taxing and still come up with enough money to keep you alive, but you'd be better off paying a lot of attention to this aspect and get the best out of your natives. Simply following the first formula above, there's nothing to it: you drop clans on a planet, you tax the natives and your clans collect taxes. How much they can collect at a certain taxlevel depends on the number of natives on the planet and their government factor. Unless you're playing with the Race+ addon you cannot influence the government factor, but it is pretty easy as a Fed to influence the number of natives. Two major ways are terraforming and taxing them through the so-called growth method (or ofcourse not taxing them at all).

6.1 Taxing your natives - different strategies
There are a couple of different ways to tax your natives. The most commonly known methods are the so-called growth method and the safetax-method. The difference between them is that the safetax-method taxes the natives every turn, and keeps their happiness at 70 points (the minimum at which the natives still grow). The growth-method taxes the natives very high every couple of turns, then waits for their happiness to reach 100 again and than yanks them for another round of taxing. The difference in the result of these methods derives from the 'native growth' formula: as you'll see the taxlevel is an influence on growth. A simple glance at the formula will show us that the natives will grow at a percentage, calculated by a multiplying a factor for the temperature (we'll get to that later) by four and then dividing it by a taxrate-factor. So at 0% taxes the temperature-factor is divided by 1; at 7% taxes it's divided by 2 and at 39% taxes by 8.

Now, in short the safetax-method would tax the natives at 7% every turn, while the growth-method taxes at for example 35% at one turn and then a four turns at 0%. The net-result over five turns looks the same at first: 5*7% equals 35%, after all. But there's the catch: now in the sixth turn the growth-method implements another 35% taxround. But this time the number of natives has grown at a maximum level for four straight turns, instead of half the maximum level as with the safetax-method. Using this advantage the growth-method earns you more money. Or at least, that's what everybody says.

6.2 Comparing different policies
Ofcourse, some just don't believe anything no matter how many people say it's so, without seeing some actual proof. In this case one of those people is me, so I fired up a spreadsheet or two and started calculating. I've used the formulas as stated on top of this page, and created my own virtual natives. I think I've used the formulas in the correct order (growth occurs after happiness change, but to be sure I didn't make a mistake there I just kept happiness at 70 or higher) and have taken a few things into account. It is reported that above a population of approximately 6.5 million natives only grow half as fast. Furthermore, native population is limited by temperature. At 50 degrees the max. populations is 15.6 million, at 84 degrees it's 12 million. My testgrounds included:

• Two different temperatures: 50 and 84 degrees
• Two different starting populations: 2 million and 9 million
• A native government type of Monarchy
• 2500 colonis clans on the surface, enough to earn 5000 MCs per turn
• 200 structures: 150 factories (max. for 2500 clans) and 50 mines
• 40 turns of virtual taxing
• A taxlimit of 5000 MCs per turn
• Happiness starts at 100 points

And just for the heck of it I also tested a third strategy I call the half-tax strategy. Tax one turn at about 10%, so that happiness drops the same amount of points as it will grow at a turn of non-taxing, than don't tax for one turn so happiness reaches 100 again and tax again, and so on and so on.

6.3 Money, money, money
To keep this at least somewhat readable I won't bother you with the sheets of the different methods (twelve in total). The following is a table with the total taxes earned over 40 turns using the different methods under different circumstances. A few remarks beforehand: I manually set the (virtual) taxlevel each turn, mostly staying under the 5000 MC limit. In some occasions one percent higher taxes would earn more money, but would lift the total earned amount for that turn over 5000 MCs. So it is possible to squeeeze some extra bucks out of the growth-method.

As youl see, for a low starting population the differences aren't that impressive. What's surprising is that the safetax-method actually earns more money than the growth-method. The difference however is negligable: a maximum of 900 MCs over 40 turns. So, since it doesn't seem to matter which method you use on low populations from this point of view it's time to take a look at the long-term strategy: the big bucks can be earned from large populations, and to get to a large populations non-taxing (only a valid option if you're really swimming in money) or the growth-method are the best ways.

Now, at a high starting population things become more interesting. I've read somewhere (I think it was in the newsgroup) that using the growth-method on high populations isn't worth the trouble because of the halved growth. But from the looks of things it's defenitely worth the trouble. The major reason for the success of the growth-tax method with high populations is that the natives will reach their maximum population faster that way, and once that's happened you don't have to worry about keeping them happy anymore. Just tax them straight down to 40 happiness points, which means taxing them high for a turn or three. That's where you make the extra bucks.

6.4 Differences other than money
Since the benefits of the growth-tas method moneywise aren't that impressive on low populations, let's just have a look at the growth results. As stated, using this method your natives grow faster, but just how much faster do they grow? The number of natives in millions we've ended up with after using the above described taxing methods for 40 turns (as above, a low population is 2 million and a high population 9 million) are as follows:

Clearly, using the growth-method you'll end up with substantially more natives. Big deal, you say. Well, yes! As seen above, once your population hase grown to a nice large amount, the bucks really begin to fly in. And what if your natives are Bovinoids? Each turn, the difference in number of natives for both method grows. So each turn, the growth-method would give you more "extra" natives and thus more extra supplies. A comparison:

So by simply using the growth-method on your Bovinoids, you've just earned yourself 5086 extra supplies over a course of 40 turns. And putting those extra supplies through a Merlin would have earned you 1695 minerals. Now, considering a base and a new Merlin together will cost you a grand total of 1871 minerals, you'll see you've just about earned yourself quite a substantial amount of extra resources. And that is just for a low starting population. Comparing both methods for a high starting population of nine million cows, we find a difference of 6299 supplies over 40 turns. This ofcourse equals 2100 minerals, or put into perspective: a starbase, a Merlin and the minerals for a Diplomacy or two Kittyhawk hulls.

6.5 Some final words on taxing
Apart from all the above mentioned, the way in which you tax a certain planet depends entirely on the situation. How long you expect to own the planet and profit from it's natives is a big influence. The growth-method din't really pay off in 30 turns, for example (Before calculating the differences for both methods over 40 turns I did it for 30 turns). The amount of clans you can put on a planet should also influence your tax-strategy. There's not much use for the growth-method when you only have 100 clans on a planet. Sure, using the growth-method allows the natives to grow faster before your ship with colonists arrives, but then again so will not taxing them at all. If it's a planet you expect to lose to your enemy in the near future, just tax the natives into a civil war and make the planet useless to him. As for my calculations, I have yet to make them for longer periods of time, and have yet to make them for Avians and have a look at the situation with Insects. If someone discovers a mistake in the formulas I've used or the conclusions I've drawn from all this, please don't hesitate to let me know.