Population Growth Rate

from GalCiv2 Forums
Greetings, I have been trying Galciv2 for quite a while and have some suggestion - that is quite much of he reason why I registered an account.

This game is indeed great, yet I would like to criticize a little so I may help to make it even better.

We know that the population growth in Galciv2 is constant, that is, a linear growth.
Yet, a high school student taking up to Gr. 12 Biology might have studied that a natural population would grow under a "logistic growth" (not exponential growth) instead if there is only limited resource.

http://en.wikipedia.org/wiki/Logistic_function

I am no professional mathematician, so I guess that the engineers in Stardock and many other Galciv2 players would understand all those.. equations better than I do.

The idea is that the linear model used by Stardock appears to be quite a fine model for population growth in the long run, that is, quite a good approximation for logistic growth over a long interval.

Yet, I believe that using a logistic growth equation to model the population growth would be more natural.

I remember using the equation " dP/dt = rP(1 - P/K) " in Gr. 12 .

dP/dt is the growth rate, P is the population, K is the carrying capacity, and r is the innate growth rate of a specific population.

..so this is what I had in mind and wish to see in Galciv2:

Say, on a colony, the population cap is 18.00b, so K in this case would be 18.00b.
Say, on the same colony, the population is 5.00b, so P in this case is 5.00b

r is of course the "innate population growth rate", which would be a constant decided by Stardock and would have a multiplication depends on what civilization colonized the planet and how it was modified by the players.

This model should present that the population growth becomes quite similar to exponential growth before reaching half of its carrying capacity. As the population is reaching its carrying capacity, it becomes harder and harder to grow (as in Galciv2, the morale also drops).

Thus, I believe that this model would be more natural to use for a great game such a Galciv2 and hope that this suggestion can be taken into consideration.

colonies
12,836 views 9 replies
Reply #1 from GalCiv2 Forums Top
Actually, if we use this model, populations would go out of whack pretty quick...

See, the thing you have to remember is there is a difference between *actual* planet population, and the population that pays taxes. The population that you're seeing is the tax paying population.The tax paying population increases exponentially with morale. This would make sense, since the more satisfied citizens there are, the more that will pay taxes.

Not to mention, basing this growth on a cap that is so quickly changed... is a joke. Most players (at least i know i do) have their population far outgrow the AI. I could make my economy sky rocket by building a farm on every planet i colonize, thereby increasing my growth rate (the 1-P/K ratio scares me) tremendously, and quickly upping my tax base. Farms are so cheap too... rush buying one would probably pay itself off in a turn or two.

Remember, and not just you, this is everyone... GC II's population is the TAX PAYING population. This settles a lot of silly arguments, not just this one.
Reply #2 from GalCiv2 Forums Top
I have to agree with your answer there, but disagree with one point. On outgrowing the AI. I think that is tied to difficulty level. On tough+ they (AI players in general) seem to be more efficient at having higher populations, taxing them and keeping morale under control.
Elemental: Reforged
Reply #3 from GalCiv2 Forums Top
@Shogun

Maybe it's just me then. I play obscene, and usually burn the first 30 turns at 100% morale and tend to match on colonies. Including the population growth attributes i always select at the beginning, i tend to have gaps in the hundred billions by the 75th turn between me and the AI. Like... usually by the time I'm ready for my first war, there are as many of my race as there are the other 9 opponents combined.
Reply #4 from GalCiv2 Forums Top
To n0v4k4n3:

Being honest, I felt that your words were.. offensive.
This is merely a suggestion to Stardock that may not even be accepted. Perhaps there is no need to.. provoke others.. at all.

I think that there might be some misunderstanding here, so.. I should clarify my idea a little more.

1. "r" is a constant that has to be determined first. Using a value too high will definitely ruin the game, but using a value too low will also make the game difficult. The (1 - P/K) ratio gives the population curve its characteristics, but the actual value of P depends quite much on "r".

2. The population displayed is indeed the tax-paying population. However, this model can still apply. I am not saying that the infants and the children are paying taxes, too; I am saying that the tax-paying population is obviously a percentage of the total population, and thus, the total population is a constant multiple of the tax-paying population. As a result, this model still applies.

3. Morale seems to be a secondary factor affecting population growth. I believe that the game manual states the population growth to be linear; this is the part that I have doubts with - not the morale factor.

4. As a result, rush buying farms will not really help so quickly... In this model, the growth rate maximizes when P/K = 0.5 , but if r is small, there is not much difference; besides, the growth rate will quickly drop overtime when P/K > 0.5 .

5. While both AI and the players have population growth using the same model, there should be no way that the player can have population outgrow the AI because of the model.


..so, I guess that this clarify the matter a little more.

Reply #5 from Stardock Forums Top
Being honest, I felt that your words were.. offensive.
This is merely a suggestion to Stardock that may not even be accepted. Perhaps there is no need to.. provoke others.. at all.

I didn't see anything that could be considered offensive in either of n0v4k4n3's posts. Believe me, if he wished to be offensive or provocative he's certainly capable.

Also I think everyone realizes that you're merely making a suggestion and I see no one denying your right to do so. All I see is a couple of folks disagreeing with the content of your suggestion.

Actually, if we use this model, populations would go out of whack pretty quick...

I have to agree with this as well. Population, taxes and morale have been heavily tweaked and adjusted in this game. There are parts of this structure that I disagree with, mostly on how strongly morale declines as the population gets to be around 20B. But regardless, it's my personal opinion that drastic changes to any of these elements is just opening a can of worms.

In your first post it seems your motivation for this suggestion is that it's more "natural". While I agree that this type of growth would be more natural, I don't think that's a sufficient reason the change the structure. In your second post your motivation appears to be balance between the AI and human populations. IMHO this is a better justification for change but it's not clear to me how your change would make the AI handle population any better.

Anyway, all this is merely my own opinion that people are free to agree or disagree with just as they are free to agree or disagree with your opinion.

BTW please don't let any of this inhibit you from contributing your thoughts and ideas about the game. I think that diverse opinions can only improve the game even though I may disagree with some of them.   
Reply #6 from GalCiv2 Forums Top
To n0v4k4n3:

Being honest, I felt that your words were.. offensive.



O_o honestly I'm shocked here. I apologize if my tone came off wrong, I actually *liked* the suggestion, just respectfully disagreed with it. And Mumble's right (he knows from personal experience), if I was trying to be a provocative jerk, there would be no subtly at all. If you don't believe me, just check some other posts I've written. I go off the deep end man.


5. While both AI and the players have population growth using the same model, there should be no way that the player can have population outgrow the AI because of the model.


This happens now because of the model *and* how the AI handles the model. The AI doesn't make population predictions based on current morale, it simply sees the current population as a means to an end. So it's not just the model itself we have to take into consideration. It's the AI's interaction with the model that is important.

The (1 - P/K) ratio gives the population curve its characteristics, but the actual value of P depends quite much on "r".


I have to respectfully disagree here. In the equation, they are *both* factors of the end derivative. So, for example, 1- 1mil/6mil = 5/6 (before farm). 1-1mil/9mil = 8/9 (after farm) 1-1mil/12mil = 11/12(double bonus tile) 1-1mil/15mil = 14/15 (triple bonus tile). As you can see, the difference between rush buying a farm on a triple and not is a whole 10 percent of rP! And since i'm *assuming* r would take into account all my pop growth bonuses, that could be a huge difference.
Reply #7 from GalCiv2 Forums Top
Now this seems slightly funny...

Yeah.. I guess I used the Yors too often.. so my mind has become.. slightly too mechanical.

I was thinking something like if r can be set to a certain number so that the population will be smaller than usual when P < K/2 and greater than usual when P > K/2 .

Also, I was thinking something like.. even if the players manipulate K to increase dP/dt, they need to keep up the morale, so this may not really be much easier at all.

Anyways... I must say that I can't really continue this discussion for much longer. No, I LIKE this discussion and I LIKE the math, but I have so much work to do that I merely spared the time just to register an account to post my idea and a few replies here. I would certainly enjoy more discussions when I have more leisure time for this game.

I must appreciate all of the replies.. and I can tell how enthusiastic you people are - Galciv2 is a good game!

Reply #8 from GalCiv2 Forums Top
I don't think we would really want to try to be more realistic with population growth.

If we did, then overpopulated unhappy planets with limited recources would experience population booms, while rich happy planets would experience population decreases!

Reply #9 from GalCiv2 Forums Top



I must appreciate all of the replies.. and I can tell how enthusiastic you people are - Galciv2 is a good game!

Yes indeed.   .
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