Population is
relatively simple, the main thing is weirdness with how environment works. The formula is:
(A - B) * CA is growth rate, which is:
0.055 (base rate, higher than normal because of your racial bonus) * 1.21 (modifier from pop growth tech) * 0.6 (loyalty, which should have increased last turn from 50% to 60%, or higher if you bought them off) = 0.03993 for you this turn
B is environmental penalty, which varies by planet. The actual formula is:
(difference between ideal and current environments * 0.0005)
You can get the difference by subtracting your race's ideal environment from the planet's current one, or vice versa, and then making it positive. So Ideal 50 and Current 100 would be the same as Ideal 100 and Current 50, since it's 50 points from current situation to ideal situation either way.
In the case of Planet 3, the difference is 0, so the penalty is 0 * 0.0005, which is also 0, so no worries there. On Planet 15, the ideal is still 160, but the current environment is 50, so we get |50 - 160| or |160 - 50|, which gives us 110 either way. You could also just eyeball it and notice that they're 110 apart, but that gets messy for most numbers.
Thus, Planet 15's environmental penalty is (110 * 0.0005), or 0.055
Combining the
(A - B) part of the equation gives us 0.03993 (your total growth rate) - 0.055 (your environmental penalty) = -0.01507, which is your total growth modifier. This is then multiplied by
C, which is just your current population, in this case 5.8 (apparently your colonists arrived from last round).
Thus, we get a grand total of (-0.01507 * 5.
= -0.087406, which unfortunately rounds the opposite way you'd prefer to -0.1
More generally speaking, your new colony has two differences from your main one- lower loyalty, and an imperfect environment.
Loyalty is applied as a modifier to production, taxes, and population growth, so a world with 50% loyalty will produce half as much production, pay half as many taxes, and grow slower (though not exactly half as slow, usually).
Environmental difference is applied as a penalty to population growth and helps determine environmental upkeep, which is 0 for a world with perfect environment.
Anyone mind if I delete loyalty entirely, though? It's bothersome to track, and is mostly just an annoyance.
I kind of like it, though I'm not sure if it's worth it or not. Also my racial penalty is to loyalty gain, so...