Maybe my 1 billion is way over-shooting the size of the Andalite poulation but 10,000 total for the whole population?!
That's why I was being hypothetical. As indicated when I used the phrase "Lets say". If I used the phrase, "And chiseled here into the stone up there next to the ten commandments is the total number of the Andalite population" I would have been in error.
Spread over several planets? You have to remember that not all members of the millitary as fighters, a ton of them would be involved in logistics, this would subtract hugely from the number of fighting adalites which means you'd only have about three thousand available fighters. Three thousand against Millions if not Billions of yeerks?!
A few points to make.
1: The Andalite fleet was, as mentioned, spread pretty thin. And the military was getting so desperate to put down the Yeerk threat that they were actually resorting to "quarantine" procedures for some worlds. What do you think would have happened if the Yeerks had won the battle on Leera?
2: As also mentioned, the Andalites were practicing population control. Which, before the Yeerks became an issue, probably involved zero population growth control. That means, the births were likely only allowed when a number of Andalites had died. So, ten thousand or one million, you probably fit the entire Andalite population into New York City comfortably.
Now, I'm no exobilogist. But even when the Electorate said, "Go ahead and have yourselves as many kids as possible", I doubt the Andalites could reproduce as much as quickly as the Yeerks.
We don't see the Andalites having multiple births. At best, we can guess that they have one child at a time and that each child takes a time approximately close to either humans or Earth based horses to come to term. To say nothing of how long it takes the child to reach maturity. From Ax's story, it's fair to say that he took about the same time growing up as the Anis. But again, we can only speculate here.
All the Yeerks have to do is have a threesome and croak. Then out pop thousands of little Yeerks.
So, either way, the Yeerks have always had the advantage of numbers over the Andalites. That, and the majority of Andalite leaders continue to think of themselves as superior in everyway. They don't consider anyone a threat to them and they pay for their arrogance with their lives and unfortunately, the lives of a lot of fine officers under their command.
How many times do we personally witness the Andalites getting their furry blue behinds handed to them? No the Andalites aren't that good. But they weren't doing all that well to begin with, which is why the Yeerks were basically winning the war.