My ideas in the first one are self-explanatory, but the second link, in short, speculates that laguz lose their power when they breed with beorc to create a better balance in the union, which would lead to more stability, which would lead to stronger families, etc., with the idea that it would promote evolution. Please note I'm using the term "evolution" generously, as I kinda sorta don't really care to research it properly or make a scientific argument. Ditto for genetics. I'll leave that to the science nerds on my Flist.
I was looking back at a half-serious post about what combining beast/bird laguz genetics would look like illustrated by Punnett Square (answer: hilarious), and ended up thinking that there might be something to see there after all. I'm not going to pull out genotype examples or anything; it made me wonder, though, if the laguz/beorc problem could be as simple as assuming that each parent has an equal contribution to make, and an uneven distribution of power screws that up. So, for example:
laguz A + laguz B = let's say each parent contributes half of what the child inherits, so A gives half of his birthright, and B gives half of hers;
beorc A + beorc B = ditto;
laguz + beorc = there's only one birthright to pass down; it's most beneficial to give it to the child, who will carry on the line;
laguz + branded = they both have equal birthrights, so there is no loss
laguz + carrier = only one birthright, see laguz/beorc ("carrier" meaning someone who was born with laguz blood, but isn't branded, eg. Sanaki).
Also, re: the carriers, I think in this version of the equation they'd be wild cards, because they're still carrying a birthright - their children might end up having brands, which would mean the carrier in question would be contributing an equal portion, so there's potential for the laguz to come out of it okay. The opposite might be true of the Branded individual, come to think of it. If brands are passed down only once the previous bearer dies, as amielleon speculated, that could complicate things further.
Unfortunately, this undercuts the essential equality we're supposed to believe the two races have, because the beorc always come out on the bottom, so to speak, not having any power or birthright to speak of unless you count magic. (Which I think is a flaw in the game's argument. I have a hard time accepting "reason" as a birthright, but that's another topic.) It's also pretty silly and one-dimensional. I'm personally still in favor of laguz/beorc pairings leading to a single people - the Branded - who bear the best characteristics of both, in balance with each other.
I've seen authors speculate on this a little bit, but the only pairing that comes to mind is (of course) Naesala/Sanaki, where this birthright thing would be a huge problem for both of them - unless you assume that Sanaki has something to offer (genetically speaking, ha ha?) that will neutralize Naesala's loss. Then again, it's more ~romantic~ for him to take the risk and not care if he keeps his birthright or not. I don't think that's quite in character, but that's one way to look at it, I guess.
So, I've kind of come full circle here; the above was how I first looked at the laguz/beorc problem, before I decided it should have something to do with the cosmic balance, and now I'm back again. To be honest, I think the most logical way to handle this in a story would be much different - Lehran's past is the backbone of the racial divide on Tellius, but I think the designers could've come up with better reasons for that and left his birthright alone. Why can't we use real genetics and pretend that laguz parents can pass on some of their attributes without neutralizing their own?
I'm thinking that's just not angsty enough. It's too logical! We need our weepy herons to be weepy, and some tragic inter-racial romance thrown in for good measure.
Not really satisfied with this post, but whatever. It looked so much better in my head.