Ok, so here it goes. My "Unified Theory of Tribble." Much credit goes to IfniLuck, without who's theories and previous work I would not have come up with this. My Tribble chart is actually a refinement of the chart he posted earlier.
So without further delay, I present my Tribble Theory chart, version 1;
http://www.yargnit.com/download/tribblesheet1.png
What does it mean? Well lets begin.
Every Tribble starts off as a basic Dotson (DOT), Sparkles (SPA), or Stahl (STL). These are what you find in the wild, these are what you will begin to breed and Tribble collection from.
From these three, any tribble they breed will become either a Susilo (SUS), Thompson (THO), or Vitales (VIT). Up to this point, which specific Tribble out have had doesn't matter. Any of the 1st three (Type 1a) can breed any of the second three (type 1b), and any of this second group will be able to breed the next Tribble. Starting at the next stage however, your breeding choices will start to matter.
The basic Tribbles are nice and cuddly, but lets say you want to get something more from you furry friend? Well in that case your next stop is Tuffli (TUF), aka the gatekeeper Tribble. Should you be unsuccessful in your attempt to breed your Type 1b you'll end up back at Type 1a, if you are successful however you'll end up with a TUF, or Type2. This is the Tribble through which all rare breeding attempts must pass.
You have your TUF, but you just bred him to get to the rare Tribbles right? Well from here you can split off down one of two paths. You can breed a Henry/Jasper (HEN/JAS) , or a Mccary/Nix (MCC/NIX) . But once you pick one line, the two never intersect again. These four Tribbles are all known as Type 3a's, and are the first Tribbles that actually provide long term buffs from using them.
From here a HEN/JAS can either result in Cavallaro/Deangelo (CAV/DEA), while a MCC/NIX can both lead too a Howe/Stacy (HOW/STC). These Tribbles give the same level of buffs as their predecessors, but are able to breed into new options. We will call these Type 3b Tribbles. The Best Buy Tribble also appears to breed Type 3b's.
Type 4's are where it starts to get fun, these Tribbles provide two different buffs, and are what most people will probably carry. CAV/DEA can result in a Mattson (MAT), while HOW/STC can result in a Ricossa (RIC). (Which seems to be the most popular Trible to carry atm)
Here we split again, Type 5's come in one of four varieties, each of which provides a single buff at double the effectiveness of their Type 3a/b cousins. Velasquez (VEL) and Highison (HIG) both come from MAT, while Griffis (GIR) and Daxter (DAX) both come from RIC.
Now we've arrived at the cutting edge. These tribbles, Type 6, buff a single stat for triple the value of Type 3a/b's. There are also still many holes in out finding at this level. From what we know so far, VEL can breed Nielson (NIE), while HIG can breed Yu (YU). GRI has been tested and found to not have a likely offspring, while DAX has not been thoroughly tested as of yet.
Now a few of these breeding lines are not confirmed as of yet, but most are, and those that are not fit well in established patterns, You may consult one of many charts avalible in this topic for breeding specifics. (My own will be updated shortly)
Why Type 1/2/3a and so forth? Well it's quite simple. Type 1 Tribbles offer no buffs, and cannot breed directly into a Tribble that provides buffs. 1a/b are olny different in the fact that you have to move from 1a to 1b before progressing. Type 2 provides no buffs, but breeding into buffing Tribbles. Type 3a and 3b are once again identical in terms of buffs, both providing a single buff at regular value, you just once again must progress from 3a to 3b before moving on.
Type 4 Tribbles provide 2 seperate buffs at regular value, while their offspring, Type 5, provide a single buff at double value. Type 6 once again provides a single buff at triple value. The Best Buy Tribble is unique, and statistically does not fit with any of the others, in breeding however, his offspring appear to be of Type 3b.
The buffs these Tribbles provide can be separated into 3 categories. Damage, Resistance, or Regen, and each provides a small bonus in their respective area.
Recent discoveries or theories;
From observed pictures from an unknown source, we have at least two varieties of Tribbles not discovered as of yet.
Also from my chart linked above, we can see there is a pattern in the naming of the Tribble types. All rows run in alphabetical order, either from right to left, or left to right. From this we can discern that if this pattern holds true, should a new Tribble be discovered above GRI (unlikely) or Dax, it's make would be something later in the alphabet than Yu.
Also, as there are three different buffs Tribbles can provide, meaning three possible combinations of two buffs, it is not unlikely that another Type 4 (one of the blue background ones) Tribble is yet to be discovered, meaning the posibility of more Type5/6 tribbles, or at the least new ways to breed them.
Another thing to not, no Tribble appears to breed any type besides 1a, or the type immediately above it. Some results saying they did were reported earlier, but as I've been testing them they have all come up false as of this point. (Even though the Best Buy one is shown even to the Type 3b's it breeds, remember it is not actually in this tier, and as it is a special issue Tribble doesn't fit into the standard rules anyhow. Functionally however it appears able to breed as if it were in either of the Type 3a groups)
I will address specific buff types as they relate in breeding, and add them to my chart later. This post is getting long enough as it is.
Again, remember this is still a work in progress, and is somewhat based off educated guesswork at this point.