The entire brotherhood started with 1 Beaver.

It was cold, scared, and alone.. It wandered across the forest floor looking for some sort of human civilization, because It can feel the bone-chilling temperature of Winter approaching, and It is not intelligent enough to create a fire.

After weeks and weeks, the beaver has found the Pig King. It has expected that there would be a human base surrounding the fat king, but the beaver wasn't as lucky. Winter is nearing closer...

2 Days until the end of Autumn. The Beaver, kiting and gnawing on the shadow creatures that chase it, tries and makes it back to the spawnpoint. It has seen multiple survivors in the hellish lands, but they fear the beaver, they run from the Beaver. The ones that are not afraid of it, do not have a sustainable base set for Winter. The Beaver is starting to get very beaten down by the shadows, and on it's presumably last breath, it finds the thing it would never thought even existed.

Another Beaver...

The Brothers inspect one another. It was like a reflection, a mirror. Once both of them realize this ISN'T a sick trick made by the villianous shadows, they jump around each other, and skip away with each other. Their chances of survival for winter has increased.

They continue their search for a base. They did not find a human settlement, but they found the next best thing. A Robot's base. The Robot supplied wood and fire. The Beaver Brothers did a last minute search for anything that they might need for winter, along with the robot. As if God has came back to the world of Don't Starve, they have found another Brother, almost near death.
If the beavers had as much IQ as a human being, they would've noticed the robot's lack of empathy. The Robot has manipulated the beavers to do his bidding, and that including sending them into a battle they will not survive...

Who are they fighting?

None other than the Bee Queen...

The Beavers run in mindlessly and start to attack the queen, being 100% loyal to their soulless robotic "Friend". They do decent damage. The Bee queen screeches in pain at the multiple bites and scratches of the relentless beavers. But alas, the Bee splatters each of the beavers with the sticky honey, pinning the beavers' feet to the ground. And then the defenders of the Bee queen are free to pick them off. The Robot, as a last resort, tries to attack the queen while it is distracted. That has cost the robot it's life...

None of the beavers survived.

Their only hope of continuing the species of beaver is to reach the touchstone on the other side of the map, before the entire island restarts.

They hurry their weightless pale bodies, trying to race against time to save the entire race.

The Clock ticks down.

5...

4...

3...

And then the first beaver's body breaks out of the stone.

Then the second.

Then the third.

The beavers have survived, for now. They used their combined knowledge to map out the entirety of the island they live on. If there was any hope of any other beavers on the island, it had to be dead, or somehow got off the island.

That only left one other way to grow in numbers.
Repopulation.

How do you jump-start any species?

Make 'em repopulate.

The island contains dozens and dozens of beavers. They have almost started a civilization, rather than forming a pack, like other wild animals. They have even started to create organized attack patterns, and defensive positions.
(As you can see, it's not perfect.)

Sadly, the beavers did not know that the moe numbers they have...

The more shadows are casted...

The Shadows have picked off numerous beavers before they realized the grave mistake of having too many beavers on a single island.

The war between the hundreds upon hundreds of shadow creatures, and about eight beavers, have begun.

Blood has been shed. Shadows has been dissapated. But for every shadow that appears, 2 more seemingly appear.

10 Shadows jump on 1 beaver at once, ripping the beaver apart.

The second beaver perishes...

The third perishes...

The fourth...

The fifth...

The rest of the Beavers that are fighting strong dies from the unemotional ruthless shadows.

Then the final beaver falls.

On the beaver's last few breaths, it looks around. His friends are all dead. The shadows are closing in. The beaver is bleeding out horribly... It coughs, and then closes it's eyes, and stops breathing...