I do not believe that animals are lower in their karma than humans. My dog shows more compassion and is less selfish than any person I ever met. How could this be?
You are confusing mental habits and Karma. Your dog's actions are due to his mental habits, not due to the fruition of Karma. An animal's karma has nothing to do with it being more or less altruistic than humans . Your dog, compared to numerous other animals, is in a good condition. Most animals live miserable lives, your dog is one of the lucky ones karmically in the first place.
The amount of Karma one single being possesses is very vast. So, the particular Karma that ripened to cause your dog to be reborn does not make up his whole store of Karma. Your dog might have a lot of good Karma too! Sometimes very virtuous beings, even highly advanced Bodhisattvas, are reborn as animals for numerous lifetimes. That could be the case too.
There is a concept called "Third Lifetime" in Buddhism which one should also understand: For one lifetime, a person might perform mundane acts of kindness. In their next life, they gained great happiness, wealth, fame and fortune. But, they might use all this fortune for selfish reasons. Therefore, in their "third" life, their bad Karma comes to fruition and they suffer.
Humans must realize how precious their existence is. If we do not utilize the happiness we have for good and not merely mundane purposes, we are only cheating ourselves.
In Buddhism, every single sentient being has the potential or inherent nature to become enlightened. Only one's Karma, conditions and afflictions create obstacles to this. Your dog's Buddha nature is no different from your own or mine.