I think it would be nice if your animals had a small chance to gain certain attributes.
What i mean is:
There is a 0.5% chance that a animal upon being born will have a random attribute, and parents will have a 10% chance per parent to pass on their genes to the next generation(20% if both parents have the gene)
If an animal has more than 1 gene, it will be a 10% chance for the first gene and 10% chance for the second, so about 5% chance to pass both. It's technically possible to have all 4 genes, but even if you achieve this, it would not be easy to pass these genes on.
Of course these are more like fun random things that can happen, hardcore people will only focus on quality though, since this is not at all efficient, but some areas would be helpful, 50% less food for a casual helps alot.
These attributes would be
Precocious: this animal will grow up 50% faster
Hardy: consumes 50% less food
Genetically Predisposed: babies born from this mother will have +50 added to a random stat.
Reproductive: Always has 2 babies when giving birth