When DNA is replicated sometimes things change and can cause mutations which are passed down to the offspring. If you have two offspring with this trait and they mate this mutation is twice as likely to be passed on to their offspring. If that offspring breeds with other offspring that mutation is even more likely to be passed on.
If the first offspring with the mutation mated with a different family there is still a chance they pass it on to their offspring, but being with someone who has the same trait increases the likelihood of getting the trait.
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