Simple genetics: the closer the parent to the offspring, the more genes it will contribute to it.
Parents contribute 50% each; grandparents 25% etc.
Unless the gene you're studying is sex-linked, the mother and father have an equal effect.
A dominant allele will be more strongly expressed through each generation compared to a recessive allele of a gene (in which case a characteristic may only pop up every few generations).
As for specifics concerning dogs, very experienced breeders will have figured out which traits travel through which generations and are expressed at which frequencies through which parents
Half your dog's chromosomes come from the "top" and half come from the "bottom" so, from the standpoint of biology, both the male lines & the female lines are equally important -- IMHO, the dam's temperament often has a bigger impact on her litters than the sire's does, because she's the one who raises her whelps...
Or did you have some other type of importance in mind ?
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