1. In some breeds of dogs, a dominant gene controls the characteristics of barking while trailing. In these dogs, another independent gene produces erect ears; it is dominant of its allele for drooping ears. Suppose a dog breeder wants to produce a pure-breeding strain of droop-eared barkers, but he knows that the genes for silent trailing and erect ears are present in his kennels. How should he proceed? Show all work involved including punnett squares.
This sentence: "but she knows that the genes for silent training and erect ears are present in her kennels" indicates that both alleles of both genes are present in her population of dogs. Some dogs will be SSEE, some SsEe, some ssEE, etc. What she wants to do is systematically make barking dogs SS (lord knows why) weeding out any s alleles, and droop ear dogs ee weeding out any E (erect) alleles. It's not a simple punnet square.
Part of the problem is that barking trait isn't clearly labeled as dominant though from the wording I believe it is dominant over silent. (I've kept your notation of "s" for the barking trait)
What she should do is breed only dogs with Droopy ears that bark- Since droopy ears is recessive, dogs with this trait will only have "e" alleles since any "E' would show in their phenotype. She could get pure-breeding droopy ears in one generation.
Barking dogs is harder (because dominant alleles mask recessive ones), she can first test a barking dog to see if it is a carrier for silent traits by doing a test cross with a silent dog (silent dogs must be ss), if any F1 dogs are silent, she knows that the barking parental is a carrier for silent (since a SS would produce all Ss F1s with a test cross and therefore be barkers). If the dog is not a carrier and is droopy eared- it will pure breed for these two traits.
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