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First, write out the genotypes of the mice being crossed. When a trait is HOMOZYGOUS, both of the alleles (versions of that gene) will be in the same case. So if the trait is dominant, like the R for running, a homozygous dominant mouse would be RR (remember that mice, and most other organisms you'll be working with for genetics problems, are diploid, so they have two sets of chromosomes - and two of each gene). If the mouse was homozygous for the recessive trait, it would be rr. If the mouse is HETEROZYGOUS, then the letters are one of each case, so one allele is dominant and the other is recessive, so Rr. Hetero = "different".
So a a heterozygous running/heterozygous black mouse has the genotype RrBb. A homozygous running/homozygous black mouse has the genotype RRBB.
Next, figure out what possible combinations of alleles can exist in the gametes from each mouse. Each gamete has to have the full "set of instructions" to produce a new mouse, so each trait has to be accounted for in each gamete. So there has to be both a "R" and a "B" in each gamete, regardless of whether it's upper or lower case. You can't have two Rs and no Bs or two Bs and no Rs. When fertilization occurs, the offspring will inherit a complete set of genes from each parent, so there will be two of each gene again.
To figure out what the possible allele combinations are for each gamete from each parent, look at their genotypes. The parent that's RRBB is easier, as this mouse can only produce RB gametes. The one that's RrBb is a little harder. There are four possibilities. The way to figure out how many possible combinations there are is that for a diploid organism, use a base 2 and raise it to the power of how many traits there are in your problem. You're using two traits (running type and color), so 2^2=4 (or you can multiply 2 twice: 2 x 2 = 4. So your problem has four possible gametes. If there were three traits, you'd use 2^3 or 2 x 2 x 2 = 8.
To figure out the possible combinations for a two-trait problem use FOIL - the First letters from each pair, the Outside two, the Inside two, and the Last two. So for RrBb the possible combinations are RB, Rb, rB, and rb. There are four from the homozygous mouse as well, but all are RB, regardless of whether you use the "first" R and B or the "last" of each pair of letters.
Now, use these letters to make your Punnett square. Each parent produces four types of gametes, so the square will be 4 x 4 blocks:
Combine the letters in each row with those at the top of the column to see what the genotypes of the offspring are from the combination of the two gametes. I did the first column for you to show you how it's done. If either trait has a dominat allele (upper case letter) write that one first - it makes it easier to see if there's a dominant allele when you go to write the phenotypes.
When you have all the blocks finished, count up how many you have of each EXACT set of letters. You'll have four that are RRBB for instance (the top row). Use these numbers to write your genotypic ratio. The genotypic ratio is only concerned with the LETTERS that are used. You should get the answer of RRBB = 4, RRBb = 4, RrBB = 4, and RrBb = 4. So your genotypic ratio will be 4:4:4:4. In a two trait cross, the number will add up to 16 (you have 4 x 4 = 16 blocks in the Punnett square. That's a way you can check to make sure you counted them all.
To figure out the phenotypic ratio, you now have to "translate" what the genotypes produce. The phenotypic ratio is concerned with how the genes are expressed, so the phenotyes will always be descriptive words, such as "running" "waltzing", "black" or "brown". When you count the phenotypes, remember that for a trait with complete dominance, both the homozygous dominant and the heterozygous genotypes will procude the dominat phenotype. That is, whether the mouse is BB or Bb, it will be black. The only way it can be brown is for the genotype to be bb. The same goes for running type, RR and Rr will be running mice, rr will be waltzing. So find what the phenotype is for each of the genotypes you found in the first part of your problem. Then write out the phenotypic ratio the same way, ___running/black : ___ running/brown : ___waltzing/black : ___waltzing brown. (NOTE: you may not get all these combinations, just write your ratio for the phenotypes you get unless your instructor wants you to show all possible phenotypes, even if they aren't produced - and sometimes all offspring will have the same phenotype even if they have different genotypes; in this case, you can say all [or 100%] were _____). I'll let you work this portion on your own.
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