Athro, Limited Biology Genetics Sheltie Coats

The standard way of working out what the possible offspring of two parents will be is the Punnett Square. Consider just the Merle gene in Shetland Sheepdogs. Since each individual has one pair of each chromosome, each has two copies of the Merle gene (one on each chromosome). A Punnett square is a simple graphical way of figuring out how the genes from each parent might combine. The reproductive cells (eggs and sperm) get only half the normal number of chromosomes. When an egg gets made, it recieves one of each pair of chromosomes. Likewise with sperm.

Since eggs and sperm each carry only one of each chromosome instead of a pair of each, they carry only one copy of each gene instead of two. Thus a female who carries two different flavors (alleles) for the Merle gene (heterozygous Mm), produces some eggs reproductive cells that carry one flavor (m), and some eggs that carry the other (M). A male with two different alleles for the same gene likewise produces some sperm carrying one allele (m) and some sperm carrying the other (M). This is the basis of the Punnet square - line up the possible reproductive cells for one parent on one side of the square, and the possible reproductive cells for the other on the other side, and combine them in the middle to show all possible combinations of alleles of this genes from the two parents.

The Merling gene has dominant M and recessive m flavors (alleles). What happens if two parents each carrying one of each allele (Mm) (heterozygous: blue merle, sable merle, or bi-blue) mate? Put the possible eggs for the mother along the top of the square (m) and (M), and the possible sperm for the father along the side (m) and (M). The square has four boxes in it, fill each box with the allele above it from the mother, and the allele beside it from the father. This is a possible combination of alleles of that gene in a puppy. The four boxes in the square represent the four possible combinations of the alleles.

A Punnett square:

This cross yeilds three possible genotypes in the offspring - MM, Mm, and mm. The Punnett square also indicates how likely a particular child of this mating is to have a given genotype. In this case, there is a 25% chance that the child would be mm, 50% that it would be Mm and 25% that it would be a double merle: MM. This is like throwing a four sided die, with mm written on one side, Mm written on two, and MM on the other. This die gets thrown once for each puppy. If the cross produces several puppies, each gets one toss of the die (except identical twins). Thus on average, about 25% of the puppies in a litter of this cross should have a genotype of mm (and not be merled). However, remember that this is a separate combination of egg and sperm, a separate toss of the dice for each individual. It is possible to throw the dice four times and get mm each time, likewise it is possible to get four out of four mm puppies from this cross (and less desirably it is equally possible to get four out of four double merles from this cross). It is simply less probable than only one out of four puppies having a genotype of mm.

The Merling gene is one gene with two alleles: M-dominant, m-recessive. Since an individual has a pair of each chromosome, they have two copies of the gene. An individual can have a genotype of BB (Homozygous dominant: Double merle), Bb (Heterozygous: Blue merle, bi-blue, or sable merle), or bb (Homozygous Recessive: Pure for sable, Trifactored, Tricolor, Bicolor) with sable, bicolor and tricolor depending on the alleles for the Agouti gene.

This simple case of a single gene is called a monohybrid cross - simply meaning that there is one gene and two possible alleles for that gene. It is quite rare for an aspect of an organism's appearance to be controled by genes as simple as this. Consider that each gene is a length of DNA with many base pairs - many possible sites where a mutation could produce a change. All genes have the potential to come in lots of mutant flavors - lots of alleles. Adding a third or fourth allele for a gene doesn't make the Punnett square any more complex though, as each parent can only have two copies (two alleles) of each gene. It is simply a matter of figuring out the alleles in each parent, lining them up on the top and side of the square and filling in the boxes with one allele from each parent.

Another step up in complexity is to consider two genes: A dihybrid cross.

In a dihybrid cross we consider Two independent genes. Think of these as being on two different chromosomes (most genes seem to assort independently but there aren't that many chromosomes - that tells us about recombination, but that's another story...) If we have two genes that are independent, either copy of each could end up in a reproductive cell with either copy of the other. Thus our Punnett Square needs to have four rows along the top, and four rows along the side - to consider all four possible combinations of the two copies of the two genes.

Thus in this case, the probablity of a puppy having the a^ba^bmm genotype is:

Also, in this case, the probablity of a puppy being a double merle is:

Other Examples of Genes

It is rare that an aspect of an organism will be controled by a single gene that has just two alleles. Most real world phenotypes are produced by complex inteactions between sets of genes.