Final answer:
The genotype of a closely linked marker to the DM animals that are homozygous for the recessive DM-allele would be homozygous. This results from linked genetic markers being inherited together. The lethal allele concept, which alters expected genotypic ratios in certain crosses, is also important in understanding inheritance but is secondary to this question.
Step-by-step explanation:
If DM animals are homozygous for the recessive DM-allele, we would expect the genotype of a closely linked marker to be homozygous. This is because linked markers tend to be inherited together due to their close proximity on the chromosome; thus, if the animals are homozygous for one allele, they are likely to be homozygous for a closely linked allele as well. For example, if the DM allele is dd and it's closely linked with a marker allele which could be represented as either MM or mm, one would expect the marker to also be mm in these animals due to the homozygous nature of the recessive allele.
An interesting case to note is when considering lethal alleles. In mating between two individuals that are heterozygous for a recessive lethal allele, a different genotypic ratio would be expected because the homozygous recessive genotype would not be viable. Here, the expected ratio would typically be 2:1 (homozygous dominant:heterozygous) in surviving offspring but this is not directly related to the initial question, just an important concept related to genetics and inheritance.