Question

A dog has 39 pairs of chromosomes. Considering only the random alignment of chromosomes, how many genetically different puppies are possible when two dogs mate? Is this number an underestimate or overestimate of the actual total? Why?

Short answer

The total number of genetically different puppies possible when two dogs mate, considering only the random alignment of chromosomes, is \(2^{39}\). However, this number is an underestimate of the total actual variability, because it doesn't consider the additional genetic diversity introduced through recombination during meiosis.

Step-by-step solution

Calculate the Genetical Variability

To calculate the genetically different puppies each dog can produce only considering the random alignment of chromosomes, the formula is \(2^n\), where \(n\) represents the number of pairs of chromosomes. In this case, n=39, representing the 39 pairs of chromosomes in each dog. To find the number of combinations, we carry out the calculation \(2^{39}\). However, keep in mind this goes for only one dog, not both.

Interpret over or underestimate

To determine if this number is an overestimate or underestimation, we need to consider recombination during meiosis, where chromosomes can cross over and exchange genes. This process generates more genetic diversity, which implies that the number calculated in Step 1 will only account for the variability from independent assortment. The recombination introduces another layer of complexity, thus the calculated number would be an underestimate of the total possible genetically different puppies.

Key concepts

Chromosome Alignment

Chromosome alignment is a critical biological process during meiosis where homologous chromosomes are paired up and aligned in the middle of the cell before being separated into different cells. In dogs, which have 39 pairs of chromosomes, this alignment is random. This means that each chromosome pair can line up in multiple ways, contributing significantly to genetic diversity.
During meiosis, each chromosome from a pair can orient differently, resulting in different mixes of chromosomes in the gametes (sperm or eggs).

• Random alignment occurs in metaphase I of meiosis where paired homologous chromosomes line up along the cell's equatorial plane.
• This random alignment ensures that each gamete receives a different set of alleles, enhancing genetic variability in offspring.

The number of possible combinations due to random alignment in dogs is calculated as \(2^{39}\), as each of the 39 chromosome pairs can align in two different ways independently.

Meiosis and Recombination

Meiosis is a special type of cell division that reduces the chromosome number by half, producing four haploid cells, each genetically distinct from the parent cell. An essential feature of meiosis is genetic recombination, which occurs during prophase I. Recombination or "crossing over" further increases genetic diversity by allowing homologous chromosomes to exchange segments.

• During crossing over, homologous chromosomes exchange genetic material at points called chiasmata.
• This process introduces new combinations of alleles on each chromosome, contributing to the uniqueness of each gamete.

Recombination ensures that the offspring carry a mix of traits that are different from either parent, intensifying genetic variability.
It is one of the reasons why the genetically distinct combinations produced by just independent assortment (chromosome alignment) is an underestimate compared to actual genetic diversity.

Genetic Variability Calculation

Genetic variability in offspring is calculated considering various factors during meiosis. One such factor is independent assortment, analyzed through the formula \(2^n\), where \(n\) equals the number of chromosome pairs. For dogs, this calculation becomes \(2^{39}\), yielding a large number of potential genetic combinations just from how chromosome pairs align randomly.
However, this calculation doesn't encompass all sources of genetic variation, as it solely perturbs permutations resulting from independent assortment.

• This number does not include additional variability introduced by recombination during meiosis.
• Each crossover event during recombination can drastically alter genetic make-up, producing even more combinations in gametes.

Consequently, while \(2^{39}\) provides a huge number of genetically distinct offspring, the actual potential is greater when taking into account recombination. Hence, the calculation is typically an underestimate.
It demonstrates how extensively processes during meiosis contribute to genetic diversity, crucial for the adaptability and evolution of species.