Yes, populations do have genomes, but they also possess gene pools. To understand this, we need to define both terms.
A genome is the complete set of genetic information – including all of its genes – in an organism. This means that every individual in a population has a genome that contains the hereditary material inherited from their ancestors. Therefore, in any given population, you will find a variety of genomes based on the genetic makeup of each individual.
On the other hand, a gene pool refers to the total collection of genes and their different alleles within that population. It encompasses all the genetic diversity available for reproduction among the individuals in that population. The gene pool provides the genetic basis for evolution, adaptation, and the potential for future generations.
In summary, while every individual in a population carries its own genome, the gene pool represents the collective genetic resources of that population. Thus, the notion that populations possess genomes but lack gene pools is not accurate. Both are integral components of population genetics.