Final answer:
The lemming population in a warming mountainous region would most likely adapt if they had alleles for heat resistance, as this would allow them to regulate their body temperature effectively in the new warmer climate.
Step-by-step explanation:
The lemming population would be MOST likely to adapt to a drier and warmer climate if individuals in the population had alleles for heat resistance. Alleles for cold resistance, tree-climbing ability, or long fur would not be as advantageous under warmer conditions. Heat resistance could help lemmings regulate their body temperature and survive in the changed environment.
When considering evolutionary adaptation, the available alleles within a population can determine the potential for survival in new conditions. As the climate becomes warmer, selective pressure would favor individuals that are more tolerant to heat, ultimately leading to a greater proportion of these traits in subsequent generations. This concept is similar to the idea of a cline, where traits vary along a gradient, in this case, a gradient of temperature. However, if heat-resistant traits are not present in the population, the lemmings may not adapt successfully and could decline in numbers or become extinct in the area.