Fur: Polar bears have thick, white fur that insulates them from the cold. In a desert environment, they would likely develop thinner fur with a lighter coloration to reflect sunlight and reduce heat absorption.
Body Size: Polar bears have large bodies that help them retain heat in the Arctic. To adapt to the desert, they might evolve smaller body sizes to reduce their surface area and minimize water loss.
Behavior: Polar bears in the Arctic hunt seals from sea ice. In the desert, they would need to develop new hunting strategies. They could become opportunistic scavengers, feeding on small desert animals or insects, and perhaps even plants if necessary.
Water conservation: Polar bears typically get their water from sea ice or by drinking seawater and filtering out the salt. In the desert, they would have to be extremely efficient at conserving water. They might develop the ability to store water more efficiently in their bodies or extract water from their food.
Hibernation: Polar bears conserve energy by hibernating during the Arctic winter. In the desert, they might develop shorter periods of dormancy or estivation to survive through extremely hot periods.
Burrowing: Polar bears could adapt by digging burrows or finding shelter under rocks or in caves to escape the scorching desert sun and extreme temperatures.
Sweat glands: Polar bears don't have sweat glands, but to survive in the desert, they might evolve sweat glands to help regulate their body temperature through evaporation.
Population Genetics: Over time, the polar bear population in the desert would experience genetic changes due to natural selection. Individuals with genetic traits that allow them to better tolerate heat and conserve water would have a higher chance of survival and reproduction, passing on these traits to future generations.
It's important to note that these adaptations would take place over an extensive evolutionary timescale, requiring thousands or even millions of years. Polar bears are highly specialized for life in the Arctic and transitioning to a desert environment would be extremely challenging, if not impossible in practice.