To solve this problem, we need to identify which gas's depletion in the atmosphere can lead to an increased incidence of skin cancers.$\newline$Let's analyze each option:$\newline \bullet$Option 1: Nitrous oxide - This gas is not directly linked to skin cancer incidence. It is a greenhouse gas and contributes to global warming.$\newline \bullet$Option 2: Ozone - Ozone in the stratosphere forms a layer that absorbs the majority of the sun's harmful ultraviolet (UV) radiation. Depletion of this ozone layer increases UV exposure, leading to a higher risk of skin cancers.$\newline \bullet$Option 3: Ammonia - This gas is not associated with skin cancer. It is commonly found in fertilizers and cleaning products.$\newline \bullet$Option 4: Methane - Methane is a potent greenhouse gas but does not have a direct link to skin cancer.$\newline$Based on this analysis, the correct answer is Option 2: Ozone.$\newline$The depletion of ozone in the atmosphere can lead to an increased incidence of skin cancers due to higher exposure to UV radiation.