To solve this problem, we need to understand the types of natural selection and how they affect the distribution of traits in a population.$\newline$Natural selection can lead to different types of changes in a population:$\newline \bullet$Stabilizing selection: This type of selection favors the average individuals in a population. It reduces variation and tends to maintain the status quo by selecting against extreme traits.$\newline \bullet$Directional selection: This type of selection favors individuals at one extreme of the trait distribution. It leads to a shift in the population's trait distribution towards that extreme.$\newline \bullet$Disruptive selection: This type of selection favors individuals at both extremes of the trait distribution, leading to a bimodal distribution.$\newline \bullet$Random change: This refers to changes that occur due to random events, not due to natural selection.$\newline$The question states that more individuals acquire a specific character value other than the mean character value. This indicates that the population is shifting towards one extreme, which is characteristic of directional selection.$\newline$Therefore, the correct answer is Option 2: Directional change.