What term describes a rapid and substantial increase in population or numbers?

The term that describes a rapid and substantial increase in population or numbers is "pullulation." This word originates from the Latin "pullulatio," which means to sprout or bud, and it specifically refers to the act of proliferating or flourishing rapidly. In demographic and ecological contexts, pullulation often pertains to the growth of populations, especially in situations where environmental conditions favor reproduction and survival.

In contrast, the other options reflect processes or states that are quite different from a population increase. For example, "decline" refers to a decrease in numbers or quality, while "stagnation" signifies a period of little to no growth or change. "Reduction," similarly, indicates a diminishment in size, quantity, or extent. Hence, pullulation stands out as the term that accurately captures the essence of a substantial increase in population.