Aphids are born pregnant, can reproduce without sex, and are fully grown in a week. Microorganisms, including fungi and bacteria, can double their number in hours or days and produce many thousands of spores in a small area. Many plants can reproduce asexually. Field bindweed spreads by way of underground rhizomes. If you break up one of these rhizomes by spading or tilling, each piece of rhizome is capable of producing a new plant.
Pests can also disperse their numbers over time.
A single musk thistle head can produce 1000 seeds. The seeds, carried by the wind, will land almost anywhere. Each seed is capable of lying dormant in the soil for many years. In other words, a successful pest species will be able to put out a sufficient number of egg, spore, or seed to be able to take advantage of the next time environmental conditions are favorable for its reproduction and growth. Think about how plants appear in nature.