The Bible doesn't say anything about overpopulation. Questions about overpopulation and population control often arise from a deeply entrenched modern mindset. Unfounded fears of overpopulation abound, showing a lack of trust in God. Overpopulation is a possibility in our world only if resources became depleted, no one ever died, and if genes and fertility rates were untainted by sin.
However, the question does not concern Adam and Eve in a fallen world but in a perfect, sinless world—the original creation that was far different from today's world. The question thus becomes hypothetical as we try to speculate about modern concerns of overpopulation in a radically different environment. A creation with sinless man wisely overseeing the earth's resources and living in charitable harmony is completely foreign to us.
This question can also arise from two other factors: not understanding how God rules the universe He created (Colossians 1:16-17) and misreading the text. The word "fill" in Genesis 1:28 means to fill to capacity, not to over-fill beyond capacity. God saw that His creation was very good (Genesis 1:31) including natural limits on the maximum capacity for both animal and human populations.
Overpopulation is the idea that humanity may become too numerous to be sustained by their environment or resources in the long term, either globally or locally. The belief that global population levels will become too large to sustain is a point of contentious debate. Human population growth has actually been decreasing since 1968 and it is predicted that the population itself will likely peak, and possibly even begin to decrease, before 2100. Previously predicted "population explosions" have not materialized; instead, population growth has slowed. Further, advancements in technology have greatly increased humanity’s ability to produce food and resources. Due to a lack of evidence, some scholars refer to human overpopulation as a myth.
Population dynamics, a branch of mathematical biology, has determined that no population can increase without limitation. Instead, populations in natural ecosystems increase or decrease in response to changes that restrict growth, such as available food, shelter and population density. Unlimited population growth in the animal kingdom doesn't happen, partly because populations compete for finite resources. Human beings are uniquely equipped to overcome some of those limitations. In an ideal, sinless world, we would always do so in responsible and reasonable ways. But even in our fallen state, the idea of global overpopulation seems unlikely.