Introduction<br>In theory, any kind of organism could take over the Earth just by reproducing. For instance, imagine that we started with a single pair of male and female rabbits. If these rabbits and their descendants reproduced at top speed ("like bunnies") for 777 years, without any deaths, we would have enough rabbits to cover the entire state of Rhode Island^{1,2,3}1,2,3start superscript, 1, comma, 2, comma, 3, end superscript. And that's not even so impressive – if we used E. coli bacteria instead, we could start with just one bacterium and have enough bacteria to cover the Earth with a 111-foot layer in just 363636 hours^44start superscript, 4, end superscript!<br>As you've probably noticed, there isn't a 111-foot layer of bacteria covering the entire Earth (at least, not at my house), nor have bunnies taken possession of Rhode Island. Why, then, don't we see these populations getting as big as they theoretically could? E. coli, rabbits, and all living organisms need specific resources, such as nutrients and suitable environments, in order to survive and reproduce. These resources aren’t unlimited, and a population can only reach a size that match the availability of resources in its local environment.<br>Population ecologists use a variety of mathematical methods to model population dynamics (how populations change in size and composition over time). Some of these models represent growth without environmental constraints, while others include "ceilings" determined by limited resources. Mathematical models of populations can be used to accurately describe changes occurring in a population and, importantly, to predict future changes.
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