Mathematics is essential in scientific inquiry. Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations, and communicating results. Species evolve over time. Populations grow or decline through the combined effects of births and deaths and through emigration and immigration into specific areas. Populations can increase through linear or exponential growth, with effects on resource use and on environmental pollution.
Populations can reach limits to growth.
Carrying capacity is the maximum number of organisms that can be supported by a given environment. Living organisms have the capacity to produce populations of arbitrarily large size, but environments and resources are finite. This fundamental tension has profound effects on the interactions between organisms. The tension between expanding populations and limited resources was a fundamental point that Darwin came to understand when he read Thomas Malthus. This understanding subsequently had an important influence on the formulation of his theory of natural selection.