was not explicitly used in 1838 by the Belgian mathematician Pierre François Verhulst when he first published his equations based on research on modelling population growth. The origins of the term "carrying capacity" are uncertain, with sources variously stating that it was originally used "in the context of international shipping" in the 1840s, or that it was first used during 19th-century laboratory experiments with micro-organisms. A 2008 review finds the first use of the term in English was an 1845 report by the US Secretary of State to the US Senate. It then became a term used generally in biology in the 1870s, being most developed in wildlife and livestock management in the early 1900s. It had become a staple term in ecology used to define the biological limits of a natural system related to population size in the 1950s. Neo-Malthusians and eugenicists popularised the use of the words to describe the number of people the Earth can support in the 1950s, although American biostatisticians Raymond Pearl and Lowell Reed had already applied it in these terms to human populations in the 1920s. Hadwen and Palmer (1923) defined carrying capacity as the density of stock that could be grazed for a definite period without damage to the range. It was first used in the context of wildlife management by the American Aldo Leopold in 1933, and a year later by the American Paul Lester Errington, a wetlands specialist. They used the term in different ways, Leopold largely in the sense of grazing animals (differentiating between a 'saturation level', an intrinsic level of density a species would live in, and carrying capacity, the most animals which could be in the field) and Errington defining 'carrying capacity' as the number of animals above which predation would become 'heavy' (this definition has largely been rejected, including by Errington himself). The important and popular 1953 textbook on ecology by Eugene Odum, Fundamentals of Ecology, popularised the term in its modern meaning as the equilibrium value of the logistic model of population growth. Mathematics The specific reason why a population stops growing is known as a limiting or regulating factor. The difference between the birth rate and the death rate is the natural increase. If the population of a given organism is below the carrying capacity of a given environment, this environment could support a positive natural increase; should it find itself above that threshold