changes in the condition of the pasture. Fisheries In fisheries, carrying capacity is used in the formulae to calculate sustainable yields for fisheries management. The maximum sustainable yield (MSY) is defined as "the highest average catch that can be continuously taken from an exploited population (=stock) under average environmental conditions". MSY was originally calculated as half of the carrying capacity, but has been refined over the years, now being seen as roughly 30% of the population, depending on the species or population. Because the population of a species which is brought below its carrying capacity due to fishing will find itself in the exponential phase of growth, as seen in the Verhulst model, the harvesting of an amount of fish at or below MSY is a surplus yield which can be sustainably harvested without reducing population size at equilibrium, keeping the population at its maximum recruitment. However, annual fishing can be seen as a modification of r in the equation -i.e. the environment has been modified, which means that the population size at equilibrium with annual fishing is slightly below what K would be without it. Note that mathematically and in practical terms, MSY is problematic. If mistakes are made and even a tiny amount of fish are harvested each year above the MSY, populations dynamics imply that the total population will eventually decrease to zero. The actual carrying capacity of the environment may fluctuate in the real world, which means that practically, MSY may actually vary from year to year (annual sustainable yields and maximum average yield attempt to take this into account). Other similar concepts are optimum sustainable yield and maximum economic yield; these are both harvest rates below MSY. These calculations are used to determine fishing quotas. Humans Human carrying capacity is a function of how people live and the technology at their disposal. The two great economic revolutions that marked human history up to 1900—the agricultural and industrial revolutions—greatly ramped up Earth’s human carrying capacity, from 5 to 10 million people 10,000 BCE to 1.5 billion in 1900. The immense technological improvements of the past 100 years—in applied chemistry, physics, computing, genetic engineering, and more—have further increased Earth’s human carrying capacity, at least in the short term. Without the Haber-Bosch process for fixing nitrogen, modern agriculture could not support 8 billion people. Without the Green Revolution of the 1950s and 60s, famine might have culled large