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A population cycle in zoology is a phenomenon where populations rise and fall over a predictable period of time. There are some species where population numbers have reasonably predictable patterns of change although the full reasons for population cycles is one of the major unsolved ecological problems.
Thomas Robert Malthus, after whom Malthusianism is named. Malthusianism is a theory that population growth is potentially exponential, according to the Malthusian growth model, while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population decline.
P 0 = P(0) is the initial population size, r = the population growth rate, which Ronald Fisher called the Malthusian parameter of population growth in The Genetical Theory of Natural Selection, [2] and Alfred J. Lotka called the intrinsic rate of increase, [3] [4] t = time. The model can also be written in the form of a differential equation:
This definition is a measure of the distance between generations rather than a renewal time of the population. Since many demographic models are female-based (that is, they only take females into account), this definition is often expressed as a mother-daughter distance (the "average age of mothers at birth of their daughters").
Ecologists have been unable to successfully explain regular population cycles for many decades; delayed density dependence may hold the answer. [2] Here populations are allowed to increase above their normal capacity because there is a time lag until negative feedback mechanisms bring the population back down.
Population pyramid of Portugal in 2023 (Stage five). Population pyramid of Belarus in 2023 (Stage five). United Nation's population projections by location. Note the vertical axis is logarithmic and represents millions of people. The original Demographic Transition model has just four stages, but additional stages have been proposed.
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The half-life of a population is the time taken for the population to decline to half its size. We can calculate the half-life of a geometric population using the equation: N t = λ t N 0 by exploiting our knowledge of the fact that the population (N) is half its size (0.5N) after a half-life. [20]