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The Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology named after Patrick H. Leslie. [1] [2] The Leslie matrix (also called the Leslie model) is one of the most well-known ways to describe the growth of populations (and their projected age distribution), in which a population is closed to migration, growing in an unlimited ...
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:
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]
Population modeling became of particular interest to biologists in the 20th century as pressure on limited means of sustenance due to increasing human populations in parts of Europe were noticed by biologist like Raymond Pearl. In 1921 Pearl invited physicist Alfred J. Lotka to assist him in his lab.
Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. [ 2 ] The global population has grown from 1 billion in 1800 to 8.1 billion in 2024. [ 3 ] The UN projected population to keep growing, and estimates have ...
In the study of age-structured population growth, probably one of the most important equations is the Euler–Lotka equation.Based on the age demographic of females in the population and female births (since in many cases it is the females that are more limited in the ability to reproduce), this equation allows for an estimation of how a population is growing.
Matrix population models are a specific type of population model that uses matrix algebra. Population models are used in population ecology to model the dynamics of wildlife or human populations. Matrix algebra, in turn, is simply a form of algebraic shorthand for summarizing a larger number of often repetitious and tedious algebraic ...
The book An Essay on the Principle of Population was first published anonymously in 1798, [1] but the author was soon identified as Thomas Robert Malthus.The book warned of future difficulties, on an interpretation of the population increasing in geometric progression (so as to double every 25 years) [2] while food production increased in an arithmetic progression, which would leave a ...