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One may then define the generation time as the time it takes for the population to increase by a factor of . For example, in microbiology , a population of cells undergoing exponential growth by mitosis replaces each cell by two daughter cells, so that R 0 = 2 {\displaystyle \textstyle R_{0}=2} and T {\displaystyle T} is the population doubling ...
The notion of doubling time dates to interest on loans in Babylonian mathematics. Clay tablets from circa 2000 BCE include the exercise "Given an interest rate of 1/60 per month (no compounding), come the doubling time." This yields an annual interest rate of 12/60 = 20%, and hence a doubling time of 100% growth/20% growth per year = 5 years.
The doubling time (t d) of a population is the time required for the population to grow to twice its size. [24] We can calculate the doubling time 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 twice its size (2N) after the doubling time. [20]
Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. [2] George Pólya writes in Mathematics and plausible reasoning: The name "generating function" is due to Laplace. Yet, without giving it a name, Euler used the device of generating functions long before Laplace [..].
A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as (p + q) 2:2(p + q)(q + r):(q + r) 2, or as p 1:2q 1:r 1, say. The interesting question is: in what circumstances will this distribution be the same as that in the generation before?
In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
As the Jewish Festival of Lights, or Hanukkah, is fast approaching (December 25, 2024 to January 2, 2025), we’re looking forward to playing dreidel (and winning gelt!), lighting the menorah with ...
Coalescent theory is a model of how alleles sampled from a population may have originated from a common ancestor.In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure, meaning that each variant is equally likely to have been passed from one generation to the next.
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