Notice sur la loi que la population suit dans son accroissement¶
Verhulst, P. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Amara's Law
- Let cumulative impact follow the S-shaped realization curve \(f(t) = L / (1 + e^{-k(t - t_0)})\), with low early slope, a steep middle, and a saturating plateau at \(L\).
This sourceOrigin of the logistic growth curve f(t)=L/(1+e^{-k(t-t0)}) used as the S-shaped realization curve.
Supported in partVerified against the publisher's abstract
The abstract confirms Verhulst introduced the logistic equation in 1838 with a saturating maximum, i.e. the shape the curve is credited with, but states no parameterization and no three-phase description.
“In 1838 the Belgian mathematician Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population.”
- Let cumulative impact follow the S-shaped realization curve \(f(t) = L / (1 + e^{-k(t - t_0)})\), with low early slope, a steep middle, and a saturating plateau at \(L\).
- Carrying Capacity
- A population N grows according to dN/dt = rN(1 − N/K), where r is the intrinsic growth rate and K is the carrying capacity.
This sourceIntroduces the logistic growth equation dN/dt = rN(1 − N/K) with K as the carrying capacity. (Link is Bacaër's annotated reproduction and translation of the original memoir.)
Supported in partVerified against the publisher's abstract
Bacaër's abstract confirms that Verhulst introduced the logistic equation with a maximum population value, but it does not state the formula dN/dt = rN(1 − N/K) or name r the intrinsic growth rate.
“In 1838 the Belgian mathematician Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population.”
- A population N grows according to dN/dt = rN(1 − N/K), where r is the intrinsic growth rate and K is the carrying capacity.
- Logistic Growth
- In population biology and ecology, the Verhulst-Pearl equation for a population growing into a fixed-resource environment is the original substrate, with the S-curve falling out of births proportional to current population and deaths rising with density.
This sourceOriginal derivation of the logistic equation dN/dt = rN(1 − N/K) for population growing against a finite ceiling, with its sigmoid solution, fixed points, and half-ceiling inflection. (Reproduced and analyzed in Bacaër 2011, ch. 6: https://doi.org/10.1007/978-0-85729-115-8_6)
Supported in partVerified against the publisher's abstract
Confirms Verhulst introduced the logistic equation with a maximum population value in 1838, but is a 2011 chapter abstract that says nothing about births proportional to population or density-dependent deaths.
“In 1838 the Belgian mathematician Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population.”
- In population biology and ecology, the Verhulst-Pearl equation for a population growing into a fixed-resource environment is the original substrate, with the S-curve falling out of births proportional to current population and deaths rising with density.
- Nonlinearity
- Biology and ecology uses nonlinearity for logistic population growth (Verhulst
This source(Originating treatment of the logistic equation `dN/dt = rN(1 − N/K)` for population growth with a carrying-capacity saturation; founding instance of saturation nonlinearity in dynamical modelling.)
- Biology and ecology uses nonlinearity for logistic population growth (Verhulst
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 3 of 4 citations: 3 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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Links previously used in the corpus¶
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