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is the density-dependent crowding effect (also known as intraspecific competition). In this equation, the population equilibrium (sometimes referred to as the
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sometimes represents the maximum number of individuals that the environment can support. In relation to the density-dependent crowding effect,
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863:
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Traité élémentaire des fonctions elliptiques : ouvrage destiné à faire suite aux traités élémentaires de calcul intégral
824:
Studies in
History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences
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66:
Verhulst developed the logistic function in a series of three papers between 1838 and 1847, based on research on modeling
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Mémoires de l'Académie Royale des
Sciences, des Lettres et des Beaux-Arts de Belgique
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Nouveaux Mémoires de l'Académie Royale des
Sciences et Belles-Lettres de Bruxelles
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614:{\displaystyle {\frac {1}{N(t)}}={\frac {1-e^{-rt}}{K}}+{\frac {e^{-rt}}{N(0)}}.}
49:
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411:. The Pearl-Reed logistic equation can be integrated exactly, and has solution
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727:[Mathematical Researches into the Law of Population Growth Increase].
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808:(Technical report). Vol. 119. Tinbergen Institute. pp. 167–178.
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because of similarity of form, it is actually more closely related to the
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Although the continuous-time logistic equation is often compared to the
725:"Recherches mathématiques sur la loi d'accroissement de la population"
33:
681:"Notice sur la loi que la population suit dans son accroissement"
364:{\displaystyle {\frac {dN}{dt}}=rN\left(1-{\frac {N}{K}}\right)}
822:
Cramer, J. S. (2004). "The early origins of the logit model".
750:"Deuxième mémoire sur la loi d'accroissement de la population"
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popularized the equation, but with a presumed equilibrium,
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that he conducted in the mid 1830s, under the guidance of
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502:(0). The solution can also be written as a weighted
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of the initial condition and the carrying capacity,
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639:derives its name from the competing dynamics of
143:{\displaystyle {\frac {dN}{dt}}=rN-\alpha N^{2}}
36:– 15 February 1849, in Brussels) was a Belgian
476:{\displaystyle N(t)={\frac {K}{1+CKe^{-rt}}}}
161:) represents number of individuals at time
262:{\displaystyle N^{*}={\frac {r}{\alpha }}}
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864:MacTutor History of Mathematics Archive
685:Correspondance mathématique et physique
498:is determined by the initial condition
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404:{\displaystyle \alpha ={\frac {r}{K}}}
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647:introduced by the equations above.
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802:The origins of logistic regression
748:Verhulst, Pierre-François (1847).
723:Verhulst, Pierre-François (1845).
704:Verhulst, Pierre-François (1841).
679:Verhulst, Pierre-François (1838).
48:in 1825. He is best known for the
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76:Logistic function § History
169:the intrinsic growth rate, and
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836:10.1016/j.shpsc.2004.09.003
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859:"Pierre François Verhulst"
632:of fisheries recruitment.
277:he named the solution the
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900:19th-century male writers
869:University of St Andrews
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494:(0) − 1/
30:Pierre François Verhulst
25:Pierre François Verhulst
183:{\displaystyle \alpha }
895:Belgian mathematicians
799:Cramer, J. S. (2002).
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81:Verhulst published in
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667:Logistic distribution
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219:{\displaystyle N^{*}}
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32:(28 October 1804, in
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637:R/K selection theory
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853:O'Connor, John J.;
814:10.2139/ssrn.360300
657:Population dynamics
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46:University of Ghent
710:. Bruxelles: Hayez
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62:Logistic function
56:Logistic equation
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50:logistic growth
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60:Main article:
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762:. Retrieved
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737:. Retrieved
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693:. Retrieved
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662:Logistic map
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626:logistic map
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890:1849 deaths
885:1804 births
787:Cramer 2002
764:18 February
739:18 February
714:18 February
695:18 February
290:Lowell Reed
879:Categories
774:References
691:: 113–121
582:−
555:−
547:−
460:−
386:α
344:−
255:α
242:∗
212:∗
178:α
128:α
125:−
44:from the
651:See also
34:Brussels
284:Later,
52:model.
760:: 1–32
735:: 1–42
486:where
374:where
153:where
74:; see
806:(PDF)
673:Works
296:, as
226:, is
766:2013
741:2013
716:2013
697:2013
643:and
490:= 1/
288:and
832:doi
810:doi
273:In
199:),
881::
867:,
861:,
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826:.
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756:.
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731:.
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600:0
597:(
594:N
588:t
585:r
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572:+
567:K
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551:e
544:1
538:=
532:)
529:t
526:(
523:N
519:1
500:N
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492:N
488:C
466:t
463:r
456:e
452:K
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446:+
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434:=
431:)
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425:(
422:N
397:K
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389:=
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341:1
337:(
333:N
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327:=
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318:d
313:N
310:d
294:K
269:.
252:r
247:=
238:N
208:N
197:K
167:r
163:t
159:t
157:(
155:N
136:2
132:N
122:N
119:r
116:=
110:t
107:d
102:N
99:d
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