Logistic Functions: Difference between revisions
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From Stephen Strogatz' Nonlinear Dynamics and Chaos | From Stephen Strogatz' Nonlinear Dynamics and Chaos | ||
"The algebraic form of the model is not to be taken literally. The model should really be regarded as a metaphor for populations that have a tendency to grow from zero population up to some carrying capacity K. Â | <blockquote>"The algebraic form of the model is not to be taken literally. The model should really be regarded as a metaphor for populations that have a tendency to grow from zero population up to some carrying capacity K. Â | ||
Originally a much stricter interpretation was proposed, and the model was argued to be a universal law of growth (Pearl 1927). The logistic equation was tested in laboratory experiments in which colonies of bacteria, yeast, or other simple organisms were grown in conditions of constant climate, food supply and absence of predators. For a good review of this literature, see Krebs (1972, pp. 190-200). These experiments often yielded sigmoid growth curves, in some cases with an impressive match to the logistic predictions. | Originally a much stricter interpretation was proposed, and the model was argued to be a universal law of growth (Pearl 1927). The logistic equation was tested in laboratory experiments in which colonies of bacteria, yeast, or other simple organisms were grown in conditions of constant climate, food supply and absence of predators. For a good review of this literature, see Krebs (1972, pp. 190-200). These experiments often yielded sigmoid growth curves, in some cases with an impressive match to the logistic predictions. | ||
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On the other hand, the agreement was much worse for fruit flies, flour beetles and other organisms that have complex life cycles, involving eggs, larvae, pupae and adults. In these organisms, the predicted asymptotic approach to a steady carrying capacity was never observed--instead the populations exhibited large, persistent fluctuations after an initial period of logistic growth. See Kregs (1927) for a discussion of the possible causes of these fluctuations, including age structure and time-delayed effects of overcrowding in the population. | On the other hand, the agreement was much worse for fruit flies, flour beetles and other organisms that have complex life cycles, involving eggs, larvae, pupae and adults. In these organisms, the predicted asymptotic approach to a steady carrying capacity was never observed--instead the populations exhibited large, persistent fluctuations after an initial period of logistic growth. See Kregs (1927) for a discussion of the possible causes of these fluctuations, including age structure and time-delayed effects of overcrowding in the population. | ||
For further reading on population biology, see Pielou (1969) or May (1981). Edelstein-Keshet (1988) and Murray (1989) are excellent textbooks on mathematical biology in general." | For further reading on population biology, see Pielou (1969) or May (1981). Edelstein-Keshet (1988) and Murray (1989) are excellent textbooks on mathematical biology in general."</blockquote> |
Revision as of 20:36, 27 November 2020
Critiques of the Logistic Model
From Stephen Strogatz' Nonlinear Dynamics and Chaos
"The algebraic form of the model is not to be taken literally. The model should really be regarded as a metaphor for populations that have a tendency to grow from zero population up to some carrying capacity K.
Originally a much stricter interpretation was proposed, and the model was argued to be a universal law of growth (Pearl 1927). The logistic equation was tested in laboratory experiments in which colonies of bacteria, yeast, or other simple organisms were grown in conditions of constant climate, food supply and absence of predators. For a good review of this literature, see Krebs (1972, pp. 190-200). These experiments often yielded sigmoid growth curves, in some cases with an impressive match to the logistic predictions.
On the other hand, the agreement was much worse for fruit flies, flour beetles and other organisms that have complex life cycles, involving eggs, larvae, pupae and adults. In these organisms, the predicted asymptotic approach to a steady carrying capacity was never observed--instead the populations exhibited large, persistent fluctuations after an initial period of logistic growth. See Kregs (1927) for a discussion of the possible causes of these fluctuations, including age structure and time-delayed effects of overcrowding in the population.
For further reading on population biology, see Pielou (1969) or May (1981). Edelstein-Keshet (1988) and Murray (1989) are excellent textbooks on mathematical biology in general."