Acta Biotheoretica 59 (3):273-289 (2011)
|Abstract||Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ( $$ \Uptheta $$ L ). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population ( N ) is divided into reproducing ( P ) and non-reproducing/quiescent ( Q ) sub-populations. The modes of the rate of change of ratio P / N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P / N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic ( T $$ \Uptheta $$ L ) since they exist when the $$ \Uptheta $$ L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid ( TS ). The $$ \Uptheta $$ L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T $$ \Uptheta $$ L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T $$ \Uptheta $$ L versus $$ \Uptheta $$ L for model growth curves|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Roger Buis (1997). Sur l'Interprétation de la Loi Logistique de Croissance: Une Re-Lecture de la Relation Entre Autocatalyse Et Croissance on the Interpretation of the Logistic Law of Growth: A New Reading of the Relationships Between Autocatalysis and Growth. Acta Biotheoretica 45 (3-4).
Roger Buis (1991). On the Generalization of the Logistic Law of Growth. Acta Biotheoretica 39 (3-4).
Peter Richerson, Homage to Malthus, Ricardo, and Boserup: Toward a General Theory of Population, Economic Growth, Environmental Deterioration, Wealth, and Poverty.
Gérard Cusset (1991). Les modeLes Sigmoides En Biologie Vegetale. Acta Biotheoretica 39 (3-4).
J.-C. Poggiale, P. Auger, D. Nérini, C. Manté & F. Gilbert (2005). Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model. Acta Biotheoretica 53 (4).
A. Steiner & I. Walker (1990). The Pattern of Population Growth as a Function of Redundancy and Repair. Acta Biotheoretica 38 (2).
Roger Buis, Marie-Thérèse L'Hardy-Halos & Cécile Lambert (1996). Caracterisation de la Structure d'Un Processus de Croissance. Acta Biotheoretica 44 (3-4).
Johan Grasman, Willem B. E. Van Deventer & Vincent van Laar (2012). Estimation of Parameters in a Bertalanffy Type of Temperature Dependent Growth Model Using Data on Juvenile Stone Loach (Barbatula Barbatula). Acta Biotheoretica 60 (4):393-405.
I. Walker (1993). Competition and Information. Acta Biotheoretica 41 (3).
Jorge Paulo Cancela & Kimon Hadjibiros (1977). Le Modele Matriciel Deterministe de Leslie Et Ses Applications En Dynamique Des Populations. Acta Biotheoretica 26 (4).
Marc Jarry, Mohamed Khaladi, Martine Hossaert-McKey & Doyle McKey (1995). Modeling the Population Dynamics of Annual Plants with Seed Bank and Density Dependent Effects. Acta Biotheoretica 43 (1-2).
Frank Dochy (1995). Human Population Growth: Local Dynamics-Global Effects. Acta Biotheoretica 43 (3).
Roger Buis (1993). Growth Activity and Structure at Various Organization Levels in Plants. Acta Biotheoretica 41 (3).
Werner Kroeber-Riel & Sighard Roloff (1973). Problems of Points of Inflection in Trend Functions as Described by a Model for the Forecast of Brand Shares. Theory and Decision 3 (3):222-230.
Added to index2011-05-04
Total downloads10 ( #114,274 of 722,700 )
Recent downloads (6 months)1 ( #60,006 of 722,700 )
How can I increase my downloads?