A theory of growth

Turner, Malcolm E.; Bradley, Edwin L.; Kirk, Katherine A.; Pruitt, Kenneth M.

doi:10.1016/0025-5564(76)90112-7

Cited by 155 publications

(140 citation statements)

References 8 publications

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“…This mathematical relationship represents the mechanism governing the growth process. This approach has been extensively used for somatic growth and a large number of growth functions have been derived, such as the monomolecular, logistic, and Gompertz ones (Turner et al, 1976;France and Thornley, 1984).…”

Section: Mathematical Description Of Growthmentioning

confidence: 99%

“…The early history of the subject was reviewed by Glass (1967). Turner et al (1976) presented a generalized theory of growth based on three postulates. The first asserts that the rate of growth is jointly proportional to the monotonic function of the generalized distance from the initial size to the present size ("reproductive capability"), and to a monotonic function of the generalized distance from the present size to the ultimate size ("the limiting factor").…”

Section: The Theory Of Growth Of Turner Et Almentioning

confidence: 99%

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Trajectories and models of individual growth

Karkach¹

2006

DemRes

135

104

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It has long been recognized that the patterns of growth play an important role in the evolution of age trajectories of fertility and mortality (Williams, 1957). Life history studies would benefit from a better understanding of strategies and mechanisms of growth, but still no comparative research on individual growth strategies has been conducted.Growth patterns and methods have been shaped by evolution and a great variety of them are observed. Two distinct patterns -determinate and indeterminate growth -are of a special interest for these studies since they present qualitatively different outcomes of evolution. We attempt to draw together studies covering growth in plant and animal species across a wide range of phyla focusing primarily on the noted qualitative features. We also review mathematical descriptions of growth, namely empirical growth curves and growth models, and discuss the directions of future research.1 Email: karkach@demogr.mpg.de http://www.demographic-research.org 347Karkach: Trajectories and models of individual growth IntroductionThe ontogenetic growth of an individual is intuitively understood to be an increase in the size of the whole organism or parts of it with age. But the very "natural" notion of growth is, in fact, very difficult to define. Living organisms are complex systems, consisting of parts that often grow at different rates and displaying different patterns. Some parts of the body may grow faster than others, some may stop growing at a certain stage while others continue to grow, and organs may grow "on demand" during regeneration. The cells of an organ may divide continuously throughout an organism's life, replacing aging cells and producing cell turn-over in the tissues; still the body size may remain constant. Growth is coordinated by a program of ontogenetic development that allows for variability in the development rates and sizes in order to adapt to environmental conditions. Size and growth rates are subject to evolutionary optimization and constraints. On the one hand, larger size usually leads to greater mating success, greater fertility, lower vulnerability to environmental hazards, and thus lower mortality. On the other, growth needs resources, and trades-off with other traits.Studies on growth and maintenance shed light on the problem of senescence. Most organisms experience cell turn-over in most tissues. Some organisms (e.g. hydra) apparently escape senescence due to a quick turn-over of cells (Martínez, 1998).Growth and body size are strongly related to other traits and fitness. Research on extant species showed a strong statistical relationship between body mass and a remarkable variety of biological features (Smith, 1996). Measures of growthGrowth as an increment in size can be measured in many different ways, each having advantages and drawbacks. An increase in mass or volume often can be measured easily, but may be only indirectly related to growth as increase in biomass. Organisms may change in content of water or fat, in mass and volume, but this i...

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Section: Mathematical Description Of Growthmentioning

confidence: 99%

Section: The Theory Of Growth Of Turner Et Almentioning

confidence: 99%

Trajectories and models of individual growth

Karkach¹

2006

DemRes

135

104

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“…Such a process can be described by the logistic (or limited growth) equation (Turner et al 1976). The rate of growth of recruited members (dN/dt) might then be modelled by the equation:…”

Section: Appendix C: the Modelling Rebel Group Growthmentioning

confidence: 99%

Potential uses of Numerical Simulation for the Modelling of Civil Conflict

Burton

Johnson

Braithwaite³

2017

Peace Economics, Peace Science and Public Policy

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This paper explores ways in which civil conflict can be simulated using numerical methods. A general two-party model of conflict is developed by extending an approach proposed by [Christia, F., (2012), Alliance Formation in Civil Wars, Cambridge University Press, New York], which is based on a metric of the 'relative power' that exists between the state and a rebel group. Various definitions of relative power are considered and one of these is chosen to illustrate different types of two-sided armed conflict, namely direct-fire, guerrilla and asymmetric warfare. The additional suggestion of Christia that random or stochastic events can lead to unexpected conflict outcomes is also further extended in this paper. The inclusion in the model of terms describing concurrent rebel recruitment of civilians and state deployment of troops are then described. Examples are presented for various hypothetical cases. It is demonstrated that numerical simulation techniques have great potential for modelling civil war. The Christia approach is shown to provide an excellent basis from which numerical models of civil conflict can be built and from which the progress of a conflict can usefully be visualised graphically.

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“…The Gompertz model is often used to obtain estimates of k, µ m and λ from microbial growth data [15], but (1) has previously been used to model the growth of rats [11] and cultured mammalian cells [7].…”

Section: C232mentioning

confidence: 99%

“…where β is related to µ m , λ and k, and n > 0 and −1 < p ≤ 1/n are constants [11] modulating the detailed shape of the growth curve. For convenience, the solution to (1) is…”

Section: Introductionmentioning

confidence: 99%

Two implications of common models of microbial growth

Brown¹

2007

ANZIAMJ

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Analysis of a generalised growth equation shows that both the maximum growth rate of a microbial culture and the duration of the lag phase are related to each other and to the maximum growth. Similar relationships apply to growth expressions, such as the logistic and Gompertz models, that are special cases of the generalised model. Moreover, the same relationships are observed qualitatively in measurements of the growth of Salmonella species. These results may allow the characterisation of microbial growth with fewer parameters than is usually the case and imply the likelihood of a fundamental physiological interdependence between maximum growth rate, the duration of the lag time and the maximum growth.

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A theory of growth

Cited by 155 publications

References 8 publications

Trajectories and models of individual growth

Trajectories and models of individual growth

Potential uses of Numerical Simulation for the Modelling of Civil Conflict

Two implications of common models of microbial growth

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