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Lower panels: Marginal posterior distribution on intercept and slope. Descending arrows point to threshold weights at which the probability of male is 50%. Logistic curves are a random sample from the MCMC posterior. Predicting gender (arbitrarily coded as male = 1, female = 0) as a function of weight (in pounds), using logistic regression. This theory can provide an additional biomarker and a predictive tool to complement experimental research.įigure 21.3. Data that describe tumor growth dynamics, for instance, can be fit to various, often similarly shaped curves (e.g., logistic and Gompertz curves). Using the theory developed in previous chapters, we investigate Gompertzian, inhomogeneous Malthusian, inhomogeneous logistic, linear-exponential, and three-stage models and identify whether the population that fits best is homogeneous or heterogeneous, whether it grows in a density-dependent or frequency-dependent manner and whether it depends on external resources during any or all stages of its development. Obtaining this information can become important in cases, when, for instance, intervention or population management strategies need to be devised.
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In this chapter, we are interested in investigating a different angle of the data-equation relationship : if a data set is best fitted by a particular curve, what information about intrinsic population dynamics can be derived from this result? That is, we are interested not in making predictions about future population dynamics, but in inferring information about population structure and conditions under which the population has been growing based on the data that have been collected. Finding the right curve to describe the trends observed in global demography is another example, where finding a correct equation influences dramatically predictions about future human population growth (see Chapter 3). For instance, tumor growth can be described by logistic or Gompertz curves, and there exists a relatively extensive debate on which curve provides a better fit see, for instance, Benzekry et al. The procedures for finding the best-fitting curves within a certain class of formulas (equations) are well developed, and the problem is often considered to be solved when the curve is found. Exponential and logistic curves for describing unrestrained and environmentally restrained population growth, respectively, are classical examples.
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Irina Kareva, Georgy Karev, in Modeling Evolution of Heterogenous Populations, 2020 11.1 Problem formulationįinding a simple curve or a justified equation that fits experimental data well is a standard problem in population dynamics, as it allows making predictions about future dynamics of the population. Because new construction of MWIs in the United States was essentially terminated in 1993, only about one-fifth of this investment had actually been made by the end of 1998. population of 300 × 10 6, technology saturation would correspond to 252 × 10 9 lbs/yr of waste incineration.
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With the optimistic value of 30% of total waste recycled, ultimate disposal would involve 840 lbs per person per year dedicated for incineration assuming that landfilling would become unacceptable. The latter was based on an assumed ultimate per capita municipal waste generation rate of 1200 lbs/person (p)-yr in view of stringent conservation efforts at the input end. Penner, in Encyclopedia of Physical Science and Technology (Third Edition), 2003 III Initial Growth Rates for MWI Use in the United Statesīefore the normal growth rate of MWIs was seriously interrupted in the United States around 1988–89 because of environmental concerns involving especially dioxin and furan emissions, a logistics curve was used to estimate the rate of market penetration as well as the ultimate value for market saturation ( Penner and Richards, 1989).