Mathematical model of population dynamics with the world population size stabilizing about a stationary level

Climate change and persistent high temperatures: does it matter?

“…Given this interpretation of the Condorcet's and Malthus principles, the interpretation of the growth or the decay of the carrying capacity and the population dynamics that is associated with that behavior is possible. Using these principles several authors have demonstrated that the historical data on world population over the entire period of human existence up to the year 2000 can be accurately described by the use of empirical mathematical models (von Foerster et al, 1960;Kapitza, 1996;Lee et al, 2008;Dolgonosov, 2009Dolgonosov, , 2012Akaev and Sadovnichii, 2012). A comprehensive review of these models and the lineage among them was discussed in Aral (2013), which will not be repeated here.…”

“…It is assumed that this growth would be limited by the homogenous carrying capacity of population growth characterized by the carrying capacity function K (P, τ 2 , τ 3 ) given as Equation 4which follows Equation (2). This carrying capacity term follows the information accumulation concept of Condorcet (Dolgonosov, 2009;Akaev and Sadovnichii, 2012). This is followed by the heterogeneous logistic function defined in terms of the carrying capacity that is associated with changing climatic conditions in association to population and temperature change.…”

“…In Equations 3and 4, P c is identified as the current population density which is tied to the rate of information accumulation of humans which influence the population growth in the sense of Condorcet (Dolgonosov, 2009;Akaev and Sadovnichii, 2012).…”

“…In Equations (3) and (4) the constant P o = 1 billion is defined as the static biocapacity of earth (Akaev and Sadovnichii, 2012), which was exceeded during 1980s, κ and γ are rate constants, τ 1 ≈ 20 − 50 years which represents the mean reproductive age, τ 2 ≈ 10 − 100 years which represents the time of diffusion of basis technologies within human population which influence population growth (Gorshkov, 1995), and τ 3 = 25 − 100 years can be chosen as the time delay in the biospheric response of earth systems to anthropogenic loads. A discussion of the theoretical analysis of the reasons behind the choice of these parameters can be found in Dolgonosov (2009) and Akaev and Sadovnichii (2012).…”

“…In Equations (3) and (4) the constant P o = 1 billion is defined as the static biocapacity of earth (Akaev and Sadovnichii, 2012), which was exceeded during 1980s, κ and γ are rate constants, τ 1 ≈ 20 − 50 years which represents the mean reproductive age, τ 2 ≈ 10 − 100 years which represents the time of diffusion of basis technologies within human population which influence population growth (Gorshkov, 1995), and τ 3 = 25 − 100 years can be chosen as the time delay in the biospheric response of earth systems to anthropogenic loads. A discussion of the theoretical analysis of the reasons behind the choice of these parameters can be found in Dolgonosov (2009) and Akaev and Sadovnichii (2012). The second logistic function that introduces the temperature effects into the population model is introduced with a scaling factor β which may be used to describe the increase or decrease in world temperatures relative to a scenario such as the IPCC 2 • C scenario beyond the year 2000 or any other temperature scenario may also be used here to define the future temperature trend (Solomon et al, 2009).…”