Taylor's power law in human mortality

Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data

“…For females and males in 12 developed countries, the temporal means and temporal variances from 1960 to 2009 of observed age-specific mortality, when one point for each age from 0 to 100 years was plotted on log-log coordinates, fell approximately along a straight line, according to the data of the Human Mortality Database (2015) ( Figures 2 and A-1 in Bohk, Rau, and Cohen 2015;and Figures 3-4 here). This approximate linearity was consistent with Taylor's law.…”

“…The changes in the log 10 temporal mean are expected from the increasing mortality with age at older a g e s a n d t h e d e c r e a s i n g m o r t a l i t y w i t h a g e f r o m i n f a n c y t o c h i l d h o o d . T h e corresponding linear changes in the log 10 temporal variance were not known prior to the work of Bohk, Rau, and Cohen (2015).…”

“…Is this empirical regularity in human mortality just a coincidence, or does it come from an underlying pattern or mechanism? Here we answer these questions by comparing the completely empirical results of Bohk, Rau, and Cohen (2015) with the results of fitting three human mortality models: those of Gompertz (1825), Makeham (1860), and Siler (1979Siler ( , 1983, which belong to the same family. We show that fitted mortality of these models obeys TL, exactly or approximately.…”

“…TL describes the population densities of hundreds of species in ecology (Taylor 1961;Kilpatrick and Ives 2003;Kendal 2004) and many other nonnegative quantities (reviewed by Eisler, Bartos, and Kertész 2008), such as numbers of cancer metastases, numbers of cases of infectious diseases, numbers of single-nucleotide polymorphisms, sizes of tornado outbreaks (Tippett and Cohen 2016), and prime numbers (Cohen 2016). In human demography, TL describes the density (people per area) of Norway's population (Cohen, Xu, and Brunborg 2013) and the agespecific force of mortality (henceforth, simply 'mortality') in developed countries (Bohk, Rau, and Cohen 2015). A restrictive view of TL limits its application to apparently random variability without dominating systematic trends, that is, to what is sometimes called 'fluctuation scaling.'…”

“…A restrictive view of TL limits its application to apparently random variability without dominating systematic trends, that is, to what is sometimes called 'fluctuation scaling.' A broader view of TL, adopted here, includes applications of TL to nonnegative quantities that may change deterministically, for example, in purely mathematical structures (Kendal and Jørgensen 2011;Kendal 2013;Cohen 2013, Kendal andJørgensen 2015;Xiao, Locey, and White 2015;Cohen 2016) or that may fluctuate apparently chaotically or randomly to some extent while dominated by systematic trends (Cohen, Xu, and Brunborg 2013;Bohk, Rau, and Cohen 2015). We discuss some unanswered questions raised by this broader view of TL in the concluding section 4.2 on future research.…”