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Contributed by James W. Vaupel, October 17, 2016 (sent for review July 26, 2016; reviewed by Michael Murphy and Deborah Roach)
Article Figures & SI
Figures
- Fig. 1.
Lifespan distributions for males and females. Each panel presents the proportion of individuals dying by age for females (red) and males (blue). Infant mortality (before age 1 y) is reported in Inset pie charts. The solid vertical lines mark life expectancies for each sex. The dashed vertical lines indicate the average number of years of life expectancy lost due to death. Keyfitz’s entropy is given by this value divided by life expectancy (Box 1). For the muriqui, capuchin, and female gorillas, the curves are extrapolated beyond maximum estimated lifespans within the dataset, as indicated by dotted curves and diagonal shading (Materials and Methods).
- Fig. S1.
Survivorship curves for each sex for the 12 datasets analyzed. Each panel represents the survivorship (proportion surviving) for females (red) and males (blue) for the seven species including six datasets for humans. The solid vertical lines mark life expectancies for each sex. The dashed vertical lines indicate the average number of years of life expectancy lost due to death. Keyfitz’s entropy is given by this value divided by life expectancy (Box 1). For the muriqui, capuchin, and female gorillas, the curves are extrapolated beyond maximum estimated lifespans within the dataset, as indicated by dotted curves and diagonal shading (Materials and Methods).
- Fig. 2.
Ranking of four measures of length of life and five measures of variation in lifespan, for females and males in the 12 focal populations. The rank ordering of the populations for each measure is shown in increasing order (lowest to the left, highest to the right).
- Fig. 3.
Scatterplots showing relationships among selected measures of the length of life and lifespan equality for the 12 datasets analyzed. A–C show scatterplots between measures of length of life, D–F show comparisons between measures of lifespan equality, and G–I show scatterplots between length of life and measures of lifespan equality. For display purposes, the values of the Gini coefficient and the coefficient of variation were transformed by subtracting each population’s value from the maximum in the dataset.
- Fig. 4.
The continuum of lifespan equality and life expectancy in primates. In A–C, the y axis shows our measure of lifespan equality, the log of the inverse of Keyfitz’s entropy; corresponding values of Keyftiz’s entropy are given in parentheses in A. (A) The evolutionary-historical continuum in lifespan equality and life expectancy for the 12 focal populations (Fig. 1) and 16 additional human populations (Table S4). The equation for the gray regression line is
- Fig. 5.
Absolute and relative male–female differences in life expectancy and lifespan equality. Absolute differences between the male and female values are shown in the Top two panels; relative differences are shown in the Bottom two panels, expressed as the percentage of difference of males from females. Dark red dashed lines represent the median of each set of values; all medians lie in the direction of a female advantage.
- Fig. S2.
Circles represent times of entry; solid circles are known times of birth and open circles are entries after birth. Squares are departure times where solid squares are known times of death and open squares are out-migration. Solid triangles indicate individuals known to be alive until the end of the study and vertical bars indicate unknown type of departure.
Tables
- Table 1.
Nonhuman primate species included in the study, showing ages at sexual maturity for each sex and the numbers of individuals for each sex for each study population
Age at adulthood, y Sample size by sex Common name Species Family Country Female Male Female Male Unknown Sifaka Propithecus verreauxi Indriidae Madagascar 6.5 5.5 266 342 385 Northern muriqui Brachyteles hypoxanthus Atelidae Brazil 8.5 6.5 263 263 5 Capuchin Cebus capucinus Cebidae Costa Rica 6.5 6.5 113 158 16 Yellow baboon Papio cynocephalus Cercopithecidae Kenya 5.5 7.5 618 706 0 Chimpanzee Pan troglodytes Hominidae Tanzania 14.5 14.5 155 133 17 Gorilla Gorilla beringei Hominidae Rwanda 9.5 15.5 151 151 19 For more detailed information on each study see refs. 11 and 12.
- Table 2.
Spearman’s (open cells) and Pearson's (shaded cells) correlation coefficients between the measures of length of life and of lifespan equality for females and males of the 12 main populations
The row and column heads correspond to the following: e0, life expectancy; eα, adult life expectancy; Ω0, exceptional age; Ωα, exceptional age for adults; ε0, lifespan equality; g0, Gini coefficient; cv0, coefficient of variation; lα, proportion surviving to maturity; e0/Ω0, life expectancy as a proportion of exceptional age (see Box 1 and Materials and Methods for a full description of the measures).
- Table S1.
Estimated means (and SEs in parentheses) of the measures of length of life for females and males for each of the main populations analyzed
Species e0 eα Ω0 Ωα Females Sifaka 5.58 (0.525) 10.6 (0.609) 32.3 (1.86) 36.1 (2.48) Muriqui 28.1 (7.37) 34.7 (11.7) 65.6 (19)* 67.1 (20.4)* Capuchin 9.6 (1.21) 11 (1.51) 33.6 (6.56) 35.5 (7.81) Baboon 9.34 (0.389) 10.3 (0.412) 27.5 (1.01) 28.4 (1.09) Chimpanzee 16.1 (1.75) 19 (1.38) 53.7 (3.17) 56.1 (3.55) Gorilla 19.4 (1.65) 24 (1.19) 44.4 (1.4) 45.1 (1.44) Liberia 2.23 (0.487) 16.5 (0.771) 38.3 (4.35) 68.4 (2.37) Hadza 37.4 (2.12) 45.4 (2.14) 86.8 (1.45) 87.3 (1.05) Ache 37 (2.06) 43.3 (2.04) 77.8 (0.762) 77.8 (0.762) Sweden 1751–1759 37.8 (0.0608) 44.3 (0.0533) 92 (0) 93.6 (0.488) Sweden 2000–2009 82.6 (0.0178) 68 (0.0163) 102 (0.01) 102 (0) Japan 2012 86.4 (0.0154) 71.8 (0.0137) 105 (0) 105 (0) Males Sifaka 5.93 (0.483) 11.5 (0.525) 25.7 (0.805) 27.1 (0.911) Muriqui 21.2 (4.39) 24.9 (6.55) 59.3 (23.3)* 60.4 (24.3)* Capuchin 8.07 (1.12) 10.7 (1.85) 28.2 (7.74) 29.7 (9.43) Baboon 8.13 (0.512) 7.94 (0.734) 24.6 (1.4) 25.7 (1.49) Chimpanzee 12.8 (1.35) 13.8 (0.964) 43 (1.64) 44.9 (1.82) Gorilla 18 (1.47) 14.5 (1.24) 39.9 (2.1) 40.5 (2.18) Liberia 1.68 (0.427) 15 (0.74) 30.9 (5.71) 65.1 (1.79) Hadza 32.4 (1.83) 38.8 (2) 84.2 (0.794) 84.5 (0.649) Ache 37.7 (1.64) 36.8 (1.57) 79.7 (1.13) 79.7 (1.05) Sweden 1751–1759 34.8 (0.0593) 41.8 (0.0558) 90 (0.217) 92 (0.0666) Sweden 2000–2009 78.3 (0.0189) 63.7 (0.0174) 99 (0) 99 (0) Japan 2012 80 (0.0162) 65.3 (0.0148) 101 (0) 101 (0) The column heads are as follows: e0, life expectancy; eα, adult life expectancy; Ω0, exceptional age; Ωα, exceptional age for adults (see Box 1 and Materials and Methods for a full description of the measures). SEs with null values for some of the exceptional ages (Ω) are the result of using integer age intervals that produced no variability in the bootstrap estimates.
↵* The exceptional ages for the muriquis have large SEs because of heavy censoring in the data and hence high uncertainty in the exceptional ages.
- Table S2.
Estimated means (and SEs in parentheses) of the measures of lifespan equality for each of the main populations analyzed
Species ε0 lα e0/Ω0 g0 cv0 Females Sifaka −0.376 (0.0573) 0.289 (0.0271) 0.173 (0.0155) 0.711 (0.0197) 1.51 (0.0893) Muriqui 0.331 (0.151) 0.629 (0.0357) 0.417 (0.0484) 0.471 (0.0479) 0.832 (0.081) Capuchin 0.0682 (0.12) 0.496 (0.0528) 0.292 (0.0438) 0.538 (0.038) 0.99 (0.101) Baboon 0.194 (0.0414) 0.55 (0.0205) 0.34 (0.0146) 0.502 (0.014) 0.896 (0.0303) Chimpanzee 0.0262 (0.0996) 0.434 (0.0485) 0.3 (0.0323) 0.573 (0.0361) 1.06 (0.0919) Gorilla 0.337 (0.111) 0.564 (0.0447) 0.437 (0.036) 0.486 (0.0386) 0.883 (0.0752) Liberia −0.911 (0.0858) 0.0342 (0.00949) 0.0578 (0.00768) 0.929 (0.0197) 2.82 (0.279) Hadza 0.357 (0.0691) 0.6 (0.0295) 0.431 (0.0245) 0.478 (0.0234) 0.852 (0.044) Ache 0.409 (0.0703) 0.609 (0.0301) 0.476 (0.0266) 0.46 (0.0229) 0.819 (0.0428) Sweden 1751–1759 0.345 (0.00201) 0.622 (0.000899) 0.411 (0.000661) 0.475 (0.000716) 0.839 (0.00135) Sweden 2000–2009 2.2 (0.00156) 0.996 (9.19e-05) 0.81 (0.000192) 0.079 (0.000139) 0.157 (0.000364) Japan 2012 2.26 (0.00148) 0.996 (8.35e-05) 0.823 (0.000146) 0.0745 (0.000124) 0.151 (0.000342) Males Sifaka −0.248 (0.057) 0.325 (0.0267) 0.231 (0.0179) 0.488 (0.0503) 0.87 (0.107) Muriqui 0.244 (0.175) 0.653 (0.0328) 0.37 (0.0647) 0.578 (0.0379) 1.09 (0.112) Capuchin 0.000787 (0.124) 0.417 (0.0483) 0.295 (0.0479) 0.513 (0.0152) 0.922 (0.0344) Baboon 0.159 (0.0455) 0.453 (0.0238) 0.331 (0.017) 0.569 (0.0317) 1.05 (0.0819) Chimpanzee 0.0224 (0.0889) 0.378 (0.0443) 0.298 (0.0299) 0.454 (0.0362) 0.816 (0.0666) Gorilla 0.416 (0.107) 0.566 (0.0438) 0.451 (0.0344) 0.944 (0.023) 3.07 (0.316) Liberia −0.977 (0.104) 0.0241 (0.00803) 0.0541 (0.0064) 0.506 (0.0209) 0.901 (0.0423) Hadza 0.25 (0.0595) 0.58 (0.0284) 0.385 (0.0215) 0.41 (0.0187) 0.717 (0.033) Ache 0.51 (0.0577) 0.706 (0.0254) 0.474 (0.0213) 0.498 (0.000707) 0.883 (0.00139) Sweden 1751–1759 0.274 (0.00194) 0.597 (0.000902) 0.387 (0.00108) 0.0905 (0.000152) 0.177 (0.000365) Sweden 2000–2009 2.07 (0.00151) 0.995 (9.68e-05) 0.791 (0.000191) 0.091 (0.000133) 0.176 (0.000322) Japan 2012 2.06 (0.00134) 0.996 (8.7e-05) 0.792 (0.000161) 0.686 (0.0197) 1.4 (0.0745) The column heads are as follows: ε0, lifespan equality; g0, Gini coefficient; cv0, coefficient of variation; lα, proportion surviving to maturity; e0/Ω0, life expectancy as a proportion of exceptional age (see Box 1 and Materials and Methods for a full description of the measures).
- Table S3.
Mammal species used in addition to the six nonhuman primates to estimate the significance of the interspecific correlation between life expectancy and lifespan equality
Common name Species Family Life expectancy, e0, y Lifespan equality, ε0 Ref. Tundra vole Microtus oeconomus Cricetidae 0.79 0.118 (73) Yellow-bellied marmot Marmota flaviventris Sciuridae 1.79 −0.079 (74) Eastern chipmunk Tamias striatus Sciuridae 5.02 0.174 (75) Plains zebra Equus burchellii Equidae 7.95 0.155 (76) Moose Alces alces Cervidae 7.08 0.186 (77) Japanese serow Naemorhedus crispus Bovidae 4.67 −0.057 (78) Gaur Bos gaurus Bovidae 7.90 0.111 (79) Wolf Canis lupus Canidae 4.31 0.012 (80) African lion Panthera leo Felidae 3.72 −0.098 (14) All datasets were obtained from the database DATLife (www.demogr.mpg.de/en/laboratories/evolutionary_biodemography_1171/projects/datlife_the_demography_of_aging_across_the_tree_of_life_database_744.htm).
- Table S4.
Time periods or years, by population, that were used in the life tables underlying the measures shown in Fig. 4 A and C
Country Period Age interval Ref. For Fig. 4A Sweden 1751–1759 1 (19) Sweden 1800–1809 1 (19) Sweden 1850–1859 1 (19) Sweden 1900–1909 1 (19) Sweden 1950–1959 1 (19) Sweden 2000–2009 1 (19) Sweden 1925–1934 1 (19) England 1600–1725 1 (56) Trinidad 1813–1816 1 (55) Ukraine 1933 1 (19) Liberia 1820–1843 5 (17, 18) Hadza 1985–2000 1 (15) Ache 1980–1994 1 (16) Acculturated hunter-gatherers* — — (57) Sweden 1773 1 (19) Iceland 1882 1 (19) India 2013 1 (54) Nigeria 2013 1 (54) Russia 2013 1 (54) United States 2013 1 (54) Japan 2012 1 (19) China 2013 1 (54) For Fig. 4C Iceland 1881 1 (19) Iceland 1883 1 (19) Sweden 1772 1 (19) Sweden 1774 1 (19) Ukraine 1931 1 (19) Ukraine 1932 1 (19) Ukraine 1934 1 (19) Ukraine 1935 1 (19) We used data for 2012 for Japan because we decided to use highly reliable HMD data (19) for this focal population and these data were not available after 2012.
↵* The estimation of the pace and shape measures for acculturated hunter-gatherers was carried out based on the Siler mortality parameter estimates provided by ref. 57.
- Table 3.
Descriptive statistics of human populations of hunter-gatherers (Ache and Hadza) and populations from Liberia, Sweden, and Japan
Population Sex Person years Deaths Ache Women 6,738 151 Men 9,368 202 Total 16,106 353 Hadza Women 6,218 182 Men 6,100 227 Total 12,318 409 Liberia, 1820–1843 Women 1,973 1,135 Men 2,318 967 Total 4,291 2,195 Sweden, 1751–1759 Women 8,736,291 232,161 Men 7,808,644 225,428 Total 16,544,934 457,589 Sweden, 2000–2009 Women 45,582,428 475,035 Men 44,832,800 446,825 Total 90,415,228 921,860 Japan, 2012 Women 64,657,932 600,833 Men 61,362,195 655,526 Total 126,020,126 1,256,359 Person years are a combined measure of the number of individuals and the number of years they contributed to the study.
- Table S5.
Sex-specific patterns of natal dispersal (dispersal from the natal group) and higher-order dispersal (subsequent dispersals after natal) for each nonhuman primate species, as well as the minimum age at which natal dispersal is observed for each sex
Common name Sex Natal dispersal Higher-order dispersal Minimum age at onset of dispersal behavior, y Weighted average proportion of study groups (G) and nonstudy groups (A) in the estimated total population Sifaka F Yes Yes 2 M Yes Yes 0.5 G = 0.70, A = 0.30 Northern muriqui F Yes No 4.8 M No No — G = 0.50, A = 0.50 Capuchin F No No 7 M Yes Yes 1.7 G = 0.76, A = 0.24 Baboon F No No — M Yes Yes 6 G = 0.72, A = 0.28 Chimpanzee F Yes Yes 9 M No No — G = 0.40, A = 0.60 Gorilla F Yes Yes 6 M Yes No 9 G = 0.75, A = 0.25 Females Males Species b0 b1 b0 b1 Sifaka −4.308 0.102 −5.033 0.191 Muriqui −7.483 0.129 −7.268 0.149 Capuchin −4.333 0.169 −6.562 0.296 Baboon −4.356 0.128 −4.940 0.216 Chimpanzee −6.300 0.099 −6.831 0.137 Gorilla −10.00 0.207 −7.947 0.182 The Siler mortality model is given by
- Table S7.
Parameters obtained for the simulation of ages at dispersal for the six species of nonhuman primates
Males Females Natal Higher Natal Higher Species α1 β1 α2 β2 α1 β1 α2 β2 Sifaka 3.628 0.907 8.001 1.347 3.331 1.141 7.367 1.293 Muriqui — — — — 3.460 3.720 — — Capuchin 2.339 0.734 4.493 0.461 2.339 0.734 — — Baboon 9.077 4.907 4.168 0.693 — — — — Chimpanzee — — — — 8.000 2.000 — — Gorilla 6.674 1.076 — — 0.888 0.181 2.123 0.208 The labels “Natal” and “Higher” refer to natal dispersal and higher-order dispersal, respectively.
Data supplements
Supporting Information
Emergence of longevous populations
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