Growth rate, evolutionary entropy and ageing across the tree of life

Figures & data

Figure 1. Sensitivity of r (red) and H (blue) with respect to $m_j$, left to right: H. sapiens (Japanese) $(r=0.00881925,H=0.100721)$, H. sapiens (Swedish) $(0.0341426,0.103543)$, L. rothschildi $(0.526852,0.529284)$, P. reticulata $(0.168432,0.328877)$, H. sapiens (hunter gatherers) $(0.0412469,0.121009)$, and F. glacialoides $(0.0930894,0.206323)$.

Figure 2. Sensitivity of r and H $\left(m_j\right)$: O. orca $(0.0466768,0.346966)$, D. longispina $(0.211085,0.226278)$, P. leo $(0.11583,0.317768)$, P. cynocephalus$(0.0357706,0.234431)$, M. quadricornifera $(0.450159,0.35105)$ and C. capreolus $(0.166879,0.39307)$.

Figure 3. Sensitivity of r and H $\left(m_j\right)$: C. elaphus $(-0.0646938,0.269369)$, C. elegans $(1.15314,0.205441)$, P. humanus $(0.797284,0.468487)$, P. troglodytes $(0.0212558,0.155512)$, D. melanogaster $(0.758004,0.458826)$ and R. rupicapra $(0.000516964,0.360327)$.

Figure 4. Sensitivity of r and H $\left(m_j\right)$: O. aries $(0.0220628,0.477351)$, C. capitata $(5.43509,0.0298147)$, A. melbus $(-0.152303,0.234593)$, C. olor $(-0.227956,0.234202)$, M. oeconomus $(0.217662,0.573796)$ and H. cumulicola $(-1.34944,0.11294)$.

Figure 5. Sensitivity of r and H $\left(m_j\right)$: P. sylvestris${}^{†}$ $(0.181038,0.234763)$, C. johnsoni $(0.0334963,0.130565)$, M. flaviventris $(-0.319723,0.280175)$, A. nisus $(0.816199,0.616241)$, C. flava $(-0.270389,0.177422)$ and A. marmorata${}^{†}$ $(-0.132842,0.135127)$.

Figure 6. Sensitivity of r and H $\left(m_j\right)$: G. orbignyan${}^{†}$ $(0.0710771,0.0994781)$, L. vivipara${}^{†}$ $(-0.459895,0.302762)$, U. minor${}^{†}$ $(0.251756,0.321232)$, B. pyrenaica $(-0.0135153,0.0928572)$, F. albicollis $(-0.508817,0.440093)$ and R. maximum${}^{†}$ $(-0.282474,0.250665)$.

Figure 7. Sensitivity of r and H $\left(m_j\right)$: P. major $(-0.493461,0.463734)$, H. magnipapillata${}^{†}†$ $(1.68592,0.478592)$, P. longicarpus${}^{†}†$ $(-0.177558,0.439018)$, A. acanthocarpa${}^{†}$ $(-0.192478,0.456595)$, H. rufescens${}^{†}$ $(-0.0369571,0.273291)$ and R. aurora${}^{†}†$ $(-0.0116635,0.43502)$.

Table 1. Population dynamics: comparison of $E_0,R_0,\text{˜}T,T,\mathrm{\Phi }$ and H of 48 species.

Species	$E_0$	$R_0$	$\text{˜}T$	T	Φ	H
H. sapiens (Japanese)	86.92	1.310	30.73	30.47	−0.0919	0,1007
H. sapiens (Swedish)	53.04	2.978	32.67	31.26	−0.0694	0.1035
Leucopsar rothschildi	9.48	9.057	5.85	3.20	−0.0024	0.5293
Poecillia reticulata (m)	26.02	6.011	13.79	8.37	−0.1604	0.3289
H. sapiens (Hunter Gatherers)	28.54	3.330	30.52	27.86	−0.0798	0.1210
Fulmarus glacialoides	21.71	4.297	17.27	14.23	−0.1132	0.2063
Orcinus orca	62.44	1.233	22.77	22.11	−0.3003	0.3470
Daphnia longispina	29.38	29.63	22.78	11.94	−0.0152	0.2263
Panthera leo	4.73	2.417	8.11	7.16	−0.2019	0.3178
Papio cynocephalus	10.52	1.524	12.13	11.45	−0.1987	0.2344
Macrotrachela quadricornifera (d)	34.67	25.88	10.27	5.54	0.0991	0.3511
Capreolus capreolus	6.67	2.472	5.95	4.97	−0.2262	0.3931
Cervus elaphus	8.63	0.559	8.69	9.32	−0.3341	0.2694
Caenorhabditis elegans (d)	14.82	287.3	5.36	4.58	0.9477	0.2054
Pediculus humanus (d)	17.58	81.68	13.05	3.24	0.3288	0.4685
Pan troglodytes	15.02	1.602	22.83	21.53	−0.1343	0.1555
Drosophila melanogaster (d)	28.27	57.30	15.11	3.142	0.2992	0.4588
Rupicapra rupicapra	4.64	1.002	4.78	4.78	−0.3598	0.3603
Ovis aries	3.47	1.113	4.92	4.77	−0.4553	0.4774
Ceratitis capitata (d)	38.71	74.22	22.84	10.05	5.4052	0.002981
Alpus melba	7.52	0.222	8.53	11.31	−0.3869	0.2346
Cygnus olor	5.54	0.105	8.64	11.23	−0.4622	0.2342
Microtus oeconomus (m)	11.00	2.033	10.64	8.979	−0.3561	0.5738
Hypericum cumulicola	2.28	0.0001515	6.33	6.66	−1.4502	0.1129
Pinus sylvestris	17.85	13.51	17.51	12.06	−0.0537	0.2348
Crocodylus johnsoni	3.26	2.360	26.57	24.77	−0.0971	0.1306
Marmota flaviventris	2.27	0.110	6.00	7.89	−0.6000	0.2802
Accipiter nisus	2.18	4.818	2.74	1.44	0.2000	0.6162
Cryptantha flava	3.61	0.069	8.25	11.46	−0.4478	0.1774
Agave marmorata	1.09	0.054	17.53	27.04	−0.2680	0.1351
Geonoma orbignyana	24.73	40.67	70.21	40.65	−0.0284	0.09948
Lacerta vivipara	1.49	0.123	4.32	4.83	−0.7627	0.3028
Ulex minor	1.80	22.45	20.53	8.25	−0.0695	0.3212
Borderea pyrenaica	9.05	0.618	28.61	48.52	−0.1064	0.09286
Ficedula albicollis	2.99	0.165	3.07	4.13	−0.9489	0.4401
Rhododendron maximum	5.87	0.078	6.82	12.69	−0.5331	0.2507
Parus major	2.23	0.219	2.74	3.51	−0.9572	0.4637
Hydra magnipapillata	45851	2017	45574	122.3	1.2075	0.4786
Pagurus longicarpus	1.26	0.452	3.86	5.32	−0.6166	0.4390
Atriplex acanthocarpa	2.18	2.429	5.17	4.16	−0.2641	0.4566
Haliotis fufescens	1.36	0.696	9.45	10.19	−0.3102	0.2733
Rana aurora	1.01	0.941	5.13	5.23	−0.4467	0.4350
Paramuricea clavata	5.85	0.292	30.08	46.43	−0.1324	0.09894
Viburnum furcatum	4.17	0.012	53.24	453.7	−0.0507	0.01512
Laminaria digitata	1.56	0.074	4.23	30.61	−0.4448	0.1427
Quercus rugosa	22.72	2.959	100.3	62.21	−0.0647	0.07866
Gopherus agassizii	3.57	1.834	32.82	28.71	−0.1103	0.1300
Avicennia marina	5.90	318.0	124.5	11.69	−0.0623	0.2729

Note: Units of study are years unless indicated otherwise: (m) refers to months and (d) to days. On average, $E_0$ is larger in more senescent populations, such as human species: since most individuals survive infancy, life expectancy at birth is higher than average, and mortality rates are initially low, increasing sharply over time. In the least senescent species, most individuals die at birth, so mortality is highest in younger classes, but, for those who survive infancy, mortality decreases with age (negative senescence). We also note that most species are equilibrium species $(\mathrm{\Phi }<0)$. The only opportunistic species are A. nisus, C. elegans, C. capitata, D. melanogaster, H. magnipapillata, M. quadricornifera, and P. humanus. These species have smaller than average values of H, typical of populations with broad reproductive spans and early age of sexual maturity (see Figures 2–5 and 7, as well as large offspring production $(R_0$ is large for these species, indicating a larger than average reproductive output)

Figure 8. Sensitivity of r and H $\left(m_j\right)$: P. clavata${}^{†}†$ $(-0.0334535,0.0989397)$, V. furcatum${}^{†}$ $(-0.0356104,0.0151249)$, L. digitata${}^{†}$ $(-0.302172,0.142665)$, Q. rugosa${}^{†}$$(0.0139858,0.0786571)$, G. agassizii${}^{†}$ $(0.0197802,0.130042)$ and A. marina${}^{†}$ $(0.210566,0.27288)$.

Figure 9. Sensitivity of r (red) and H (blue) with respect to $b_j$, left to right: H. sapiens (Japanese) $(r=0.00881925,H=0.100721)$, H. sapiens (Swedish) $(0.0341426,0.103543)$, L. rothschildi $(0.526852,0.529284)$, P. reticulata $(0.168432,0.328877)$, H. sapiens (hunter gatherers) $(0.0412469,0.121009)$, and F. glacialoides $(0.0930894,0.206323)$.

Figure 10. Sensitivity of r and H $\left(b_j\right)$: O. orca $(0.0466768,0.346966)$, D. longispina $(0.211085,0.226278)$, P. leo $(0.11583,0.317768)$, P. cynocephalus$(0.0357706,0.234431)$, M. quadricornifera $(0.450159,0.35105)$ and C. capreolus $(0.166879,0.39307)$.

Figure 11. Sensitivity of r and H $\left(b_j\right)$: C. elaphus $(-0.0646938,0.269369)$, C. elegans $(1.15314,0.205441)$, P. humanus $(0.797284,0.468487)$, P. troglodytes $(0.0212558,0.155512)$, D. melanogaster $(0.758004,0.458826)$ and R. rupicapra $(0.000516964,0.360327)$.

Figure 12. Sensitivity of r and H $\left(b_j\right)$: O. aries $(0.0220628,0.477351)$, C. capitata $(5.43509,0.0298147)$, A. melbus $(-0.152303,0.234593)$, C. olor $(-0.227956,0.234202)$, M. oeconomus $(0.217662,0.573796)$ and H. cumulicola $(-1.34944,0.11294)$.

Figure 13. Sensitivity of r and H $\left(b_j\right)$: P. sylvestris${}^{†}$ $(0.181038,0.234763)$, C. johnsoni $(0.0334963,0.130565)$, M. flaviventris $(-0.319723,0.280175)$, A. nisus $(0.816199,0.616241)$, C. flava $(-0.270389,0.177422)$ and A. marmorata${}^{†}$ $(-0.132842,0.135127)$.

Figure 14. Sensitivity of r and H $\left(b_j\right)$: G. orbignyan${}^{†}$ $(0.0710771,0.0994781)$, L. vivipara${}^{†}$ $(-0.459895,0.302762)$, U. minor${}^{†}$ $(0.251756,0.321232)$, B. pyrenaica $(-0.0135153,0.0928572)$, F. albicollis $(-0.508817,0.440093)$ and R. maximum${}^{†}$ $(-0.282474,0.250665)$.

Figure 15. Sensitivity of r and H $\left(b_j\right)$: P. major $(-0.493461,0.463734)$, H. magnipapillata${}^{†}†$ $(1.68592,0.478592)$, P. longicarpus${}^{†}†$ $(-0.177558,0.439018)$, A. acanthocarpa${}^{†}$ $(-0.192478,0.456595)$, H. rufescens${}^{†}$ $(-0.0369571,0.273291)$ and R. aurora${}^{†}†$ $(-0.0116635,0.43502)$.

Figure 16. Sensitivity of r and H $\left(b_j\right)$: P. clavata${}^{†}†$ $(-0.0334535,0.0989397)$, V. furcatum${}^{†}$ $(-0.0356104,0.0151249)$, L. digitata${}^{†}$ $(-0.302172,0.142665)$, Q. rugosa${}^{†}$$(0.0139858,0.0786571)$, G. agassizii${}^{†}$ $(0.0197802,0.130042)$ and A. marina${}^{†}$ $(0.210566,0.27288)$.