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Density dependence triggers runaway selection of reduced senescence.

Seymour RM, Doncaster CP - PLoS Comput. Biol. (2007)

Bottom Line: Across a realistic spectrum of senescent age profiles, density regulation of recruitment can trigger runaway selection for ever-reducing senescence.The evolution of nonsenescence from senescence is robust to the presence of exogenous adult mortality, which tends instead to increase the age-independent component of vitality loss.We simulate examples of runaway selection leading to negligible senescence and even intrinsic immortality.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University College London, London, United Kingdom.

ABSTRACT
In the presence of exogenous mortality risks, future reproduction by an individual is worth less than present reproduction to its fitness. Senescent aging thus results inevitably from transferring net fertility into younger ages. Some long-lived organisms appear to defy theory, however, presenting negligible senescence (e.g., hydra) and extended lifespans (e.g., Bristlecone Pine). Here, we investigate the possibility that the onset of vitality loss can be delayed indefinitely, even accepting the abundant evidence that reproduction is intrinsically costly to survival. For an environment with constant hazard, we establish that natural selection itself contributes to increasing density-dependent recruitment losses. We then develop a generalized model of accelerating vitality loss for analyzing fitness optima as a tradeoff between compression and spread in the age profile of net fertility. Across a realistic spectrum of senescent age profiles, density regulation of recruitment can trigger runaway selection for ever-reducing senescence. This novel prediction applies without requirement for special life-history characteristics such as indeterminate somatic growth or increasing fecundity with age. The evolution of nonsenescence from senescence is robust to the presence of exogenous adult mortality, which tends instead to increase the age-independent component of vitality loss. We simulate examples of runaway selection leading to negligible senescence and even intrinsic immortality.

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Simulated Adult Population in Presence of a Low Rate of Extrinsic Adult Mortality(A) Evolution over time in x (population mean and minimum), showing progressively later onset of vitality loss until most have negligible or zero senescence.(B) Concurrent reduction in μ0 (mean and minimum) until some have zero aging; the dashed line is the optimum μ0* = 0.017, determined by the Marginal Value Theorem (see Appendix B of Text S1).(C) Adult population (upper black line) and intrinsic immortals (lower red); the dashed line is the carrying capacity K.(D) Adult age (mean and maximum) showing extended span for intrinsic immortals. Input parameter values: αb = αd = 0.5; random mutational increments of up to ±0.01 in x and μ0; δt = 0.01; B0 = 10, D0 = 0.3; ω0 = B0μ0/(D0 + μ0); g = 0.001; and b0(x) = ω0(1 + 0.2xe−1/x).
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pcbi-0030256-g004: Simulated Adult Population in Presence of a Low Rate of Extrinsic Adult Mortality(A) Evolution over time in x (population mean and minimum), showing progressively later onset of vitality loss until most have negligible or zero senescence.(B) Concurrent reduction in μ0 (mean and minimum) until some have zero aging; the dashed line is the optimum μ0* = 0.017, determined by the Marginal Value Theorem (see Appendix B of Text S1).(C) Adult population (upper black line) and intrinsic immortals (lower red); the dashed line is the carrying capacity K.(D) Adult age (mean and maximum) showing extended span for intrinsic immortals. Input parameter values: αb = αd = 0.5; random mutational increments of up to ±0.01 in x and μ0; δt = 0.01; B0 = 10, D0 = 0.3; ω0 = B0μ0/(D0 + μ0); g = 0.001; and b0(x) = ω0(1 + 0.2xe−1/x).

Mentions: Stochastic simulations were developed to exploit the Gaussian example of Equation 12 using a partition of the form of Equation 15a and 15b; i.e., with Φt(x) = ½(xt)2 (see Methods below). Populations evolved towards smaller x, and thus slower senescence, given sufficiently small C and large D for Equation 14. Figure 4 shows an example of a population with extrinsic adult mortality set to a low value (small g), in addition to the extrinsic mortality imposed on juveniles by their inability to dislodge resident adults from any of the 200 habitable sites. The individuals making up the population were given life histories characterized by a relatively large R0 (as in Figure 2A), and an equal partition of senescence between birth rate and period survival (αb = αd = 0.5). The size of x and μ0 diminished rapidly (Figure 4A and 4B) after population size had equilibrated (Figure 4C), with eventual production of some intrinsically immortal individuals (Figure 4C, red line). These immortals did not senesce, because they had zero age-dependent loss of vitality (x = 0), nor did they age, because they had zero intrinsic mortality (μ0 = 0). They could never accumulate to displace all mortals, however, because each remained susceptible to extrinsic adult mortality. The mean value of x stabilized just above zero, probably due to an ever-increasing time to fixation in the population of ever-longer lived individuals. The simulation departed from the analytical model with respect to genetic variation, by allowing every offspring to carry a (small) mutation rather than having a linear sequence of mutation followed by fixation.


Density dependence triggers runaway selection of reduced senescence.

Seymour RM, Doncaster CP - PLoS Comput. Biol. (2007)

Simulated Adult Population in Presence of a Low Rate of Extrinsic Adult Mortality(A) Evolution over time in x (population mean and minimum), showing progressively later onset of vitality loss until most have negligible or zero senescence.(B) Concurrent reduction in μ0 (mean and minimum) until some have zero aging; the dashed line is the optimum μ0* = 0.017, determined by the Marginal Value Theorem (see Appendix B of Text S1).(C) Adult population (upper black line) and intrinsic immortals (lower red); the dashed line is the carrying capacity K.(D) Adult age (mean and maximum) showing extended span for intrinsic immortals. Input parameter values: αb = αd = 0.5; random mutational increments of up to ±0.01 in x and μ0; δt = 0.01; B0 = 10, D0 = 0.3; ω0 = B0μ0/(D0 + μ0); g = 0.001; and b0(x) = ω0(1 + 0.2xe−1/x).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2230684&req=5

pcbi-0030256-g004: Simulated Adult Population in Presence of a Low Rate of Extrinsic Adult Mortality(A) Evolution over time in x (population mean and minimum), showing progressively later onset of vitality loss until most have negligible or zero senescence.(B) Concurrent reduction in μ0 (mean and minimum) until some have zero aging; the dashed line is the optimum μ0* = 0.017, determined by the Marginal Value Theorem (see Appendix B of Text S1).(C) Adult population (upper black line) and intrinsic immortals (lower red); the dashed line is the carrying capacity K.(D) Adult age (mean and maximum) showing extended span for intrinsic immortals. Input parameter values: αb = αd = 0.5; random mutational increments of up to ±0.01 in x and μ0; δt = 0.01; B0 = 10, D0 = 0.3; ω0 = B0μ0/(D0 + μ0); g = 0.001; and b0(x) = ω0(1 + 0.2xe−1/x).
Mentions: Stochastic simulations were developed to exploit the Gaussian example of Equation 12 using a partition of the form of Equation 15a and 15b; i.e., with Φt(x) = ½(xt)2 (see Methods below). Populations evolved towards smaller x, and thus slower senescence, given sufficiently small C and large D for Equation 14. Figure 4 shows an example of a population with extrinsic adult mortality set to a low value (small g), in addition to the extrinsic mortality imposed on juveniles by their inability to dislodge resident adults from any of the 200 habitable sites. The individuals making up the population were given life histories characterized by a relatively large R0 (as in Figure 2A), and an equal partition of senescence between birth rate and period survival (αb = αd = 0.5). The size of x and μ0 diminished rapidly (Figure 4A and 4B) after population size had equilibrated (Figure 4C), with eventual production of some intrinsically immortal individuals (Figure 4C, red line). These immortals did not senesce, because they had zero age-dependent loss of vitality (x = 0), nor did they age, because they had zero intrinsic mortality (μ0 = 0). They could never accumulate to displace all mortals, however, because each remained susceptible to extrinsic adult mortality. The mean value of x stabilized just above zero, probably due to an ever-increasing time to fixation in the population of ever-longer lived individuals. The simulation departed from the analytical model with respect to genetic variation, by allowing every offspring to carry a (small) mutation rather than having a linear sequence of mutation followed by fixation.

Bottom Line: Across a realistic spectrum of senescent age profiles, density regulation of recruitment can trigger runaway selection for ever-reducing senescence.The evolution of nonsenescence from senescence is robust to the presence of exogenous adult mortality, which tends instead to increase the age-independent component of vitality loss.We simulate examples of runaway selection leading to negligible senescence and even intrinsic immortality.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University College London, London, United Kingdom.

ABSTRACT
In the presence of exogenous mortality risks, future reproduction by an individual is worth less than present reproduction to its fitness. Senescent aging thus results inevitably from transferring net fertility into younger ages. Some long-lived organisms appear to defy theory, however, presenting negligible senescence (e.g., hydra) and extended lifespans (e.g., Bristlecone Pine). Here, we investigate the possibility that the onset of vitality loss can be delayed indefinitely, even accepting the abundant evidence that reproduction is intrinsically costly to survival. For an environment with constant hazard, we establish that natural selection itself contributes to increasing density-dependent recruitment losses. We then develop a generalized model of accelerating vitality loss for analyzing fitness optima as a tradeoff between compression and spread in the age profile of net fertility. Across a realistic spectrum of senescent age profiles, density regulation of recruitment can trigger runaway selection for ever-reducing senescence. This novel prediction applies without requirement for special life-history characteristics such as indeterminate somatic growth or increasing fecundity with age. The evolution of nonsenescence from senescence is robust to the presence of exogenous adult mortality, which tends instead to increase the age-independent component of vitality loss. We simulate examples of runaway selection leading to negligible senescence and even intrinsic immortality.

Show MeSH
Related in: MedlinePlus