Limits...
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.

Show MeSH

Related in: MedlinePlus

Graphs of R(x) as Functions of the Senescence Variable x for Various Initial Recruitment Functions b0(x)Graphs of b0(x) are shown in the inset panels.(A) As in Equation 14 with C = 1 and D = μ. In this case, R(x) is monotonically decreasing in x, and the evolutionary optimum is at the nonsenescent state x = 0.(B) As in Equation 14 with C = 8 and D = μ. In this case, R(x) has a minimum at a positive value of x.(C) As in Equation 14 with C = 20 and D = μ. In this case, R(x) is monotonically increasing, and the evolutionary optimum is the most extreme compressed life history, x = ∞.(D) A recruitment function not in the class of Equation 14: 							. In all cases, ω0 = 1, μ = μ0 + g = 0.1, and R0 = ω0/μ, R∞ = κCω0 with 							.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2230684&req=5

pcbi-0030256-g002: Graphs of R(x) as Functions of the Senescence Variable x for Various Initial Recruitment Functions b0(x)Graphs of b0(x) are shown in the inset panels.(A) As in Equation 14 with C = 1 and D = μ. In this case, R(x) is monotonically decreasing in x, and the evolutionary optimum is at the nonsenescent state x = 0.(B) As in Equation 14 with C = 8 and D = μ. In this case, R(x) has a minimum at a positive value of x.(C) As in Equation 14 with C = 20 and D = μ. In this case, R(x) is monotonically increasing, and the evolutionary optimum is the most extreme compressed life history, x = ∞.(D) A recruitment function not in the class of Equation 14: . In all cases, ω0 = 1, μ = μ0 + g = 0.1, and R0 = ω0/μ, R∞ = κCω0 with .

Mentions: If D = 0, this is linear in x with slope C, and with D > 0, it is asymptotically linear as x → ∞. The exponential factor is important for small x, since it ensures that b0(x) is very flat, increasing only slowly near x = 0. In Appendix C of Text S1, it is shown that, for D > 0 and C sufficiently small, and with relative vitality given by Equation 12 (and for the more general forms considered in Appendix A of Text S1), R(x) in Equation 13 is monotonically decreasing in x, with R(x) → κCω0, a positive constant, as x → ∞ (where ). Clearly, if R(x) is decreasing and Cω0 ≥ 1, then R(x) > 1 for all x, and so there is a viable equilibrium population for every value of x, representing an evolutionary continuum from the most extreme compressed life history (x → ∞) to the most extreme spread, nonsenescent life history (x = 0). Examples of behaviors of R(x) for b0(x) in the family of Equation 14 are shown in Figure 2A–2C. Figure 2D shows an example in which b0(x) increases rapidly for small x, and then only slowly approaches its straight-line asymptote. The corresponding R(x) has a complicated shape, with two evolutionary optima, one near x = 0, and a more prominent one at a value near x = 1.


Density dependence triggers runaway selection of reduced senescence.

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

Graphs of R(x) as Functions of the Senescence Variable x for Various Initial Recruitment Functions b0(x)Graphs of b0(x) are shown in the inset panels.(A) As in Equation 14 with C = 1 and D = μ. In this case, R(x) is monotonically decreasing in x, and the evolutionary optimum is at the nonsenescent state x = 0.(B) As in Equation 14 with C = 8 and D = μ. In this case, R(x) has a minimum at a positive value of x.(C) As in Equation 14 with C = 20 and D = μ. In this case, R(x) is monotonically increasing, and the evolutionary optimum is the most extreme compressed life history, x = ∞.(D) A recruitment function not in the class of Equation 14: 							. In all cases, ω0 = 1, μ = μ0 + g = 0.1, and R0 = ω0/μ, R∞ = κCω0 with 							.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2230684&req=5

pcbi-0030256-g002: Graphs of R(x) as Functions of the Senescence Variable x for Various Initial Recruitment Functions b0(x)Graphs of b0(x) are shown in the inset panels.(A) As in Equation 14 with C = 1 and D = μ. In this case, R(x) is monotonically decreasing in x, and the evolutionary optimum is at the nonsenescent state x = 0.(B) As in Equation 14 with C = 8 and D = μ. In this case, R(x) has a minimum at a positive value of x.(C) As in Equation 14 with C = 20 and D = μ. In this case, R(x) is monotonically increasing, and the evolutionary optimum is the most extreme compressed life history, x = ∞.(D) A recruitment function not in the class of Equation 14: . In all cases, ω0 = 1, μ = μ0 + g = 0.1, and R0 = ω0/μ, R∞ = κCω0 with .
Mentions: If D = 0, this is linear in x with slope C, and with D > 0, it is asymptotically linear as x → ∞. The exponential factor is important for small x, since it ensures that b0(x) is very flat, increasing only slowly near x = 0. In Appendix C of Text S1, it is shown that, for D > 0 and C sufficiently small, and with relative vitality given by Equation 12 (and for the more general forms considered in Appendix A of Text S1), R(x) in Equation 13 is monotonically decreasing in x, with R(x) → κCω0, a positive constant, as x → ∞ (where ). Clearly, if R(x) is decreasing and Cω0 ≥ 1, then R(x) > 1 for all x, and so there is a viable equilibrium population for every value of x, representing an evolutionary continuum from the most extreme compressed life history (x → ∞) to the most extreme spread, nonsenescent life history (x = 0). Examples of behaviors of R(x) for b0(x) in the family of Equation 14 are shown in Figure 2A–2C. Figure 2D shows an example in which b0(x) increases rapidly for small x, and then only slowly approaches its straight-line asymptote. The corresponding R(x) has a complicated shape, with two evolutionary optima, one near x = 0, and a more prominent one at a value near x = 1.

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