Perturbation Analysis of Indices of Lifespan Variability

Food availability modulates survival in interaction with (for example) competition, disease and predators, but to what extent food availability in natural populations affects survival independent of these factors is not well known. We tested the effect of food availability on lifespan and actuarial senescence in a large population of captive zebra finches by increasing the effort required to obtain food, reflecting natural contrasts in food availability. Food availability may not affect all individuals equally and we therefore created heterogeneity in phenotypic quality by raising birds with different numbers of siblings. Low food availability had no effect on lifespan for individuals from benign developmental conditions (raised in small broods), but shortened lifespan for individuals from harsh developmental conditions. The lifespan difference arose through higher baseline mortality rate of individuals from harsh developmental conditions, despite a decrease in the rate of actuarial senescence. We found no evidence for sex-specific environmental sensitivity, but females lived shorter than males due to increased actuarial senescence. Thus, low food availability by itself shortens lifespan, but only in individuals from harsh developmental conditions. Our food availability manipulation resembles dietary restriction as applied to invertebrates, where it extends lifespan in model organisms and we discuss possible reasons for the contrasting results.

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“…), and other measures of lifespan inequality correlate well with the s.d. [52]. We found that the s.d.…”

Section: (B) Senescencementioning

confidence: 74%

Food availability affects adult survival trajectories depending on early developmental conditions

Briga¹,

Koetsier²,

Boonekamp³

et al. 2017

Proc. R. Soc. B.

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“…There is a large literature examining patterns of variation in the age at death and a variety of indices of discrepancy in longevity (Anand and Nanthikesan 2000;van Raalte and Caswell 2013). Like all life table calculations, these assume that all individuals experience the same set of specified vital rates, and hence the calculated variation is due to individual stochasticity (van Raalte and Caswell 2013).…”

Section: Individual Stochasticity and Its Componentsmentioning

confidence: 99%

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation

Daalen¹,

Caswell²

2015

DemRes

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“…The matrixŨ in (17) is the transient matrix of an absorbing Markov chain (Feichtinger 1971;Caswell 2001Caswell , 2006Caswell , 2009van Raalte and Caswell 2013). The transition matrix of this chain is…”

Section: The Absorbing Markov Chainmentioning

confidence: 99%

“…Many statistics of longevity can be obtained from the marginal fundamental matrix N * (e.g., Caswell 2001Caswell , 2006Caswell , 2009Caswell , 2013van Raalte and Caswell 2013;Engelman, Caswell, and Agree 2014). These statistics describe the marginal results for the cohort starting with the initial frailty distribution π(0), including:…”

Section: Longevity Variation and Disparitymentioning

confidence: 99%

A matrix approach to the statistics of longevity in the gamma-Gompertz and related mortality models

Caswell¹

2014

DemRes

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BACKGROUNDThe gamma-Gompertz model is a fixed frailty model in which baseline mortality increases exponentially with age, frailty has a proportional effect on mortality, and frailty at birth follows a gamma distribution. Mortality selects against the more frail, so the marginal mortality rate decelerates, eventually reaching an asymptote. The gammaGompertz is one of a wider class of frailty models, characterized by the choice of baseline mortality, effects of frailty, distributions of frailty, and assumptions about the dynamics of frailty. OBJECTIVETo develop a matrix model to compute all the statistical properties of longevity from the gamma-Gompertz and related models. METHODSI use the vec-permutation matrix formulation to develop a model in which individuals are jointly classified by age and frailty. The matrix is used to project the age and frailty dynamics of a cohort and the fundamental matrix is used to obtain the statistics of longevity. RESULTSThe model permits calculation of the mean, variance, coefficient of variation, skewness and all moments of longevity, the marginal mortality and survivorship functions, the dynamics of the frailty distribution, and other quantities. The matrix formulation extends naturally to other frailty models. I apply the analysis to the gamma-Gompertz model (for humans and laboratory animals), the gamma-Makeham model, and the gamma-Siler model, and to a hypothetical dynamic frailty model characterized by diffusion of frailty with reflecting boundaries.The matrix model permits partitioning the variance in longevity into components due to heterogeneity and to individual stochasticity. In several published human data sets, Caswell: A matrix approach to the statistics of longevity in heterogeneous frailty models heterogeneity accounts for less than 10% of the variance in longevity. In laboratory populations of five invertebrate animal species, heterogeneity accounts for 46% to 83% of the total variance in longevity. IntroductionThe gamma-Gompertz (hereafter, G-G) model is one of a class of models that investigate the effects of hidden heterogeneity -heterogeneity that is either unobservable or unobserved -on mortality rates. It calculates various consequences of that heterogeneity for the dynamics of cohorts (e.g. Vaupel, Manton, and Stallard 1979;Vaupel and Yashin 1985;Yashin, Iachine, and Begun 2000;Vaupel 2010;Wienke 2010;Missov 2013). I refer to this heterogeneity as frailty, making no assumptions about its causes. The goal of this paper is to present a matrix formulation that permits easy computation of all the properties of the G-G and other frailty models. Frailty models can be characterized by their components:1. the baseline mortality rate, 2. the effects of frailty on the baseline mortality rate, 3. the dynamics of individual frailty over time, and 4. the initial distribution of frailty.The baseline mortality rate in the G-G model is the Gompertz model, in which mortality increases exponentially with age t, µ(t) = ae bt .Frailty affects mortality as a proportio...

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Perturbation Analysis of Indices of Lifespan Variability

Cited by 122 publications

References 53 publications

Food availability affects adult survival trajectories depending on early developmental conditions

Food availability affects adult survival trajectories depending on early developmental conditions

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation

A matrix approach to the statistics of longevity in the gamma-Gompertz and related mortality models

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