Stochasticity, heterogeneity, and variance in longevity in human populations
MetadataShow full item record
KeywordIndividual stochasticity; Heterogeneous frailty; Variance; Longevity; Age–frailty classified matrix model; Gamma-Gompertz–Makeham
Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751–1899), France (1816–1903), and Italy (1872–1899), and also for a selection of period data for the same countries. Heterogeneity in mortality is described by the gamma-Gompertz–Makeham model, in which a gamma distributed “frailty” modifies a baseline Gompertz–Makeham mortality schedule. Model parameters were estimated by maximum likelihood for a range of starting ages. The estimates were used to construct an age××frailty-classified matrix model, from which we compute the variance of longevity and its components due to heterogeneous frailty and to individual stochasticity. The estimated fraction of the variance in longevity due to heterogeneous frailty (averaged over time) is less than 10% for all countries and for both sexes. These results suggest that most of the variance in human longevity arises from stochasticity, rather than from heterogeneous frailty.
© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Theoretical Population Biology 114 (2017): 107-116, doi:10.1016/j.tpb.2017.01.001.
Suggested CitationTheoretical Population Biology 114 (2017): 107-116
The following license files are associated with this item:
Showing items related by title, author, creator and subject.
van Daalen, Silke F.; Hernández, Christina M.; Caswell, Hal; Neubert, Michael G.; Gribble, Kristin E. (The University of Chicago Press, 2022-03-28)Variance among individuals in fitness components reflects both genuine heterogeneity between individuals and stochasticity in events experienced along the life cycle. Maternal age represents a form of heterogeneity that ...
Interacting effects of unobserved heterogeneity and individual stochasticity in the life-history of the Southern fulmar Jenouvrier, Stephanie; Aubry, Lise M.; Barbraud, Christophe; Weimerskirch, Henri; Caswell, Hal (2017-09-19)Individuals are heterogeneous in many ways. Some of these differences are incorporated as individual states (e.g., age, size, breeding status) in population models. However, substantial amounts of heterogeneity may remain ...
The extraordinary longevity of kleptoplasts derived from the Ross Sea haptophyte Phaeocystis antarctica within dinoflagellate host cells relates to the diminished role of the oxygen-evolving Photosystem II and to supplementary light harvesting by mycosporine-like amino acid/s Stamatakis, Kostas; Vayenos, Dimitris; Kotakis, Christos; Gast, Rebecca J.; Papageorgiou, George C. (2016-12)The haptophyte Phaeocystis antarctica and the novel Ross Sea dinoflagellate that hosts kleptoplasts derived from P. antarctica (RSD; R.J. Gast et al., 2006, J. Phycol. 42 233–242) were compared for photosynthetic light ...