Trajectories of senescence through Markov models

Lead Research Organisation: University of Oxford
Department Name: Statistics


Ageing is a process, in most species, that is both inexorable and individually variable. Measuring that individual variation (the individual ageing that is distinct from the calendar age) has long proved elusive.
A major goal of current theoretical research is to untangle the population-level measures of ageing (most crudely, age-specific mortality rates, but also cross-sectional measures of specific physiological capacities) into individual measures of ageing.
This project aims to develop new statistical and mathematical models that will sharpen the focus on an individual-level senescence process, and to apply these models to real data from an experimental system.
The modelling work is based on hidden Markov models, in which a hidden "senescence" state drives surface-level observable processes. It is connected to recent theoretical work that has attempted to link basic structural properties of Markov processes to observed mortality rates, but goes farther in considering continuous observables, rather than merely a single endpoint (time of death).
The project is linked to a set of experiments being carried out in continuous behavioural observation of fruit flies, by entomologists and physicists in California and Mexico.
Analogous mathematical tools are being developed to improve the estimation of growth rates of age-structured populations in changing environments.


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Catalano RA (2015) Hormonal evidence of selection in utero revisited. in American journal of human biology : the official journal of the Human Biology Council

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Kolb M (2012) Quasilimiting behavior for one-dimensional diffusions with killing in The Annals of Probability

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Steinsaltz D (2011) Derivatives of the stochastic growth rate. in Theoretical population biology

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Steinsaltz D (2012) Markov models of aging: theory and practice. in Experimental gerontology

Description • We have a new formula for computing the sensitivity of population growth in age-structured natural populations to environmental changes. This has practical implications for studying ecological response to climate change and other environmental shifts, and theoretical implications for the evolution of ageing.
• The patterns of total movement through the life course among flies were too variable to analysed with the basic monotone-ageing hidden diffusion model that had initially been proposed. This work helped to inspire a new dynamical generalised linear model, that is now being made operational, and will be applied to a cleaner and larger set of data.
• We were able in principle to "filter" the individual pattern of ageing for flies on the basis of patterns of behaviour other than movement, in this case the frequency of eating. On the other hand, the individual trajectories were too variable to be demonstrably useful for predicting remaining lifespan.
• We have new theorems giving general conditions for the stabilisation over the life course ("convergence to quasistationarity") of diffusion models for ageing.
• We have drawn up a classification of statistical models of ageing in terms of the way the models treat random variation.
• We have shown how information measures can be used to evaluate the theoretical utility of features of mathematical models that purport to describe the ageing process.
Exploitation Route We have now produced software for computing the algorithms we developed for analysing the growth of ageing populations in random environments, and these are now being tested by groups in the US working in applied and theoretical population ecology.

The approach that we developed for analysing survival with longitudinal covariates has led us to procedures for studying longitudinal data sets for the impact of variability of blood pressure. We are working on extending these to general procedures for medical monitoring.
Sectors Healthcare,Pharmaceuticals and Medical Biotechnology
Description NCRM Methodological Research Projects
Amount £162,000 (GBP)
Funding ID ES/N011856/1 
Organisation Economic and Social Research Council 
Sector Public
Country United Kingdom of Great Britain & Northern Ireland (UK)
Start 01/2016 
End 12/2018
Title Stochastic growth software 
Description Software package for computing changes in population growth rates in changing environments. 
Type Of Material Improvements to research infrastructure 
Year Produced 2014 
Provided To Others? Yes  
Impact None yet.