STATISTICS and DEMOGRAPHY


The Bridge of Life
Sovereigns may sway materials, but not matter,
and wrinkles (the damned democrats) won't flatter.

And Death -- the sovereign's sovereign, though the great
Gracchus of all mortality, who levels
With his agrarian laws, the high estate
Of him who feasts and fights and roars and revels
To one small grass-grown patch (which must await
Corruption for its crop) with the poor devils
Who never had a foot of land till now --
Death's a reformer, all men must allow.
-- Lord Byron, Don Juan
"The Bridge of Life". Painting commissioned by Francis Galton.


Summary of my research

Since July, 2001, I have been working to understand the connection between population level data and individual-level processes, particularly with regard to aging and mortality   Until June 2005 this work was funded by a career development grant from the National Institute on Aging.  From 2006 to 2007 this work was funded by a Discovery Grant from the Canadian NSERC.

Attempts to understand aging in a broad biological context, in particular evolutionary models, have suffered at times from antiquated mathematical technology.  I have been working to extend and reanalyze existing models, and to develop new models, based on modern mathematical (particularly stochastic-process) methods. Click here for slides from a recent presentation I gave at the Santa Fe Institute.

An account of some not-yet mathematized ideas about modeling the aging process, written
jointly with Lloyd Goldwasser, may be found as Aging and Total Quality Management:
Extending the reliability metaphor for longevity. In Evolutionary Ecology Research 8 (2006), pp. 1445--59.

One of the most exciting developments in aging research is the extension of theories of senescence down to protozoans.  An analysis of the evolutionary consequences of unequal inheritance of damage in fissioning organisms may be found as:
Damage segregation at fissioning may increase growth rates: A superprocess model.
Theoretical Population Biology 71:4 (2007), pp. 473-90.

So far, I have written several papers on modeling mortality plateaus. Two papers, written jointly with Steven Evans, look at the implications of convergence to quasistationarity for Markov models of mortality. “Markov mortality models” describes the implications for mathematical modeling. “Quasistationary distributions” is a mathematical paper, proving some of the results referred to in “Markov mortality models”.  

Markov mortality models: Implications of quasistationarity and initial distributions (Joint with Steven N. Evans). Theoretical Population Biology 65:4 (June 2004).

Quasistationary distributions for one-dimensional diffusions (Joint with Steven N. Evans).  Transactions of the American Mathematical Society 359:3 (March 2007), pp. 1285--1324.

A major effort, of late, has been to develop more flexible models of mutation-selection balance, a fundamental component of evolutionary explanations for aging.

A generalized model of mutation-selection balance with applications to aging (Joint with Steven N. Evans and Kenneth W. Wachter).  Advances in Applied Mathematics 35:1 (2005), pp. 16--33.

This has been extended to a (quite different) limit process that incorporates recombination:
A mutation-selection model for general genotypes with recombination

Some recent work has concerned statistical issues in fitting lifetime models to small data sets.
"Validated analysis of mortality rates demonstrates distinct genetic mechanisms that influence lifespan.” (Joint with Kelvin Yen and Charles Mobbs).  Experimental Gerontology, 43:12 (2008), pp. 1044--51.  (published version doi:10.1016/j.exger.2008.09.006)

I have also been working on mathematical and statistical questions connected with a demographic explanation of mortality plateaus.  If the initial population were composed of subpopulations with differing initial robustness, this would produce an appearance of flattening mortality at advanced ages, even if individual hazards kept increasing.

"Reevaluating a test of the heterogeneity explanation for mortality plateaus".  (Experimental Gerontology 40:1-2 (Jan/Feb 2005), pp. 101-13) considers some statistical issues that arise in fitting plateaued Gompertz curves to small-population survival data.  It reanalyzes data from an experiment which purported to show that there was no heterogeneity effect in Drosophila mortality plateaus.


Understanding mortality rate deceleration and heterogeneity  (Joint with Kenneth W. Wachter).   (Mathematical Population Studies, 13:1 (2006), pp. 19--37). This paper uses an Abelian theorem to clarify the connection between high initial robustness and the mortality plateau. Qualitative behavior of the heterogeneity model is linked to human and invertebrate mortality data.


Relevant links

Presentations on Aging


For the more mathematically inclined

Santa Fe Institute review of theories of ageing

Lecture notes on mortality in heterogeneous populations from Second Annual Stanford Workshop on Formal Methods in Demography:
  1. Mortality plateaus and fixed frailty models
  2. Changing frailty models (slides)

Last updated 29 July, 2009

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