My research focuses on population models, usually based on matrices, for plants, animals, and humans.  I am interested in stochastic processes in demography, including individual stochasticity (random outcomes of individual lives, affecting indices such as longevity), demographic stochasticity (random growth of populations generated by the stochastic outcomes of survival and reproduction), and environmental stochasticity (fluctuations in the vital rates that affect all members of the population). I study both basic theory and the application of that theory, especially to evolutionary questions and to environmental questions related to climate change.

Beyond individuals, it is notable that family dynamics are important for the life histories of humans and of some kinds of animals: primates, whales, some birds, and social insects in particular. Matrix population models may provide an important analytical tool to explore the patterns of kinship and family structures implied by particular sets of demographic processes.

Some of the projects I am currently involved in:

• Stochasticity and heterogeneity in lifetime reproductive output and longevity. Using Markov chains with rewards to calculate the variance in lifetime reproductive output that is implied by any set of age- or stage-specific demographic rates, without the need to invoke individual heterogeneity. Comparisons across species and in historical series of human populations. Applications to studies of socio-economic inequality.
• Eco-evolutionary dynamics. Combining ecological and demographic processes, using matrix population models, with evolutionary dynamics at the level of single-locus Mendelian genetics.
• Mathematics of demographic models and Markov chains. Developing comprehensive mathematical treatments of second-order demographic models, ageXstage-classified models, cause of death analyses, and properties of multistate Markov chains. New mathematical methods for Markov chains with rewards.
• Matrix approaches to health demography. Using matrices to incorporate both prevalence-based and incidence-based models for healthy longevity. Focusing on extending results from a preoccupation with means to inclusion of variances and higher moments.
• Matrix methods for the analysis of family and kinship structures. Funded by an ERC Advanced Grant; see the tab for that project on this web page.
• Sensitivity analysis in ecology and demography.  Any population model implies a relationship between the parameter values and the outcomes of the model. Sensitivity analysis attempts to determine how changes in the parameters would translate into changes in the outcomes. I am applying matrix calculus methods to carry out sensitivity analysis of population projections, demographic variances, second-order demographic models, ageXstage-classified models, and models for cause of death.
• Seabird ecology. In collaboration with researchers at Woods Hole Oceanographic Institution, I am working on demographic models for Antarctic seabirds (fulmars, albatrosses) with a focus on identifying and projecting effects of climate change.
• A matrix formulation of the analysis of causes of death. Organisms, including humans, are subject to a variety of causes of death. These causes are competing risks, because while the individual is at risk from all of them, only one can, in the end, be the cause of death. There is a long tradition of calculating the results of competing risks; this project is using matrix methods to carry out all the traditional analyses and more.

You can download a CV with a complete list of publications here.

I have been fortunate enough to receive two Advanced Grants from the European Research Commission. The new one, beginning in June 2018, is The Formal Demography of Kinship and Family. Its goal is to develop a complete formal demographic structure for studying kinship at the individual, cohort, and population levels. Kinship structures arise from the relation betwen parents and offspring and spread out in directions both earlier (ancestors) and later (descendents) in time. This project is funded through the social science panel at ERC, and is focused on human kinship dynamics. However, it has not escaped my notice that kinship is also an important issue for some non-human species. I intend to investigate these interactions as well; the complexity of life cycles in the plant and animal kingdoms provides plenty of challenges for analysis.

My previous ERC Advanced Grant, Individual stochasticity and population heterogeneity in plant and animal demography (2013-2018) has developed new approaches to partitioning variance in demographic outcomes into contributions from heterogeneity (genuine differences among individuals) and stochasticity (random differences from probabilistic demographic events). A series of publications from the research team has produced new methods for matrix population models, Markov chains, sensitivity analysis, and statistical analyses. We have applied the results to populations of humans, laboratory studies of insects, and field studies of birds. Results will continue to accumulate for quite some time!  My list of publications available on another tab here will give an idea of where we are at this point.