We study populations by developing concepts of demography, epidemiology, ecology and population genetics. In our book, How Many People Can the Earth Support?, we examine how the interaction of natural constraints with human choices affects carrying capacity. In other studies, we are developing spatially explicit mathematical models of Chagas disease transmission in Argentina, to improve interventions and disease control. To understand ecological communities of human and nonhuman species, we focus on food webs, flowcharts of who eats whom. We are developing a new data structure to integrate food webs with species abundances and body sizes. Many descriptions of community structure can be derived as special cases of this data structure. We analyze quantitatively age patterns of senescence-related variables, including total and cause-specific rates of mortality, morbidity and disability, as well as biomarkers of aging. We develop mathematical models and statistical methods to explain observed quantitative patterns and differentials.
We study populations, and theories relevant to them. Populations exhibit phenomena that are difficult to deduce from the characteristics of an isolated member. For example, the prevalence of a disease is indirectly connected to the course of disease in an individual, aging in a population differs in causes and consequences from aging in an individual. To develop concepts helpful for understanding populations, we study concrete problems in demography, epidemiology, ecology, and population genetics.
Some of my projects include:
- Demography: How Many People Can the Earth Support ( details )
- Epidemiology: Chagas Disease in Northwest Argentina
- Ecology: Food Webs in Rice Paddies in the Philippines; Spectral Properties of Chaotic Population Models.
- Mathematical Studies: Entropy Inequalities in Information Theory; Paradoxes of Congested Networks;
- Nonassociative Algebras: Paper, Scissors, Stone.