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Individual stochasticity and population heterogeneity in plant and animal demography

Final Report Summary - INDSTOCH (Individual stochasticity and population heterogeneity in plant and animal demography)

The most basic biological observation might be that individuals, of any species, vary among themselves. This variation is critically important for the growth of populations, for their extinction or persistence, for the structure and composition of populations, and for the evolution of species. The variation depends on rates of birth, death, and development, and how those rates differ among individuals.

Some of those differences are due to heterogeneity: differences in age, size, health, developmental stage, etc. Some of the differences are due to stochasticity, the random outcomes of probabilistic events. Who lives or dies, who reproduces or does not, is partly a matter of chance. The goal of this project was to develop new demographic theory for stochasticity and heterogeneity in population biology, including plants, animals, and humans.

Part of the effort was the development of new mathematical models to calculate the amount of stochasticity created by life cycle processes. Part involved creating new ways to incorporate heterogeneity, both observed and unobserved, into models. Another part developed new mathematical methods to analyze models and data. And yet another part developed applications, to evolution, climate change, pollution, and social effects, in plants, animals, and humans. These different directions of research were pursued in three major directions: sensitivity analysis of matrix population models, the incorporation of what are called “reward structures” into population models, and models that combine heterogeneity and stochasticity.

Sensitivity analysis is a branch of mathematics that quantifies the change in the outcome of some model in response to a change in the parameters of the model. We developed new sensitivity analysis methods for longevity and the special case of healthy longevity, for causes of death, and for multistate demographic models. We applied the methods to data on human mortality, laboratory data on insects and other invertebrates, and field data on seabirds, and evolutionary questions about senescence and the creation of genetic variation.

Reward structures are a new concept in population biology. As an individual organism proceeds through its life cycle, it accumulates stuff. We call these “rewards,” but there is no limitation that they be positive or desired. Examples include accumulating reproductive output, accumulating long-term income, and accumulating years spent in good (or bad) health. We developed this new mathematical framework in relation to Markov chain models for the individual life cycle, and applied it to a wide range of species and problems.

The final, synthetic, component of the project was to combine heterogeneity and stochasticity into a unified framework. This was accomplished by developing models that can include multiple dimensions of individual classification (age and stage and health and ...). This permits the heterogeneity due to these factors to be analyzed using the mathematical methods we developed. We developed models for humans, invertebrate animals, and seabirds, and incorporated heterogeneity due to prior conditions, male-female differences, genetic differences, health effects, maternal age, and socioeconomic conditions.

The results of the project have provided the basis for an entirely new approach to individual variation and its sources in heterogeneity and stochasticity.