Populations of insects, birds, or plants, for example, that have more individuals, on the average, frequently have more variability in the numbers of individuals over time, or from one place to another, or both. Taylor's law says that a statistical measure of the variability of population size, the variance, increases linearly with increasing average population size. Taylor's law has attracted intellectual interest in ecology, population biology, physics, computer science, and finance. This project aims to develop new theory and data to deepen the mathematical and biological understanding of Taylor's law.
Variability of the sizes of populations is a major practical concern in fisheries, agriculture, forestry, and epidemiology. Better understanding of spatial and temporal variability in population sizes can benefit people in all these areas. This project will contribute to public education in science and training of scientists at levels from primary school through post-doctoral training through collaborations with the Black Rock Forest Consortium and the University of Montpellier II, France.
INTELLECTUAL MERIT The present project added to our understanding of the patterns, origins and consequences of variability over time or across space in the size or density of populations. The project focused on a remarkable empirical regularity: in populations of a single species and interspecifically among related species, the variance of population size is often well described as a power law function of the mean population size: variance = a×meanb, a > 0. This empirical regularity is commonly called Taylor’s law, after the British agricultural entomologist L. R. Taylor (1924-2007), although it was discovered earlier by others. Taylor’s law has attracted intellectual interest in ecology, population biology, forestry, agricultural entomology, physics, computer science, and finance, and is the subject of more than 1000 publications. But many questions have remained unanswered. This project illuminated the scope of validity, the limitations, and the interpretation of the form and the parameters of Taylor's law by the coordinated analysis of mathematical models and empirical data. The approaches were inter- and multi-disciplinary, involving mathematics, statistics, computation, experimental laboratory populations, and long-term ecological field observations. The project deepened mathematical understanding of Taylor’s law; linked Taylor’s law, which is a pattern of ensembles of populations, to variation in individual body mass; and linked Taylor’s law to interspecific interactions at the level of an ecological community through multi-species experiments with bacterial microcosms. These advances and additional related work were reported in peer-reviewed scientific publications and lectures for scientific and public audiences. BROADER IMPACTS As a result of its conceptual and methodological breadth, the research offered exceptional educational opportunities to young scientists at the Rockefeller University and in other collaborating institutions. This research added to our understanding of how and why population sizes and densities vary in space and time. These variations have practical and scientific importance. For example, large increases in the size of populations of mosquitoes that transmit infectious diseases like West Nile virus or malaria may cause outbreaks of disease among humans. Large increases in populations of weedy plants or insect pests may impair timber and crop production. Large decreases in the size of populations of honeybees that pollinate agricultural crops may lower agricultural production and raise the cost of food and other agricultural crops. Large decreases in game animals may impair hunting for recreation and food. Large decreases in population size interest scientists because they may bring about genetic bottlenecks and increase the risk of extinction of a species. Variations in human population density in space affect the possibility and costs of delivering services like education, healthcare, telecommunications, public transportation, and electrical power. For these and many more reasons, it is important to understand how and why population size and population density fluctuate across space and over time. This project developed and tested mathematical and statistical models that make it possible to understand, predict, and interpret patterns of population fluctuation in species ranging from bacteria to forest trees, including humans.
