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Random fluctuations in population dynamics are fundamentally important in pure and applied ecology. This book introduces demographic and environmental stochasticity, and illustrates statistical methods for estimating them from field data. The concept of long-run growth rate of a population is explained and extended to age-structured populations. Diffusion approximations show how stochastic factors affect extinction in single populations and metapopulations. Delayed density dependence in populations with discrete annual reproduction is estimated from time series of adult numbers combined with basic life history data. The spatial scale of population fluctuations and local extinction risk depend on the scales of spatial environmental autocorrelation and individual dispersal, and the strength of density dependence. Stochastic dynamics and statistical uncertainty in population parameters are incorporated in Population Viability Analysis and sustainable harvesting. Statistics of species diversity measures and species abundance distributions are described, with implications for rapid assessments of biodiversity, and methods are developed for partitioning species diversity into components. Analysis of stochastic community dynamics indicates that real communities are far from neutral.