Steinar Engen

Spatial Scale of Population Synchrony: Environmental Correlation versus Dispersal and Density Regulation.

A stochastic model is developed to analyze the equilibrium spatial pattern of population synchrony, the correlation of temporal fluctuations in population density between localities. The expected population dynamics and the distribution of individual dispersal distance are homogeneous in space. Environmental stochasticity is caused by temporal fluctuations in the intrinsic rate of increase and/or carrying capacity of local populations that are correlated in space (but not time), the environmental correlation decreasing with distance. We analyze a linearized model for small fluctuations. Employing the standard deviation of a function in a given direction as a measure of scale, the spatial scale of population synchrony, lρ, is related to the spatial scales of environmental correlation, le, and individual dispersal, l, by the simple general formula \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Optimal Harvesting of Fluctuating Populations with a Risk of Extinction

l^{2}_{\rho }=l^{2}_{e}+ml^{2}/ \gamma

Generation time and temporal scaling of bird population dynamics.

\end{document} , where m is the individual dispersal rate and γ is the strength of population density regulation (or rate of return to equilibrium, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Environmental Stochasticity and Extinction Risk in a Population of a Small Songbird, the Great Tit

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Individual Heterogeneity in Vital Parameters and Demographic Stochasticity

\end{document} in the logistic model). Relative to environmental correlation (the Moran effect), the contribution of individual dispersal to the spatial scale of synchrony is magnified by the ratio of the individual dispersal rate to the strength of density regulation. Thus, even if the scale of individual dispersal is smaller than that of environmental correlation, dispersal can substantially increase the scale of population synchrony for weakly regulated populations.

Estimating density dependence from population time series using demographic theory and life-history data

Publisher Summary This chapter reviews studies that have analyzed the effects of local weather and large-scale climate phenomenon on fluctuations in the size of bird populations. Population size depends upon birth rates and death rates and how these interact with density. The variation in these relationships is also important. By understanding how these interact to affect variation in population size, one can examines how climate change may affect the future fluctuations of bird populations. There are three major issues to consider in understanding how climate change may result in changes in population size: whether the climate responses are density dependent or density independent; whether climate change largely affects the reproductive success or the survival; and whether climate change primarily affects the mean values or the variability. The chapter outlines a general theoretical framework based on Lande et al. for analyzing avian population dynamics and describes how an expected change in climate may affect avian population dynamics and thus help resolve the three issues. Modeling and estimating the effects of the density dependence as well as changes in the mean and variance of the relevant climate variables have been discussed.