JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 165.123.34.86 on Wed, 17 Jun 2015 18:34:14 UTC All use subject to JSTOR Terms and Conditions Editor's Note Invasions of new territory-by plants, animals, or genes-are an old topic in ecology, but hardly obsolete: the spread of pests such as the gypsy moth, exotic plants, recurrent and emerging infectious diseases, and genetically engineered organisms are important contemporary problems for ecology. For nearly half a . . ~~century, reaction-diffusion models have been the main analytic framework for Emphasizing9 modeling spatial spread, in part because of the well-developed mathematical theory new ideas that tells us how to compute things like the long-term rate of spread and the conditions for spatial pattern formation. In this paper, we are given the tools to to study the rate of spread for invading organisms in a very different kind of model, integrodifference equations. Unlike diffusion equations, these models can accomstimulate research modate leptokurtic (broad-tailed) dispersal patterns, and in such cases they can exhibit the accelerating rates of spread that have been observed in some invasions.in ecology Of course this does not mean that we should stop using diffusion models, but it gives us an alternative with a different set of assumptions that is likely to be more accurate when the dispersal pattern of individuals is far from the Gaussian distribution implicit in a diffusion model. AbstractModels that describe the spread of invading organisms often assume that the dispersal distances of propagules are normally distributed. In contrast, measured dispersal curves are typically leptokurtic, not normal. In this paper, we consider a class of models, integrodifference equations, that directly incorporate detailed dispersal data as well as population growth dynamics. We provide explicit formulas for the speed of invasion for compensatory growth and for different choices of the propagule redistribution kernel and apply these formulas to the spread of D. pseudoobscura. We observe that: (1) the speed of invasion of a spreading population is extremely sensitive to the precise shape of the redistribution kernel and, in particular, to the tail of the distribution; (2) fat-tailed kernels can generate accelerating invasions rather than constant-speed travelling waves; (3) normal redistribution kernels (and by inference, many reaction-diffusion models) may grossly underestimate rates of spread of invading populations in comparison with models that incorporate more realistic leptokurtic distributions; and (4) the relative superiority of different redistribution kernels depends, in general, on the precise magnitude of the net reproductive rate. The addition of...

Summary 1.A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define availability?Step selection analysis deals with this problem at the scale of the observed positional data, by matching each 'used step' (connecting two consecutive observed positions of the animal) with a set of 'available steps' randomly sampled from a distribution of observed steps or their characteristics. 2. Here we present a simple extension to this approach, termed integrated step selection analysis (iSSA), which relaxes the implicit assumption that observed movement attributes (i.e. velocities and their temporal autocorrelations) are independent of resource selection. Instead, iSSA relies on simultaneously estimating movement and resource selection parameters, thus allowing simple likelihood-based inference of resource selection within a mechanistic movement model. 3. We provide theoretical underpinning of iSSA, as well as practical guidelines to its implementation. Using computer simulations, we evaluate the inferential and predictive capacity of iSSA compared to currently used methods. 4. Our work demonstrates the utility of iSSA as a general, flexible and user-friendly approach for both evaluating a variety of ecological hypotheses, and predicting future ecological patterns.

Numbers of non-indigenous species-species introduced from elsewhere-are increasing rapidly worldwide, causing both environmental and economic damage. Rigorous quantitative risk-analysis frameworks, however, for invasive species are lacking. We need to evaluate the risks posed by invasive species and quantify the relative merits of different management strategies (e.g. allocation of resources between prevention and control). We present a quantitative bioeconomic modelling framework to analyse risks from nonindigenous species to economic activity and the environment. The model identi es the optimal allocation of resources to prevention versus control, acceptable invasion risks and consequences of invasion to optimal investments (e.g. labour and capital). We apply the model to zebra mussels (Dreissena polymorpha), and show that society could bene t by spending up to US$324 000 year 21 to prevent invasions into a single lake with a power plant. By contrast, the US Fish and Wildlife Service spent US$825 000 in 2001 to manage all aquatic invaders in all US lakes. Thus, greater investment in prevention is warranted.

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Ecological Society of America is collaborating with JSTOR to digitize, preserve and extend access to Ecology. Abstract.Most of the fundamental elements of ecology, ranging from individual behavior to species abundance, diversity, and population dynamics, exhibit spatial variation. Partial differential equation models provide a means of melding organism movement with population processes and have been used extensively to elucidate the effects of spatial variation on populations. While there has been an explosion of theoretical advances in partial differential equation models in the past two decades, this work has been generally neglected in mathematical ecology textbooks. Our goal in this paper is to make this literature accessible to experimental ecologists.Partial differential equations are used to model a variety of ecological phenomena; here we discuss dispersal, ecological invasions, critical patch size, dispersal-mediated coexistence, and diffusion-driven spatial patterning. These models emphasize that simple organism movement can produce striking large-scale patterns in homogeneous environments, and that in heterogeneous environments, movement of multiple species can change the outcome of competition or predation. In the classical applications of PDE models to population ecology, organisms are assumed to have Brownian random motion, the rate of which is invariant in time and space. This assumption leads to the diffusion model (Okubo 1980, Edelstein-Keshet 1986, Murray 1989): au (x, y, t) (02U a2U _ _ _ _= LITERATURE CITED Allee, W. C. 1931. Animal aggregations, a study on general sociology. University of Chicago Press, Chicago, Illinois, USA. Alt, W. 1985. Models for mutual attraction and aggregation of motile individuals. Pages 33-38 in V. Capasso, E. Grosso, and S. L. Paveri-Fontana, editors. Lecture Notes in Biomathematics Number 57. Ammerman, A. J., and L. L. Cavalli-Sforza. 1984. The Neolithic transition and the genetics of populations in Europe. . 1988. Analyzing field studies of insect dispersal using two-dimensional transport equations. Environmental Entomology 17:815-820. Bertsch, M., M. E. Gurtin, D. Hilhorst, and L. A. Peletier. 1984. On interacting populations that disperse to avoid crowding: the effect of a sedentary colony. Journal of Mathematical Biology 19:1-12. Bertsch, M., M. E. Gurtin, D. Hilhorst, and L. A. Peletier. 1985. On interacting populations that disperse to avoid crowding: preservation of segregation. Journal of Mathematical Biology 23:1-13. Bradford, E., and J. P. Philip. 1970a. Stability of steady distributions of asocial populations in one dimension. Journal of Theoretical Biology 29:13-26.