Alan Hastings

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  Ecological dynamics through time
  Alan Hastings
  A challenge for ecological modeling is to focus on appropriate time scales. A caricature of classical ecological theory is that it is typically based on the asymptotic behavior of deterministic systems with constant parameters. Yet answering the questions of interest for many real ecological systems requires approaches that use none of these assumptions. Work over recent decades has focused on just such approaches, with some of the most recent work focusing on transient dynamics and time varying parameters, which raises substantial mathematical challenges. I will give both ecological examples where these ideas are essential and describe some recent work in this area.
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  Dynamics and control of spatial ecological populations
  Alan Hastings
  I will focus on two important themes in contemporary ecology that draw upon mathematical tools: the dynamics of populations in space and management of populations. I will consider both deterministic and stochastic models of spatial population dynamics. For the management questions, I will consider both the issue of controlling invasive species in space and approaches for maintaining endangered species. Mathematical tools will be diverse, ranging from partial differential equations to stochastic models to different optimization approaches. Issues of time scales and the interface between models and data will be emphasized.
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  Dynamics and control of Spartina alterniflora and related issues
  Alan Hastings
  I will discuss models that include the kinds of spatial dynamics and control and life history appropriate for this plant. The ideas will focus on developing simple analytic models and using approaches that into account not only control but restoration and bio-economic aspects. Mathematical tools will include linear and quadratic programming in addition to optimization and other approaches to try and obtain general rules.
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  Ecological Modeling
  Alan Hastings
  Some underlying issues of modeling in ecology
  2 species predator prey dynamics and analysis
  Aquatic ecological systems - basic issues
  NPZ modeling basics
  NPZ "applications" and extensions
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  Intoductions and questions/panel with morning speakers
  Alan Hastings
  Panel discussion with morning speakers David Thomas and Alan Hastings
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  Spatial population dynamics and uncertainty in Tribolium: Lab Experiments and Models
  Alan Hastings
  In joint work with Brett Melbourne we have studied highly replicated spatial population dynamics of flour beetles in a lab setting. I will describe the results of experiments on single species and spatial spread, and corresponding models. The models have to incorporate stochasticity of different forms to provide a good match to the data. In particular, demographic heterogeneity, fixed differences among individuals, are critical for understanding the dynamics.
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  Role of time scales in sustainability of complex systems
  Alan Hastings

  Role of time scales in sustainability of complex systems

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  Challenges in the management of natural systems
  Alan Hastings

  I will give an overview of mathematical challenges that arise in developing management strategies for natural systems. The emphasis will be on issues that arise from the nature of the biological systems, including, but not limited to, limited data, nonlinearities, stochasticity, constraints that arise from biological issues, and time scales. I will illustrate the concepts by starting with some of the best studied examples, which come from fisheries, then discuss issues of invasive species, and finally move on to lesser studied and more poorly specified areas. The goal of the talk will be to set the stage for the workshop and initial discussions.

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  Parallels between metapopulations and disease dynamics
  Alan Hastings

  Within host dynamics in diseases is essentially the same as dynamics within metapopulations in an ecological context. I will review results from metapopulation models, and draw parallels to disease dynamics. I will emphasize both similarities and differences. The goal will be to see how various assumptions about within host (equivalently within patch) dynamics reduce the complexity of the model and study and lead to models which can be studied analytically.

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  Ricker models and complexity in ecology
  Alan Hastings

  Ricker models and complexity in ecology

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  Predictability, uncertainty and the persistence of ecological populations
  Alan Hastings
  I will develop simple approaches for the incorporation of large noise in ecological models, and indicate how this leads to open questions, both mathematical and biological. I will provide examples from both response to resource pulses and the dynamics of spatiotemporal synchrony in masting (production of seeds).