Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-29T05:34:46.044Z Has data issue: false hasContentIssue false

20 - Moment Methods for Ecological Processes in Continuous Space

Published online by Cambridge University Press:  14 January 2010

Ulf Dieckmann
Affiliation:
International Institute for Applied Systems Analysis, Austria
Richard Law
Affiliation:
University of York
Johan A. J. Metz
Affiliation:
Rijksuniversiteit Leiden, The Netherlands
Get access

Summary

Introduction

Spatial dynamics of populations have long been of interest to ecologists (Skellam 1951; Levin and Paine 1974; Andow et al. 1990), but recent advances in data collection and in computational power have put these concepts within the reach of many ecologists for the first time. Computational models (Wilson et al. 1993, 1995b; McCauley et al. 1993; Pacala and Deutschman 1995) suggest important and previously unexplored effects of space and discrete individuals on population dynamics. Analytic approaches that capture these effects are emerging, building on methods developed in other contexts. This chapter presents a general method for deriving approximate equations for spatial dynamics in continuous space and time that has advantages over classical and many modern approaches.

We are interested in spatial pattern formation in plant communities and in the effects of pattern on plant competition. Our goal is to find general methods for exploring this problem that are

  • analytically tractable, so that we can gain insight into qualitative behaviors of the system and analyze how they depend on the parameters;

  • sufficiently general, so that some of the same tools can be applied to answer a range of different questions about spatial dynamics in ecology; and

  • close enough to the characteristics of real populations that we can eventually fit the models to field data on individual behavior.

We focus on spatial point processes (Diggle 1983; Gandhi et al. 1998), continuous-time dynamical systems for discrete individuals interacting in a continuous habitat.

Type
Chapter
Information
The Geometry of Ecological Interactions
Simplifying Spatial Complexity
, pp. 388 - 411
Publisher: Cambridge University Press
Print publication year: 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×