Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-24T17:58:16.803Z Has data issue: false hasContentIssue false

7 - The basics of stochastic population dynamics

Published online by Cambridge University Press:  05 June 2012

Marc Mangel
Affiliation:
University of California, Santa Cruz
Get access

Summary

In this and the next chapter, we turn to questions that require the use of all of our tools: differential equations, probability, computation, and a good deal of hard thinking about biological implications of the analysis. Do not be dissuaded: the material is accessible. However, accessing this material requires new kinds of thinking, because funny things happen when we enter the realm of dynamical systems with random components. These are generally called stochastic processes. Time can be measured either discretely or continuously and the state of the system can be measured either continuously or discretely. We will encounter all combinations, but will mainly focus on continuous time models. Much of the groundwork for what we will do was laid by physicists in the twentieth century and adopted in part or wholly by biologists as we moved into the twentyfirst century (see, for example, May (1974), Ludwig (1975), Voronka and Keller (1975), Costantino and Desharnais (1991), Lande et al. (2003)). Thus, as you read the text you may begin to think that I have physics envy; I don't, but I do believe that we should acknowledge the source of great ideas. Both in the text and in Connections, I will point towards biological applications, and the next chapter is all about them.

Thinking along sample paths

To begin, we need to learn to think about dynamic biological systems in a different way.

Type
Chapter
Information
The Theoretical Biologist's Toolbox
Quantitative Methods for Ecology and Evolutionary Biology
, pp. 248 - 284
Publisher: Cambridge University Press
Print publication year: 2006

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
×