Featured Research

from universities, journals, and other organizations

Predator-prey made simple: Simplifying studies of predator-prey interactions and other 'bistable' systems

Date:
May 6, 2014
Source:
American Institute of Physics (AIP)
Summary:
Scientists have developed a way to dramatically reduce the complexity of modeling "bistable" systems which involve the interaction of two evolving species where one changes faster than the other (“slow-fast systems”). The work paves the way for easier computational simulations and predictions involving such systems, which are found in fields as diverse as chemistry, biology and ecology.

Computed stationary density of a slow-fast system with metastable transitions is shown.
Credit: M. Bruna/University of Oxford

A team of U.K. researchers has developed a way to dramatically reduce the complexity of modeling "bistable" systems which involve the interaction of two evolving species where one changes faster than the other ("slow-fast systems"). Described in The Journal of Chemical Physics, the work paves the way for easier computational simulations and predictions involving such systems, which are found in fields as diverse as chemistry, biology and ecology.

Imagine, for instance, trying to predict how a population of whales would fare based on the impact of fluctuating ocean levels of plankton, if that was their primary food source. It might seem easy enough to estimate how many happy whales you will have given a relatively constant supply of plankton, but it's much harder to reckon what will happen to the population when their food source fluctuates dramatically.

That's much closer to reality: over their lifetimes, your average whale could endure multiple feasts and famines according to plankton's fickle blooms, and accurately predicting the impacts these will have on the whale population are made possible only by accounting for both the slow whale population dynamics and the much faster and widely fluctuating plankton population dynamics. This situation can be represented as a classic "bistable" problem: conceptually challenging, mathematically complicated, computationally intensive and, until now, nearly impossible to solve.

But hitting upon a solution that was in itself somewhat bistable, Maria Bruna and colleagues at the University of Oxford's Mathematical Institute and at Microsoft Research's Computational Science Laboratory in Cambridge, England developed a new method for deriving simpler models of bistable systems.

Their solution involved combining two existing mathematical techniques called "slow manifold theory," which is applied to slow-fast systems; and "perturbation theory," which is used for the study of metastable transitions. They tested this approach against the more standard, computationally expensive model that exhaustively treated the fast processes to predict the slow. What their results showed was that their simpler method worked just as well at predicting the slow process. Then they applied this to a predator-prey model and showed that it could accurately calculate the time to extinction of the predator (the slow species, like the whale) when the abundance of its prey (the fast species, like the plankton) fluctuates around two alternative states.

A key advantage of the new approach is that it allowed the researchers to obtain the accurate time-dependent behavior of the slow variable, in contrast to earlier methods that are only useful to compute equilibrium quantities.

"Using this method one can obtain accurate simulations of the process of interest that take into account the effect of the fast bistable processes, but much more cheaply," Bruna said.

"Since the reduction method is systematic, it can be easily applied to other systems and extended to higher dimensions," she added. For instance, the method could be extended to help understand why some ecosystems, consisting of multiple fast-slow interaction processes, fail to return to their original state after being perturbed by harvesting.


Story Source:

The above story is based on materials provided by American Institute of Physics (AIP). Note: Materials may be edited for content and length.


Journal Reference:

  1. Maria Bruna, S. Jonathan Chapman and Matthew J. Smith. Model reduction for slow-fast stochastic systems with metastable behaviour,. The Journal of Chemical Physics, 2014 DOI: 10.1063/1.4873343

Cite This Page:

American Institute of Physics (AIP). "Predator-prey made simple: Simplifying studies of predator-prey interactions and other 'bistable' systems." ScienceDaily. ScienceDaily, 6 May 2014. <www.sciencedaily.com/releases/2014/05/140506115617.htm>.
American Institute of Physics (AIP). (2014, May 6). Predator-prey made simple: Simplifying studies of predator-prey interactions and other 'bistable' systems. ScienceDaily. Retrieved July 23, 2014 from www.sciencedaily.com/releases/2014/05/140506115617.htm
American Institute of Physics (AIP). "Predator-prey made simple: Simplifying studies of predator-prey interactions and other 'bistable' systems." ScienceDaily. www.sciencedaily.com/releases/2014/05/140506115617.htm (accessed July 23, 2014).

Share This




More Computers & Math News

Wednesday, July 23, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Robot Parking Valet Creates Stress-Free Travel

Robot Parking Valet Creates Stress-Free Travel

AP (July 23, 2014) 'Ray' the robotic parking valet at Dusseldorf Airport in Germany lets travelers to avoid the hassle of finding a parking spot before heading to the check-in desk. (July 23) Video provided by AP
Powered by NewsLook.com
The Reviews Are In For The Amazon Fire Phone

The Reviews Are In For The Amazon Fire Phone

Newsy (July 23, 2014) Amazon's first smartphone, the Fire Phone, is set to ship this week, and so far the reviews have been pretty mixed. Video provided by Newsy
Powered by NewsLook.com
Bigger Apple Phone, Bigger Orders

Bigger Apple Phone, Bigger Orders

Reuters - Business Video Online (July 22, 2014) Apple is asking suppliers to make 70 to 80 million units of its new larger screen iPhone, a lot more initially than its current model. Fred Katayama reports. Video provided by Reuters
Powered by NewsLook.com
AP Review: Amazon Fire Adds Spark to Smartphones

AP Review: Amazon Fire Adds Spark to Smartphones

AP (July 22, 2014) Amazon's new Fire phone uses tweaks to the Android operating system and some innovative features to set it apart from smartphones from the likes of Apple and Samsung. (July 22) Video provided by AP
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins