Modeling and analysis of stoichiometric two-patch consumer-resource systems

Christian R. Miller, Yang Kuang, William F. Fagan, James Elser

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Ecological stoichiometry studies the balance of energy and multiple chemical elements in ecological interactions to establish how the laws of thermodynamics affect food-web dynamics and nutrient cycling in ecosystems. In this paper, we incorporate stoichiometric principles in a model with habitat heterogeneity and dispersal in order to better understand population growth dynamics. This model describes a situation where a resource is separated into two patches by a barrier. Growth of the resource in each patch is limited by soil fertility and self-crowding. The consumer disperses between the two patches and is not affected by the barrier. The consumer's growth is potentially limited by the phosphorus content of the acquired resource. Mathematical analysis of this model and simulations are performed. Several biological implications, including an observed 'stoichiometric extinction effect,' are demonstrated with simulation where the stoichiometric mechanism appears to promote extinction in a patchy environment. This is in sharp contrast to the notion that stoichiometry mechanism promotes diversity in spatially homogeneous settings. Another important result is the rediscovery of a simple and plausible biological mechanism that generates local and global extinction. In this setting, which can be considered a spatially mediated form of apparent competition, the dispersal of the consumer from the rich patch can des the growth of the resource in the poor patch and in some situations can lead to the extinction of the resource in the poor patch.

Original languageEnglish (US)
Pages (from-to)153-184
Number of pages32
JournalMathematical Biosciences
Volume189
Issue number2
DOIs
StatePublished - Jun 2004

Fingerprint

Patch
extinction
Extinction
Resources
Ecosystem
stoichiometry
resource
Growth
Modeling
Stoichiometry
modeling
Food Chain
Population Growth
Population Dynamics
Thermodynamics
chemical elements
Phosphorus
balance studies
Fertility
apparent competition

Keywords

  • Biodiversity
  • Consumer-resource model
  • Extinction
  • Patch model
  • Stoichiometry

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Modeling and analysis of stoichiometric two-patch consumer-resource systems. / Miller, Christian R.; Kuang, Yang; Fagan, William F.; Elser, James.

In: Mathematical Biosciences, Vol. 189, No. 2, 06.2004, p. 153-184.

Research output: Contribution to journalArticle

Miller, Christian R. ; Kuang, Yang ; Fagan, William F. ; Elser, James. / Modeling and analysis of stoichiometric two-patch consumer-resource systems. In: Mathematical Biosciences. 2004 ; Vol. 189, No. 2. pp. 153-184.
@article{1b14f94abed54c7faa3bf486ef968e54,
title = "Modeling and analysis of stoichiometric two-patch consumer-resource systems",
abstract = "Ecological stoichiometry studies the balance of energy and multiple chemical elements in ecological interactions to establish how the laws of thermodynamics affect food-web dynamics and nutrient cycling in ecosystems. In this paper, we incorporate stoichiometric principles in a model with habitat heterogeneity and dispersal in order to better understand population growth dynamics. This model describes a situation where a resource is separated into two patches by a barrier. Growth of the resource in each patch is limited by soil fertility and self-crowding. The consumer disperses between the two patches and is not affected by the barrier. The consumer's growth is potentially limited by the phosphorus content of the acquired resource. Mathematical analysis of this model and simulations are performed. Several biological implications, including an observed 'stoichiometric extinction effect,' are demonstrated with simulation where the stoichiometric mechanism appears to promote extinction in a patchy environment. This is in sharp contrast to the notion that stoichiometry mechanism promotes diversity in spatially homogeneous settings. Another important result is the rediscovery of a simple and plausible biological mechanism that generates local and global extinction. In this setting, which can be considered a spatially mediated form of apparent competition, the dispersal of the consumer from the rich patch can des the growth of the resource in the poor patch and in some situations can lead to the extinction of the resource in the poor patch.",
keywords = "Biodiversity, Consumer-resource model, Extinction, Patch model, Stoichiometry",
author = "Miller, {Christian R.} and Yang Kuang and Fagan, {William F.} and James Elser",
year = "2004",
month = "6",
doi = "10.1016/j.mbs.2004.01.004",
language = "English (US)",
volume = "189",
pages = "153--184",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",
number = "2",

}

TY - JOUR

T1 - Modeling and analysis of stoichiometric two-patch consumer-resource systems

AU - Miller, Christian R.

AU - Kuang, Yang

AU - Fagan, William F.

AU - Elser, James

PY - 2004/6

Y1 - 2004/6

N2 - Ecological stoichiometry studies the balance of energy and multiple chemical elements in ecological interactions to establish how the laws of thermodynamics affect food-web dynamics and nutrient cycling in ecosystems. In this paper, we incorporate stoichiometric principles in a model with habitat heterogeneity and dispersal in order to better understand population growth dynamics. This model describes a situation where a resource is separated into two patches by a barrier. Growth of the resource in each patch is limited by soil fertility and self-crowding. The consumer disperses between the two patches and is not affected by the barrier. The consumer's growth is potentially limited by the phosphorus content of the acquired resource. Mathematical analysis of this model and simulations are performed. Several biological implications, including an observed 'stoichiometric extinction effect,' are demonstrated with simulation where the stoichiometric mechanism appears to promote extinction in a patchy environment. This is in sharp contrast to the notion that stoichiometry mechanism promotes diversity in spatially homogeneous settings. Another important result is the rediscovery of a simple and plausible biological mechanism that generates local and global extinction. In this setting, which can be considered a spatially mediated form of apparent competition, the dispersal of the consumer from the rich patch can des the growth of the resource in the poor patch and in some situations can lead to the extinction of the resource in the poor patch.

AB - Ecological stoichiometry studies the balance of energy and multiple chemical elements in ecological interactions to establish how the laws of thermodynamics affect food-web dynamics and nutrient cycling in ecosystems. In this paper, we incorporate stoichiometric principles in a model with habitat heterogeneity and dispersal in order to better understand population growth dynamics. This model describes a situation where a resource is separated into two patches by a barrier. Growth of the resource in each patch is limited by soil fertility and self-crowding. The consumer disperses between the two patches and is not affected by the barrier. The consumer's growth is potentially limited by the phosphorus content of the acquired resource. Mathematical analysis of this model and simulations are performed. Several biological implications, including an observed 'stoichiometric extinction effect,' are demonstrated with simulation where the stoichiometric mechanism appears to promote extinction in a patchy environment. This is in sharp contrast to the notion that stoichiometry mechanism promotes diversity in spatially homogeneous settings. Another important result is the rediscovery of a simple and plausible biological mechanism that generates local and global extinction. In this setting, which can be considered a spatially mediated form of apparent competition, the dispersal of the consumer from the rich patch can des the growth of the resource in the poor patch and in some situations can lead to the extinction of the resource in the poor patch.

KW - Biodiversity

KW - Consumer-resource model

KW - Extinction

KW - Patch model

KW - Stoichiometry

UR - http://www.scopus.com/inward/record.url?scp=1942470971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1942470971&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2004.01.004

DO - 10.1016/j.mbs.2004.01.004

M3 - Article

VL - 189

SP - 153

EP - 184

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 2

ER -