### Abstract

Mutualism refers to any species interaction in which the presence of one species benefits the others. While many specific models of two-species mutualism have been developed and analyzed, comparatively, more attention has been devoted to antagonistic interactions among species (i.e., predation and competition). However, recent work revisited the problem of modeling mutualistic interactions with a focus on two basic objectives: an attempt at unifying existing particular models into a smaller set of general models and at providing a qualitative analysis of their solutions in order to reveal the fundamental role of mutualism in the dynamics of the population under consideration. In this chapter we provide an overview on the most important results concerning general models of mutualism. In particular, we place the development of these models in the general context of establishing realistic “building blocks” in ecological models. To this end, particular attention is paid on the mathematical conditions necessary to separate bounded solutions from unbounded ones and, whenever possible, on the conditions leading to a unique, globally stable, coexistence equilibrium. We show how these results can be extended to an unspecified number of mutualistic species and how one can identify a subset of these species most likely to cause unbounded solutions. Last but not least, we argue for the importance of developing general models with carefully selected assumptions that are not too restrictive but, at the same time, still useful in potential experimental research.

Original language | English (US) |
---|---|

Title of host publication | Handbook of Statistics |

Editors | Arni S.R. Srinivasa Rao, C.R. Rao |

Publisher | Elsevier B.V. |

Pages | 85-130 |

Number of pages | 46 |

ISBN (Print) | 9780444641526 |

DOIs | |

State | Published - Jan 1 2019 |

### Publication series

Name | Handbook of Statistics |
---|---|

Volume | 40 |

ISSN (Print) | 0169-7161 |

### Fingerprint

### Keywords

- Bounding thresholds
- Coexistence equilibrium
- Generalization
- Global stability
- Mutualism

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics

### Cite this

*Handbook of Statistics*(pp. 85-130). (Handbook of Statistics; Vol. 40). Elsevier B.V.. https://doi.org/10.1016/bs.host.2018.09.001

**Mathematical Modeling of Multispecies Mutualism : From Particular Models Toward a Generalization of the Concept.** / Georgescu, Paul; Maxin, Daniel; Sega, Laurentiu M; Zhang, Hong.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Handbook of Statistics.*Handbook of Statistics, vol. 40, Elsevier B.V., pp. 85-130. https://doi.org/10.1016/bs.host.2018.09.001

}

TY - CHAP

T1 - Mathematical Modeling of Multispecies Mutualism

T2 - From Particular Models Toward a Generalization of the Concept

AU - Georgescu, Paul

AU - Maxin, Daniel

AU - Sega, Laurentiu M

AU - Zhang, Hong

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Mutualism refers to any species interaction in which the presence of one species benefits the others. While many specific models of two-species mutualism have been developed and analyzed, comparatively, more attention has been devoted to antagonistic interactions among species (i.e., predation and competition). However, recent work revisited the problem of modeling mutualistic interactions with a focus on two basic objectives: an attempt at unifying existing particular models into a smaller set of general models and at providing a qualitative analysis of their solutions in order to reveal the fundamental role of mutualism in the dynamics of the population under consideration. In this chapter we provide an overview on the most important results concerning general models of mutualism. In particular, we place the development of these models in the general context of establishing realistic “building blocks” in ecological models. To this end, particular attention is paid on the mathematical conditions necessary to separate bounded solutions from unbounded ones and, whenever possible, on the conditions leading to a unique, globally stable, coexistence equilibrium. We show how these results can be extended to an unspecified number of mutualistic species and how one can identify a subset of these species most likely to cause unbounded solutions. Last but not least, we argue for the importance of developing general models with carefully selected assumptions that are not too restrictive but, at the same time, still useful in potential experimental research.

AB - Mutualism refers to any species interaction in which the presence of one species benefits the others. While many specific models of two-species mutualism have been developed and analyzed, comparatively, more attention has been devoted to antagonistic interactions among species (i.e., predation and competition). However, recent work revisited the problem of modeling mutualistic interactions with a focus on two basic objectives: an attempt at unifying existing particular models into a smaller set of general models and at providing a qualitative analysis of their solutions in order to reveal the fundamental role of mutualism in the dynamics of the population under consideration. In this chapter we provide an overview on the most important results concerning general models of mutualism. In particular, we place the development of these models in the general context of establishing realistic “building blocks” in ecological models. To this end, particular attention is paid on the mathematical conditions necessary to separate bounded solutions from unbounded ones and, whenever possible, on the conditions leading to a unique, globally stable, coexistence equilibrium. We show how these results can be extended to an unspecified number of mutualistic species and how one can identify a subset of these species most likely to cause unbounded solutions. Last but not least, we argue for the importance of developing general models with carefully selected assumptions that are not too restrictive but, at the same time, still useful in potential experimental research.

KW - Bounding thresholds

KW - Coexistence equilibrium

KW - Generalization

KW - Global stability

KW - Mutualism

UR - http://www.scopus.com/inward/record.url?scp=85054669737&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054669737&partnerID=8YFLogxK

U2 - 10.1016/bs.host.2018.09.001

DO - 10.1016/bs.host.2018.09.001

M3 - Chapter

SN - 9780444641526

T3 - Handbook of Statistics

SP - 85

EP - 130

BT - Handbook of Statistics

A2 - Srinivasa Rao, Arni S.R.

A2 - Rao, C.R.

PB - Elsevier B.V.

ER -