Numerical Methods in Mathematical Ecology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (15 November 2022) | Viewed by 13159

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Department of Marine Sciences, Faculty of the Environment, University of the Aegean, University Hill, GR81100 Mytilene, Lesvos Island, Greece
Interests: complexity/diversity and stability; species coexistence; community ecology; conservation biology; biostatistics
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Special Issue Information

Dear Colleagues,

Although almost a century has passed since the seminal work of Lotka and Volterra, who developed mathematical models to study competition and predation between biological species, there are still many people who do not consider mathematics as the tool of choice when studying ecological questions. Mathematical modeling has offered a framework for simplifying the complex natural world and seeking answers to pressing ecological questions. Ecologists are mostly interested in individual organisms, groups of individuals comprising populations, and groups of populations of different species comprising biological communities as well as communities together with their environment, comprising an ecosystem. Understanding how these entities that correspond to different levels of biological organization change in time and space—or in other words, their dynamics—has been facilitated by a particular branch of mathematics termed dynamical systems. In the tradition of mathematical ecology, very important scientific disciplines have been developed, almost in parallel, such as mathematical epidemiology. Besides the use of dynamical systems, several other tools have been utilized to study biological systems, notably network theory. Network models are used to investigate the effects of network topology on different properties of biological communities. At the same time, the relationship between some component of the complexity/diversity of ecosystems and the different measures of stability has historically been the cornerstone of mathematical ecology. It is often pointed out that increase in computational power has allowed us to investigate different scenarios in the development of the natural world, especially in light of global change.

We invite our colleagues to submit papers related to ecology as studied using different mathematical methods. We especially encourage contributions employing novel methods in the study of questions in mathematical ecology.

Prof. Dr. Giorgos Kokkoris
Guest Editor

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Keywords

  • mathematical ecology
  • theoretical ecology
  • population ecology
  • community ecology
  • ecosystem ecology
  • complexity and stability
  • food webs
  • ecological networks
  • dynamical systems

Published Papers (2 papers)

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17 pages, 639 KiB  
Article
A Numerical Method for Multispecies Populations in a Moving Domain Using Combined Masses
by M. J. Baines and Katerina Christou
Mathematics 2022, 10(7), 1124; https://doi.org/10.3390/math10071124 - 01 Apr 2022
Viewed by 1428
Abstract
This paper concerns the numerical evolution of two interacting species satisfying coupled reaction–diffusion equations in one dimension which inhabit the same part of a moving domain. The domain has both moving external boundaries and moving interior interfaces where species may arise, overlap, or [...] Read more.
This paper concerns the numerical evolution of two interacting species satisfying coupled reaction–diffusion equations in one dimension which inhabit the same part of a moving domain. The domain has both moving external boundaries and moving interior interfaces where species may arise, overlap, or disappear. Numerically, a moving finite volume method is used in which node movement is generated by local mass preservation, which includes a general combined mass strategy for species occupying overlapping domains. The method is illustrated by a test case in which a range of parameters is explored. Full article
(This article belongs to the Special Issue Numerical Methods in Mathematical Ecology)
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34 pages, 29251 KiB  
Article
Predator–Prey Models: A Review of Some Recent Advances
by Érika Diz-Pita and M. Victoria Otero-Espinar
Mathematics 2021, 9(15), 1783; https://doi.org/10.3390/math9151783 - 28 Jul 2021
Cited by 18 | Viewed by 10671
Abstract
In recent years, predator–prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper is to give a state-of-the-art review of recent [...] Read more.
In recent years, predator–prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper is to give a state-of-the-art review of recent predator–prey models which include some interesting characteristics such as Allee effect, fear effect, cannibalism, and immigration. We compare the qualitative results obtained for each of them, particularly regarding the equilibria, local and global stability, and the existence of limit cycles. Full article
(This article belongs to the Special Issue Numerical Methods in Mathematical Ecology)
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