Permanent coexistence in a resource-based competition system

Mitra, Debolina; Mukherjee, Debasis; Roy, Aidan; Ray, Santanu

doi:10.1016/0304-3800(92)90014-6

Cited by 16 publications

(15 citation statements)

References 11 publications

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“…Earlier, the structure and function of this ecosystem particularly the virgin parts were investigated using deterministic models [15,17,18,23] and disturbed part also studied by some authors [9,21]. The two or three species models these investigators employed were unable to afford them a full understanding of this system.…”

Section: Introductionmentioning

confidence: 99%

Network Analysis of a Benthic Food Web Model of a Partly Reclaimed Island in the Sundarban Mangrove Ecosystem, India

et al. 2000

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Network analysis is performed on a 14 species food web model of the ecosystem occupying a mudflat on a partly reclaimed island of the Sundarban mangrove ecosystem. The results demonstrate a dramatic difference between this heavily impacted mangrove ecosystem in its modes of primary and secondary production and its diminished role of detritus vis-a-vis its less disturbed counterparts. Unlike most benthic mangrove systems, the Sundarban bottom community receives a large contribution from the phytoplankton populations. In this system herbivory and detritivory are virtually equal, in contrast to the usual herbivory:detritivory ratio of 1:5. Anthropogenic impacts have changed the physiography of this system so as to increase the relative importance of zooplankton and meiobenthos as herbivores. Although a slight degree of omnivory is exhibited by the populations of larger organisms, all flows of each integer of trophic length into a food chain may be aggregated that represents the underlying trophic status of the starting food web. Only a small number of pathways of recycle can be identified (31), and the Finn cycling index for this system is quite low (8.4%). Litterfall comprises only 16% of the total system input, which is very little in comparison with most mangrove systems. Pathway redundancy is rather high in this ecosystem, indicating that the surviving system is probably highly resilient to further perturbations, as one might expect for a highly impacted system.

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Section: Introductionmentioning

confidence: 99%

Network Analysis of a Benthic Food Web Model of a Partly Reclaimed Island in the Sundarban Mangrove Ecosystem, India

et al. 2000

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“…In the following theorem we are able to show that the model system (4) is uniformly persistent [13,14]. By the persistence of a system we mean that both the political parties are present and none of them will go to extinction.…”

Section: Stability Analysismentioning

confidence: 95%

A simple mathematical model for the spread of two political parties

Misra

2012

NAMC

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In this paper, a non-linear mathematical model for the spread of two political parties has been proposed and analyzed by using epidemiological approach. The whole population is assumed to be a constant and homogeneously mixed. Equilibria have been obtained analytically and their local and global stability have been discussed. Conditions for the co-existence of both the political parties have been obtained. Numerical simulation is also performed to support the analytical results.

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“…However, the criterion for persistence and stability in such systems was proposed later by Freedman and Waltman (1984) and Gopalsamy (1986). The fate of the two predators attacking a single prey and their co-existence depends on the ratio between their numerical responses (Mitra et al 1992). Dubey and Das (2000) propose a model for two predators foraging for a single species of prey based on a Gause-type model.…”

Section: One-prey -Two-predator Systemmentioning

confidence: 99%

Ecological perspective of the diversity of functional responses

Pervez

Singh²,

Bozdoğan

2018

European Journal of Environmental Sciences

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Prey-predator interactions have been modelled by numerous workers. Ecologists have continuously modified Lotka-Volterra equations in order to provide more realistic descriptions of the complexity of these interactions. The response of predator(s) to increasing prey density can be best described in terms of a functional response, which is an important criterion determining the success or failure of predator(s) to control fluctuating prey populations. The functional response of a predator is further differentiated into Holling's Type I, II, III, IV and V. We discuss one-prey and one-predator interactions, in which the models are modified by the inclusion of steady-state satiation and growth factors. We review situations where two prey and one predator interact, and vice versa. We also discuss Holling's Type IV model relevant to competition and food chains. There is a need to examine functional responses as these models were mostly developed by pure mathematicians and their relevance to field conditions remains largely untested. Prey-predator interactions can be affected even by small factors and ecologists should include these models in their experimental design when attempting to predict realistic interactions.

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Permanent coexistence in a resource-based competition system

Cited by 16 publications

References 11 publications

Network Analysis of a Benthic Food Web Model of a Partly Reclaimed Island in the Sundarban Mangrove Ecosystem, India

Network Analysis of a Benthic Food Web Model of a Partly Reclaimed Island in the Sundarban Mangrove Ecosystem, India

A simple mathematical model for the spread of two political parties

Ecological perspective of the diversity of functional responses

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