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Miled El Hajji - One of the best experts on this subject based on the ideXlab platform.
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How can inter-specific interferences explain coexistence or confirm the Competitive Exclusion Principle in a chemostat?
International Journal of Biomathematics, 2020Co-Authors: Miled El HajjiAbstract:In this paper, I consider two species feeding on limiting substrate in a chemostat taking into account some possible effects of each species on the other one. System of differential equations is proposed as model of these effects with general inter-specific density-dependent growth rates. Three cases were considered. The first one for a mutual inhibitory relationship where it is proved that at most one species can survive which confirms the Competitive Exclusion Principle. Initial concentrations of species have great importance in determination of which species is the winner. The second one for a food web relationship where it is proved that under general assumptions on the dilution rate, both species persist for any initial conditions. Finally, a third case dealing with an obligate mutualistic relationship was discussed. It is proved that initial condition has a great importance in determination of persistence or extinction of both species.
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How the Fractional-order Improve and Extend the Well-known Competitive Exclusion Principle in the Chemostat Model with n Species Competing for a Single Resource?
Asian Research Journal of Mathematics, 2019Co-Authors: Sayed Sayari, Miled El HajjiAbstract:In this paper, a fractional-order mathematical model for n species competing, in a chemostat,for a single resource is proposed. The global dynamics was studied using Lyapunov theory, forany set of increasing growth functions. Obtained results generalize and improve the well-knownCompetitive Exclusion Principle in the chemostat, that one species will eliminate all other species.
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how the Competitive Exclusion Principle can be validated using optical density measurements collected on artificially reconstituted soil ecosystems
Open Journal of Environmental Biology, 2019Co-Authors: Miled El HajjiAbstract:A mathematical model, validated on experimental data aiming at describing and predicting soil bacteria growth on an essential limited substrate in batch pure cultures is proposed as an extension of the Monod’s one in revisiting the way where the optical density is modelled. This model takes into account viable cell growth, substrate consumption, cell mortality, non-viable cell accumulation in the culture medium and partial dead cell recycling into substrate. The least squares method is used to identify model parameters. The model is extended and validated for mixed cultures proving, for artificially reconstituted soil ecosystems, that there is only competition for the substrate. Mathematics Subject Classification: 34D23, 35N25, 37B25, 49K40, 00A71.
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How the Competitive Exclusion Principle can be validated using optical density measurements collected on artificially reconstituted soil ecosystems
2019Co-Authors: Miled El HajjiAbstract:A mathematical model, validated on experimental data aiming at describing and predicting soil bacteria growth on an essential limited substrate in batch pure cultures is proposed as an extension of the Monod’s one in revisiting the way where the optical density is modelled.
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how can inter specific interferences explain coexistence or confirm the Competitive Exclusion Principle in a chemostat
International Journal of Biomathematics, 2018Co-Authors: Miled El HajjiAbstract:In this paper, I consider two species feeding on limiting substrate in a chemostat taking into account some possible effects of each species on the other one. System of differential equations is pr...
Christian C Voigt - One of the best experts on this subject based on the ideXlab platform.
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how bats escape the Competitive Exclusion Principle seasonal shift from intraspecific to interspecific competition drives space use in a bat ensemble
Frontiers in Ecology and Evolution, 2018Co-Authors: Manuel Roeleke, Lilith Johannsen, Christian C VoigtAbstract:Finding prey is crucial for predators that hunt on patchily distributed prey aggregations. At prey-rich patches, intraspecific and interspecific competition should be high. While the Competitive Exclusion Principle suggests that species can only coexist if their ecological niches show considerable differences, newer theory suggests stabilizing and equalizing mechanisms besides classical niche differences that facilitate local coexistence. To identify such mechanisms, the understanding of the strength and nature (i.e. interference or exploitation) of competition in a species ensemble is a prerequisite. Here, we investigated intra- and interspecific competition between aerial-hawking insectivores, using the interactions between two open-space foraging bats as a model. In particular, we tested for shifts in space use of the common noctule bat Nyctalus noctula in response to simulated aggregations of conspecific and heterospecific competitors at foraging patches. When confronted with playbacks of heterospecific Pipistrellus nathusii, N. noctula increased their activity in the experimental area in early summer, but decreased activity in late summer. When confronted with playbacks of conspecifics, activity of N. noctula remained the same, irrespective of season. This pattern was accompanied by a decrease in the proportion of large insects during late summer. Our results suggest that intraspecific competition is more severe than interspecific competition for aerial insectivores in early summer. Probably, conspecifics engage in interference competition for flight space, and in the case of echolocating bats, may interfere with each other’s echolocation calls. Interspecific competition may be mediated by fine scale vertical partitioning and the use of different, non-interfering echolocation frequencies during insect rich times. In contrast, during late summer, bats may rather compete for the exploitation of relatively scarce large prey items. We speculate that N. noctula decreased activity in response to P. nathusii playbacks due to its inferior manoeuvrability and thus probably inferior hunting success in the presence of smaller, more agile bat species. However, N. noctula’s specialization on fast and efficient flight may enable them to use farther away and possibly less rich foraging patches, thus equalizing for a lower fitness compared to superior hunters.
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How Bats Escape the Competitive Exclusion Principle—Seasonal Shift From Intraspecific to Interspecific Competition Drives Space Use in a Bat Ensemble
Frontiers in Ecology and Evolution, 2018Co-Authors: Manuel Roeleke, Lilith Johannsen, Christian C VoigtAbstract:Finding prey is crucial for predators that hunt on patchily distributed prey aggregations. At prey-rich patches, intraspecific and interspecific competition should be high. While the Competitive Exclusion Principle suggests that species can only coexist if their ecological niches show considerable differences, newer theory suggests stabilizing and equalizing mechanisms besides classical niche differences that facilitate local coexistence. To identify such mechanisms, the understanding of the strength and nature (i.e. interference or exploitation) of competition in a species ensemble is a prerequisite. Here, we investigated intra- and interspecific competition between aerial-hawking insectivores, using the interactions between two open-space foraging bats as a model. In particular, we tested for shifts in space use of the common noctule bat Nyctalus noctula in response to simulated aggregations of conspecific and heterospecific competitors at foraging patches. When confronted with playbacks of heterospecific Pipistrellus nathusii, N. noctula increased their activity in the experimental area in early summer, but decreased activity in late summer. When confronted with playbacks of conspecifics, activity of N. noctula remained the same, irrespective of season. This pattern was accompanied by a decrease in the proportion of large insects during late summer. Our results suggest that intraspecific competition is more severe than interspecific competition for aerial insectivores in early summer. Probably, conspecifics engage in interference competition for flight space, and in the case of echolocating bats, may interfere with each other’s echolocation calls. Interspecific competition may be mediated by fine scale vertical partitioning and the use of different, non-interfering echolocation frequencies during insect rich times. In contrast, during late summer, bats may rather compete for the exploitation of relatively scarce large prey items. We speculate that N. noctula decreased activity in response to P. nathusii playbacks due to its inferior manoeuvrability and thus probably inferior hunting success in the presence of smaller, more agile bat species. However, N. noctula’s specialization on fast and efficient flight may enable them to use farther away and possibly less rich foraging patches, thus equalizing for a lower fitness compared to superior hunters.
Vyacheslav L Kalmykov - One of the best experts on this subject based on the ideXlab platform.
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Coexistence of complete competitors with fitness inequality
bioRxiv, 2017Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:There was a long standing contradiction between formulations of the Competitive Exclusion Principle and natural species richness, which is known as the biodiversity paradox. Here we investigate a role of fitness differences in coexistence of two completely competing species using individual-based cellular automata. According to the classical formulations of the Competitive Exclusion Principle such coexistence is impossible. Earlier we found that coexistence of complete competitors is possible with a 100% difference in fitness, but only under certain initial conditions. Here we verify a hypothesis that completely competing species may coexist with less than 100% difference in fitness regardless of different initial location of competing individuals in the ecosystem. We have found a new fact that two aggressively propagating complete competitors can stably coexist in one limited, stable and homogeneous habitat, when one species has some advantage in fitness over the other and all other characteristics of the species are equal, in particular any trade-offs and cooperations are absent. This fact is established theoretically on the rigorous model. The found Competitive coexistence occurred regardless of the initial location of individuals in the ecosystem. When colonization of free habitat started from a single individual of each species, then the complete competitors coexisted up to 31% of their difference in fitness. And when on initial stage half of the territory was probabilistically occupied, the complete competitors coexisted up to 22% of their difference in fitness. These results additionally support our reformulation of the Competitive Exclusion Principle, which we consider as resolving of the biodiversity paradox.
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On ecological modelling problems in the context of resolving the biodiversity paradox
Ecological Modelling, 2016Co-Authors: Vyacheslav L Kalmykov, Lev V KalmykovAbstract:Abstract The biodiversity paradox has been a long-standing enigma in theoretical ecology. It emerged as a contradiction between the Competitive Exclusion Principle and the natural species richness. There are two competing ecological theories which try to explain this issue: niche theory and neutral theory. The problem is that both theories are based on nontransparent models which ignore local interactions between individuals and cannot provide an understanding of interspecific competition mechanisms. Mathematical models of complex systems may be of three general types: black-box, grey-box and white-box models. Classical ecological models – Malthusian, Verhulst and Lotka–Volterra models are of black-box type. Black-box models are nonmechanistic. They cannot help to create a mechanistic ecological theory as they do not provide a direct insight into individual-based mechanisms. Here we make some critical notes on the recent attempts to resolve the paradox by black-box and grey-box approaches. We critically discuss a contribution of the neutral theory and the attempts to solve the paradox by methods of the classical quantum mechanics. These attempts are rather ineffective due to the lack of mechanicalness and likely lead to more confusion than clarity in understanding of biodiversity mechanisms. We also discuss our solution to the biodiversity paradox through a verification of the Competitive Exclusion Principle with using the white-box approach to mathematical modelling of Competitive coexistence.
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A solution to the biodiversity paradox by logical deterministic cellular automata
Acta Biotheoretica, 2015Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the Competitive Exclusion Principle and the observed biodiversity. The Principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations of the Competitive Exclusion Principle. This mechanism is based on timely recovery of limiting resources and their spatio-temporal allocation between competitors. Because of limitations of the black-box modeling there was a problem to formulate the Exclusion Principle correctly. Our white-box multiscale model of two-species competition is based on logical deterministic individual-based cellular automata. This approach provides an automatic deductive inference on the basis of a system of axioms, and gives a direct insight into mechanisms of the studied system. It is one of the most promising methods of artificial intelligence. We reformulate and generalize the Competitive Exclusion Principle and explain why this formulation provides a solution of the biodiversity paradox. In addition, we propose a Principle of Competitive coexistence.
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A solution to the biodiversity paradox by logical deterministic cellular automata
bioRxiv, 2014Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the Competitive Exclusion Principle and the observed biodiversity. This Principle was formulated incorrectly because of limitations of the traditional black-box models of interspecific competition. Our white-box models are based on logical deterministic individual-based cellular automata. Here, we show a mechanism of Competitive coexistence which violates the known formulations of the Principle. We reformulate and generalize the Competitive Exclusion Principle and explain why our formulations provide a solution of the biodiversity paradox. In addition, we propose a Principle of Competitive coexistence.
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On a solution of the biodiversity paradox and a Competitive coexistence Principle
bioRxiv, 2014Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:The biodiversity paradox is the central problem in theoretical ecology. The paradox consists in the contradiction between the Competitive Exclusion Principle and the observed biodiversity. This contradiction is the key subject of the long-standing and continuing biodiversity debates. The paradox impedes our insights into biodiversity conservation. Previously we proved that due to a soliton-like behaviour of population waves complete competitors can indefinitely coexist in one closed homogeneous habitat on one and the same limiting resource under constant conditions of environment, without any trade-offs and cooperations. As this fact violates the known formulations of the Competitive Exclusion Principle we have reformulated the Principle. Here we explain why this reformulation of the Principle results in a solution of the biodiversity paradox. In addition, we generalize the Competitive Exclusion Principle. Reasoning by contradiction, we formulate a generalized Principle of Competitive coexistence. These Principles expand theoretical basis for biodiversity conservation and sustainable development.
Manuel Roeleke - One of the best experts on this subject based on the ideXlab platform.
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how bats escape the Competitive Exclusion Principle seasonal shift from intraspecific to interspecific competition drives space use in a bat ensemble
Frontiers in Ecology and Evolution, 2018Co-Authors: Manuel Roeleke, Lilith Johannsen, Christian C VoigtAbstract:Finding prey is crucial for predators that hunt on patchily distributed prey aggregations. At prey-rich patches, intraspecific and interspecific competition should be high. While the Competitive Exclusion Principle suggests that species can only coexist if their ecological niches show considerable differences, newer theory suggests stabilizing and equalizing mechanisms besides classical niche differences that facilitate local coexistence. To identify such mechanisms, the understanding of the strength and nature (i.e. interference or exploitation) of competition in a species ensemble is a prerequisite. Here, we investigated intra- and interspecific competition between aerial-hawking insectivores, using the interactions between two open-space foraging bats as a model. In particular, we tested for shifts in space use of the common noctule bat Nyctalus noctula in response to simulated aggregations of conspecific and heterospecific competitors at foraging patches. When confronted with playbacks of heterospecific Pipistrellus nathusii, N. noctula increased their activity in the experimental area in early summer, but decreased activity in late summer. When confronted with playbacks of conspecifics, activity of N. noctula remained the same, irrespective of season. This pattern was accompanied by a decrease in the proportion of large insects during late summer. Our results suggest that intraspecific competition is more severe than interspecific competition for aerial insectivores in early summer. Probably, conspecifics engage in interference competition for flight space, and in the case of echolocating bats, may interfere with each other’s echolocation calls. Interspecific competition may be mediated by fine scale vertical partitioning and the use of different, non-interfering echolocation frequencies during insect rich times. In contrast, during late summer, bats may rather compete for the exploitation of relatively scarce large prey items. We speculate that N. noctula decreased activity in response to P. nathusii playbacks due to its inferior manoeuvrability and thus probably inferior hunting success in the presence of smaller, more agile bat species. However, N. noctula’s specialization on fast and efficient flight may enable them to use farther away and possibly less rich foraging patches, thus equalizing for a lower fitness compared to superior hunters.
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How Bats Escape the Competitive Exclusion Principle—Seasonal Shift From Intraspecific to Interspecific Competition Drives Space Use in a Bat Ensemble
Frontiers in Ecology and Evolution, 2018Co-Authors: Manuel Roeleke, Lilith Johannsen, Christian C VoigtAbstract:Finding prey is crucial for predators that hunt on patchily distributed prey aggregations. At prey-rich patches, intraspecific and interspecific competition should be high. While the Competitive Exclusion Principle suggests that species can only coexist if their ecological niches show considerable differences, newer theory suggests stabilizing and equalizing mechanisms besides classical niche differences that facilitate local coexistence. To identify such mechanisms, the understanding of the strength and nature (i.e. interference or exploitation) of competition in a species ensemble is a prerequisite. Here, we investigated intra- and interspecific competition between aerial-hawking insectivores, using the interactions between two open-space foraging bats as a model. In particular, we tested for shifts in space use of the common noctule bat Nyctalus noctula in response to simulated aggregations of conspecific and heterospecific competitors at foraging patches. When confronted with playbacks of heterospecific Pipistrellus nathusii, N. noctula increased their activity in the experimental area in early summer, but decreased activity in late summer. When confronted with playbacks of conspecifics, activity of N. noctula remained the same, irrespective of season. This pattern was accompanied by a decrease in the proportion of large insects during late summer. Our results suggest that intraspecific competition is more severe than interspecific competition for aerial insectivores in early summer. Probably, conspecifics engage in interference competition for flight space, and in the case of echolocating bats, may interfere with each other’s echolocation calls. Interspecific competition may be mediated by fine scale vertical partitioning and the use of different, non-interfering echolocation frequencies during insect rich times. In contrast, during late summer, bats may rather compete for the exploitation of relatively scarce large prey items. We speculate that N. noctula decreased activity in response to P. nathusii playbacks due to its inferior manoeuvrability and thus probably inferior hunting success in the presence of smaller, more agile bat species. However, N. noctula’s specialization on fast and efficient flight may enable them to use farther away and possibly less rich foraging patches, thus equalizing for a lower fitness compared to superior hunters.
Lev V Kalmykov - One of the best experts on this subject based on the ideXlab platform.
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Coexistence of complete competitors with fitness inequality
bioRxiv, 2017Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:There was a long standing contradiction between formulations of the Competitive Exclusion Principle and natural species richness, which is known as the biodiversity paradox. Here we investigate a role of fitness differences in coexistence of two completely competing species using individual-based cellular automata. According to the classical formulations of the Competitive Exclusion Principle such coexistence is impossible. Earlier we found that coexistence of complete competitors is possible with a 100% difference in fitness, but only under certain initial conditions. Here we verify a hypothesis that completely competing species may coexist with less than 100% difference in fitness regardless of different initial location of competing individuals in the ecosystem. We have found a new fact that two aggressively propagating complete competitors can stably coexist in one limited, stable and homogeneous habitat, when one species has some advantage in fitness over the other and all other characteristics of the species are equal, in particular any trade-offs and cooperations are absent. This fact is established theoretically on the rigorous model. The found Competitive coexistence occurred regardless of the initial location of individuals in the ecosystem. When colonization of free habitat started from a single individual of each species, then the complete competitors coexisted up to 31% of their difference in fitness. And when on initial stage half of the territory was probabilistically occupied, the complete competitors coexisted up to 22% of their difference in fitness. These results additionally support our reformulation of the Competitive Exclusion Principle, which we consider as resolving of the biodiversity paradox.
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On ecological modelling problems in the context of resolving the biodiversity paradox
Ecological Modelling, 2016Co-Authors: Vyacheslav L Kalmykov, Lev V KalmykovAbstract:Abstract The biodiversity paradox has been a long-standing enigma in theoretical ecology. It emerged as a contradiction between the Competitive Exclusion Principle and the natural species richness. There are two competing ecological theories which try to explain this issue: niche theory and neutral theory. The problem is that both theories are based on nontransparent models which ignore local interactions between individuals and cannot provide an understanding of interspecific competition mechanisms. Mathematical models of complex systems may be of three general types: black-box, grey-box and white-box models. Classical ecological models – Malthusian, Verhulst and Lotka–Volterra models are of black-box type. Black-box models are nonmechanistic. They cannot help to create a mechanistic ecological theory as they do not provide a direct insight into individual-based mechanisms. Here we make some critical notes on the recent attempts to resolve the paradox by black-box and grey-box approaches. We critically discuss a contribution of the neutral theory and the attempts to solve the paradox by methods of the classical quantum mechanics. These attempts are rather ineffective due to the lack of mechanicalness and likely lead to more confusion than clarity in understanding of biodiversity mechanisms. We also discuss our solution to the biodiversity paradox through a verification of the Competitive Exclusion Principle with using the white-box approach to mathematical modelling of Competitive coexistence.
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A solution to the biodiversity paradox by logical deterministic cellular automata
Acta Biotheoretica, 2015Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the Competitive Exclusion Principle and the observed biodiversity. The Principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations of the Competitive Exclusion Principle. This mechanism is based on timely recovery of limiting resources and their spatio-temporal allocation between competitors. Because of limitations of the black-box modeling there was a problem to formulate the Exclusion Principle correctly. Our white-box multiscale model of two-species competition is based on logical deterministic individual-based cellular automata. This approach provides an automatic deductive inference on the basis of a system of axioms, and gives a direct insight into mechanisms of the studied system. It is one of the most promising methods of artificial intelligence. We reformulate and generalize the Competitive Exclusion Principle and explain why this formulation provides a solution of the biodiversity paradox. In addition, we propose a Principle of Competitive coexistence.
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A mechanistic model of the S-shaped population growth
bioRxiv, 2014Co-Authors: Lev V KalmykovAbstract:The main idea of this note is to show the most basic and purely mechanistic model of population growth, which has been used by us to create models of interspecific competition for verification of the Competitive Exclusion Principle (1, 2). Our logical deterministic individual-based cellular automata model demonstrates a spatio-temporal mechanism of the S-shaped population growth.
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A solution to the biodiversity paradox by logical deterministic cellular automata
bioRxiv, 2014Co-Authors: Lev V Kalmykov, Vyacheslav L KalmykovAbstract:The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the Competitive Exclusion Principle and the observed biodiversity. This Principle was formulated incorrectly because of limitations of the traditional black-box models of interspecific competition. Our white-box models are based on logical deterministic individual-based cellular automata. Here, we show a mechanism of Competitive coexistence which violates the known formulations of the Principle. We reformulate and generalize the Competitive Exclusion Principle and explain why our formulations provide a solution of the biodiversity paradox. In addition, we propose a Principle of Competitive coexistence.