Social behavior-induced multistability in minimal competitive ecosystems

On Predation-Commensalism Processes as Models of Bi-stability and Constructive Role of Systemic Extinctions

We propose a mathematical model for a class of predator-prey systems more complex than the usual one, involving a commensalism effect consisting in an influence of the predator on the sustainability of the prey. This effect induces interesting new features, including bi-stability (two attractors with disjoint attraction basins). The question of the possibility of reaching a certain attractor starting from initial conditions with a small population of predators, which presents an interest from the vewpoint of the onset of the predator in evolution, is addressed. We propose two possibilities: the classical one involving adapted conditions in the far past and a new (up to our knowledge) one using biodiversity, specifically the presence of another predator which operates as a starter, being displaced in the sequel.

The competition model with Holling type II competitive response to interfering time

In Nature, species coexistence is much more frequent than what the classical competition model predicts, so that scientists look for mechanisms that explain such a coexistence. We revisit the classical competition model assuming that individuals invest time in competing individuals of the other species. This assumption extends the classical competition model (that becomes a particular case of the model presented) under the form of a Holling type II term, that we call competitive response to interfering time. The resulting model expands the outcomes allowed by the classical model by (i) enlarging the range of parameter values that allow coexistence scenarios and (ii) displaying dynamical scenarios not allowed by the classical model: namely, bi-stable conditional coexistence in favour of i (either species coexist or species i wins) or tri-stable conditional coexistence (either species coexist or any of them goes extinct), being exclusion in both cases due to priority effects.

Evolution of the Individual Attitude in the Risk Decision of Waste Incinerator Construction: Cellular Automaton Model

In current work, the phenomenon of NIMBY (not in my back yard) for a municipal solid waste incinerator was recognized through an investigation for the evolution of individual risk attitude to group risk attitude (ItGRA). The cellular automaton model was employed to evaluate the risk attitude status with different frequencies of social interaction between residents. In the simulation case, the risk attitude of residents in the pseudo-rational state and non-pseudo-rational state was evaluated, which indicates the sheep-flock effect on the exaggeration of public NIMBY attitude. To the incinerator, the individual risk attitude evolved to supportive group risk attitude at a social interaction frequency 100 times higher than that in family or local neighborhoods, when the initial number of residents in opposition and support was equal. This was supported by the result of the model in the evaluation of resident risk attitude around the incinerator in Shanghai. On the contrary, for those in a non-pseudo-rational state, the ultimate group risk attitude depends on the probability that the residents have a supportive or opposing risk attitude as the concept of individuals was difficult to change. Accordingly, the decision strategy of incinerator construction should consider the influence of the sheep-flock effect, which can increase the attitude of residents in support and lead to the evolution of a group risk attitude to support attitude. Therefore, this study provides insight into the evolution of public attitude to NIMBY attitude and a promising evaluation method to quantify and guide the individual and group risk attitudes.

Some fractal thoughts about the COVID-19 infection outbreak

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Criticism on the “Mass Hypothesis” in models of epidemic spreading.

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Review of the Generalized Richards Model of epidemic outbreaks.

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Review of the form of segregation named “herd behaviour” in the Trophic Web Theory.

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Adaptation of “herd behaviour” to epidemic outbreak description, as a motivation to the Generalized Richards Model.

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Interpretation of the exponents p and α of the Generalized Richards Model with particular reference to the COVID-19 case.

Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the complex, possibly fractal, structure of the locus describing the “contagion event set”, and on what can be learnt from the models of trophic webs with “herd behaviour”.

Under the hypothesis that the total number of cases, as a function of time, is fitted by a solution of the Generalized Richards Model, it is argued that the exponents appearing in that differential equation, usually determined empirically, represent the geometric signature of the non-space filling, network-like locus on which contagious contacts take place.

Invasion waves in the biochemical warfare between living organisms

Microorganisms and plants very commonly release toxic secondary chemical compounds (allelochemicals) that inhibit or kill sensitive strains or individuals from their own or other species. In this work we study a model that describes two species interacting through allelopathic suppression and competing for resources. Employing linear stability analysis, the conditions for coexistence or extinction of species in spatially homogeneous systems were determined. We found that the borders between the regimes of bistability, coexistence, and the extinction of the weaker by the stronger competitor, are altered by allelopathic interactions. In addition, traveling wave solutions for one species invasion were obtained considering the spatially explicit nature of the model. Our findings indicate that the minimum speed of the invasion wavefronts depends primarily on the competition coefficients and the parameters characterizing the species' functional responses to their allelochemicals. As a general rule, the species provided with the most effective chemical weapons dominates the population dynamics. Finally, we found a tristability at the coexistence region due to the combination of allelopathy and patchy population distributions in space. So, our model provides a distinct mechanism, independent of social behaviors, that produces such unexpected tristability impossible in classical competition models involving one-to-one individual interactions.