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Register a new userA dynamical population modeling of invasive species with reference to the crayfish Procambarus Clarkii
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In this paper we present a discrete dynamical population modeling of invasive species, with reference to the swamp crayfish Procambarus clarkii. Since this species can cause environmental damage of various kinds, it is necessary to evaluate its expected in not yet infested areas. A structured discrete model is built, taking into account all biological information we were able to find, including the environmental variability implemented by means of stochastic parameters (coefficients of fertility, death, etc.). This model is based on a structure with 7 age classes, i.e. a Leslie mathematical population modeling type and it is calibrated with laboratory data provided by the Department of Evolutionary Biology (DEB) of Florence (Italy). The model presents many interesting aspects: the population has a high initial growth, then it stabilizes similarly to the logistic growth, but then it exhibits oscillations (a kind of limit-cycle attractor in the phase plane). The sensitivity analysis shows a good resilience of the model and, for low values of reproductive female fraction, the fluctuations may eventually lead to the extinction of the species: this fact might be exploited as a controlling factor. Moreover, the probability of extinction is valuated with an inverse Gaussian that indicates a high resilience of the species, confirmed by experimental data and field observation: this species has diffused in Italy since 1989 and it has shown a natural tendency to grow. Finally, the spatial mobility is introduced in the model, simulating the movement of the crayfishes in a virtual lake of elliptical form by means of simple cinematic rules encouraging the movement towards the banks of the catchment (as it happens in reality) while a random walk is imposed when the banks are reached.
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As impacts of introduced species cascade through trophic levels, they can cause indirect and counter-intuitive effects. To investigate the impact of invasive species at the network scale, we use a generalized food web model, capable of propagating changes through networks with a series of ecologically realistic criteria. Using data from a small British offshore island, we quantify the impacts of four virtual invasive species (an insectivore, a herbivore, a carnivore and an omnivore whose diet is based on a rat) and explore which clusters of species react in similar ways. We find that the predictions for the impacts of invasive species are ecologically plausible, even for large networks robust predictions for the impacts of invasive species can be obtained. Species in the same taxonomic group are similarly impacted by a virtual invasive species. However, interesting differences within a given taxonomic group can occur. The results suggest that some native species may be at risk from a wider range of invasives than previously believed. The implications of these results for ecologists and land managers are discussed.
The evolution of antimicrobial resistance can be strongly affected by variations of antimicrobial concentration. Here, we study the impact of periodic alternations of absence and presence of antimicrobial on resistance evolution in a microbial population, using a stochastic model that includes variations of both population composition and size, and fully incorporates stochastic population extinctions. We show that fast alternations of presence and absence of antimicrobial are inefficient to eradicate the microbial population and strongly favor the establishment of resistance, unless the antimicrobial increases enough the death rate. We further demonstrate that if the period of alternations is longer than a threshold value, the microbial population goes extinct upon the first addition of antimicrobial, if it is not rescued by resistance. We express the probability that the population is eradicated upon the first addition of antimicrobial, assuming rare mutations. Rescue by resistance can happen either if resistant mutants preexist, or if they appear after antimicrobial is added to the environment. Importantly, the latter case is fully prevented by perfect biostatic antimicrobials that completely stop division of sensitive microorganisms. By contrast, we show that the parameter regime where treatment is efficient is larger for biocidal drugs than for biostatic drugs. This sheds light on the respective merits of different antimicrobial modes of action.
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is shown that random events cause the population mean of each specie to make smooth transition from far above to far below of its growth rate threshold. At the same time, the population mean of the weaker specie never reaches the extinction point. It is also shown that, as a result of competition, the relative population fluctuations do not die out as the growth rates of both species are raised far above their respective thresholds. This behavior is most remarkable at the maximum competition point where the weaker species population statistics becomes completely chaotic regardless of how far its growth rate in raised.
Eigens quasi-species model describes viruses as ensembles of different mutants of a high fitness master genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When the mutation rate is sufficiently high, the master type no longer survives and gets replaced by a wide range of mutant types, thus destroying the quasi-species. It is the so-called error catastrophe. But natural selection acts on phenotypes, not genotypes, and huge amounts of genotypes yield the same phenotype. An important consequence of this is the appearance of beneficial mutations which increase the fitness of mutants. A model has been recently proposed to describe quasi-species in the presence of beneficial mutations. This model lacks the error catastrophe of Eigens model and predicts a steady state in which the viral population grows exponentially. Extinction can only occur if the infectivity of the quasi-species is so low that this exponential is negative. In this work I investigate the transient of this model when infection is started from a small amount of low fitness virions. I prove that, beyond an initial regime where viral population decreases (and can go extinct), the growth of the population is super-exponential. Hence this population quickly becomes so huge that selection due to lack of host cells to be infected begins to act before the steady state is reached. This result suggests that viral infection may widespread before the virus has developed its optimal form.
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