1,720,969 research outputs found
How do predator interference, prey herding and their possible retaliation affect prey-predator coexistence?
Full text linkIn this paper, focusing on individualistic generalist predators and prey living in herds which coexist in a common area, we propose a generalization of a previous model, namely, a two-population system that accounts for the prey response to predator attacks. In particular, we suggest a new prey-predator interaction term with a denominator of the Beddington-DeAngelis form and a function in the numerator that behaves as N for small values of N, and as N^alpha for large values of N, where N denotes the number of prey. We can take the savanna biome as a reference example, concentrating on large herbivores inhabiting it and some predators that feed on them. Only two conditionally stable equilibrium points have emerged from the model analysis: the predator-only equilibrium and the coexistence one. Transcritical bifurcations from the former to the latter type of equilibrium, as well as saddle-node bifurcations of the coexistence equilibrium have been identified numerically by using MATLAB. In addition, the model was found to exhibit bistability. Bistability is studied by using the MATLAB toolbox bSTAB, paying particular attention to the basin stability values. Comparison of coexistence equilibria with other prey-predator models in the literature essentially shows that, in this case, prey thrive in greater numbers and predators in smaller numbers. The population changes due to parameter variations were found to be significantly less pronounced
Fare gruppo cambia tutto. Capire l’evoluzione degli ecosistemi con la matematica
No full textUn secolo fa, i primi modelli matematici per popolazioni interagenti che descrivevano le popolazioni di animali consideravano solo le interazioni tra individui isolati. Ma in natura molte specie vivono in gruppo, perché ciò aumenta la loro capacità di difesa e sopravvivenza. Noi studiamo modelli che tengono conto del comportamento collettivo di alcune specie animali, in modo da poter prevedere meglio come si comportano prede, predatori, competitori e specie mutualiste e nell'ottica di comprendere e preservare meglio gli ecosistemi reali
Mitigating negative effects of EBHSV-infected eastern cottontail invasion in Italy using Z-type control on a four-population system
No full textThe introduction in Italy of eastern cottontails (Sylvilagus floridanus) for hunting purposes has influenced the local predator-prey dynamics of the red foxes (Vulpes vulpes) and native European hares (Lepus europaeus). Although no direct competition seems to occur between the two lagomorphs, the cottontail invasion damages the indigenous hare population. Indeed, the invasive lagomorphs cause hyperpredation of red foxes on native hares and are also carriers of viruses and parasites. This paper focuses on the situation in which EBHSV-infected eastern cottontails are introduced in a region of virus-free European hares. To avoid the extinction of native lagomorphs and to contain the invasive ones, we look at two possible biological control actions using the Z-type control method on a four-population reference system. In particular, we consider an indirect control of the invasive prey acting on predators and a combination of this indirect control with direct control on native prey. The corresponding Z-controlled models are investigated analytically and numerically. In both cases, the Z-type control significantly reduces the number of equilibria and the convergence of the cottontail population to the desired state is ensured. The hare survival, instead, is guaranteed only in the second case. Overall, mathematically speaking, the second Z-type control action seems the best solution. However, in the cases in which the indirect control on cottontails allows the native prey survival, this control may be preferable since it involves only one control function and seems more practicable. In any case, in the choice of control action, ecosystem managers need to consider each specific situation, taking into account various elements from a biological and practical point of view
A Note on an Epidemic Model with Cautionary Response in the Presence of Asymptomatic Individuals
Full text linkWe analyse a simple disease transmission model accounting for demographic features and an illness appearing in two forms, asymptomatic and symptomatic. Its main feature is the epidemic-induced fear of the population, for which contacts are reduced, responding to increasing symptomatic numbers. We find that in the presence of asymptomatic individuals, if the progression rate to symptomatic is high, protection measures may prevent the whole population becoming infected. The results also elucidate the importance of assessing transmission rates as quickly as possible
On the impact of migratory flows on the residential species of a region
No full textMigrations can trigger biological invasions. Indeed, when a migrant population finds favorable conditions in a region, it can settle there permanently. This can pose a threat to local biodiversity. Moreover, even when a biological invasion does not occur, a migratory transit affecting a territory can harm residential species. In this paper, we focus on a migrant population that either only touches the border of the region occupied by residents or crosses it altogether. We investigate the possible negative consequences due to a migratory flow for a native species that interacts with the migrants in some particular scenarios. Specifically, we consider the following situations: migratory interference with negative or positive effects on the native species, migrant predation on the residential population, competition and symbiosis of the two populations. By analytically and numerically exploring the mathematical models for the migrant-resident interactions of interest, we find that in the interference scenarios migrant biological invasions cannot occur, while in the others they do. The only migrant disturbance action, however, could still have serious consequences for the native population, which may even be driven to extinction. We can also have the resident extinction in the models of migrant predation on residents and competition. In the positive interference and symbiosis scenarios, instead, the system can only evolve toward coexistence. The residents, in these last two situations, benefit from the migratory transit. These general results are valid for both marginal and non-marginal migrant-resident contacts, but we also observe some differences in these two cases
Pathways to sustainability or collapse in inland small-scale aquaculture systems: insights from a social–ecological systems model
Full text linkDespite the promise of small-scale aquaculture for improving food security and alleviating poverty, its long-term sustainability remains poorly understood, particularly in contexts where economic and ecological processes reinforce each other. This paper develops a stylized social-ecological model that captures feedbacks between producer wealth, fish biomass, and nutrient dynamics in pond aquaculture. The model reveals how these intertwined feedbacks shape the long-term dynamics of the system and lead to monostability, bistability, or multistability. These regimes correspond to collapse, a high-yield but high-risk, and a sustainable equilibrium in fish production. Using bifurcation and stability analysis, we identify six dynamic scenarios: Clearwater, Overload, Flux, Knife-edge, Tipping pond and Decay, that represent qualitatively different long-term outcomes. Rather than predicting specific outcomes, the model gives a structural understanding of small-scale aquaculture dynamics and highlights the importance of local context and producers' heterogeneity in shaping the outcomes. It also provides a theoretical foundation for scenario-based management and empirical model development
Modeling the insect-vectors-mediated phytoplasm transmission in agroecosystems
Full text linkTwo models for the herbivore-insects-plants interactions are formulated, differing in the way the farmer’s behavior is accounted for. In the first one the farmer regularly checks the crop and possibly removes infected plants, reimplanting new healthy ones in their place. The second one instead considers a large crop where this behavior is not possible and where therefore the infection may propagate freely in it, via the action of insect vectors. Effector proteins are known to affect the insect-plant dynamics and their influence is here investigated. Although they cannot influence the ultimate ecosystem behavior, they do impact the speed at which the equilibria are attained, in some fortunate cases favoring a faster infection eradication
Prey herding and predators’ feeding satiation induce multiple stability
No full textIn this paper we study a predator–prey model assuming that the prey population gather together in herd and considering feeding satiation for the predator population as well. After analyzing the equilibrium points of the model, their stability and the existence of bifurcations we show the existence of multistability for three different equilibrium points via numerical simulations. This last analysis is performed using the bSTAB software and its extensions. It allows to compute the basin of stability values and to plot bifurcation diagram surfaces with respect to the model parameters
Investigating the Spread of Chytridiomycosis in Native Amphibians by Invading Bd-Carrier Bullfrogs
No full textThe amphibians are undergoing a dramatic decline and are the most globally threatened class of vertebrates. Among the main causes of this problem, we have biological invasions and the spread of diseases. The most worrisome amphibian disease is chytridiomycosis, which predominantly affects the skin of adult amphibians. This is a fungal disease that can be spread by several amphibian and non-amphibian vectors. These include the bullfrog (Lithobates catesbeianus), which is a large voracious frog native to eastern North America, particularly known to be a highly invasive species and a tolerant carrier of Batrachochytrium dendrobatidis (Bd). The latter is one of the chytridiomycosis pathogens, specifically a chytrid fungus with two life stages, i.e., environmental and on the host. In this chapter, we consider an aquatic ecosystem invaded by bullfrogs. In particular, we are interested in studying the possible consequences of this biological invasion for native amphibian species. We propose and analyze a four-population model, considering the interaction dynamics between Bd carrier and noncarrier bullfrogs, noninfected native amphibians, and free fungus zoospores in the environment
An Exploration of the Effects of Periodic Top Predator Interference and Hunting on a Predator-Prey System
Full text linkWe introduce two models for the investigation of damages that periodic passages of migrating animals may have on established ecosystems of a smaller scale. In the first one, the damage is only of "physical" nature, in which the population at the highest trophic layer ravages the territory where the other interacting species live, thereby reducing their survival capabilities but not obtaining any benefit out of this. In the second one, it is assumed that the periodic damage comes from a moving top predator, periodically crossing the habitat of the lower trophic level populations, chasing both of them and therefore getting a reward from this hunt. The underlying model is assumed to be of minimalist predator-prey type, in order to better elucidate the effect of the action of the top predator. While the pure interference model does not seem to produce relevant effects other than the presence in a two-dimensional subspace of neutrally stable trajectories, a behavior that is forbidden in the underlying basic predator-prey model, the superpredation of a migrating population in suitable conditions induces a stable equilibrium, which may undergo a Hopf bifurcation with specific parameter choices. This elementary investigation elucidates therefore a possible invasion mechanism where the migrating population spots an attracting ecosystem in which thriving is possible and settles in it, substantially altering it and affecting the native populations
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