Search Results (12)

In this paper, the local and global structure of positive solutions for a general predator–prey model in a multi-dimension with ratio-dependent predator influence and prey taxis is investigated. By analyzing the corresponding characteristic equation, we first obtain the local stability conditions of the positive equilibrium caused by prey taxis. Secondly, taking the prey-taxis coefficient as a bifurcation parameter, we obtain the local structure of the positive solution by resorting to an abstract bifurcation theorem, and then extend the local solution branch to a global one. Finally, the local stability of such bifurcating positive solutions is discussed by the method of the perturbation of simple eigenvalues and spectrum theory. The results indicate that attractive prey taxis can stabilize positive equilibrium and inhibits the emergence of spatial patterns, while repulsive prey taxis can lead to Turing instability and induces the emergence of spatial patterns. Full article

Turing’s instability has been widely introduced to explain the formation of several biological and ecological patterns, such as the skin patterning of fish or animals, wings of butterflies, pigmentation, and labyrinth patterns of the cerebral cortex of mammals. Such a mechanism may occur in the ecosystem due to the differential diffusion dispersal that happen if one of the constituent species results in the activator or the prey, showing a tendency to undergo autocatalytic growth. The diffusion of the constituent species activator is a random mobility function called passive diffusion. If the other species in the system (the predator/inhibitor) disperses sufficiently faster than the activator, then the spatially uniform distribution of species becomes unstable, and the system will settle into a stationary state. This paper introduced Turing’s mechanism in our reaction–taxis–diffusion model to simulate the harmful algal bloom (HAB) pattern. A numerical approach, the Runge–Kutta method, was used to deal with this system of reaction–taxis–diffusion equations, and the findings were qualitatively compared to the aerial patterns obtained by a drone flying over Torment Lake in Nova Scotia (Canada) during the bloom season of September 2023. Full article

We consider two models of the predator–prey community with prey-taxis. Both models take into account the capability of the predators to respond to prey density gradients and also to one more signal, the production of which occurs independently of the community state (such a signal can be due to the spatiotemporal inhomogeneity of the environment arising for natural or artificial reasons). We call such a signal external. The models differ to one another through the description of their responses: the first one employs the Patlak–Keller–Segel law for both responses, and the second one employs Cattaneo’s model of heat transfer for both responses following to Dolak and Hillen. Assuming a short-wave external signal, we construct the complete asymptotic expansions of the short-wave solutions to both models. We use them to examine the effect of the short-wave signal on the formation of spatiotemporal patterns. We do so by comparing the stability of equilibria with no signal to that of the quasi-equilibria forced by the external signal. Such an approach refers back to Kapitza’s theory for an upside-down pendulum. The overall conclusion is that the external signal is likely not capable of creating the instability domain in the parametric space from nothing but it can substantially widen the one that is non-empty with no signal. Full article

We investigate a new event of accelerated environmental change that was recorded during the late Barremian in the pelagic Subbetic Basin (Western Tethys). Two pelagic sections have been studied using a multi-proxy approach based on C-isotope stratigraphy and a high-resolution quantitative study of nannofossil assemblages, along with major and trace elements and biomarkers. Our results provide a detailed biostratigraphy and C-isotope stratigraphy, and outline the paleoenvironmental conditions recorded during the early stages of the Taxy Episode. A disturbance has been identified in the C-isotope record, called the IFeNE (Intra-Feradianus negative C-excursion), which is coeval with environmental and biotic changes that predate the well-known ISNE (Intra-Sarasini negative C-excursion). The combined analysis of nannofossil associations, C-isotopes, major and trace elements, and biomarker distributions indicates a separate episode of warming heralding the ISNE, resulting in the acceleration of the hydrological cycle and a consequent increase in continental inputs and the fertilization of surface waters. The origin of the Taxy Episode (the IFeNE and ISNE) has been related to orbital factors (high-eccentricity cycles), and to a global increase in volcanism, probably related to the early phases of the Ontong Java Plateau. Full article

In this paper, we consider a predator-prey diffusion model incorporating hunting cooperation and predator-taxis. Firstly, we establish the global existence of a classical solution for the model in any spatial dimension. Secondly, we analyze the stability/instability caused by predator-taxis, and we observe that predator-taxis play a key role in inducing stability changes. Specifically, if the positive equilibrium is stable for the corresponding reaction-diffusion model, the attractive predator-taxis can further stabilize the system, while the repulsive predator-taxis may lead to a change in spatial stability, if the positive equilibrium is unstable for the corresponding reaction-diffusion model, the attractive predator-taxis makes the model remain unstable, while the repulsive predator-taxis has a stabilizing effect. Finally, numerical simulations are employed to validate the obtained results. Full article

The spatiotemporal dynamics of a three-component model of a food web are considered. The model describes the interactions between populations of resources, prey, and predators that consume both species. It assumes that the predator responds to the spatial change in the resource and prey densities by occupying areas where species density is higher (prey-taxis) and that the prey population avoids areas with a high predator density (predator-taxis). This work studies the conditions for the taxis-driven instability leading to the emergence of stationary patterns resulting from Turing instability and autowaves caused by wave instability. The existence of nonconstant positive steady states for the system is assessed through a rigorous bifurcation analysis. Meanwhile, the conditions for the existence of both types of instabilities are obtained by linear stability analysis. It is shown that the presence of cross-diffusion in the system supports the formation of spatially heterogeneous patterns. For low values of the resource-tactic and predator-tactic coefficients, Turing and wave instabilities coexist. The system undergoes only Turing instability for high levels of these parameters. Full article

The concept of an ideal free distribution (IFD) is extended to a predator–prey system in a heterogeneous environment. We consider reaction–diffusion–advection equations which describe the evolution of spatial distributions of predators and prey under directed migration. Modification of local interaction terms is introduced, if some coefficients depend on resource. Depending on coefficients of local interaction, the different scenarios of predator distribution are possible. We pick out three cases: proportionality to prey (and respectively to resource), indifferent distribution and inversely proportional to the prey. These scenarios apply in the case of nonzero diffusion and taxis under additional conditions on diffusion and migration rates. We examine migration functions for which there are explicit stationary solutions with nonzero densities of both species. To analyze solutions with violation of the IFD conditions, we apply asymptotic expansions and a numerical approach with staggered grids. The results for a two-dimensional domain with no-flux boundary conditions are presented. Full article

Age-disparate transactional sex relationships are often coerced and exploitative. The gender and economic disparities between affluent men and economically disadvantaged girls often perpetuate these relationships, resulting in their exploitation. This qualitative study assessed men’s understanding of factors influencing schoolgirls’ engagement in age-disparate transactional sex relationships in two rural districts in Kenya. Four focus group sessions were conducted with men from two primary professions: motorcycle taxi operators (Boda Boda) and teachers from primary and secondary schools from two districts in Kitui South, Sub County, Kenya. Focus group data were analyzed using conventional content analysis. Several influential factors associated with schoolgirls’ engagement in these transactional relationships are discussed in three broad themes: access and coercion, parental influence, and peer-related factors. Study results indicate that schoolgirls in rural areas are more susceptible to predation by men willing to trade sexual favors with underage girls. These findings make it imperative to address the predation of adolescent girls by men involved in these transactional relationships by implementing comprehensive sex education programs that empower schoolgirls to recognize and resist coercion. Additionally, implementing measures involving community leaders, parents, and other stakeholders in a collective effort to combat the exploitation of underage girls is paramount. These measures should be accompanied by the stricter enforcement of laws and regulations to hold perpetrators accountable for their actions. Full article

This paper will explore a predator–prey model that incorporates prey-taxis and a general functional response in a bounded domain. Firstly, we will examine the stability and pattern formation of both local and nonlocal models. Our main finding is that the inclusion of nonlocal terms enhances linear stability, and the system can generate patterns due to the effects of prey-taxis. Secondly, we consider the nonlinear prey-taxis as the bifurcation parameter in order to analyze the global bifurcation of this model. Specifically, we identify a branch of nonconstant solutions that emerges from the positive constant solution when the prey-tactic sensitivity is repulsive. Finally, we will validate the effectiveness of the theoretical conclusions using numerical simulation methods. Full article

Combining explicit modelling of predator movements with the Kostitzin demo-genetic equations, we study conditions promoting natural selection of consumer motility. The model is a system of partial differential equations describing spatial movements of predators pursuing the diffusing prey. Local predator–prey interactions are described by the classical Rosenzweig–MacArthur model, which additionally accounts for the Allee effect affecting reproduction of predators. Spatial activity of predators is determined by the coefficients of diffusion and indirect prey-taxis. The latter characterizes the predator ability to move directionally up the gradient of taxis stimulus (odor, pheromone, exometabolite) continuously emitted by prey. Assuming that the consumer movement ability is governed by a single diallelic locus with recessive ‘mobile’ and dominant ‘settled’ alleles, the predator population in the model consists of three competing genotypes differing by diffusion and taxis coefficients; other parameters characterizing the genotypes are assumed to be equal. Numerical simulations with different spatial patterns imitating habitat deterioration demonstrate that the direction of selection among the consumer genotypes alternates, depending on the degree of habitat deterioration affecting the overall production of the prey population. Theoretical implications of the results are discussed in relation with problems of biological control, predator interference, and evolution of animal motility. Full article

Development, survival and reproduction of Ambyseius andersoni (Chant), a predatory mite widely distributed in Europe, were assessed on different food items. These included two key pests of ornamental coniferous plants, i.e., Oligonychus ununguis (Jacobi) and Pentamerismus taxi (Haller) and pollen of Pinus sylvestris L. The rationale behind these experiments was to provide a preliminary assessment of the potential of A. andersoni as a biocontrol agent of the above phytophagous arthropods and evaluate pine pollen as an alternative food source for the predator. Under laboratory conditions (23 ± 0.5 °C, 70 ± 10% RH and 16L:8D) A. andersoni was able to feed, develop and reproduce on all tested diets. The shortest development time (egg to female) was obtained when the predator fed on P. taxi (mean = 5.12 d) and the longest was on pine pollen (mean = 6.55 d). The r_m value was significantly higher on both tested prey (0.166 on P. taxi and 0.160 on O. ununguis) than on pollen (0.139). Thus, we do not recommend pine pollen for mass rearing of A. andersoni; however, we conclude that pollen may provide sufficient sustenance for the predator population under field conditions when prey are absent. The potential of A. andersoni as a biocontrol agent of O. ununguis and P. taxi is discussed. Full article

A simple mathematical model capable of reproducing formation of small-scale spatial structures in prey–predator system is presented. The migration activity of predators is assumed to be determined by the degree of their satiation. The hungrier individual predators migrate more frequently, randomly changing their spatial position. It has previously been demonstrated that such an individual response to local feeding conditions leads to prey–taxis and emergence of complex spatiotemporal dynamics at population level, including periodic, quasi-periodic and chaotic regimes. The proposed taxis–diffusion–reaction model is applied to describe the trophic interactions in system consisting of benthic diatom microalgae and harpacticoid copepods. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence is given. The model parameters are identified on the basis of field observation data and knowledge on the species ecology in order to explain micro-scale spatial patterns of these organisms, which still remain obscure, and to reproduce in numerical simulations characteristic size and the expected lifetime of density patches. Full article