Ecological system with fear induced group defence and prey refuge

In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defence of prey against predators; and (iii) prey refuge. We provide comprehensive mathematical analysis of extinction and persistence scenarios for both prey and predator species. To better explore the dynamics of the system, a thorough investigation of bifurcation analysis has been performed using fear level, prey birth rate, and prey death rate caused by intra-prey competition as bifurcation parameter. All potential occurrences of bi-stability dynamics have also been investigated for some relevant sets of parametric values. Our numerical evaluations show that high levels of fear can stabilize the prey-predator system by ruling out the possibility of periodic solutions. Also, our model Hopf bifurcation is subcritical in contrast to traditional prey-predator models, which ignore the cost of fear and have supercritical Hopf bifurcations in general. In contrast to the general trend, predator species go extinct at higher values of prey birth rates. We have also found that, contrary to the typical tendency for prey species to go extinct, both prey and predator populations may coexist in the system as intra-prey competition level grows noticeably. The stability and Turing instability of associated spatial model have also been investigated analytically. We also perform the numerical simulation to observe the effect of different parameters on the density distribution of species. Different types of spatiotemporal patterns like spot, mixture of spots and stripes have been observed via variation of time evolution, diffusion coefficient of predator population, level of fear factor and prey refuge. The fear level parameter (k) has a great impact on the spatial dynamics of model system

Studying Both Direct and Indirect Effects in Predator-Prey Interaction

Studying and modelling the interaction between predators and prey have been one of the central topics in ecology and evolutionary biology. In this thesis, we study two different aspects of predator-prey interaction: direct effect and indirect effect. Firstly, we study the direct predation between predators and prey in a patchy landscape. Secondly, we study indirect effects between predators and prey. Thirdly, we extend our previous model by incorporating a stage-structure into prey. Finally, we further extend our previous model by incorporating spatial structures into modelling

Modelling dispersal processes in impala-cheetah-lion ecosystems with infection in the lions

The study involved the predator-prey interaction of three species namely the predator (Cheetah Acinonyx jubatus), the super-predator (Lion Panthera leo), and their common prey (Impala Aepyceros melampus). The study area is the Kruger National Park. The predator being an endangered species, faces a survival problem. It is frequently killed by the super-predator to reduce competition for prey. The super-predator also scares away the predator o_ its kills. The prey forms the main diet of the predator. The plight of the predator motivated the author to formulate disease and reaction-diffusion models for the species interactions. The purpose of the models were to predict and explain the effect of large competition from the super-predator on the predator population. Important parameters related to additional predator mortality due to presence of super-predator, the disease incidence rate and induced death rate formed the focal points of the analysis. The dynamics of a predator-prey model with disease in super-predator were investigated. The super-predator species is infected with bovine Tuberculosis. In the study, the disease is considered as biological control to allow the predator population to regain from low numbers. The results highlight that in the absence of additional mortality on the predator by the super-predator, the predator population survives extinction. Furthermore, at current levels of disease incidence, the super-predator population is wiped out by the disease. However, the super-predator population survives extinction if the disease incidence rate is low. Persistence of all populations is possible in the case of low disease incidence rate and no additional mortality imparted on the predator. Furthermore, a two-species subsystem, prey and predator, is considered as a special case to determine the effect of super-predator removal from the system, on the survival of the predator. This is treated as a contrasting case from the smaller parks. The results show that the predator population thrives well in the total absence of its main competitor, with its population rising to at least twice the initial value. A reaction-diffusion three-species predator-prey model was formulated and analysed. Stability of the temporal and the spatio-temporal systems, existence and non-existence of stationary steady state solutions were studied. Conditions for the emergence of stationary patterns were deduced. The results show that by choosing the diffusion coeffcient d2 > _D 2 suffciently large, a non-constant positive solution is generated, that is, stationary patterns emerge, depicting dispersal of species. Predators were observed to occupy habitats surrounding prey. However, super-predators were observed to alternate their habitats, from staying away from prey to invading prey habitat. In the investigation, strategies to determine ways in which the predator species could be saved from extinction and its population improved were devised, and these included isolation of the predator from the super-predator

Spatiotemporal dynamics of a diffusive predator-prey model with delay and Allee effect in predator

It has been shown that Allee effect can change predator-prey dynamics and impact species persistence. Allee effect in the prey population has been widely investigated. However, the study on the Allee effect in the predator population is rare. In this paper, we investigate the spatiotemporal dynamics of a diffusive predator-prey model with digestion delay and Allee effect in the predator population. The conditions of stability and instability induced by diffusion for the positive equilibrium are obtained. The effect of delay on the dynamics of system has three different cases: (a) the delay doesn't change the stability of the positive equilibrium, (b) destabilizes and stabilizes the positive equilibrium and induces stability switches, or (c) destabilizes the positive equilibrium and induces Hopf bifurcation, which is revealed (numerically) to be corresponding to high, intermediate or low level of Allee effect, respectively. To figure out the joint effect of delay and diffusion, we carry out Turing-Hopf bifurcation analysis and derive its normal form, from which we can obtain the classification of dynamics near Turing-Hopf bifurcation point. Complex spatiotemporal dynamical behaviors are found, including the coexistence of two stable spatially homogeneous or inhomogeneous periodic solutions and two stable spatially inhomogeneous quasi-periodic solutions. It deepens our understanding of the effects of Allee effect in the predator population and presents new phenomena induced be delay with spatial diffusion

Biological control via "ecological" damping: An approach that attenuates non-target effects

In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous" levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in earlier work. Lastly, we confirm the existence of spatio-temporal chaos

Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response

In this paper, considering the aggregation effect and Allee effect of cyanobacteria populations and the harvesting of both cyanobacteria and fish by human beings, a new cyanobacteria-fish model with two harvesting terms and a modified Holling type Ⅳ functional response function is proposed. The main purpose of this paper is to further elucidate the influence of harvesting terms on the dynamic behavior of a cyanobacteria-fish model. Critical conditions for the existence and stability of several interior equilibria are given. The economic equilibria and the maximum sustainable total yield problem are also studied. The model exhibits several bifurcations, such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. It is concluded from a biological perspective that the survival mode of cyanobacteria and fish can be determined by the harvesting terms. Finally, concrete examples of our model are given through numerical simulations to verify and enrich the theoretical results

Behavioural and ecological energetics of elasmobranchs

Understanding the capacity of animals to behaviourally and physiologically cope with environmental change is becoming crucial for developing process-based approaches to wildlife management. Energy is one of the most basic resources of animals, and the need to acquire energy to fuel daily activities, growth, and reproduction drives many aspects of ecology. Decades of comparative physiology work have shown the metabolic rates of animals systematically vary based on a suite of organismal traits and environmental factors. However, it is poorly understood how such metabolic variation influences animal’s behaviours in the wild, and as such, their capacity to adapt to environmental change. Recently, novel technologies have allowed physiological research to be conducted in the field, facilitating investigations of how animal physiology drives the behaviours of animals in natural settings. In this thesis, I present a number of studies that investigate how the three primary factors governing the physiology of ectotherms, namely body size, temperature, and habitat shape an animals’ capacity to cope with anthropogenic threats and environmental change. Using a combination of respirometry experiments, on-animal motion-sensing, biotelemetry tracking tools, and sophisticated behavioural modelling, I examined how changes in metabolism drive the behavioural and spatial ecology of sharks. First, I demonstrate how local environmental pressures place constraints on a species ability to expand home ranges to escape local resource limitations. Second, investigations of the drivers of behavioural and activity patterns of sharks revealed that within these spatial constraints, sharks’ ability to adjust their foraging and resting patterns are relatively limited. While metabolic changes associated with increased environmental temperatures pressure sharks to forage more often, functional traits limit their ability to forage outside short temporal windows. Taken together, these results indicate that physiological requirements place substantial constraints on the behavioural flexibility of sharks, which will likely have serious impacts on their life history, fitness, and survival in the face of continued environmental change. Lastly, I discuss the implications of physiological and behavioural constraints for the management of threatened shark population

Myxobacteria

Myxobacteria are fascinating and important prokaryotes. They have large genomes and exhibit a wide range of interesting behaviors, including multicellular fruiting body formation, social interaction, predation, and secondary metabolite production. Substantial progress is being made in understanding their ecological roles and the evolutionary forces that have shaped their phenotypes and behaviors. Novel species of myxobacteria are regularly described, often producing unusual metabolites and enzymes which can be of significant biotechnological interest. Molecular studies, ranging in subject from individual enzymes to entire ‘omes, continue to provide rich insights into myxobacterial biology. This collected volume brings together five research articles and three reviews, to provide a snapshot of current myxobacterial research in all its diversity