Large-scale Natural Systems Research Articles

Spatiotemporal dynamics of a predator-prey system with fear effect

Recent field experiments on vertebrates show that though mere presence of a predator causes a dramatic change in prey demography, the fear of predators increases the survival probability of prey leading to a cost of prey production. Based on the experimental findings, we proposed and analyzed a mathematical model that incorporates the fear-induced birth reduction in the prey population due to presence of predator. A modified and more realistic fear function is proposed in this study. Qualitative behavior of the model is performed including positivity and boundedness of solutions, existence of critical points and their local stability analysis, existence of transcritical and Hopf bifurcation. We analyzed Hopf bifurcation with respect to the prey growth rate and the level of fear. Transcritical bifurcation is analyzed by varying the prey growth rate. Distribution of the population of interacting species in a large scale natural system is heterogeneous and subject to alter for different reasons. Thus, we investigate how behavioral modification in prey population due to fear for predators and mutual interference among predator species can create various spatiotemporal pattern formation in population distribution. In the spatially extended system, we provide a detailed stability analysis and obtain the conditions for Turing instability. Numerical simulations are performed to validate analytical results for both non-spatial and spatial models. Warm spot patterns are obtained by considering three different types of initial data and discussed the biological significance of these patterns for the two-dimensional spatial model. Our numerical simulation demonstrates that the fear effect in a diffusive predator-prey system with mutual interference between predators may exhibit more complicated dynamics.

Dynamics of turbidity in gypsum-precipitating brines: The case of the Red Sea – Dead Sea project

Authigenic processes in aqueous environments, such as mineral precipitation, can create turbidity which may have undesired effects on the natural environment and in industrial processes. Turbidity is often used to monitor such environments, as a mean to determine water quality and to follow the industrial processes. However, turbidity develops and grows or dissipates with time as the processes underlying its development advance. This dynamic nature of turbidity has yet to be studied.The proposed pilot Red Sea – Dead Sea project (RSDSP) is to desalinate seawater from the Gulf of Aqaba/Eilat and convey the reject brine, with or without additional seawater, to the Dead Sea to slow down the rate of its water level decline. The pilot is considered environmentally safe and will be used as a mean to determine if increased inflow volumes to stabilize the Dead Sea level will not negatively affect the lake. The mixing of the two very different solutions will lead to gypsum precipitation in the Dead Sea. In a large-scale project, if this gypsum remains in suspension, it may result in increased turbidity and whitening of the Dead Sea's surface water, thereby impacting the lake's appearance, its energy balance, and its touristic and mineral industries.We have studied the dynamic nature of turbidity as gypsum crystals form, grow and sink out of the water column in enriched mixtures of Dead Sea brine with seawater from the Red Sea. Our laboratory experiments suggest that precipitation from simple mixtures is likely to proceed without creating a significant spontaneous increase in turbidity. Turbidity did however develop in sulfate-enriched mixtures that had higher initial oversaturation. In these enriched solutions increased turbidity was observed, which developed faster and to higher values with increasing initial oversaturation. A linear relationship was found between the mass of gypsum precipitated and turbidity. However, this relationship was not universal; a unit mass of precipitated gypsum resulted in higher turbidity when the gypsum precipitated from mixtures having higher %wt of Dead Sea.This study shows that under laboratory conditions, mixtures of Dead Sea - seawater or Dead Sea – reject brine, do not develop turbidity due to gypsum precipitation. However, precipitation process in large scale natural systems can differ from those in the lab. Therefore, our findings cannot unequivocally conclude whether a whitening of the Dead Sea would develop following the implementation of the full scale RSDSP. Nevertheless, it does set forth the factors that need to be monitored during the pilot stage. Moreover, the study also demonstrates that: 1) authigenic processes do not lead to a one-to-one relationship between particulate matter and turbidity; and 2) turbidity readings must first be calibrated before used as a monitoring tool to identify and quantify gypsum formation (e.g., in desalination plants) or for the determination of induction times (e.g., in experiments).

Diffusion-induced regular and chaotic patterns in a ratio-dependent predator-prey model with fear factor and prey refuge.

Population distribution of interacting species in a large scale natural system is heterogeneous and subject to change for various reasons. Here, we explore how behavioral modification in prey species due to fear of predator and mutual interference between predators can create different spatiotemporal patterns in population distribution. We show that the fear factor and diffusion in a ratio-dependent predator-prey model may show more complex dynamics than observed earlier. It is shown that when prey diffusivity is low, prey remains concentrated at different patches throughout the domain. However, prey density becomes low at the patches as they disperse at a higher rate. Mixed and stripe patterns are observed during the transition from a hot spot pattern at the lower prey diffusivity to a cold spot pattern at its higher value. Pattern transition is, however, completely opposite if the antipredator behavior is gradually increased. Our simulation results reveal that the spatiotemporal chaotic pattern may also be observed in the Hopf-Turing region of instability provided prey shows a higher level of antipredator behavior. The chaotic pattern of the Hopf-Turing region may be shifted to a spot type pattern of the Turing region depending on the refuge level of the habitat.

Field tests and multiphysics analysis of a flooded shaft for geothermal applications with mine water

This paper introduces the scientific part of a large-scale study in the Upper Peninsula (U.P.) of Michigan, a historical mining area, for exploring the water in deep abandoned copper mines as a geothermal energy resource. The main focus of the paper is placed on the scientific understanding of the natural mine water-geologic formation system, especially the transport of heat and mass in this large-scale natural system, which is critical to the efficiency and sustainability of the energy renovation. For this purpose, a field study involving measurements of temperatures and chemicals in a local mine shaft in the U.P. is conducted to reveal the major issue in recovering geothermal energy in the water from the shaft, i.e., the temperature distribution. Water samples are also collected in situ to investigate the distribution and concentrations of major chemicals. Afterward, a theoretical framework for the thermo-hydrodynamic process in the mine water coupled with heat transfer in the surrounding geologic formations is developed to outline a mathematical description for studying the scientific issue. Simulations are finally conducted, based on the real geologic information, to preliminarily investigate the quasi-equilibrium water movement in this local mine shaft due to geothermal gradients to provide insights into the phenomena observed in the field study.

Local knowledge regarding ecosystem services and disservices from invasive alien plants in the arid Kalahari, South Africa

Across the globe, many invasive alien plants were purposefully introduced because of their usefulness. These plants continue to provide multiple goods and services, such as fodder, fuelwood, medicines, fruits, shade and aesthetic appeal. However, as they invade negative impacts arise. This often leads to conflicts of interests and trade-offs between the benefits and costs of these species and, ultimately, the environment and local livelihoods. Traditionally, invasive plant species research in dryland systems has tended to focus on the impacts of these species on large-scale natural systems, primarily rangelands and river courses. Limited work has been undertaken regarding the role of these species in providing services and disservices within homesteads and settlements in these harsh environments. Such knowledge is important with regards to management. The primary aim of this study was therefore to assess the assimilation of invasive plant species into the lives of households in several small farming settlements in the arid Kalahari region of the Northern Cape, South Africa. Specific objectives were to: 1) assess the diversity, prevalence and size structure of invasive plants in resident's homesteads; 2) identify sources, local practices, knowledge and beliefs related to the invasive plants present as well as local management practices; and 3) understand residents' perceptions of the ecosystem services and disservices these species deliver. To do this, we used household and ‘drive-past’ surveys, in-depth interviews and measurement of plants in homesteads. From the ‘drive-past’ survey, we identified 12 officially listed and one proposed invasive plant species in the settlements, 10 of which were covered in the household survey. Eight native tree species were also present, but these were at much lower frequency and density than introduced species. Thirteen different goods and services from the invasive plants were recognised with the most common being shade, aesthetics and fuelwood. Some species, such as Morus alba and Opuntia ficus-indica, were important for fruit, while eight species were mentioned as being used for fodder. Respondents also mentioned that O. ficus-indica, Prosopis spp., Leucaena leucocephala and Melia azedarach imposed costs. These disservices included reductions in water supply, damage to buildings and human health impacts. Some of these species were also perceived to be spreading beyond homesteads in some settlements and invading rangeland. Less than a quarter of households had no invasive plants in their yards, and these were mainly new dwellings in the growing informal areas around the settlements. Invasive plants were obtained from variety of sources suggesting various pathways of introduction. We conclude by discussing some options for management focusing on Prosopis, as the invasive plant perceived to most rapidly expanding and generating the most disservices. We also highlight what further research is needed with regard to filling research gaps on invasive plant species within social-ecological systems in arid areas.

Wave chaos in rapidly rotating stars

The effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens fresh perspectives for rapidly rotating star seismology and also provides a potentially observable manifestation of wave chaos in a large-scale natural system.

Coupling in predator-prey dynamics: Ratio-Dependence

In continuous-time predator-prey models, the per capita rate of consumption (the functional response or “trophic function”) is usually interpreted as a behavioral phenomenon. The classical assumptions are that predators encounter prey at random and that the trophic function depends on prey abundance only. We argue that this approach is not always appropriate. The trophic function must be considered on the slow time scale of population dynamics at which the models operate—not on the fast behavioral time scale. We propose that, in cases where these two time scales differ, it is reasonable to assume that the trophic function depends on the ratio of prey to predator abundances. Several field and laboratory observations support this hypothesis. We compare the consequences of the two types of dependence with respect to the dynamical properties of the models and the responses of population equilibria to variations in primary production. In traditional prey-dependent models, only the predator population responds to primary production, while both levels respond in ratio-dependent models. This result is generalized to food chains. We suggest that the ratio-dependent form of the trophic function is a simple way of accounting for many types of heterogeneity that occur in large scale natural systems, while the prey-dependent form may be more appropriate for homogeneous systems like chemostats.