Repulsive-attractive models for the impact of two predators on prey species varying in anti-predator response

This study considers the dynamical interaction of two predatory carnivores (Lions (Panthera leo) and Spotted Hyaenas (Crocuta crocuta)) and three of their common prey (Buffalo (Syncerus caffer), Warthog (Phacochoerus africanus) and Kudu (Tragelaphus strepsiceros)). The dependence on spatial structure of species’ interaction stimulated the author to formulate reaction-diffusion models to explain the dynamics of predator-prey relationships in ecology. These models were used to predict and explain the effect of threshold populations, predator additional food and prey refuge on the general species’ dynamics. Vital parameters that model additional food to predators, prey refuge and population thresholds were given due attention in the analyses. The stability of a predator-prey model for an ecosystem faced with a prey out-flux which is analogous to and modelled as an Allee effect was investigated. The results highlight the bounds for the conversion efficiency of prey biomass to predator biomass (fertility gain) for which stability of the three species ecosystem model can be attained. Global stability analysis results showed that the prey (warthog) population density should exceed the sum of its carrying capacity and threshold value minus its equilibrium value i.e., W >(Kw + $) −W . This result shows that the warthog’s equilibrium population density is bounded above by population thresholds, i.e., W < (Kw+$). Besides showing the occurrence under parameter space of the so-called paradox of enrichment, early indicators of chaos can also be deduced. In addition, numerical results revealed stable oscillatory behaviour and stable spirals of the species as predator fertility rate, mortality rate and prey threshold were varied. The stabilising effect of prey refuge due to variations in predator fertility and proportion of prey in the refuge was studied. Formulation and analysis of a robust mathematical model for two predators having an overlapping dietary niche were also done. The Beddington-DeAngelis functional and numerical responses which are relevant in addressing the Principle of Competitive Exclusion as species interact were incorporated in the model. The stabilizing effect of additional food in relation to the relative diffusivity D, and wave number k, was investigated. Stability, dissipativity, permanence, persistence and periodicity of the model were studied using the routine and limit cycle perturbation methods. The periodic solutions (b 1 and b 3), which influence the dispersal rate (') of the interacting species, have been shown to be controlled by the wave number. For stability, and in order to overcome predator natural mortality, the nutritional value of predator additional food has been shown to be of high quality that can enhance predator fertility gain. The threshold relationships between various ecosystem parameters and the carrying capacity of the game park for the prey species were also deduced to ensure ecosystem persistence. Besides revealing irregular periodic travelling wave behaviour due to predator interference, numerical results also show oscillatory temporal dynamics resulting from additional food supplements combined with high predation rates

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

The paradox of the plankton: Investigating the effect of inter-species competition of phytoplankton and its sensitivity to nutrient supply and external forcing

Hutchinson (1961) first posed the paradox of the plankton: Why do so many phytoplankton species coexist while competing for a limited number of resources? High biodiversity has been explained in terms of the phytoplankton system not reaching an equilibrium state. Spatial and temporal variability can be achieved through externally imposed physical variability or internally-induced behaviour including periodic oscillations or irregular, chaotic behaviour. The research presented in this thesis investigates whether the non-equilibrium, chaotic response of the phytoplankton community is a likely outcome within the aquatic ecosystems. The thesis addresses the extent that chaotic behaviour remains a robust response with externally-imposed environmental variability. The sparsity of long-term time-series data and infrequent sampling inhibits the ability to verify whether marine ecosystems exhibit complex behaviour. The analysis of the time-series records of phytoplankton taxa in the English Channel suggests that chaos might occur within diatom and dinoflagellates abundance time series. However, simulations using a chemostat model for phytoplankton and nutrients suggests that time series sampled every 1-2 days for more than 5 years are required to confidently distinguish deterministic chaos from noise. The model simulations suggest that the community response depends on the phytoplankton requirement for nutrients and attributed physiological traits allowing each species to be a stronger competitor for a different resource. A wider inter-species specialization increases the likelihood of oscillatory and chaotic responses, with competitive exclusion decreasing from 50% to 20% of the cases. Higher departures from the Redfield ratio in the elemental composition of species favour complex community behaviour and act to increase biodiversity. Whether chaotic response can be sustained is sensitive to the strength of the diffusive feedback between nutrient supply and ambient nutrient concentration that acts to sustain steady-state nutrient concentrations. Including seasonal and stochastic variability in the nutrient supply reveals that the frequency of chaotic dynamics increases by 20% and 45% respectively. In addition, seasonal forcing leads to temporal variability in the strength of the chaotic response, with chaos becoming more prevalent in the summer. In contrast to a well-mixed, homogeneous environment, physical dispersal can stir different phytoplankton communities together, which might act to inhibit chaos, but at the same time enhance phytoplankton diversity. Idealised model simulations are conducted to mimic the small and large scale transport processes by including 2 or 3 well-mixed boxes. Locally generated chaotic response is sustained if: 1) there is a low rate of exchange with a strong nutrient competitor that maintains the contrasts in the community structure; 2) a strong competitor is inhibited by a high mortality rate. In addition, if the local community is outcompeted, chaos can be exported through the advection of stronger competitors that exhibit chaotic fluctuations. This study highlights the importance of understanding the interactions between ambient nutrients and phytoplankton community. The variability in the nutrient supply and connectivity between ecosystems shape the community response to inter-species competition. Complex behaviour arising from inter-species competition is suggested to have a significant contribution in driving biodiversity. Future research on assessing the extent of chaos requires extending and analysing the available time-series data obtained from stable or isolated marine provinces

YOUMARES 8 – Oceans Across Boundaries: Learning from each other

This open access book presents the proceedings volume of the YOUMARES 8 conference, which took place in Kiel, Germany, in September 2017, supported by the German Association for Marine Sciences (DGM). The YOUMARES conference series is entirely bottom-up organized by and for YOUng MARine RESearchers. Qualified early career scientists moderated the scientific sessions during the conference and provided literature reviews on aspects of their research field. These reviews and the presenters’ conference abstracts are compiled here. Thus, this book discusses highly topical fields of marine research and aims to act as a source of knowledge and inspiration for further reading and research

Trophic relationships in soil communities: how abiotic stress affects biotic interactions in the McMurdo Dry Valleys, Antarctica

2018 Summer.Includes bibliographical references.To view the abstract, please see the full text of the document

YOUMARES 8 – Oceans Across Boundaries: Learning from each other

This open access book presents the proceedings volume of the YOUMARES 8 conference, which took place in Kiel, Germany, in September 2017, supported by the German Association for Marine Sciences (DGM). The YOUMARES conference series is entirely bottom-up organized by and for YOUng MARine RESearchers. Qualified early career scientists moderated the scientific sessions during the conference and provided literature reviews on aspects of their research field. These reviews and the presenters’ conference abstracts are compiled here. Thus, this book discusses highly topical fields of marine research and aims to act as a source of knowledge and inspiration for further reading and research

Investigating summer thermal stratification in Lake Ontario

Summer thermal stratification in Lake Ontario is simulated using the 3D hydrodynamic model Environmental Fluid Dynamics Code (EFDC). Summer temperature differences establish strong vertical density gradients (thermocline) between the epilimnion and hypolimnion. Capturing the stratification and thermocline formation has been a challenge in modeling Great Lakes. Deviating from EFDC's original Mellor-Yamada (1982) vertical mixing scheme, we have implemented an unidimensional vertical model that uses different eddy diffusivity formulations above and below the thermocline (Vincon-Leite, 1991; Vincon-Leite et al., 2014). The model is forced with the hourly meteorological data from weather stations around the lake, flow data for Niagara and St. Lawrence rivers; and lake bathymetry is interpolated on a 2-km grid. The model has 20 vertical layers following sigma vertical coordinates. Sensitivity of the model to vertical layers' spacing is thoroughly investigated. The model has been calibrated for appropriate solar radiation coefficients and horizontal mixing coefficients. Overall the new implemented diffusivity algorithm shows some successes in capturing the thermal stratification with RMSE values between 2-3°C. Calibration of vertical mixing coefficients is under investigation to capture the improved thermal stratification