Monitoring in a Lotka-Volterra model

The problem of monitoring arises when in an ecosystem, in particular in a system of several populations, observing some components, we want to recover the state of the whole system in function of time. Due to the difficulty to construct exactly this state process, we look for an auxiliary system called observer, the solution of which reproduces this process with certain approximation. This means, that the solution of the observer tends to that of the original system. For this work an important concept is observability which means, that from the observation it is possible to recover the state process in a unique way, however without determining a constructive method to obtain it. If observability holds for the original system, it guarantees the existence of an auxiliary matrix which makes it possible to construct an observer of the system. The considered system of populations is described by the classical Lotka-Volterra model with one predator and two preys and the construction of its observer is illustrated with a numerical example. Finally, it is shown how the observer can be used for the estimation of the level of an abiotic effect on the population system

Identification and incorporation of quantitative indicators of ecosystem function into single-species fishery stock assessment models and the associated biological reference points

The move towards an ecosystem approach to fisheries management requires baseline information on the biotic communities and an understanding of the interactions among species. The two objectives of this study were to describe the demersal fish community (DFC) associated with the northwestern Gulf shrimp trawl fishery, and to utilize a multispecies Lotka-Volterra model to examine possible community level effects of fishing. Community level effects include predator-prey interactions and the responses of fish in the same community to fishing pressure. The summer and fall Southeast Area Monitoring and Assessment Program (SEAMAP) bottomfish trawl surveys were used to identify spatial and temporal indicators in the northwestern Gulf. Cluster analysis and nonmetric multidimensional scaling analysis identified four distinct demersal fish communities (DFCs) from the summer survey data and three distinct spatial DFCs from the fall survey data. Indicator species analysis identified two different dominant communities within each DFC during the summer and fall survey periods. No statistically significant temporal trends were identifiable in the SEAMAP data over the selected time period (1986-2007). However, the community metrics from the DFCs were used to create initial parameters for a multispecies Lotka-Volterra simulation model. The Lotka-Volterra model was developed to study the implications of estimating single-species biological reference points from multispecies data and to determine the effect of fishing on other species in the same community. Three series of simulations were created to explore connectance, rebuilding plans, and multispecies fisheries in the Lotka-Volterra model. Across all simulations, the single-species FMSY rates were estimated between 10-75% of the expected values from the Lotka-Volterra model, indicating that fishing mortality rate buffers are needed to account for predator-prey interactions. No trends were detected as to the magnitude of the buffer for the species examined across all levels of community connectance. The magnitude of biomass changes in unfished species decreased as community connectance increased. The projected time for a species to rebuild was longer in the multispecies model versus the single-species model in four of five case studies. Indirect effects were important in all simulations and these results indicate a need for ecological buffers when determining single-species fishing mortality rates

Noise Induced Phenomena in the Dynamics of Two Competing Species

Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise delayed extinction, and noise induced pattern formation. In addition, our theoretical results are validated with experimental findings. Specifically the results, obtained by a coupled map lattice model, well reproduce the spatial distributions of anchovies and sardines, observed in a marine ecosystem. Moreover, the experimental dynamical behavior of two competing bacterial populations in a meat product and the probability distribution at long times of one of them are well reproduced by a stochastic microbial predictive model.Comment: 23 pages, 8 figures; to be published in Math. Model. Nat. Phenom. (2016

Smart Grid communications in high traffic environments

The establishment of a previously non-existent data class known as the Smart Grid will pose many difficulties on current and future communication infrastructure. It is imperative that the Smart Grid (SG), as the reactionary and monitory arm of the Power Grid (PG), be able to communicate effectively between grid controllers and individual User Equipment (UE). By doing so, the successful implementation of SG applications can occur, including support for higher capacities of Renewable Energy Resources. As the SG matures, the number of UEs required is expected to rise increasing the traffic in an already burdened communications network. This thesis aims to optimally allocate radio resources such that the SG Quality of Service (QoS) requirements are satisfied with minimal effect on pre-existing traffic. To address this resource allocation problem, a Lotka-Volterra (LV) based resource allocation and scheduler was developed due to its ability to easily adapt to the dynamics of a telecommunications environment. Unlike previous resource allocation algorithms, the LV scheme allocated resources to each class as a function of its growth rate. By doing so, the QoS requirements of the SG were satisfied, with minimal effect on pre-existing traffic. Class queue latencies were reduced by intelligent scheduling of periodic traffic and forward allocation of resources. This thesis concludes that the SG will have a large effect on the telecommunications environment if not successfully controlled and monitored. This effect can be minimized by utilizing the proposed LV based resource allocation and scheduler system. Furthermore, it was shown that the allocation of periodic SG radio channels was optimized by continual updates of the LV model. This ensured the QoS requirements of the SG are achieved and provided enhanced performance. Successful integration of SG UEs in a wireless network can pave the way for increased capacity of Renewable and Intermittent Energy Resources operating on the PG

Vortex dynamics in a three-state model under cyclic dominance

The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate which is increased by the spiral formation due to the cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle antiparticle system with density dependent pair creation rate. Numerical estimates for the critical indices of the vortex density ($\beta=0.29(4)$) and of its fluctuation ($\gamma=0.34(6)$) improve an earlier Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic voter model in two dimensions.Comment: 5 pages, 6 figures, to appear in PR