An Optimal Harvesting Strategy of a Three Species Syn-ecosystem with Commensalism and Stochasticity

In this paper we have studied the stability of three typical species syn-ecosystem. The system comprises of one commensal S1 and two hosts S2 and S3 . Both S2 and S2 benefit S1 without getting themselves affected either positively or adversely. Further S2 is a commensal of S3 and S3 is a host of both S1 and S2. Limited resources have been considered for all the three species in this case. The model equations of the system constitute a set of three first order non-linear ordinary differential equations. The possible equilibrium points of the model are identified. We have also studied the local and global stabilities. We have analyzed the bionomic equilibrium and optimal harvesting strategy using Pontryagin’s maximum principle. We have investigated the inhabitant intensities of the fluctuations (variances) around the positive equilibrium due to noise and have investigated the stability. We have also checked the MATLAB numerical simulations for stability of the system

Influence of impreciseness in designing tritrophic level complex food chain modeling in interval environment

Abstract In this paper, we construct a tritrophic level food chain model considering the model parameters as fuzzy interval numbers. We check the positivity and boundedness of solutions of the model system and find out all the equilibrium points of the model system along with its existence criteria. We perform stability analysis at all equilibrium points of the model system and discuss in the imprecise environment. We also perform meticulous numerical simulations to study the dynamical behavior of the model system in detail. Finally, we incorporate different harvesting scenarios in the model system and deploy maximum sustainable yield (MSY) policies to determine optimum level of harvesting in the imprecise environment without putting any unnecessary extra risk on the species toward its possible extinction

Ecological Process and the Blister Rust Epidemic: Cone Production, Cone Predation, and Seed Dispersal in Whitebark Pine (Pinus albicaulis)

Whitebark pine (Pinus albicaulis), a high elevation foundation species, is experiencing population declines throughout the northern part of its range. The introduced fungal pathogen, Cronartium ribicola (white pine blister rust), infects whitebark pine and kills cone-bearing branches and trees. Blister rust has spread nearly rangewide and damage and mortality are highest in the northwest US and southwest Canada. Mortality caused by mountain pine beetle (Dendroctonus ponderosae) population upsurges, and successional replacement and loss of regeneration opportunities from fire suppression, are also impacting some whitebark pine populations. Within this dissertation, I present three manuscripts that address the impact of whitebark pine\u27s decline on species interactions and ecological processes within subalpine forests. Research was conducted in three ecosystems in the Rocky Mountains USA that are distinct in whitebark pine health conditions (rust infection and mortality) and abundance. In the first manuscript, I explore how the relationship between whitebark pine and Clark\u27s Nutcracker (Nucifraga columbiana), its primary seed disperser, is being affected by whitebark\u27s decline. Nutcrackers were less likely to use and disperse seeds from forests where cone production is below a threshold. In the second manuscript, I describe habitat use of whitebark pine forests by red squirrels (Tamiasciurus hudsonicus). Squirrel residency and impact of cone predation increased with decreasing whitebark pine abundance. The third manuscript focuses on the tree-level ecological process, predispersal cone survival, as a function of coarse scale whitebark pine abundance. Surviving trees in high mortality forests were found to have a lower rate and higher variability of cone survival, suggesting that the putative levels of rust-resistance in surviving trees of high mortality forests may not be passed on to future generations. At the ecosystem level, the Northern Divide had the highest levels of rust infection and tree mortality and lowest nutcracker interaction and regeneration levels; the Greater Yellowstone had the lowest infection and mortality levels and nutcrackers were present and dispersing seeds at all research sites in all years, while the Bitterroot Mountains were intermediate in these comparisons. These findings provide important components for developing a long-term strategy to conserve and restore whitebark pine ecosystems in the Rocky Mountains

Biofuels from micro-organisms: Thermodynamic analysis of sustainability

L'abstract è presente nell'allegato / the abstract is in the attachmen

Optimal economic planning and control for the management of ecosystems

In recent years the interest on sustainable systems has increased significantly. Among the many interested problems, creating and restoring sustainable ecosystems is a challenging and complex problem. One of the fundamental problems within this area is the imbalance between species that have a predator-prey relationship. Solutions involving management have become an integral player in many environments. Management systems typically use ad hoc methods to develop harvesting policies to control the populations of species to desired numbers. In order to amalgamate intelligence and structure, ecological systems require a diverse research effort from three primary fields: ecology, economics, and control theory. In this thesis, all three primary fields aforementioned are researched to develop a theoretical framework that includes an optimal trajectory planning system that exploits an ecosystem to maximize profits for the supporting community, and a robust control system design to track the optimal trajectories subjected to exogenous disturbances. Population ecology is used to select a model that identifies the key characteristics a management system needs to understand the behavior of the natural environment. A bioeconomic model is developed to relate the species populations to revenue. The nonlinear ecosystem is transformed into a linear parameter-varying (LPV) system that is then controlled using hinf synthesis and the gain scheduling methodology. The consequences of the results in this thesis are that optimal trajectories of an ecosystem can be obtained by constructing and solving a nonlinear programming problem (NLP), and the LPV based gain scheduling approach produces a robust controller that rejects disturbances and advises quality control policies to the manager an ecosystem. The LPV controller achieves comparable profits with satisfactory tracking performance while minding the induced costs of its high frequency output. Implications of constraining the control effort when designing for robustness are observed. Overall, the theoretical framework provides a solid foundation for future research on the understanding and improvement of ecosystem management

Evolutionary dynamics of cancer cell populations under immune selection pressure and optimal control of chemotherapy

Increasing experimental evidence suggests that epigenetic and microenvironmental factors play a key role in cancer progression. In this respect, it is now generally recognized that the immune system can act as an additional selective pressure, which modulates tumor development and leads, through cancer immunoediting, to the selection for resistance to immune effector mechanisms. This may have serious implications for the design of effective anti-cancer protocols. Motivated by these considerations, we present a mathematical model for the dynamics of cancer and immune cells under the effects of chemotherapy and immunity-boosters. Tumor cells are modeled as a population structured by a continuous phenotypic trait, that is related to the level of resistance to receptor-induced cell death triggered by effector lymphocytes. The level of resistance can vary over time due to the effects of epigenetic modifications. In the asymptotic regime of small epimutations, we highlight the ability of the model to reproduce cancer immunoediting. In an optimal control framework, we tackle the problem of designing effective anti-cancer protocols. The results obtained suggest that chemotherapeutic drugs characterized by high cytotoxic effects can be useful for treating tumors of large size. On the other hand, less cytotoxic chemotherapy in combination with immunity-boosters can be effective against tumors of smaller size. Taken together, these results support the development of therapeutic protocols relying on combinations of less cytotoxic agents and immune-boosters to fight cancer in the early stages. © EDP Sciences, 2014