Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

This article discussed about a dynamic analysis of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously

Doctor of Philosophy

dissertationThis dissertation investigates the competitive environment of craft based specialist organizations. These are often characterized as entrepreneurial, craft based firms that leverage a collective identity of authenticity (and include, but are not restricted to: microbreweries and microdistilleries, artisan cheese producers, custom snowboard, surfboard and bicycle manufacturers, farm to table restaurants, and organic food producers). In this context, I investigate how these entrepreneurial firms leverage reputation, identity, and legitimacy to compete with much larger organizations, despite their inability to garner competitive advantages based on scope and scale economies. The findings are consistent with the notion that craft based organizations operate much differently than mainstream markets

Generalizations and Models in Ecology : Lawlikeness, Invariance, Stability, and Robustness

The question at issue in this dissertation is the epistemic role played by ecological generalizations and models. I investigate and analyze such properties of generalizations as lawlikeness, invariance, and stability, and I ask which of these properties are relevant in the context of scientific explanations. I will claim that there are generalizable and reliable causal explanations in ecology by generalizations, which are invariant and stable. An invariant generalization continues to hold or be valid under a special change called an intervention that changes the value of its variables. Whether a generalization remains invariant during its interventions is the criterion that determines whether it is explanatory. A generalization can be invariant and explanatory regardless of its lawlike status. Stability deals with a generality that has to do with holding of a generalization in possible background conditions. The more stable a generalization, the less dependent it is on background conditions to remain true. Although it is invariance rather than stability of generalizations that furnishes us with explanatory generalizations, there is an important function that stability has in this context of explanations, namely, stability furnishes us with extrapolability and reliability of scientific explanations. I also discuss non-empirical investigations of models that I call robustness and sensitivity analyses. I call sensitivity analyses investigations in which one model is studied with regard to its stability conditions by making changes and variations to the values of the model s parameters. As a general definition of robustness analyses I propose investigations of variations in modeling assumptions of different models of the same phenomenon in which the focus is on whether they produce similar or convergent results or not. Robustness and sensitivity analyses are powerful tools for studying the conditions and assumptions where models break down and they are especially powerful in pointing out reasons as to why they do this. They show which conditions or assumptions the results of models depend on. Key words: ecology, generalizations, invariance, lawlikeness, philosophy of science, robustness, explanation, models, stabilityEkologiset yleistykset ja mallit tieteellisissä selityksissä Viime aikoina ekologit ovat kysyneet, onko ekologisia lakeja olemassa. Keskeinen motivaatio tälle kysymykselle liittyy lakien rooliin tieteissä. Traditionaalisen (filosofisen) käsityksen mukaan tieteelliset lait ovat välttämättömiä tieteellisille selityksille. Ilmiöt selitetään osoittamalla, miten jotkin lait kattavat ko. ilmiöt erikoistapauksinaan. Väitöskirjassani tutkin ekologisten yleistysten ja mallien tiedollisia rooleja. Keskityn yleistyksien ominaisuuksiin lainomaisuus, invarianssi ja stabiilius, ja kysyn, mitkä näistä ominaisuuksista ovat relevantteja tieteellisten selityksien kannalta. Väitän että on olemassa yleistettäviä ja luotettavia kausaalisia selityksiä ekologisilla yleistyksillä, jotka ovat invariantteja ja stabiileja. Invariantti yleistys kuvaa, miten jotkin yleistyksen variaabeleiden arvot muuttuisivat, jos joitakin muita sen variaabeleiden arvoja manipuloitaisiin tai muutettaisiin tiettyjen ehtojen alaisena. Yleistys voi olla invariantti ja selityksellinen riippumatta yleistyksen lainomaisuuden statuksesta, ts. siitä kuvaako yleistys lain vai ei. Yleistysten stabiilius liittyy taas yleistyksien pätemiseen taustaolosuhteiden muuttuessa. Mitä stabiilimpi yleistys (tai säännönmukaisuus) on, sitä vähemmän riippuvainen se on taustaolosuhteista. Vaikka invarianssi tarjoaa meille selityksellisiä yleistyksiä, stabiiliudelle on toinen rooli: se tarjoaa tieteellisten selityksien yleistettävyyttä ja luotettavuutta. Ekologiset yleistykset kykenevät siis tarjoamaan meille jotakin muuta kuin vain tapaustutkimuksia . Ekologia on myös selityksellinen tiede riippumatta siitä, onko ekologisia lakeja olemassa vai ei. Tutkin myös tieteellisten mallien robustius- ja sensitiivisyysanalyyseja. Kutsun sensitiivisyysanalyyseiksi tutkimuksia, jossa mallia ja sen pätemistä eri taustaolosuhteissa tutkitaan muuntelemalla mallin parametri(e)n arvoja. Robustiusanalyysit ovat tutkimuksia siitä, tuottavatko saman ilmiön eri mallit, jotka sisältävät erilaisia mallinnusoletuksia, samanlaisia tuloksia vai eivät. Robustius- ja sensitiivisyysanalyysit ovat ei-empiirisiä keinoja tutkia, minkä olosuhteiden tai oletuksien alaisena mallit tuottavat joitakin tuloksia. Tässä mielessä ne voivat kertoa, mistä olosuhteista tai oletuksista mallien tulokset ovat riippuvaisia. Jani Raerinteen väitöskirja Generalizations and Models in Ecology: Lawlikeness, Invariance, Stability, and Robustness julkaistaan sarjassa Filosofisia tutkimuksia Helsingin yliopistosta. Väitöskirja kuuluu ekologian tieteenfilosofian alaan

Dynamic Behavior of a Commensalism Model with Nonmonotonic Functional Response and Density-Dependent Birth Rates

In this paper, we propose and analyze a commensalism model with nonmonotonic functional response and density-dependent birth rates. The model can have at most four nonnegative equilibria. By applying the differential inequality theory, we show that each equilibrium can be globally attractive under suitable conditions. However, commensalism can be established only when resources for both species are large enough