3 resultados para mathematical model

em Helda - Digital Repository of University of Helsinki


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XVIII IUFRO World Congress, Ljubljana 1986.

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Flow experience is often defined either as an experience of high concentration and enjoyment or as a situation, where high challenges are matched with high skills. According to core-emotion theories, the experience of any emotion contains two core emotions: valence and arousal. Through an accurate mathematical model, the present study investigated, whether the experience of concentration and enjoyment is related to situations where both challenge and skills are high and in balance. Further, it was investigated what sort of core emotions are related to differing relationships between challenge and skills. Finally, university students’ experiences of their natural study environments were described in terms of core emotions and in terms of relationships between challenge and skills. Participants were 55 university students who participated two weeks research period. Altogether 3367 questionnaire answers were collected with the CASS experience-sampling method, operating in 3G-mobile phones. The relationship between challenge and skills (competence) was defined in an exact way in polar coordinates. An enjoyable and concentrated flow experience was defined as a sum variable of absorption, interest and enthusiasm. Core emotions were calculated with factor analysis from nine emotion variables. As expected, an experience of concentration and enjoyment was, on average, related to the situations where both challenge and skills were high and in balance. This was not, however, the case in every situation. Thus, it should be taken into consideration how flow experience is operationalised in experience sampling studies. When flow experience was defined as a situation of high challenge and high skills, it was often related to high valence and arousal emotions such as excitement or enthusiasm. A happier or a more tranquil enjoyment was related to situations of moderate challenge and high skills. Experiences differed clearly between various natural study environments. At lectures students were often bored or mentally absent, and did not experience challenges. In a small group students were often excited or enthusiastic, and showed optimal balance between challenge and skills. At library students felt satisfied and were engaged in highly challenging work.

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Ecology and evolutionary biology is the study of life on this planet. One of the many methods applied to answering the great diversity of questions regarding the lives and characteristics of individual organisms, is the utilization of mathematical models. Such models are used in a wide variety of ways. Some help us to reason, functioning as aids to, or substitutes for, our own fallible logic, thus making argumentation and thinking clearer. Models which help our reasoning can lead to conceptual clarification; by expressing ideas in algebraic terms, the relationship between different concepts become clearer. Other mathematical models are used to better understand yet more complicated models, or to develop mathematical tools for their analysis. Though helping us to reason and being used as tools in the craftmanship of science, many models do not tell us much about the real biological phenomena we are, at least initially, interested in. The main reason for this is that any mathematical model is a simplification of the real world, reducing the complexity and variety of interactions and idiosynchracies of individual organisms. What such models can tell us, however, both is and has been very valuable throughout the history of ecology and evolution. Minimally, a model simplifying the complex world can tell us that in principle, the patterns produced in a model could also be produced in the real world. We can never know how different a simplified mathematical representation is from the real world, but the similarity models do strive for, gives us confidence that their results could apply. This thesis deals with a variety of different models, used for different purposes. One model deals with how one can measure and analyse invasions; the expanding phase of invasive species. Earlier analyses claims to have shown that such invasions can be a regulated phenomena, that higher invasion speeds at a given point in time will lead to a reduction in speed. Two simple mathematical models show that analysis on this particular measure of invasion speed need not be evidence of regulation. In the context of dispersal evolution, two models acting as proof-of-principle are presented. Parent-offspring conflict emerges when there are different evolutionary optima for adaptive behavior for parents and offspring. We show that the evolution of dispersal distances can entail such a conflict, and that under parental control of dispersal (as, for example, in higher plants) wider dispersal kernels are optimal. We also show that dispersal homeostasis can be optimal; in a setting where dispersal decisions (to leave or stay in a natal patch) are made, strategies that divide their seeds or eggs into fractions that disperse or not, as opposed to randomized for each seed, can prevail. We also present a model of the evolution of bet-hedging strategies; evolutionary adaptations that occur despite their fitness, on average, being lower than a competing strategy. Such strategies can win in the long run because they have a reduced variance in fitness coupled with a reduction in mean fitness, and fitness is of a multiplicative nature across generations, and therefore sensitive to variability. This model is used for conceptual clarification; by developing a population genetical model with uncertain fitness and expressing genotypic variance in fitness as a product between individual level variance and correlations between individuals of a genotype. We arrive at expressions that intuitively reflect two of the main categorizations of bet-hedging strategies; conservative vs diversifying and within- vs between-generation bet hedging. In addition, this model shows that these divisions in fact are false dichotomies.