Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Other Side of This Life : Death, Value, and Social Being in Thomas Pynchon's Fiction

This dissertation analyzes the interrelationship between death, the conditions of (wo)man s social being, and the notion of value as it emerges in the fiction of the American novelist Thomas Pynchon (1937 ). Pynchon s present work includes six novels V. (1963), The Crying of Lot 49 (1966), Gravity s Rainbow (1973), Vineland (1990), Mason & Dixon (1997), Against the Day (2006) and several short stories. Death constitues a central thematic in Pynchon s work, and it emerges through recurrent questions of mortality, suicide, mass destruction, sacrifice, afterlife, entropy, the relationship between the animate and the inanimate, and the limits of representation. In Pynchon, death is never a mere biological given (or event); it is always determined within a certain historical, cultural, and ideological context. Throughout his work, Pynchon questions the strict ontological separation of life and death by showing the relationship between this separation and social power. Conceptual divisions also reflect the relationship between society and its others, and death becomes that through which lines of social demarcation are articulated. Determined as a conceptual and social "other side", death in Pynchon forms a challenge to modern culture, and makes an unexpected return: the dead return to haunt the living, the inanimate and the animate fuse, and technoscientific attempts at overcoming and controlling death result in its re-emergence in mass destruction and ecological damage. The questioning of the ontological line also affects the structuration of Pynchon's prose, where the recurrent narrated and narrative desire to reach the limits of representation is openly associated with death. Textualized, death appears in Pynchon's writing as a sudden rupture within the textual functioning, when the "other side", that is, the bare materiality of the signifier is foregrounded. In this study, Pynchon s cultural criticism and his poetics come together, and I analyze the subversive role of death in his fiction through Jean Baudrillard s genealogy of the modern notion of death from L échange symbolique et la mort (1976). Baudrillard sees an intrinsic bond between the social repression of death in modernity and the emergence of modern political economy, and in his analysis economy and language appear as parallel systems for generating value (exchange value/ sign-value). For Baudrillard, the modern notion of death as negativity in relation to the positivity of life, and the fact that death cannot be given a proper meaning, betray an antagonistic relation between death and the notion of value. As a mode of negativity (that is, non-value), death becomes a moment of rupture in relation to value-based thinking in short, rationalism. Through this rupture emerges a form of thinking Baudrillard labels the symbolic, characterized by ambivalence and the subversion of conceptual opposites.

Assessing university students' prior knowledge

The aim of this dissertation was to explore how different types of prior knowledge influence student achievement and how different assessment methods influence the observed effect of prior knowledge. The project started by creating a model of prior knowledge which was tested in various science disciplines. Study I explored the contribution of different components of prior knowledge on student achievement in two different mathematics courses. The results showed that the procedural knowledge components which require higher-order cognitive skills predicted the final grades best and were also highly related to previous study success. The same pattern regarding the influence of prior knowledge was also seen in Study III which was a longitudinal study of the accumulation of prior knowledge in the context of pharmacy. The study analysed how prior knowledge from previous courses was related to student achievement in the target course. The results implied that students who possessed higher-level prior knowledge, that is, procedural knowledge, from previous courses also obtained higher grades in the more advanced target course. Study IV explored the impact of different types of prior knowledge on students’ readiness to drop out from the course, on the pace of completing the course and on the final grade. The study was conducted in the context of chemistry. The results revealed again that students who performed well in the procedural prior-knowledge tasks were also likely to complete the course in pre-scheduled time and get higher final grades. On the other hand, students whose performance was weak in the procedural prior-knowledge tasks were more likely to drop out or take a longer time to complete the course. Study II explored the issue of prior knowledge from another perspective. Study II aimed to analyse the interrelations between academic self-beliefs, prior knowledge and student achievement in the context of mathematics. The results revealed that prior knowledge was more predictive of student achievement than were other variables included in the study. Self-beliefs were also strongly related to student achievement, but the predictive power of prior knowledge overruled the influence of self-beliefs when they were included in the same model. There was also a strong correlation between academic self-beliefs and prior-knowledge performance. The results of all the four studies were consistent with each other indicating that the model of prior knowledge may be used as a potential tool for prior knowledge assessment. It is useful to make a distinction between different types of prior knowledge in assessment since the type of prior knowledge students possess appears to make a difference. The results implied that there indeed is variation between students’ prior knowledge and academic self-beliefs which influences student achievement. This should be taken into account in instruction.

Opettajan uskomukset opetustyön lähtökohtana : näkökulmia pedagogiseen ajatteluun

The purpose of this research was to examine teacher’s pedagogical thinking based on beliefs. It aimed to investigate and identify beliefs from teachers’ speech when they were reflecting their own teaching. Placement of beliefs in levels of pedagogical thinking was also examined. The second starting point for a study was the Instrumental Enrichment -intervention, which aims to enhance learning potential and cognitive functioning of students. The goal of this research was to investigate how five main principles of the intervention come forward in teachers’ thinking. Specifying research question was: how similar teachers’ beliefs are to the main principles of intervention. The teacher-thinking paradigm provided the framework for this study. The essential concepts of this study are determined exactly in the theoretical framework. Model of pedagogical thinking was important in the examination of teachers’ thinking. Beliefs were approached through the referencing of varied different theories. Feuerstein theory of Structural cognitive modifiability and Mediated learning experience completed the theory of teacher thinking. The research material was gathered in two parts. In the first part two mathematics lessons of three class teachers were videotaped. In second part the teachers were interviewed by using a stimulated recall method. Interviews were recorded and analysed by qualitative content analysis. Teachers’ beliefs were divided in themes and contents of these themes were described. This part of analysis was inductive. Second part was deductive and it was based on theories of pedagogical thinking levels and Instrumental Enrichment -intervention. According to the research results, three subcategories of teachers’ beliefs were found: beliefs about learning, beliefs about teaching and beliefs about students. When the teachers discussed learning, they emphasized the importance of understanding. In teaching related beliefs student-centrality was highlighted. The teachers also brought out some demands for good education. They were: clarity, diversity and planning. Beliefs about students were divided into two groups. The teachers believed that there are learning differences between students and that students have improved over the years. Because most of the beliefs were close to practice and related to concrete classroom situation, they were situated in Action level of pedagogical thinking. Some teaching and learning related beliefs of individual teachers were situated in Object theory level. Metatheory level beliefs were not found. Occurrence of main principles of intervention differed between teachers. They were much more consistent and transparent in the beliefs of one teacher than of the other two teachers. Differences also occurred between principles. For example reciprocity came up in every teacher’s beliefs, but modifiability was only found in the beliefs of one teacher. Results of this research were consistent with other research made in the field. Teachers’ beliefs about teaching were individual. Even though shared themes were found, the teachers emphasized different aspects of their work. Occurrence of beliefs that were in accordance with the intervention were teacher-specific. Inconsistencies were also found within teachers and their individual beliefs.

Becoming a teacher: emerging teacher identity in mathematics teacher education

This research examines three aspects of becoming a teacher, teacher identity formation in mathematics teacher education: the cognitive and affective aspect, the image of an ideal teacher directing the developmental process, and as an on-going process. The formation of emerging teacher identity was approached in a social psychological framework, in which individual development takes place in social interaction with the context through various experiences. Formation of teacher identity is seen as a dynamic, on-going developmental process, in which an individual intentionally aspires after the ideal image of being a teacher by developing his/her own competence as a teacher. The starting-point was that it is possible to examine formation of teacher identity through conceptualisation of observations that the individual and others have about teacher identity in different situations. The research uses the qualitative case study approach to formation of emerging teacher identity, the individual developmental process and the socially constructed image of an ideal mathematics teacher. Two student cases, John and Mary, and the collective case of teacher educators representing socially shared views of becoming and being a mathematics teacher are presented. The development of each student was examined based on three semi-structured interviews supplemented with written products. The data-gathering took place during the 2005 2006 academic year. The collective case about the ideal image provided during the programme was composed of separate case displays of each teacher educator, which were mainly based on semi-structured interviews in spring term 2006. The intentions and aims set for students were of special interest in the interviews with teacher educators. The interview data was analysed following the modified idea of analytic induction. The formation of teacher identity is elaborated through three themes emerging from theoretical considerations and the cases. First, the profile of one s present state as a teacher may be scrutinised through separate affective and cognitive aspects associated with the teaching profession. The differences between individuals arise through dif-ferent emphasis on these aspects. Similarly, the socially constructed image of an ideal teacher may be profiled through a combination of aspects associated with the teaching profession. Second, the ideal image directing the individual developmental process is the level at which individual and social processes meet. Third, formation of teacher identity is about becoming a teacher both in the eyes of the individual self as well as of others in the context. It is a challenge in academic mathematics teacher education to support the various cognitive and affective aspects associated with being a teacher in a way that being a professional and further development could have a coherent starting-point that an individual can internalise.

Yhdessä ajattelu ja osallistuminen : Interventiotutkimus yhteistoiminnallisen oppimisen kehittymisestä kahdessa alakoulun pienryhmässä

Participation and social modes of thinking - An intervention study on the development of collaborative learning in two primary school small groups This study explores the thinking together -intervention programme in three primary school classes. The object of the intervention was to teach pupils to use exploratory talk in small group collaboratory learning. Exploratory talk is a type of talk in which joint reasoning is made explicit. Research has shown that exploratory talk can improve mathematics and science learning, argumentative skills and competence in reasoning tests. The object of this study was to investigate the theory of social modes of thinking which the intervention program is based on. I tried to find out how the thinking together -intervention programme suits the Finnish context. Therefore my study is part of an international research project of interventions that have been implemented for example in Great-Britain and in Mexico. One essential drawback in former research made on thinking together -approach is that the nature of participation has not been studied properly. In this study I also examine how the nature of participation develops in small groups. In addition to that I aim to develope a theoretical framework which includes both the perspectives of the social modes of thinking and the nature of participation. The perspective of this study is sociocultural. The research material consists of video recordings of collaborative learning tasks of two small groups. In groups there were pupils of age groups 9 - 11. I study the nature of participation using both qualitative and quantitative methods. Quantitative methods include for example IR-analysis method and counting of turns at talk and words. I also use qualitative content analysis to analyze both the nature of participation and social modes of thinking. As a result of my study I found out that the interaction of the other group was leadership based and in the other group the interaction was without leadership relations. In both groups the participation was quantitatively more symmetrical in the end of the intervention. In the group in which the interaction was leadership based the participation of the pupils was more symmetrical. Exploratory talk was found more in the group without leadership relations, but in both groups the amount of exploratory talk was increased during the intervention. Leadership based interaction was further divided into interaction of alienating and inclusive leadership according to how symmetrical the participation was in the dialogue. Exploratory talk was found only when the leadership was inclusive or the interaction was without leadership relations. The main result of the study was that the exploratory talk was further divided into four subcategories according to the nature of participation. In open and inclusive exploratory talk all group members participated initiatively and their initiatives were responded by others. In closed and uneven exploratory talk some group members couldn't participate properly. Therefore it cannot be said that exploratory talk guarantees symmetrical participation. The nature of participation must be investigated separately.

Orphan nuclear receptor subfamily NR4A their interplay with other nuclear receptors and functions in osteoblasts

Nurr1, NGFI-B and Nor1 (NR4A2, NR4A1 and NR4A3, respectively) belong to the NR4A subfamily of nuclear receptors. The NR4A receptors are orphan nuclear receptors which means that activating or repressing ligands for these receptors have not been found. NR4A expression is rapidly induced in response to various stimuli including growth factors and the parathyroid hormone (PTH). The studies concerning the NR4A receptors in the central nervous system have demonstrated that they have a major role in the development and function of the dopaminergic neurons of the midbrain and in regulating hypothalamus-pituitary-adrenal-axis. However, the peripheral functions of the NR4A family are largely unknown. Cultured mouse primary osteoblasts, a preosteoblastic cell line and several osteoblastic cell lines were used to investigate the role of NR4A receptors in osteoblasts. NR4A receptors were shown to directly bind to and activate the promoter of the osteopontin gene (OPN) in osteoblastic cells, thus regulating its expression. OPN is a major bone matrix protein expressed throughout the differentiation of preosteoblastic cells into osteoblasts. The activation of the OPN promoter was shown to be dependent on the activation function-1 located in the N-terminal part of Nurr1 and to occur in both monomeric and RXR heterodimeric forms of NR4A receptors. Furthermore, PTH was shown to upregulate OPN expression through the NR4A family. It was also demonstrated that the fibroblast growth factor-8b (FGF-8b) induces the expression of NR4A receptors in osteoblasts as immediate early genes. This induction involved phosphatidylinositol-3 kinase, protein kinase C, and mitogen activated protein kinase, which are all major pathways of FGF signalling. Nurr1 and NGFI-B were shown to induce the proliferation of preosteoblastic cells and to reduce their apoptosis. FGF-8b was shown to stimulate the proliferation of osteoblastic cells through the NR4A receptors. These results suggest that NR4A receptors have a role both in the differentiation of osteoblasts and in the proliferation and apoptosis of preosteoblast. The NR4A receptors were found to bind to the same response element on OPN as the members of the NR3B family of orphan receptors do. Mutual repression was observed between the NR4A receptors and the NR3B receptors. This repression was shown to be dependent on the DNA-binding domains of both receptor families, but to result neither from the competition of DNA binding nor from the competition for coactivators. As the repression was dependent on the relative expression levels of the NR4As and NR3Bs, it seems likely that the ratio of the receptors mediates their activity on their response elements. Rapid induction of the NR4As in response to various stimuli and differential expression of the NR3Bs can effectively control the gene activation by the NR4A receptors. NR4A receptors can bind DNA as monomers, and Nurr1 and NGFI-B can form permissive heterodimers with the retinoid X receptor (RXR). Permissive heterodimers can be activated with RXR agonists, unlike non-permissive heterodimers, which are formed by RXR and retinoic acid receptor or thyroid hormone receptor (RAR and TR, respectively). Non-permissive heterodimers can only be activated by the agonists of the heterodimerizing partner. The mechanisms behind differential response to RXR agonists have remained unresolved. As there are no activating or repressing ligands for the NR4A receptors, it would be important to find out, how they are regulated. Permissiviness of Nurr1/RXR heterodimers was linked to the N-terminal part of Nurr1 ligand-binding domain. This region has previously been shown to mediate the interaction between NRs and corepressors. Non-permissive RAR and TR, permissive Nurr1 and NGFI-B, and RXR were overexpressed with corepressors silencing mediator for retinoic acid and thyroid hormone receptors (SMRT), and with nuclear receptor corepressor in several cell lines. Nurr1 and NGFI-B were found to be repressed by SMRT. The interaction of RXR heterodimers with corepressors was weak in permissive heterodimers and much stronger in non-permissive heterodimers. Non-permissive heterodimers also released corepressors only in response to the agonist of the heterodimeric partner of RXR. In the permissive Nurr1/RXR heterodimer, however, SMRT was released following the treatment with RXR agonists. Corepressor release in response to ligands was found to differentiate permissive heterodimers from non-permissive ones. Corepressors were thus connected to the regulation of NR4A functions. In summary, the studies presented here linked the NR4A family of orphan nuclear receptors to the regulation of osteoblasts. Nurr1 and NGFI-B were found to control the proliferation and apoptosis of preosteoblasts. The studies also demonstrated that cross-talk with the NR3B receptors controls the activity of these orphan receptors. The results clarified the mechanism of permissiviness of RXR-heterodimers. New information was obtained on the regulation and functions of NR4A receptors, for which the ligands are unknown.

Statistical analysis of the associations of hereditary factors with the risk of Type 1 diabetes and Diabetic Nephropathy based on the familial data collected through ascertaiment from population-based registers

In genetic epidemiology, population-based disease registries are commonly used to collect genotype or other risk factor information concerning affected subjects and their relatives. This work presents two new approaches for the statistical inference of ascertained data: a conditional and full likelihood approaches for the disease with variable age at onset phenotype using familial data obtained from population-based registry of incident cases. The aim is to obtain statistically reliable estimates of the general population parameters. The statistical analysis of familial data with variable age at onset becomes more complicated when some of the study subjects are non-susceptible, that is to say these subjects never get the disease. A statistical model for a variable age at onset with long-term survivors is proposed for studies of familial aggregation, using latent variable approach, as well as for prospective studies of genetic association studies with candidate genes. In addition, we explore the possibility of a genetic explanation of the observed increase in the incidence of Type 1 diabetes (T1D) in Finland in recent decades and the hypothesis of non-Mendelian transmission of T1D associated genes. Both classical and Bayesian statistical inference were used in the modelling and estimation. Despite the fact that this work contains five studies with different statistical models, they all concern data obtained from nationwide registries of T1D and genetics of T1D. In the analyses of T1D data, non-Mendelian transmission of T1D susceptibility alleles was not observed. In addition, non-Mendelian transmission of T1D susceptibility genes did not make a plausible explanation for the increase in T1D incidence in Finland. Instead, the Human Leucocyte Antigen associations with T1D were confirmed in the population-based analysis, which combines T1D registry information, reference sample of healthy subjects and birth cohort information of the Finnish population. Finally, a substantial familial variation in the susceptibility of T1D nephropathy was observed. The presented studies show the benefits of sophisticated statistical modelling to explore risk factors for complex diseases.

Degradation of lignin and other 14C-labelled compounds in compost and soil with an emphasis on white-rot fungi

Puu, ruohokasvit ja näistä tehdyt tuotteet kuten mekaanisesta massasta valmistettu sanomalehtipaperi sisältävät ligniiniä, joka hajoaa yleensä hyvin hitaasti luonnossa. Valkolahosienet hajottavat ligniiniä tehokkaimmin, ja koska niiden tuottamat entsyymit hajottavat myös muita vaikeasti hajoavia yhdisteitä, voidaan valkolahosienten avulla mahdollisesti puhdistaa saastuneita maita. Tässä työssä haluttiin selvittää, säilyttävätkö valkolahosienet (Abortiporus biennis, Bjerkandera adusta, Dichomitus squalens, Phanerochaete chrysosporium, Phanerochaete sordida, Phlebia radiata, Pleurotus ostreatus, Trametes hirsuta ja Trametes versicolor) aktiivisuutensa ja kasvavatko ne maassa. Aktiivisuutta mitattiin seuraamalla sienten synteettisen ligniinin (14C-DHP) hajotuskykyä. T. versicolor (silkkivyökääpä) osoittautui tehokkaimmaksi ligniinin hajottajaksi ja sen pentakloorifenolin (PCP) hajotuskykyä tutkittiin erillisessä kokeessa. Entiset tai pitkään käytössä olleet saha-alueet ovat yhä saastuneet puun käsittelyaineista peräisin olevilla kloorifenoleilla. Biohajoavien muovien kehitystyö sekä kompostoinnin yleistyminen jätteiden käsittelymenetelmänä ovat luoneet tarpeen materiaalien biohajoavuuden määrittämiseen. Euroopan standardisoimisjärjestön (CEN) kontrolloidussa kompostitestissä biohajoavuus määritetään materiaalin hajoamisen aikana muodostuvan hiilidioksidin perusteella. Hiilidioksidin tuotto mitataan sekä näytettä sisältävästä kompostista että kompostista ilman näytettä, ja tällöin oletetaan, että kompostin orgaaninen aines molemmissa komposteissa (tausta) tuottaa yhtä paljon hiilidioksidia. Testin puutteeksi saattaa osoittautua kompostissa tai maassa esiintyvä "priming effect". Tällä tarkoitetaan materiaalin lisäämisen jälkeen esiintyvää epänormaalin suurita tai pientä hiilidioksidin muodostusta, minkä seurauksena testin tulosksena saatava biohajoavuus on virheellinen. Ligniinin hajotessa muodostuu enemmän humusta kuin hiilidioksidia, koska ligniini on humuksen tärkein lähtöaine. Näin ollen ligniiniä sisältävät paperituotteet saattavat testin mukaan vaikuttaa biologisesti hajoamattomilta. Valkolahosienet hajottivat 4-23% ligniinistä hiilidioksidiksi ja T. versicolor 29% PCP:sta. Kompostissa ligniini hajosi hiilidioksidiksi 58°C:ssa huomattavasti vähemmän (8%) kuin lämpötiloissa 35°C ja 50°C (23-24%). Kompostin todennäköisesti tärkeimpien ligniinin hajottajien, termofiilisten sienten, tyypillinen optimilämpötila on 45°C, eivätkä ne ole enää aktiivisia 58°C:ssa. Sekä maassa että kompostissa ligniini sitoutui kuitenkin suurimmaksi osaksi humukseen. Valkolahosienet hajottivat sekä humukseen sitoutunutta ligniiniä että PCP:ia, mutta kompostin sekapopulaatio ei tähän pystynyt, ja ligniiniä sitoutui humukseen yhä enemmän kompostoinnin aikana. T. versicolor hajotti PCP:ia tehokkaasti, eikä se tuottanut myrkyllisiä kloorianisoleja, joita jotkut valkolahosienet saattavat muodostaa kloorifenoleista. Priming effect ilmiötä tutkittiin eri ikäisissä ja kypsyydeltään erilaisissa komposteissa. Kompostit erosvat toisistaan myös hajoamattoman jätteen määrän ja mikrobipopulaation suhteen. Negatiivinen priming effect havaittiin kaikissa epästabiileissa komposteissa (ikä enintään 6 kk), ja sen lisäksi yhdessä näistä komposteista positiivinen priming effect kokeen lopussa. Stabiileissa komposteissa (ikä vähintään 6 kk) ilmiötä ei sen sijaan havaittu. Epästabiileissa komposteissa biohajoavuudelle saadut tulokset eivät siis ole luotettavia. Työn tulosten perusteella valkolahosienet, ja erityisesti T. versicolor, ovat lupaavia saastuneen maan puhdistukseen, joskin sienirihmaston mahdollisuudet säilyä aktiivisena maan alkuperäisen mikrobipopulaation kanssa täytyy vielä selvittää. Kompostin sekapopulaatio, joka ei sisällä valkolahosieniä, hajotti ligniiniä yllättävän tehokkaasti termofiilisille sienille sopivissa lämpötiloissa, vaikka ligniini sitoutuikin pääasiallisesti humukseen. Kompostin kypsyys osoittautui tärkeäksi tekijäksi kontrolloidun kompostitestin onnistumisen kannalta. Priming effect ilmiön välttämiseksi on varmistettava, että testissä käytetty komposti on riittävän kypsä. Kompostien mikrobipopulaation koostumusta kompostoinnin eri vaiheissa tulisi tarkemmin selvittää, koska stabiilien ja epästabiilien kompostien ero aiheutui todennäköisesti populaatioiden rakenteessa vallitsevista eroista. Näin myös priming effect ilmiön syyt voitaisiin selittää paremmin.

Individuals on the Move : Body Condition Dependent Dispersal and Quasi-Local Competition in Metapopulations

Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.