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.

Should I stay or should I go? : Reproductive and dispersal strategies of site-specific liverwort species

The area of intensively managed forests, in which required conditions for several liverwort species are seldom found, has expanded over the forest landscape during the last century. Liverworts are very sensitive to habitat changes, because they demand continuously moist microclimate. Consequently, about third of the forest liverworts have been classified as threatened or near threatened in Finland. The general objective of this thesis is to increase knowledge of the reproductive and dispersal strategies of the substrate-specific forest bryophytes. A further aim was to develop recommendations for conservation measures for species inhabiting unstable and stable habitats in forest landscape. Both population ecological and genetic methods have been applied in the research. Anastrophyllum hellerianum inhabits spatially and temporally limited substrate patches, decaying logs, which can be considered as unstable habitats. The results show that asexual reproduction by gemmae is the dominant mode of reproduction, whereas sexual reproduction is considerably infrequent. Unlike previously assumed, not only spores but also the asexual propagules may contribute to long-distance dispersal. The combination of occasional spore production and practically continuous, massive gemma production facilitates dispersal both on a local scale and over long distances, and it compensates for the great propagule losses that take place preceding successful establishment at suitable sites. However, establishment probability of spores may be restricted because of environmental and biological limitations linked to the low success of sexual reproduction. Long-lasting dry seasons are likely to result in a low success of sexual reproduction and decreased release rate of gemmae from the shoots, and consequent fluctuations in population sizes. In the long term, the substratum limitation is likely to restrict population sizes and cause local extinctions, especially in small-sized remnant populations. Contrastingly, larger forest fragments with more natural disturbance dynamics, to which the species is adapted, are pivotal to species survival. Trichocolea tomentella occupies stable spring and mesic habitats in woodland. The relatively small populations are increasingly fragmented with a high risk for extinction for extrinsic reasons. The results show that T. tomentella mainly invests in population persistence by effective clonal growth via forming independent ramets and in competitive ability, and considerably less in sexuality and dispersal potential. The populations possess relatively high levels of genetic diversity regardless of population size and of degree of isolation. Thus, the small-sized populations inhabiting stable habitats should not be neglected when establishing conservation strategies for the species and when considering the habitat protection of small spring sites. Restricted dispersal capacity, also on a relatively small spatial scale, is likely to prevent successful (re-)colonization in the potential habitat patches of recovering forest landscapes. By contrast, random short-range dispersal of detached vegetative fragments within populations at suitable habitat seems to be frequent. Thus, the restoration actions of spring and streamside habitats close to the populations of T. tomentella may contribute to population expansion. That, in turn, decreases the harmful effects of environmental stochasticity.

The range expansion of the European map butterfly in Finland

Climate change will influence the living conditions of all life on Earth. For some species the change in the environmental conditions that has occurred so far has already increased the risk of extinction, and the extinction risk is predicted to increase for large numbers of species in the future. Some species may have time to adapt to the changing environmental conditions, but the rate and magnitude of the change are too great to allow many species to survive via evolutionary changes. Species responses to climate change have been documented for some decades. Some groups of species, like many insects, respond readily to changes in temperature conditions and have shifted their distributions northwards to new climatically suitable regions. Such range shifts have been well documented especially in temperate zones. In this context, butterflies have been studied more than any other group of species, partly for the reason that their past geographical ranges are well documented, which facilitates species-climate modelling and other analyses. The aim of the modelling studies is to examine to what extent shifts in species distributions can be explained by climatic and other factors. Models can also be used to predict the future distributions of species. In this thesis, I have studied the response to climate change of one species of butterfly within one geographically restricted area. The study species, the European map butterfly (Araschnia levana), has expanded rapidly northwards in Finland during the last two decades. I used statistical and dynamic modelling approaches in combination with field studies to analyse the effects of climate warming and landscape structure on the expansion. I studied possible role of molecular variation in phosphoglucose isomerase (PGI), a glycolytic enzyme affecting flight metabolism and thereby flight performance, in the observed expansion of the map butterfly at two separate expansion fronts in Finland. The expansion rate of the map butterfly was shown to be correlated with the frequency of warmer than average summers during the study period. The result is in line with the greater probability of occurrence of the second generation during warm summers and previous results on this species showing greater mobility of the second than first generation individuals. The results of a field study in this thesis indicated low mobility of the first generation butterflies. Climatic variables alone were not sufficient to explain the observed expansion in Finland. There are also problems in transferring the climate model to new regions from the ones from which data were available to construct the model. The climate model predicted a wider distribution in the south-western part of Finland than what has been observed. Dynamic modelling of the expansion in response to landscape structure suggested that habitat and landscape structure influence the rate of expansion. In southern Finland the landscape structure may have slowed down the expansion rate. The results on PGI suggested that allelic variation in this enzyme may influence flight performance and thereby the rate of expansion. Genetic differences of the populations at the two expansion fronts may explain at least partly the observed differences in the rate of expansion. Individuals with the genotype associated with high flight metabolic rate were most frequent in eastern Finland, where the rate of range expansion has been highest.

Studies of the star-forming structures in the dense interstellar medium: a view by dust extinction

New stars in galaxies form in dense, molecular clouds of the interstellar medium. Measuring how the mass is distributed in these clouds is of crucial importance for the current theories of star formation. This is because several open issues in them, such as the strength of different mechanism regulating star formation and the origin of stellar masses, can be addressed using detailed information on the cloud structure. Unfortunately, quantifying the mass distribution in molecular clouds accurately over a wide spatial and dynamical range is a fundamental problem in the modern astrophysics. This thesis presents studies examining the structure of dense molecular clouds and the distribution of mass in them, with the emphasis on nearby clouds that are sites of low-mass star formation. In particular, this thesis concentrates on investigating the mass distributions using the near infrared dust extinction mapping technique. In this technique, the gas column densities towards molecular clouds are determined by examining radiation from the stars that shine through the clouds. In addition, the thesis examines the feasibility of using a similar technique to derive the masses of molecular clouds in nearby external galaxies. The papers presented in this thesis demonstrate how the near infrared dust extinction mapping technique can be used to extract detailed information on the mass distribution in nearby molecular clouds. Furthermore, such information is used to examine characteristics crucial for the star formation in the clouds. Regarding the use of extinction mapping technique in nearby galaxies, the papers of this thesis show that deriving the masses of molecular clouds using the technique suffers from strong biases. However, it is shown that some structural properties can still be examined with the technique.