Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

Asymptotic behaviour of point processes with Markov-dependent intervals

This splitting techniques for MARKOV chains developed by NUMMELIN (1978a) and ATHREYA and NEY (1978b) are used to derive an imbedded renewal process in WOLD's point process with MARKOV-correlated intervals. This leads to a simple proof of renewal theorems for such processes. In particular, a key renewal theorem is proved, from which analogues to both BLACKWELL's and BREIMAN's forms of the renewal theorem can be deduced.

Living on the edge : Population genetics of Finno-Ugric-speaking humans in North Eurasia

The major aim of this thesis was to examine the origins and distribution of uniparental and autosomal genetic variation among the Finno-Ugric-speaking human populations living in Boreal and Arctic regions of North Eurasia. In more detail, I aimed to disentangle the underlying molecular and population genetic factors which have produced the patterns of uniparental and autosomal genetic diversity in these populations. Among Finno-Ugrics the genetic amalgamation and clinal distribution of West and East Eurasian gene pools were observed within uniparental markers. This admixture indicates that North Eurasia was colonized through Central Asia/ South Siberia by human groups already carrying both West and East Eurasian lineages. The complex combination of founder effects, gene flow and genetic drift underlying the genetic diversity of the Finno-Ugric- speaking populations were emphasized by low haplotype diversity within and among uniparental and biparental markers. A high prevalence of lactase persistence allele among the North Eurasian Finno- Ugric agriculturalist populations was also shown indicating a local adaptation to subsistence change with lactose rich diet. Moreover, the haplotype background of lactase persistence allele among the Finno- Ugric-speakers strongly suggested that the lactase persistence T-13910 mutation was introduced independently more than once to the North Eurasian gene pool. A significant difference in genetic diversity, haplotype structure and LD distribution within the cytochrome P450 CYP2C and CYP2D regions revealed the unique gene pool of the Finno-Ugric Saami created mainly by population genetic processes compared to other Europeans and sub-Saharan Mandenka population. From all studied populations the Saami showed also significantly the highest allele frequency of a CYP2C19 gene mutation causing variable drug reactions. The diversity patterns observed within CYP2C and CYP2D regions emphasize the strong effect of demographic history shaping genetic diversity and LD especially among such small and constant size populations as the Finno-Ugric-speaking Saami. Moreover, the increased LD in Saami due to genetic drift and/or admixture was shown to offer an advantage for further attempts to identify alleles associated to common complex pharmacogenetic traits.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

Plant secondary compounds and soil microbial processes in carbon and nitrogen cycling in relation to tree species

The aim of this study was to explore soil microbial activities related to C and N cycling and the occurrence and concentrations of two important groups of plant secondary compounds, terpenes and phenolic compounds, under silver birch (Betula pendula Roth), Norway spruce (Picea abies (L.) Karst) and Scots pine (Pinus sylvestris L.) as well as to study the effects of volatile monoterpenes and tannins on soil microbial activities. The study site, located in Kivalo, northern Finland, included ca. 70-year-old adjacent stands dominated by silver birch, Norway spruce and Scots pine. Originally the soil was very probably similar in all three stands. All forest floor layers (litter (L), fermentation layer (F) and humified layer (H)) under birch and spruce showed higher rates of CO2 production, greater net mineralisation of nitrogen and higher amounts of carbon and nitrogen in microbial biomass than did the forest floor layers under pine. Concentrations of mono-, sesqui-, di- and triterpenes were higher under both conifers than under birch, while the concentration of total water-soluble phenolic compounds as well as the concentration of condensed tannins tended to be higher or at least as high under spruce as under birch or pine. In general, differences between tree species in soil microbial activities and in concentrations of secondary compounds were smaller in the H layer than in the upper layers. The rate of CO2 production and the amount of carbon in the microbial biomass correlated highly positively with the concentration of total water-soluble phenolic compounds and positively with the concentration of condensed tannins. Exposure of soil to volatile monoterpenes and tannins extracted and fractionated from spruce and pine needles affected carbon and nitrogen transformations in soil, but the effects were dependent on the compound and its molecular structure. Monoterpenes decreased net mineralisation of nitrogen and probably had a toxic effect on part of the microbial population in soil, while another part of the microbes seemed to be able to use monoterpenes as a carbon source. With tannins, low-molecular-weight compounds (also compounds other than tannins) increased soil CO2 production and nitrogen immobilisation by soil microbes while the higher-molecular-weight condensed tannins had inhibitory effects. In conclusion, plant secondary compounds may have a great potential in regulation of C and N transformations in forest soils, but the real magnitude of their significance in soil processes is impossible to estimate.

Context-dependent mate choice in the sand goby, Pomatoschistus minutus

The results presented in this thesis show that all females of a given population do not necessarily choose similar mating partners. Specifically, partner preferences of a fish, the sand goby (Pomatoschistus minutus), varied among individual females and depended on the social context at the time of choice. I also show that females assess multiple mate choice cues simultaneously; partner preferences were based more strongly on an interaction effect between different choice cues than on any individual cue. Furthermore, I found that preferred matings involved fitness benefits in the form of increased offspring success, but these benefits were not significantly affected by mate compatibility. Hence, mate choice for partner compatibility does not appear to be an important determinant of the observed variation in female mate preferences in this species. The context-dependency of female mating preferences revealed is relevant to how genetic variation in sexually selected traits might be maintained: as the mating success of a certain male type varies according to the choice context, directional sexual selection on male traits is shown to be less intense than generally thought making for a slower loss of genetic variation in these traits. Mating preferences of sand gobies were assessed by giving females a binary choice between males that differed in body size and/or other focus traits. These association preferences were found to be sexually motivated, repeatable and to correspond to actual mating decisions.

Dispersal and related life history traits in the Glanville fritillary butterfly

Most studies of life history evolution are based on the assumption that species exist at equilibrium and spatially distinct separated populations. In reality, this is rarely the case, as populations are often spatially structured with ephemeral local populations. Therefore, the characteristics of metapopulations should be considered while studying factors affecting life history evolution. Theoretical studies have examined spatial processes shaping the evolution of life history traits to some extent, but there is little empirical data and evidence to investigate model predictions. In my thesis I have tried to bridge the gap between theoretical and empirical studies by using the well-known Glanville fritillary (Melitaea cinxia) metapopulation as a model system. The long-term persistence of classic metapopulations requires sufficient dispersal to establish new local populations to compensate for local extinctions. Previous studies on the Glanville fritillary have shown that females establishing new populations are not a random sample from the metapopulation, but they are in fact more dispersive than females in old populations. Many other life-history traits, such as body size, fecundity and lifespan, may be related to dispersal rate. Therefore, I examined a range of correlated traits for their evolutionary and ecological consequences. I was particularly interested in how the traits vary under natural environmental conditions, hence all studies were conducted in a large (32 x 26 m) outdoor population cage built upon a natural habitat patch. Individuals for the experiments were sampled from newly-established and old populations within a large metapopulation. Results show that females originating from newly-established populations had higher within-habitat patch mobility than females from old populations. I showed that dispersal rate is heritable and that flight activity is related to variation in a gene encoding the glycolytic enzyme phosphoglucose isomerase. Both among-individual and among-population variation in dispersal are correlated with the reproductive performance of females, though I found no evidence for a trade-off between dispersal and fecundity in terms of lifetime egg production or clutch size. Instead, the results suggest that highly dispersive females from newly-established populations have a shorter lifespan than females from old populations, and that dispersive females may pay a cost in terms of reduced lifetime reproductive success due to increased time spent outside habitat patches. In summary, the results of this thesis show that genotype-dependent dispersal rate correlates with other life history traits in the Glanville fritillary, and that the rapid turnover of local populations (extinctions and re-colonisations) is likely to be the mechanism that maintains phenotypic variation in many life history traits at the metapopulation level.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Reproduction and population structure in European aspen

The European aspen (Populus tremula) is a keystone species for biodiversity in boreal forests. However, the future of aspen may be threatened, because large aspens have mostly been removed from managed forests, whereas regeneration and the long-term persistence of mature trees are subjects of concern in protected areas. Aspen is a pioneer tree, and it can reproduce both sexually by seed and asexually by root suckers. Through asexual reproduction aspen forms clones, groups of genetically identical trees (ramets). In my thesis, I have studied the structure of aspen populations in terms of number, size, clonal and demographic properties. Additionally, I have investigated the emergence and survival of seedlings as well as the seed quantity and quality in crosses between the European and hybrid aspen. To study the regeneration and population structure, mature aspens were recorded in old-growth and managed forests in eastern Finland based on a large-scale inventory (11 400 ha). In addition, small aspen trees were surveyed on sample plots. Clonal structure was investigated both by morphological characters and by DNA-based markers (microsatellites). Seedling emergence and survival was studied with two sowing experiments. With crosses between European and hybrid aspens we wanted to study whether elevated temperatures due to climate change would benefit the different crosses of European and hybrid aspen unequally and thus affect the gene flow between the two species. The average volumes of mature aspen were 5.3 m3/ha in continuous old-growth, and 0.8 m3/ha in managed forests. Results indicate also that large aspen trees in managed forests are a legacy of the past less intensively managed forest landscapes. Long-term persistence of aspen in protected areas can only be secured by restoration measures creating sufficiently large gaps for regeneration. More emphasis should be given to sparing aspens in thinnings and to retaining of mature aspens in regeneration cutting in managed forests. Aspen was found to be spatially aggregated in the landscape. This could be explained by site type, disturbance history and / or limitations in seed dispersal. Clonal structure does not explain the spatial aggregation, since average size of the clones was only 2.3 ramets, and most clones (70 %) consisted of just one ramet. The small size of the clones suggests that most of them are relatively young. Therefore, sexual reproduction may be more common than has previously been thought. Seedling emergence was most successful in mineral soil especially, when the site had been burned. Only few seedlings occurred on humus. Survival of the seedlings was low, and strongly dependent on moisture, but also on seedbed conditions. The seeds were found to maintain their germinability longer than has earlier been thought to be possible. Interspecific crosses produced more seeds with higher quality than intraspecific crosses. When temperature was elevated, germination of hybrid aspen seeds increased more than seeds from P. tremula x P. tremula crosses. These results suggest that hybrid aspen may have a significant genetic impact on the European aspen, and this effect may become strengthened by climate warming.

Cyclosporine population pharmacokinetics in pediatric renal transplant recipients

Cyclosporine is an immunosuppressant drug with a narrow therapeutic index and large variability in pharmacokinetics. To improve cyclosporine dose individualization in children, we used population pharmacokinetic modeling to study the effects of developmental, clinical, and genetic factors on cyclosporine pharmacokinetics in altogether 176 subjects (age range: 0.36–20.2 years) before and up to 16 years after renal transplantation. Pre-transplantation test doses of cyclosporine were given intravenously (3 mg/kg) and orally (10 mg/kg), on separate occasions, followed by blood sampling for 24 hours (n=175). After transplantation, in a total of 137 patients, cyclosporine concentration was quantified at trough, two hours post-dose, or with dose-interval curves. One-hundred-four of the studied patients were genotyped for 17 putatively functionally significant sequence variations in the ABCB1, SLCO1B1, ABCC2, CYP3A4, CYP3A5, and NR1I2 genes. Pharmacokinetic modeling was performed with the nonlinear mixed effects modeling computer program, NONMEM. A 3-compartment population pharmacokinetic model with first order absorption without lag-time was used to describe the data. The most important covariate affecting systemic clearance and distribution volume was allometrically scaled body weight i.e. body weight**3/4 for clearance and absolute body weight for volume of distribution. The clearance adjusted by absolute body weight declined with age and pre-pubertal children (< 8 years) had an approximately 25% higher clearance/body weight (L/h/kg) than did older children. Adjustment of clearance for allometric body weight removed its relationship to age after the first year of life. This finding is consistent with a gradual reduction in relative liver size towards adult values, and a relatively constant CYP3A content in the liver from about 6–12 months of age to adulthood. The other significant covariates affecting cyclosporine clearance and volume of distribution were hematocrit, plasma cholesterol, and serum creatinine, explaining up to 20%–30% of inter-individual differences before transplantation. After transplantation, their predictive role was smaller, as the variations in hematocrit, plasma cholesterol, and serum creatinine were also smaller. Before transplantation, no clinical or demographic covariates were found to affect oral bioavailability, and no systematic age-related changes in oral bioavailability were observed. After transplantation, older children receiving cyclosporine twice daily as the gelatine capsule microemulsion formulation had an about 1.25–1.3 times higher bioavailability than did the younger children receiving the liquid microemulsion formulation thrice daily. Moreover, cyclosporine oral bioavailability increased over 1.5-fold in the first month after transplantation, returning thereafter gradually to its initial value in 1–1.5 years. The largest cyclosporine doses were administered in the first 3–6 months after transplantation, and thereafter the single doses of cyclosporine were often smaller than 3 mg/kg. Thus, the results suggest that cyclosporine displays dose-dependent, saturable pre-systemic metabolism even at low single doses, whereas complete saturation of CYP3A4 and MDR1 (P-glycoprotein) renders cyclosporine pharmacokinetics dose-linear at higher doses. No significant associations were found between genetic polymorphisms and cyclosporine pharmacokinetics before transplantation in the whole population for which genetic data was available (n=104). However, in children older than eight years (n=22), heterozygous and homozygous carriers of the ABCB1 c.2677T or c.1236T alleles had an about 1.3 times or 1.6 times higher oral bioavailability, respectively, than did non-carriers. After transplantation, none of the ABCB1 SNPs or any other SNPs were found to be associated with cyclosporine clearance or oral bioavailability in the whole population, in the patients older than eight years, or in the patients younger than eight years. In the whole population, in those patients carrying the NR1I2 g.-25385C–g.-24381A–g.-205_-200GAGAAG–g.7635G–g.8055C haplotype, however, the bioavailability of cyclosporine was about one tenth lower, per allele, than in non-carriers. This effect was significant also in a subgroup of patients older than eight years. Furthermore, in patients carrying the NR1I2 g.-25385C–g.-24381A–g.-205_-200GAGAAG–g.7635G–g.8055T haplotype, the bioavailability was almost one fifth higher, per allele, than in non-carriers. It may be possible to improve individualization of cyclosporine dosing in children by accounting for the effects of developmental factors (body weight, liver size), time after transplantation, and cyclosporine dosing frequency/formulation. Further studies are required on the predictive value of genotyping for individualization of cyclosporine dosing in children.

Critical age-dependent branching Markov processes and their scaling limits

This paper studies:(i)the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction;and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

Supercritical age-dependent branching Markov processes and their scaling limits

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time t converges as t -> infinity to a deterministic product measure.

On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.