Antti Penttinen

An evaluation of the microscopical counting methods of the tape in hirst-burkard pollen and spore trap

Abstract Three different sampling units in current use and different sampling strategies were tested. Randomly placed microscope fields are good in estimating the daily mean concentration, but very big sample size is needed. Traverses across the slide in systematic order are best to estimate the shortterm concentrations and diurnal variation. A formula for the estimation of the error in one transverse traverse is given. Twelve transverse traverses in systematic order is also enough to estimate the daily mean concentration. One or two traverses along the length of the slide give often unreliable estimates because of the irregularities in the transverse variation of the particle concentrations on the slide. For the same reason it is not safe to choose an “effectively collecting area”. Instead the whole width of the tape should be studied.

Statistical Analysis and Modelling of Spatial Point Patterns: Illian/Statistical Analysis and Modelling of Spatial Point Patterns

Preface. List of Examples. 1. Introduction. 1.1 Point process statistics. 1.2 Examples of point process data. 1.2.1 A pattern of amacrine cells. 1.2.2 Gold particles. 1.2.3 A pattern of Western Australian plants. 1.2.4 Waterstriders. 1.2.5 A sample of concrete. 1.3 Historical notes. 1.3.1 Determination of number of trees in a forest. 1.3.2 Number of blood particles in a sample. 1.3.3 Patterns of points in plant communities. 1.3.4 Formulating the power law for the pair correlation function for galaxies. 1.4 Sampling and data collection. 1.4.1 General remarks. 1.4.2 Choosing an appropriate study area. 1.4.3 Data collection. 1.5 Fundamentals of the theory of point processes. 1.6 Stationarity and isotropy. 1.6.1 Model approach and design approach. 1.6.2 Finite and infinite point processes. 1.6.3 Stationarity and isotropy. 1.6.4 Ergodicity. 1.7 Summary characteristics for point processes. 1.7.1 Numerical summary characteristics. 1.7.2 Functional summary characteristics. 1.8 Secondary structures of point processes. 1.8.1 Introduction. 1.8.2 Random sets. 1.8.3 Random fields. 1.8.4 Tessellations. 1.8.5 Neighbour networks or graphs. 1.9 Simulation of point processes. 2. The Homogeneous Poisson point process. 2.1 Introduction. 2.2 The binomial point process. 2.2.1 Introduction. 2.2.2 Basic properties. 2.2.3 The periodic binomial process. 2.2.4 Simulation of the binomial process. 2.3 The homogeneous Poisson point process. 2.3.1 Introduction. 2.3.2 Basic properties. 2.3.3 Characterisations of the homogeneous Poisson process. 2.4 Simulation of a homogeneous Poisson process. 2.5 Model characteristics. 2.5.1 Moments and moment measures. 2.5.2 The Palm distribution of a homogeneous Poisson process. 2.5.3 Summary characteristics of the homogeneous Poisson process. 2.6 Estimating the intensity. 2.7 Testing complete spatial randomness. 2.7.1 Introduction. 2.7.2 Quadrat counts. 2.7.3 Distance methods. 2.7.4 The J-test. 2.7.5 Two index-based tests. 2.7.6 Discrepancy tests. 2.7.7 The L-test. 2.7.8 Other tests and recommendations. 3. Finite point processes. 3.1 Introduction. 3.2 Distributions of numbers of points. 3.2.1 The binomial distribution. 3.2.2 The Poisson distribution. 3.2.3 Compound distributions. 3.2.4 Generalised distributions. 3.3 Intensity functions and their estimation. 3.3.1 Parametric statistics for the intensity function. 3.3.2 Non-parametric estimation of the intensity function. 3.3.3 Estimating the point density distribution function. 3.4 Inhomogeneous Poisson process and finite Cox process. 3.4.1 The inhomogeneous Poisson process. 3.4.2 The finite Cox process. 3.5 Summary characteristics for finite point processes. 3.5.1 Nearest-neighbour distances. 3.5.2 Dilation function. 3.5.3 Graph-theoretic statistics. 3.5.4 Second-order characteristics. 3.6 Finite Gibbs processes. 3.6.1 Introduction. 3.6.2 Gibbs processes with fixed number of points. 3.6.3 Gibbs processes with a random number of points. 3.6.4 Second-order summary characteristics of finite Gibbs processes. 3.6.5 Further discussion. 3.6.6 Statistical inference for finite Gibbs processes. 4. Stationary point processes. 4.1 Basic definitions and notation. 4.2 Summary characteristics for stationary point processes. 4.2.1 Introduction. 4.2.2 Edge-correction methods. 4.2.3 The intensity lambda. 4.2.4 Indices as summary characteristics. 4.2.5 Empty-space statistics and other morphological summaries. 4.2.6 The nearest-neighbour distance distribution function. 4.2.7 The J-function. 4.3 Second-order characteristics. 4.3.1 The three functions: K, L and g. 4.3.2 Theoretical foundations of second-order characteristics. 4.3.3 Estimators of the second-order characteristics. 4.3.4 Interpretation of pair correlation functions. 4.4 Higher-order and topological characteristics. 4.4.1 Introduction. 4.4.2 Third-order characteristics. 4.4.3 Delaunay tessellation characteristics. 4.4.4 The connectivity function. 4.5 Orientation analysis for stationary point processes. 4.5.1 Introduction. 4.5.2 Nearest-neighbour orientation distribution. 4.5.3 Second-order orientation analysis. 4.6 Outliers, gaps and residuals. 4.6.1 Introduction. 4.6.2 Simple outlier detection. 4.6.3 Simple gap detection. 4.6.4 Model-based outliers. 4.6.5 Residuals. 4.7 Replicated patterns. 4.7.1 Introduction. 4.7.2 Aggregation recipes. 4.8 Choosing appropriate observation windows. 4.8.1 General ideas. 4.8.2 Representative windows. 4.9 Multivariate analysis of series of point patterns. 4.10 Summary characteristics for the non-stationary case. 4.10.1 Formal application of stationary characteristics and estimators. 4.10.2 Intensity reweighting. 4.10.3 Local rescaling. 5. Stationary marked point processes. 5.1 Basic definitions and notation. 5.1.1 Introduction. 5.1.2 Marks and their properties. 5.1.3 Marking models. 5.1.4 Stationarity. 5.1.5 First-order characteristics. 5.1.6 Mark-sum measure. 5.1.7 Palm distribution. 5.2 Summary characteristics. 5.2.1 Introduction. 5.2.2 Intensity and mark-sum intensity. 5.2.3 Mean mark, mark d.f. and mark probabilities. 5.2.4 Indices for stationary marked point processes. 5.2.5 Nearest-neighbour distributions. 5.3 Second-order characteristics for marked point processes. 5.3.1 Introduction. 5.3.2 Definitions for qualitative marks. 5.3.3 Definitions for quantitative marks. 5.3.4 Estimation of second-order characteristics. 5.4 Orientation analysis for marked point processes. 5.4.1 Introduction. 5.4.2 Orientation analysis for non-isotropic processes with angular marks. 5.4.3 Orientation analysis for isotropic processes with angular marks. 5.4.4 Orientation analysis with constructed marks. 6. Modelling and simulation of stationary point processes. 6.1 Introduction. 6.2 Operations with point processes. 6.2.1 Thinning. 6.2.2 Clustering. 6.2.3 Superposition. 6.3 Cluster processes. 6.3.1 General cluster processes. 6.3.2 Neyman-Scott processes. 6.4 Stationary Cox processes. 6.4.1 Introduction. 6.4.2 Properties of stationary Cox processes. 6.5 Hard-core point processes. 6.5.1 Introduction. 6.5.2 Matern hard-core processes. 6.5.3 The dead leaves model. 6.5.4 The RSA model. 6.5.5 Random dense packings of hard spheres. 6.6 Stationary Gibbs processes. 6.6.1 Basic ideas and equations. 6.6.2 Simulation of stationary Gibbs processes. 6.6.3 Statistics for stationary Gibbs processes. 6.7 Reconstruction of point patterns. 6.7.1 Reconstructing point patterns without a specified model. 6.7.2 An example: reconstruction of Neyman-Scott processes. 6.7.3 Practical application of the reconstruction algorithm. 6.8 Formulas for marked point process models. 6.8.1 Introduction. 6.8.2 Independent marks. 6.8.3 Random field model. 6.8.4 Intensity-weighted marks. 6.9 Moment formulas for stationary shot-noise fields. 6.10 Space-time point processes. 6.10.1 Introduction. 6.10.2 Space-time Poisson processes. 6.10.3 Second-order statistics for completely stationary event processes. 6.10.4 Two examples of space-time processes. 6.11 Correlations between point processes and other random structures. 6.11.1 Introduction. 6.11.2 Correlations between point processes and random fields. 6.11.3 Correlations between point processes and fibre processes. 7. Fitting and testing point process models. 7.1 Choice of model. 7.2 Parameter estimation. 7.2.1 Maximum likelihood method. 7.2.2 Method of moments. 7.2.3 Trial-and-error estimation. 7.3 Variance estimation by bootstrap. 7.4 Goodness-of-fit tests. 7.4.1 Envelope test. 7.4.2 Deviation test. 7.5 Testing mark hypotheses. 7.5.1 Introduction. 7.5.2 Testing independent marking, test of association. 7.5.3 Testing geostatistical marking. 7.6 Bayesian methods for point pattern analysis. Appendix A Fundamentals of statistics. Appendix B Geometrical characteristics of sets. Appendix C Fundamentals of geostatistics. References. Notation index. Author index. Subject index.

On initial populations of a genetic algorithm for continuous optimization problems

Genetic algorithms are commonly used metaheuristics for global optimization, but there has been very little research done on the generation of their initial population. In this paper, we look for an answer to the question whether the initial population plays a role in the performance of genetic algorithms and if so, how it should be generated. We show with a simple example that initial populations may have an effect on the best objective function value found for several generations. Traditionally, initial populations are generated using pseudo random numbers, but there are many alternative ways. We study the properties of different point generators using four main criteria: the uniform coverage and the genetic diversity of the points as well as the speed and the usability of the generator. We use the point generators to generate initial populations for a genetic algorithm and study what effects the uniform coverage and the genetic diversity have on the convergence and on the final objective function values. For our tests, we have selected one pseudo and one quasi random sequence generator and two spatial point processes: simple sequential inhibition process and nonaligned systematic sampling. In numerical experiments, we solve a set of 52 continuous test functions from 16 different function families, and analyze and discuss the results.

Spatiotemporal Structure of Host‐Pathogen Interactions in a Metapopulation

The ecological and evolutionary dynamics of species are influenced by spatiotemporal variation in population size. Unfortunately, we are usually limited in our ability to investigate the numerical dynamics of natural populations across large spatial scales and over long periods of time. Here we combine mechanistic and statistical approaches to reconstruct continuous‐time infection dynamics of an obligate fungal pathogen on the basis of discrete‐time occurrence data. The pathogen, Podosphaera plantaginis, infects its host plant, Plantago lanceolata, in a metapopulation setting where the presence of the pathogen has been recorded annually for 6 years in ∼4,000 host populations across an area of 50 km × 70 km in Finland. The dynamics are driven by strong seasonality, with a high extinction rate during winter and epidemic expansion in summer for local pathogen populations. We are able to identify with our model the regions in the study area where overwintering has been most successful. These overwintering sites represent foci that initiate local epidemics during the growing season. There is striking heterogeneity at the regional scale in both the overwintering success of the pathogen and the encounter intensity between the host and the pathogen. Such heterogeneity has profound implications for the coevolutionary dynamics of the interaction.

Plant colonization of a bare peat surface: population changes and spatial patterns

. Changes in size and spatial arrangement of plant populations established on an initially bare peat surface were described over a period of 5 yr by following plant individuals on a 1-cm grid in an area of 10 m x 25 m. The spatial pattern of populations and association between species was analyzed statistically. The study site was very slowly colonized by 14 perennial plant species. The early successional stage was dominated by Carex rostrata, with a clumped spatial distribution, and the homogeneously distributed Eriophorum vaginatum and Pinus sylvestris. Both the growth in size of populations and changes in their spatial distribution were interpreted as a result of species dispersal ability, tolerance to severity of the substrate and pattern of reproduction.

Bayesian smoothing in the estimation of the pair potential function of Gibbs point processes

A exible Bayesian method is suggested for the pair potential estimation with a high-dimensional parameter space. The method is based on a Bayesian smoothing technique, commonly applied in statistical image analysis. For the calculation of the posterior mode estimator a new Monte Carlo algorithm is developed. The method is illustrated through examples with both real and simulated data, and its extension into truly nonparametric pair potential estimation is discussed.

Probabilistic small area risk assessment using GIS-based data : a case study on Finnish childhood diabetes

A Bayesian hierarchical spatial model is constructed to describe the regional incidence of insulin dependent diabetes mellitus (IDDM) among the under 15-year-olds in Finland. The model exploits aggregated pixel-wise locations for both the cases and the population at risk. Typically such data arise from combining geographic information systems (GIS) with large databases. The dates of diagnosis and locations of the cases are observed from 1987 to 1996. The population at risk counts are available for every second year during the same period. A hierarchical model is suggested for the pixel wise case counts, including a population model to account for the uncertainty of the population at risk over the years. The model is applied in the construction of disease maps (aggregated 100 km(2) pixels), and spatial posterior predictive distributions are computed to study whether there can be found a statistically exceptional number of cases in a small area of interest.

Cancer risk near a polluted river in Finland

The River Kymijoki in southern Finland is heavily polluted with polychlorinated dibenzo-p-dioxins and dibenzofurans and may pose a health threat to local residents, especially farmers. In this study we investigated cancer risk in people living near the river (< 20.0 km) in 1980. We used a geographic information system, which stores registry data, in 500 m × 500 m grid squares, from the Population Register Centre, Statistics Finland, and Finnish Cancer Registry. From 1981 to 2000, cancer incidence in all people (N = 188,884) and in farmers (n = 11,132) residing in the study area was at the level expected based on national rates. Relative risks for total cancer and 27 cancer subtypes were calculated by distance of individuals to the river in 1980 (reference: 5.0–19.9 km, 1.0–4.9 km, < 1.0 km), adjusting for sex, age, time period, socioeconomic status, and distance of individuals to the sea. The respective relative risks for total cancer were 1.00, 1.09 [95% confidence interval (CI), 1.04–1.13], and 1.04 (95% CI, 0.99–1.09) among all residents, and 1.00, 0.99 (95% CI, 0.85–1.15), and 1.13 (95% CI, 0.97–1.32) among farmers. A statistically significant increase was observed for basal cell carcinoma of the skin (not included in total cancers) in all residents < 5.0 km. Several other common cancers, including cancers of the breast, uterine cervix, gallbladder, and nervous system, showed slightly elevated risk estimates at < 5.0 km from the river. Despite the limitations of exposure assessment, we cannot exclude the possibility that residence near the river may have contributed to a small increase in cancer risk, especially among farmers.

Bayesian Mapping of Lichens Growing on Trees

Suitability of trees as hosts for epiphytic lichens are studied in a forest stand of size 25 ha. Suitability is measured as occupation probabilites which are modelled using hierarchical Bayesian approach. These probabilities are useful for an ecologist. They give smoothed spatial distribution map of suitability for each of the species and can be used in detecting high- and low-probability areas. In addition, suitability is explained by tree-level covariates. Spatial dependence, which is due to unobserved spatially structured covariates, is modelled through an unobserved Markov random field. Markov chain Monte Carlo method has been applied in Bayesian computation. The extensive spatial data consist of the occurrences of eight lichen species and one bryophyte on all of the 1253 potential host trees. In addition, coordinates of the trees and several tree characteristics have been recorded. The data have been analysed for four most abundant species: Lobaria pulmonaria, Nephroma bellum, Nephroma parile and Peltigera praetextata. The tree level parameters, subject to estimation, consist of the occurrence probabilities for each tree and for each lichen species. Model validation is discussed in detail and, in addition to Bayesian validation tools, the autologistic model and case-control design based on logistic regression have been suggested for validation of covariate effects. As a result we present suitability maps for the four lichen species. We observed, that among the observed tree covariates, the diameter at breast height (DBH) correlates with lichen occurrence. ()ur modelling approach has close connections to disease mapping in spatial epidemiology.

Mechanical-Statistical Modeling in Ecology: From Outbreak Detections to Pest Dynamics

Knowledge about large-scale and long-term dynamics of (natural) populations is required to assess the efficiency of control strategies, the potential for long-term persistence, and the adaptability to global changes such as habitat fragmentation and global warming. For most natural populations, such as pest populations, large-scale and long-term surveys cannot be carried out at a high resolution. For instance, for population dynamics characterized by irregular abundance explosions, i.e., outbreaks, it is common to report detected outbreaks rather than measuring the population density at every location and time event. Here, we propose a mechanical-statistical model for analyzing such outbreak occurrence data and making inference about population dynamics. This spatio-temporal model contains the main mechanisms of the dynamics and describes the observation process. This construction enables us to account for the discrepancy between the phenomenon scale and the sampling scale. We propose the Bayesian method to estimate model parameters, pest densities and hidden factors, i.e., variables involved in the dynamics but not observed. The model was specified and used to learn about the dynamics of the European pine sawfly (Neodiprion sertifer Geoffr., an insect causing major defoliation of pines in northern Europe) based on Finnish sawfly data covering the years 1961–1990. In this application, a dynamical Beverton–Holt model including a hidden regime variable was incorporated into the model to deal with large variations in the population densities. Our results gave support to the idea that pine sawfly dynamics should be studied as metapopulations with alternative equilibria. The results confirmed the importance of extreme minimum winter temperatures for the occurrence of European pine sawfly outbreaks. The strong positive connection between the ratio of lake area over total area and outbreaks was quantified for the first time.