Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

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.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Estimation of cosmological parameters using adaptive importance sampling

We present a Bayesian sampling algorithm called adaptive importance sampling or population Monte Carlo (PMC), whose computational workload is easily parallelizable and thus has the potential to considerably reduce the wall-clock time required for sampling, along with providing other benefits. To assess the performance of the approach for cosmological problems, we use simulated and actual data consisting of CMB anisotropies, supernovae of type Ia, and weak cosmological lensing, and provide a comparison of results to those obtained using state-of-the-art Markov chain Monte Carlo (MCMC). For both types of data sets, we find comparable parameter estimates for PMC and MCMC, with the advantage of a significantly lower wall-clock time for PMC. In the case of WMAP5 data, for example, the wall-clock time scale reduces from days for MCMC to hours using PMC on a cluster of processors. Other benefits of the PMC approach, along with potential difficulties in using the approach, are analyzed and discussed.

Bayesian model comparison in cosmology with Population Monte Carlo

We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour of each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zel'dovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0.

A novel method for the age estimation of Saddletail snapper (Lutjanus malabaricus) using Fourier Transform-near infrared (FT-NIR) spectroscopy

Near infrared (NIR) spectroscopy was investigated as a potential rapid method of estimating fish age from whole otoliths of Saddletail snapper (Lutjanus malabaricus). Whole otoliths from 209 Saddletail snapper were extracted and the NIR spectral characteristics were acquired over a spectral range of 800–2780 nm. Partial least-squares models (PLS) were developed from the diffuse reflectance spectra and reference-validated age estimates (based on traditional sectioned otolith increments) to predict age for independent otolith samples. Predictive models developed for a specific season and geographical location performed poorly against a different season and geographical location. However, overall PLS regression statistics for predicting a combined population incorporating both geographic location and season variables were: coefficient of determination (R2) = 0.94, root mean square error of prediction (RMSEP) = 1.54 for age estimation, indicating that Saddletail age could be predicted within 1.5 increment counts. This level of accuracy suggests the method warrants further development for Saddletail snapper and may have potential for other fish species. A rapid method of fish age estimation could have the potential to reduce greatly both costs of time and materials in the assessment and management of commercial fisheries.

Bayesian Inference for Retrospective Population Genetics Models Using Markov Chain Monte Carlo Methods

Genetics, the science of heredity and variation in living organisms, has a central role in medicine, in breeding crops and livestock, and in studying fundamental topics of biological sciences such as evolution and cell functioning. Currently the field of genetics is under a rapid development because of the recent advances in technologies by which molecular data can be obtained from living organisms. In order that most information from such data can be extracted, the analyses need to be carried out using statistical models that are tailored to take account of the particular genetic processes. In this thesis we formulate and analyze Bayesian models for genetic marker data of contemporary individuals. The major focus is on the modeling of the unobserved recent ancestry of the sampled individuals (say, for tens of generations or so), which is carried out by using explicit probabilistic reconstructions of the pedigree structures accompanied by the gene flows at the marker loci. For such a recent history, the recombination process is the major genetic force that shapes the genomes of the individuals, and it is included in the model by assuming that the recombination fractions between the adjacent markers are known. The posterior distribution of the unobserved history of the individuals is studied conditionally on the observed marker data by using a Markov chain Monte Carlo algorithm (MCMC). The example analyses consider estimation of the population structure, relatedness structure (both at the level of whole genomes as well as at each marker separately), and haplotype configurations. For situations where the pedigree structure is partially known, an algorithm to create an initial state for the MCMC algorithm is given. Furthermore, the thesis includes an extension of the model for the recent genetic history to situations where also a quantitative phenotype has been measured from the contemporary individuals. In that case the goal is to identify positions on the genome that affect the observed phenotypic values. This task is carried out within the Bayesian framework, where the number and the relative effects of the quantitative trait loci are treated as random variables whose posterior distribution is studied conditionally on the observed genetic and phenotypic data. In addition, the thesis contains an extension of a widely-used haplotyping method, the PHASE algorithm, to settings where genetic material from several individuals has been pooled together, and the allele frequencies of each pool are determined in a single genotyping.

Ambient air pollution exposure estimation for the global burden of disease 2013

Exposure to ambient air pollution is a major risk factor for global disease. Assessment of the impacts of air pollution on population health and the evaluation of trends relative to other major risk factors requires regularly updated, accurate, spatially resolved exposure estimates. We combined satellite-based estimates, chemical transport model (CTM) simulations and ground measurements from 79 different countries to produce new global estimates of annual average fine particle (PM2.5) and ozone concentrations at 0.1° × 0.1° spatial resolution for five-year intervals from 1990-2010 and the year 2013. These estimates were then applied to assess population-weighted mean concentrations for 1990 – 2013 for each of 188 countries. In 2013, 87% of the world’s population lived in areas exceeding the World Health Organization (WHO) Air Quality Guideline of 10 μg/m3 PM2.5 (annual average). Between 1990 and 2013, decreases in population-weighted mean concentrations of PM2.5 were evident in most high income countries, in contrast to increases estimated in South Asia, throughout much of Southeast Asia, and in China. Population-weighted mean concentrations of ozone increased in most countries from 1990 - 2013, with modest decreases in North America, parts of Europe, and several countries in Southeast Asia.

Habitat use and population dynamics of brown bears (Ursus arctos) in Scandinavia

Large carnivore populations are currently recovering from past extirpation efforts and expanding back into their original habitats. At the same time human activities have resulted in very few wilderness areas left with suitable habitats and size large enough to maintain populations of large carnivores without human contact. Consequently the long-term future of large carnivores depends on their successful integration into landscapes where humans live. Thus, understanding their behaviour and interaction with surrounding habitats is of utmost importance in the development of management strategies for large carnivores. This applies also to brown bears (Ursus arctos) that were almost exterminated from Scandinavia and Finland at the turn of the century, but are now expanding their range with the current population estimates being approximately 2600 bears in Scandinavia and 840 in Finland. This thesis focuses on the large-scale habitat use and population dynamics of brown bears in Scandinavia with the objective to develop modelling approaches that support the management of bear populations. Habitat analysis shows that bear home ranges occur mainly in forested areas with a low level of human influence relative to surrounding areas. Habitat modelling based on these findings allows identification and quantification of the potentially suitable areas for bears in Scandinavia. Additionally, this thesis presents novel improvements to home range estimation that enable realistic estimates of the effective area required for the bears to establish a home range. This is achieved through fitting to the radio-tracking data to establish the amount of temporal autocorrelation and the proportion of time spent in different habitat types. Together these form a basis for the landscape-level management of the expanding population. Successful management of bears requires also assessment of the consequences of harvest on the population viability. An individual-based simulation model, accounting for the sexually selected infanticide, was used to investigate the possibility of increasing the harvest using different hunting strategies, such as trophy harvest of males. The results indicated that the population can sustain twice the current harvest rate. However, harvest should be changed gradually while carefully monitoring the population growth as some effects of increased harvest may manifest themselves only after a time-delay. The results and methodological improvements in this thesis can be applied to the Finnish bear population and to other large carnivores. They provide grounds for the further development of spatially-realistic management-oriented models of brow bear dynamics that can make projections of the future distribution of bears while accounting for the development of human activities.

Heritability analysis of surface-based cortical thickness estimation on a large twin cohort

The aim of this paper is to assess the heritability of cerebral cortex, based on measurements of grey matter (GM) thickness derived from structural MR images (sMRI). With data acquired from a large twin cohort (328 subjects), an automated method was used to estimate the cortical thickness, and EM-ICP surface registration algorithm was used to establish the correspondence of cortex across the population. An ACE model was then employed to compute the heritability of cortical thickness. Heritable cortical thickness measures various cortical regions, especially in frontal and parietal lobes, such as bilateral postcentral gyri, superior occipital gyri, superior parietal gyri, precuneus, the orbital part of the right frontal gyrus, right medial superior frontal gyrus, right middle occipital gyrus, right paracentral lobule, left precentral gyrus, and left dorsolateral superior frontal gyrus.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Population characteristics of gulf menhaden, Brevoortia patronus

The status of the Gulf menhaden, Brevoortia patronus, fishery was assessed with purse-seine landings data from 1946 to 1997 and port sampling data from 1964 to 1997. These data were analyzed to determine growth rates, biological reference points for fi shing mortality from yield per recruit and maximum spawning potential analyses, spawner-recruit relationships, and maximum sustainable yield (MSY). The separable virtual population approach was used for the period 1976–97 (augmented by earlier analyses for 1964–75) to obtain point estimates of stock size, recruits to age 1, spawning stock size, and fishing mortality rates. Exploitation rates for age-1 fi sh ranged between 11% and 45%, for age-2 fi sh between 32% and 72%, and for age-3 fi sh between 32% and 76%. Biological reference points from yield per recruit (F0.1: 1.5–2.5/yr) and spawning potential ratio (F20: 1.3–1.9/yr and F30: 0.8–1.2/yr) were obtained for comparison with recent estimates of F (0.6–0.8/yr). Recent spawning stock estimates (as biomass or eggs) are above the long-term average, while recent recruits to age 1 are comparable to the long-term average. Parameters from Ricker-type spawner-recruit relations were estimated, although considerable unexplained variability remained. Recent survival to age-1 recruitment has generally been below that expected based on the Ricker spawner-recruit relation. Estimates of long-term MSY from PRODFIT and ASPIC estimation of production model ranged between 717,000 t and 753,000 t, respectively. Declines in landings between 1988 and 1992 raised concerns about the status of the Gulf menhaden stock. Landings have fl uctuated without trend since 1992, averaging about 571,000 t. However, Gulf menhaden are short lived and highly fecund. Thus, variation in recruitment to age 1, largely mediated by environmental conditions, infl uences fi shing success over the next two years (as age-1 and age-2 fi sh). Comparisons of recent estimates of fi shing mortality to biological reference points do not suggest overfishing. (PDF file contains 22 pages.)

Estimation of year class abundance and mortality of yellowfin tuna in the Eastern Tropical Pacific

ENGLISH: Age composition of catch, and growth rate, of yellowfin tuna have been estimated by Hennemuth (1961a) and Davidoff (1963). The relative abundance and instantaneous total mortality rate of yellowfin tuna during 1954-1959 have been estimated by Hennenmuth (1961b). It is now possible to extend this work, because more data are available; these include data for 1951-1954, which were previously not available, and data for 1960-1962, which were collected subsequent to Hennemuth's (1961b) publication. In that publication, Hennemuth estimated the total instantaneous mortality rate (Z) during the entire time period a year class is present in the fishery following full recruitment. However, this method may lead to biased estimates of abundance, and hence mortality rates, because of both seasonal migrations into or out of specific fishing areas and possible seasonal differences in availability or vulnerability of the fish to the fishing gear. Schaefer, Chatwin and Broadhead (1961) and Joseph etl al. (1964) have indicated that seasonal migrations of yellowfin occur. A method of estimating mortality rates which is not biased by seasonal movements would be of value in computations of population dynamics. The method of analysis outlined and used in the present paper may obviate this bias by comparing the abundance of an individual yellowfin year class, following its period of maximum abundance, in an individual area during a specific quarter of the year with its abundance in the same area one year later. The method was suggested by Gulland (1955) and used by Chapman, Holt and Allen (1963) in assessing Antarctic whale stocks. This method, and the results of its use with data for yellowfin caught in the eastern tropical Pacific from 1951-1962 are described in this paper. SPANISH: La composición de edad de la captura, y la tasa de crecimiento del atún aleta amarilla, han sido estimadas por Hennemuth (1961a) y Davidoff (1963). Hennemuth (1961b), estimó la abundancia relativa y la tasa de mortalidad total instantánea del atún aleta amarilla durante 1954-1959. Se puede ampliar ahora, este trabajo, porque se dispone de más datos; éstos incluyen datos de 1951 1954, de los cuales no se disponía antes, y datos de 1960-1962 que fueron recolectados después de la publicación de Hennemuth (1961b). En esa obra, Hennemuth estimó la tasa de mortalidad total instantánea (Z) durante todo el período de tiempo en el cual una clase anual está presente en la pesquería, consecutiva al reclutamiento total. Sin embargo, este método puede conducir a estimaciones con bias (inclinación viciada) de abundancia, y de aquí las tasas de mortalidad, debidas tanto a migraciones estacionales dentro o fuera de las áreas determinadas de pesca, como a posibles diferencias estacionales en la disponibilidad y vulnerabilidad de los peces al equipo de pesca. Schaefer, Chatwin y Broadhead (1961) y Joseph et al. (1964) han indicado que ocurren migraciones estacionales de atún aleta amarilla. Un método para estimar las tasas de mortalidad el cual no tuviera bias debido a los movimientos estacionales, sería de valor en los cómputos de la dinámica de las poblaciones. El método de análisis delineado y usado en el presente estudio puede evitar este bias al comparar la abundancia de una clase anual individual de atún aleta amarilla, subsecuente a su período de abundancia máxima en un área individual, durante un trimestre específico del año, con su abundancia en la misma área un año más tarde. Este método fue sugerido por Gulland (1955) y empleado por Chapman, Holt y Allen (1963) en la declaración de los stocks de la ballena antártica. Este método y los resultados de su uso, en combinación con los datos del atún aleta amarilla capturado en el Pacífico oriental tropical desde 1951-1962, son descritos en este estudio.

Contribution of haematological factors to the distributions and estimation of Eustrongyliides africanus larvae densities in Clarias gariepinus and Clarias anguillaris from Bida floodplain of Nigeria

The contributions of hematological factors to the distribution and estimations of Eustrongylides africanus larvae densities in Clarias gariepinus and C. anguillaris of Bida floodplain of Nigeria were documented for the first time. The hematological factors making the most important contributions to the distributions of E. africanus larvae infections in clarias species are mean corpuscular haemoglobin concentration (MCHC), mean corpuscular haemoglobin (MCH), mean corpuscular volume (MCV) and neutrophils count, in descending order of magnitude; having the manifestations for the months of January, March, September, and December of the year being closely related. Five haematological factors (neutrophils, lymphocytes and eosinophils counts; MCH and MCV) having positive or negative correlation coefficient (r) between 0.50 and 0.85 contributed to the estimated of E.africanus larvae densities in the wild population of Clarias species

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.