Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Population of computational rabbit-specific ventricular action potential models for investigating sources of variability in cellular repolarisation

Variability is observed at all levels of cardiac electrophysiology. Yet, the underlying causes and importance of this variability are generally unknown, and difficult to investigate with current experimental techniques. The aim of the present study was to generate populations of computational ventricular action potential models that reproduce experimentally observed intercellular variability of repolarisation (represented by action potential duration) and to identify its potential causes. A systematic exploration of the effects of simultaneously varying the magnitude of six transmembrane current conductances (transient outward, rapid and slow delayed rectifier K(+), inward rectifying K(+), L-type Ca(2+), and Na(+)/K(+) pump currents) in two rabbit-specific ventricular action potential models (Shannon et al. and Mahajan et al.) at multiple cycle lengths (400, 600, 1,000 ms) was performed. This was accomplished with distributed computing software specialised for multi-dimensional parameter sweeps and grid execution. An initial population of 15,625 parameter sets was generated for both models at each cycle length. Action potential durations of these populations were compared to experimentally derived ranges for rabbit ventricular myocytes. 1,352 parameter sets for the Shannon model and 779 parameter sets for the Mahajan model yielded action potential duration within the experimental range, demonstrating that a wide array of ionic conductance values can be used to simulate a physiological rabbit ventricular action potential. Furthermore, by using clutter-based dimension reordering, a technique that allows visualisation of multi-dimensional spaces in two dimensions, the interaction of current conductances and their relative importance to the ventricular action potential at different cycle lengths were revealed. Overall, this work represents an important step towards a better understanding of the role that variability in current conductances may play in experimentally observed intercellular variability of rabbit ventricular action potential repolarisation.

Population genetic models can be used to study the evolution of the interacting behaviours of parents and their progeny

An example of the evolution of the interacting behaviours of parents and progeny is studied using iterative equations linking the frequencies of the gametes produced by the progeny to the frequencies of the gametes in the parental generation. This population genetics approach shows that a model in which both behaviours are determined by a single locus can lead to a stable equilibrium in which the two behaviours continue to segregate. A model in which the behaviours are determined by genes at two separate loci leads eventually to fixation of the alleles at both loci but this can take many generations of selection. Models of the type described in this paper will be needed to understand the evolution of complex behaviour when genomic or experimental information is available about the genetic determinants of behaviour and the selective values of different genomes. (c) 2007 Elsevier Inc. All rights reserved.

Population based models of cortical drug response: insights from anaesthesia

A great explanatory gap lies between the molecular pharmacology of psychoactive agents and the neurophysiological changes they induce, as recorded by neuroimaging modalities. Causally relating the cellular actions of psychoactive compounds to their influence on population activity is experimentally challenging. Recent developments in the dynamical modelling of neural tissue have attempted to span this explanatory gap between microscopic targets and their macroscopic neurophysiological effects via a range of biologically plausible dynamical models of cortical tissue. Such theoretical models allow exploration of neural dynamics, in particular their modification by drug action. The ability to theoretically bridge scales is due to a biologically plausible averaging of cortical tissue properties. In the resulting macroscopic neural field, individual neurons need not be explicitly represented (as in neural networks). The following paper aims to provide a non-technical introduction to the mean field population modelling of drug action and its recent successes in modelling anaesthesia.

Population genomic tests of models of adaptive radiation in Lake Victoria Region cichlid fish

Adaptive radiation is usually thought to be associated with speciation, but the evolution of intraspecific polymorphisms without speciation is also possible. The radiation of cichlid fish in Lake Victoria (LV) is perhaps the most impressive example of a recent rapid adaptive radiation, with 600+ very young species. Key questions about its origin remain poorly characterized, such as the importance of speciation versus polymorphism, whether species persist on evolutionary time scales, and if speciation happens more commonly in small isolated or in large connected populations. We used 320 individuals from 105 putative species from Lakes Victoria, Edward, Kivu, Albert, Nabugabo and Saka, in a radiation-wide amplified fragment length polymorphism (AFLP) genome scan to address some of these questions. We demonstrate pervasive signatures of speciation supporting the classical model of adaptive radiation associated with speciation. A positive relationship between the age of lakes and the average genomic differentiation of their species, and a significant fraction of molecular variance explained by above-species level taxonomy suggest the persistence of species on evolutionary time scales, with radiation through sequential speciation rather than a single starburst. Finally the large gene diversity retained from colonization to individual species in every radiation suggests large effective population sizes and makes speciation in small geographical isolates unlikely.

Comparison of eight published static finite element models of the intact lumbar spine : predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values. Eight well-established FE models of the lumbar spine (L1-5) of different research centres around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values. In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.

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.

Sibling rivalry between seeds within a fruit: Some population genetic models

Competition between seeds within a fruit for parental resources is described using one-locus-two-allele models. While a �normal� allele leads to an equitable distribution of resources between seeds (a situation which also corresponds to the parental optimum), the �selfish� allele is assumed to cause the seed carrying it to usurp a higher proportion of the resources. The outcome of competition between �selfish� alleles is also assumed to lead to an asymmetric distribution of resources, the �winner� being chosen randomly. Conditions for the spread of an initially rare selfish allele and the optimal resource allocation corresponding to the evolutionarily stable strategy, derived for species with n-seeded fruits, are in accordance with expectations based on Hamilton�s inclusive fitness criteria. Competition between seeds is seen to be most intense when there are only two seeds, and decreases with increasing number of seeds, suggesting that two-seeded fruits would be rarer than one-seeded or many-seeded ones. Available data from a large number of plant species are consistent with this prediction of the model.

Identification of a novel population of Langerin+ dendritic cells.

Langerhans cells (LCs) are antigen-presenting cells that reside in the epidermis of the skin and traffic to lymph nodes (LNs). The general role of these cells in skin immune responses is not clear because distinct models of LC depletion resulted in opposite conclusions about their role in contact hypersensitivity (CHS) responses. While comparing these models, we discovered a novel population of LCs that resides in the dermis and does not represent migrating epidermal LCs, as previously thought. Unlike epidermal LCs, dermal Langerin(+) dendritic cells (DCs) were radiosensitive and displayed a distinct cell surface phenotype. Dermal Langerin(+) DCs migrate from the skin to the LNs after inflammation and in the steady state, and represent the majority of Langerin(+) DCs in skin draining LNs. Both epidermal and dermal Langerin(+) DCs were depleted by treatment with diphtheria toxin in Lang-DTREGFP knock-in mice. In contrast, transgenic hLang-DTA mice lack epidermal LCs, but have normal numbers of dermal Langerin(+) DCs. CHS responses were abrogated upon depletion of both epidermal and dermal LCs, but were unaffected in the absence of only epidermal LCs. This suggests that dermal LCs can mediate CHS and provides an explanation for previous differences observed in the two-model systems.

Front spreading in population dynamic models. Theory and application to the Neolithic transition

This thesis presents population dynamics models that can be applied to predict the rate of spread of the Neolithic transition (change from hunter-gathering to farming economics) across the European continent, which took place about 9000 to 5000 years ago. The first models in this thesis provide predictions at a continental scale. We develop population dynamics models with explicit kernels and apply realistic data. We also derive a new time-delayed reaction-diffusion equation which yields speeds about a 10% slower than previous models. We also deal with a regional variability: the slowdown of the Neolithic front when reaching the North of Europe. We develop simple reaction-diffusion models that can predict the measured speeds in terms of the non-homogeneous distribution of pre-Neolithic (Mesolithic) population in Europe, which were present in higher densities at the North of the continent. Such models can explain the observed speeds.

Evidence of a genetic bottleneck in an El Nino affected population of South American fur seals, Arctocephalus australis

The South American fur seal, Arctocephalus australis, was one of the earliest otariid seals to be exploited by humans: at least 6000 years ago on the Atlantic coast and 4000 on the Pacific coast of South America. More than 750,000 fur seals were killed in Uruguay until 1991. However, a climatological phenomenon-the severe 1997-1998 El Nino Southern Oscillation (ENSO)-was responsible for the decline of 72% Of the Peruvian fur seal population due to starvation as a consequence of warming of sea-surface temperatures and primary productivity reduction. Currently, there is no precise information on global population size or on the species` conservation status. The present study includes the first bottleneck test for the Pacific and Atlantic populations of A. australis based on the analysis of seven microsatellite loci. Genetic bottleneck compromises the evolutionary potential of a population to respond to environmental changes. The perspective becomes even more alarming due to current global warming models that predict stronger and more frequent ENSO events in the future. Our analysis found moderate support for deviation from neutrality-equilibrium for the Pacific population of fur seals and none for the Atlantic population. This difference among population reflects different demographic histories, and is consistent with a greater reduction in population size in the Pacific. Such an event could be a result of the synergic effects of recurrent ENSO events and the anthropogenic impact (sealing and prey overfishing) on this population.

Mating system of a population of Myracrodruon urundeuva F.F. & M.F. Allemão using the fAFLP molecular marker

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)