Biomedical subjects

M Gyllenberg

Publications and source records attributed to M Gyllenberg.

At least 19 recordsLinked to original sources

PubMed2003

Steady-state analysis of structured population models.

Our systematic formulation of nonlinear population models is based on the notion of the environmental condition. The defining property of the environmental condition is that individuals are independent of one another (and hence equations are linear) when this condition is prescribed (in principle as an arbitrary function of time, but when focussing on steady states we shall restrict to constant functions). The steady-state problem has two components: (i). the environmental condition should be such that the existing populations do neither grow nor decline; (ii). a feedback consistency condition relating the environmental condition to the community/population size and composition should hold. In this paper we develop, justify and analyse basic formalism under the assumption that individuals can be born in only finitely many possible states and that the environmental condition is fully characterized by finitely many numbers. The theory is illustrated by many examples. In addition to various simple toy models introduced for explanation purposes, these include a detailed elaboration of a cannibalism model and a general treatment of how genetic and physiological structure should be combined in a single model.

Cannibalism↗

PubMed2002

Adjustment of the human respiratory system to increased upper airway resistance during sleep.

A cardiorespiratory model incorporating control of the human upper airway during sleep is described. Most previous models have not considered the possibility that the upper airway could be a limiting factor for gas exchange. Our model was developed to also predict certain pathophysiological phenomena in the cardiorespiratory system that characterize heavy snoring or sleep apnea. We started by adapting our collapsible upper airway model to include the impact of nasal passage and larynx, and extended the model with equations for gas exchange in the lungs. A feedback loop both to the respiratory pump and the upper airway dilator muscles was included. The model enabled successful breath-by-breath simulations of obstructive events of the upper airway. Although the model incorporates several physiologically relevant components of the system, the simulation results suggest that only few parameters suffice to predict the key adjustments that the cardiorespiratory system is known to make in patients with heavy snoring.

Airway Obstruction↗

PubMed2002

Invasion dynamics and attractor inheritance.

We study the dynamics of a population of residents that is being invaded by an initially rare mutant. We show that under relatively mild conditions the sum of the mutant and resident population sizes stays arbitrarily close to the initial attractor of the monomorphic resident population whenever the mutant has a strategy sufficiently similar to that of the resident. For stochastic systems we show that the probability density of the sum of the mutant and resident population sizes stays arbitrarily close to the stationary probability density of the monomorphic resident population. Attractor switching, evolutionary suicide as well as most cases of "the resident strikes back" in systems with multiple attractors are possible only near a bifurcation point in the strategy space where the resident attractor undergoes a discontinuous change. Away from such points, when the mutant takes over the population from the resident and hence becomes the new resident itself, the population stays on the same attractor. In other words, the new resident "inherits" the attractor from its predecessor, the former resident.

Animals↗

PubMed2001

A fragment library based on Gaussian mixtures predicting favorable molecular interactions.

Here, a protein atom-ligand fragment interaction library is described. The library is based on experimentally solved structures of protein-ligand and protein-protein complexes deposited in the Protein Data Bank (PDB) and it is able to characterize binding sites given a ligand structure suitable for a protein. A set of 30 ligand fragment types were defined to include three or more atoms in order to unambiguously define a frame of reference for interactions of ligand atoms with their receptor proteins. Interactions between ligand fragments and 24 classes of protein target atoms plus a water oxygen atom were collected and segregated according to type. The spatial distributions of individual fragment - target atom pairs were visually inspected in order to obtain rough-grained constraints on the interaction volumes. Data fulfilling these constraints were given as input to an iterative expectation-maximization algorithm that produces as output maximum likelihood estimates of the parameters of the finite Gaussian mixture models. Concepts of statistical pattern recognition and the resulting mixture model densities are used (i) to predict the detailed interactions between Chlorella virus DNA ligase and the adenine ring of its ligand and (ii) to evaluate the "error" in prediction for both the training and validation sets of protein-ligand interaction found in the PDB. These analyses demonstrate that this approach can successfully narrow down the possibilities for both the interacting protein atom type and its location relative to a ligand fragment.

Algorithms↗

PubMed2001

How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies.

We define a fitness concept applicable to structured metapopulations consisting of infinitely many equally coupled patches. In addition, we introduce a more easily calculated quantity Rm that relates to fitness in the same manner as R0 relates to fitness in ordinary population dynamics: the Rm of a mutant is only defined when the resident population dynamics converges to a point equilibrium and Rm is larger (smaller) than 1 if and only if mutant fitness is positive (negative). Rm corresponds to the average number of newborn dispersers resulting from the (on average less than one) local colony founded by a newborn disperser. Efficient algorithms for calculating its numerical value are provided. As an example of the usefulness of these concepts we calculate the evolutionarily stable conditional dispersal strategy for individuals that can account for the local population density in their dispersal decisions. Below a threshold density x, at which staying and leaving are equality profitable, everybody should stay and above x everybody should leave, where profitability is measured as the mean number of dispersers produced through lines of descent consisting of non-dispersers.

Algorithms↗

PubMed2001

Necessary and sufficient conditions for evolutionary suicide.

Evolutionary suicide is an evolutionary process where a viable population adapts in such a way that it can no longer persist. It has already been found that a discontinuous transition to extinction is a necessary condition for suicide. Here we present necessary and sufficient conditions, concerning the bifurcation point, for suicide to occur. Evolutionary suicide has been found in structured metapopulation models. Here we show that suicide can occur also in unstructured population models. Moreover, a structured model does not guarantee the possibility of suicide: we show that suicide cannot occur in age-structured population models of the Gurtin-MacCamy type. The point is that the mutant's fitness must explicitly depend not only on the environmental interaction variable, but also on the resident strategy.

Adaptation, Biological↗

PubMed2001

On fitness in structured metapopulations.

In this paper we derive a general expression measuring fitness in general structured metapopulation models. We apply the theory to a model structured by local population size and in which local dynamics is explicitly modelled. In particular, we calculate the evolutionarily stable dispersal strategy for individuals that can assess the local population density in the case where only dispersal is subject to evolutionary control but all other model in gredients are assumed fixed. We show that there exists a threshold size such that at ESS everyone should stay as long as the population size is below the threshold and everyone should disperse immediately as the population size reaches the threshold.

Animals↗

PubMed2001

On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory.

This paper is as much about a certain modelling methodology, as it is about the constructive definition of future population states from a description of individual behaviour and an initial population state. The key idea is to build a nonlinear model in two steps, by explicitly introducing the environmental condition via the requirement that individuals are independent from one another (and hence equations are linear) when this condition is prescribed as a function of time. A linear physiologically structured population model is defined by two rules, one for reproduction and one for development and survival, both depending on the initial individual state and the prevailing environmental condition. In Part I we showed how one can constructively define future population state operators from these two ingredients. A nonlinear model is a linear model together with a feedback law that describes how the environmental condition at any particular time depends on the population size and composition at that time. When applied to the solution of the linear problem, the feedback law yields a fixed point problem. This we solve constructively by means of the contraction mapping principle, for any given initial population state. Using subsequently this fixed point as input in the linear population model, we obtain a population semiflow. We then say that we solved the nonlinear problem.

Animals↗

PubMed2001

A model of a snorer's upper airway.

In snorers, the physiologic decrease of postural muscle tone during sleep results in increased collapsibility of the upper airway. Measurement of nasal pressure changes with prongs is increasingly used to monitor flow kinetics through a collapsing upper airway. This report presents a mathematical model to predict nasal flow profile from three critical components that control upper airway patency during sleep. The model includes the respiratory pump drive, the stiffness of the pharyngeal soft tissues, and the dynamic support of the muscles surrounding the upper airway. Depending on these three components, the proposed model is able to reproduce the characteristic changes in flow profile that are clinically observed in snorers and non-snorers during sleep.

Humans↗

PubMed2000

Detection of high-frequency respiratory movements during sleep.

Sleep-related breathing disorders are common in adults and they have a significant impact on vigilance and quality of life. Previous studies have shown the validity of the static-charge-sensitive bed (SCSB) in monitoring breathing abnormalities during sleep. A whole nights sleep study produces a signal with considerable length, and therefore an automated analysis system would be of great need. In this work we focus on detection of high-frequency respiratory movement (HFRM) patterns which are related to increased respiratory efforts. The paper documents four methods to automatically detect these patterns. The first two are based on classical statistical tests applied to the SCSB signal, and the other two use spectral characteristics in order to adaptively segment the SCSB signal. Finally we adjust each method to detect patterns that coincide with the HFRMs determined by an expert, and evaluate the performance of the methods using independent test data.

Algorithms↗

PubMed2000

Minimizing stochastic complexity using local search and GLA with applications to classification of bacteria.

In this paper, we compare the performance of two iterative clustering methods when applied to an extensive data set describing strains of the bacterial family Enterobacteriaceae. In both methods, the classification (i.e. the number of classes and the partitioning) is determined by minimizing stochastic complexity. The first method performs the minimization by repeated application of the generalized Lloyd algorithm (GLA). The second method uses an optimization technique known as local search (LS). The method modifies the current solution by making global changes to the class structure and it, then, performs local fine-tuning to find a local optimum. It is observed that if we fix the number of classes, the LS finds a classification with a lower stochastic complexity value than GLA. In addition, the variance of the solutions is much smaller for the LS due to its more systematic method of searching. Overall, the two algorithms produce similar classifications but they merge certain natural classes with microbiological relevance in different ways.

Algorithms↗

PubMed1999

Bayesian predictive identification and cumulative classification of bacteria.

In this paper we give a mathematically precise formulation of an old idea in bacterial taxonomy, namely cumulative classification, where the taxonomy is continuously updated and possibly augmented as new strains are identified. Our formulation is based on Bayesian predictive probability distributions. The criterion for founding a new taxon is given a firm theoretical foundation based on prediction and it is given a clear-cut interpretation. We formulate an algorithm for cumulative classification and apply it to a large database of bacteria belonging to the family Enterobacteriaceae. The resulting taxonomy makes microbiological sense.

Bacteria↗

PubMed1999

Allee effects can both conserve and create spatial heterogeneity in population densities.

In order to determine conditions which allow the Allee effect (caused by biparental reproduction) to conserve and create spatial heterogeneity in population densities, we studied a deterministic model of a symmetric two-patch metapopulation. We proved that under certain conditions there exist stable equilibria with unequal population densities in the two patches, a situation which can be interpreted as conserved heterogeneity. Furthermore, the Allee effect can lead to instability of the equilibrium with equal population densities if some degree of competition is assumed to occur between the subpopulations (non-local competition). This indicates the potential of the Allee effect to create spatial heterogeneity. Neither of these effects appear under biologically realistic parameter values in a model where uniparental reproduction is assumed. We proved that both the between-patch migration intensity and the degree of non-local competition are decisive in determining boundaries between these types of behaviour of the spatial system with Allee effect. Therefore, we propose that the Allee effect, migration intensity, and non-local competition should be considered jointly in studies focusing on problems like pattern formation in space and invasions of spreading species.

Animals↗

PubMed1999

Improving the false nearest neighbors method with graphical analysis.

We introduce a graphical presentation for the false nearest neighbors (FNN) method. In the original method only the percentage of false neighbors is computed without regard to the distribution of neighboring points in the time-delay coordinates. With this presentation it is much easier to distinguish deterministic chaos from noise. The graphical approach also serves as a tool to determine better conditions for detecting low-dimensional chaos, and to get a better understanding on the applicability of the FNN method.

Journal Article↗

PubMed1998

Ontogenetic scaling of foraging rates and the dynamics of a size-structured consumer-resource model.

The ontogenetic scaling of foraging capacity strongly influences the competitive ability of differently sized individuals within a species. We develop a physiologically structured model to investigate the effect of different ontogenetic size scalings of the attack rate on the population dynamics of a consumer-resource system. The resource is assumed to reproduce continuously whereas the consumer only reproduces at discrete time instants. Depending on the ontogenetic size scaling, the model exhibited recruit-driven cycles, stable fixed point dynamics, non-recruit juvenile-driven cycles, quasiperiodic orbits, or chaotic dynamics. The kind of dynamics observed was related to the maintenance resource levels required of differently sized individuals. Stable fixed point dynamics was, besides at the persistence boundary, only observed when the minimum resource levels were similar for newborns and mature individuals. The tendency for large population fluctuations over a wide range of the parameter space was due to the consumer's pulsed reproduction. Background mortality and length of season were major determinants of cycle length. Model dynamics strongly resembled empirically observed dynamics from fish and Daphnia populations with respect to both patterns and mechanisms. The non-recruit juvenile-driven dynamics is suggested to occur in populations with size-dependent interference or preemptive competition like cicada populations.

Animals↗

PubMed1998

Stochastic complexity as a taxonomic tool.

In this paper we propose a method of constructing a hierarchical classification based on the notion of stochastic complexity. Minimization of stochastic complexity amounts to maximization of the information content of the classification. A dendrogram is obtained by first finding the classification which minimizes stochastic complexity and then by step-wise merging of groups such that at each step there is a minimum loss of information. The method was applied to a database containing 5313 strains of Enterobacteriaceae. The results are in reasonable accordance with present-day views on the taxonomy of Enterobacteriaceae.

Enterobacteriaceae↗

PubMed1997

Uniting Two General Patterns in the Distribution of Species

Two patterns in the distribution of species have become firmly but independently established in ecology: the species-area curve, which describes how rapidly the number of species increases with area, and the positive relation between species' geographical distribution and average local abundance. There is no generally agreed explanation of either pattern, but for both the two main hypotheses are essentially the same: divergence of species along the ecological specialist-generalist continuum and colonization- extinction dynamics. A model is described that merges the two mechanisms, predicts both patterns, and thereby shows how the two general, but formerly disconnected, patterns are interrelated.

Journal Article↗

PubMed1997

Habitat Deterioration, Habitat Destruction, and Metapopulation Persistence in a Heterogenous Landscape

Levins's unstructured metapopulation model predicts that the equilibrium fraction of empty habitat patches is a constant function of the fraction h of suitable patches in the landscape and that this constant equals the threshold value for metapopulation persistence. Levins's model thus suggests that the minimum amount of suitable habitat necessary for metapopulation persistence can be estimated from the fraction of empty patches at steady state. In this paper we construct several more realistic structured metapopulation models that include variation in patch quality and the rescue effect. These models predict both positive and negative correlations between the fractions of suitable patches and empty patches. The type of correlation depends in an intricate manner on the strength of the rescue effect and on the quality distribution of the patches to be destroyed. Empty patches can be considered as the resource limiting metapopulation growth. Our results demonstrate that the correlation between the fractions of suitable patches and empty patches is positive if and only if the average value of the resource decreases as the number of patches increases. Copyright 1997 Academic Press. Copyright 1997 Academic Press

Journal Article↗