Search results for "Population model"
showing 10 items of 43 documents
Graphical representation of some duality relations in stochastic population models
2007
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching diffusion with logistic growth (cf. math/0509612). The two dual processes are approximated by particle processes which are forward and backward processes in a graphical representation. We identify duality relations between the basic building blocks of the particle processes which lead to the two dualities mentioned above.
Ancestral processes in population genetics-the coalescent.
2000
A special stochastic process, called the coalescent, is of fundamental interest in population genetics. For a large class of population models this process is the appropriate tool to analyse the ancestral structure of a sample of n individuals or genes, if the total number of individuals in the population is sufficiently large. A corresponding convergence theorem was first proved by Kingman in 1982 for the Wright-Fisher model and the Moran model. Generalizations to a large class of exchangeable population models and to models with overlying mutation processes followed shortly later. One speaks of the "robustness of the coalescent, as this process appears in many models as the total populati…
Probabilistic small area risk assessment using GIS-based data: a case study on Finnish childhood diabetes
2000
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 ov…
The coalescent in population models with time-inhomogeneous environment
2002
AbstractThe coalescent theory, well developed for the class of exchangeable population models with time-homogeneous reproduction law, is extended to a class of population models with time-inhomogeneous environment, where the population size is allowed to vary deterministically with time and where the distribution of the family sizes is allowed to change from generation to generation. A new class of time-inhomogeneous coalescent limit processes with simultaneous multiple mergers arises. Its distribution can be characterized in terms of product integrals.
Chemically Stressed Bacterial Communities in Anaerobic Digesters Exhibit Resilience and Ecological Flexibility
2020
Anaerobic digestion is a technology known for its potential in terms of methane production. During the digestion process, multiple metabolites of high value are synthesized. However, recent works have demonstrated the high robustness and resilience of the involved microbiomes; these attributes make it difficult to manipulate them in such a way that a specific metabolite is predominantly produced. Therefore, an exact understanding of the manipulability of anaerobic microbiomes may open up a treasure box for bio-based industries. In the present work, the effect of nalidixic acid, γ-aminobutyric acid (GABA), and sodium phosphate on the microbiome of digested sewage sludge from a water treatmen…
Environmental noise and population dynamics of the ciliated protozoa Tetrahymena thermophila in aquatic microcosms
2003
Population theory predicts that the reddened environmental noise, especially in combination with high population growth rate, reddens population dynamics, increases population variability and strengthens environment–population correlation. We tested these predictions with axenic populations of ciliated protozoa Tetrahymena thermophila. Populations with low and high growth rate were cultured in a stable environment, and in environments with sublethal temperature fluctuations that had blue, white and red spectra (i.e. negatively autocorrelated, uncorrelated, or positively autocorrelated, respectively). Population size and biomass of individuals were determined at 3-h intervals for 18 days. Dy…
The use of Markovian metapopulation models: Reducing the dimensionality of transition matrices by self-organizing Kohonen networks
2006
Abstract Markovian population models are used in conservation biology to find an accurate estimate of a population's extinction probability. Such models require handling of large transition matrices and calculations are thus extremely time-consuming when large populations have to be studied. To accomplish these problems, some authors have suggested to group together several states/sizes of the population. Unfortunately, this so-called binning frequently results in errors in estimates obtained. The main problem with binning is that it assumes that grouped states behave nearly identical with respect to the underlying stochastic population process and that so far binning methods implicitly vio…
An existence and uniqueness principle for a nonlinear version of the Lebowitz-Rubinow model with infinite maximum cycle length
2017
The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.
Population dynamics of the Swedish Ornithological Society
2003
It has recently been recognized that there is declining interest in ornithology among the younger generations. In this paper we analyse the short and long-term dynamics of the Swedish Ornithological Society (SOF) and the Swedish Society for Nature Conservation (SNF) by using analytical tools from population ecology. We first show that the increasing number of SOF and SNF members is not the result of a constant proportion of ornithologists or people interested in nature conservation among a growing Swedish population. Hence, the number of members most likely reflects the true interest in joining organizations such as SOF. We also demonstrate that the growth rate of SOF can be fairly well est…
On the qualitative analysis of the solutions of a mathematical model of social dynamics
2006
Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.