A stochastic dispersal-limited trait-based model of community dynamics

I present a model of stochastic community dynamics in which death occurs randomly in the community, propagules disperse randomly from a regional pool, and recruitment of new individuals of a species is proportional to the species local abundance multiplied by its local competitive ability. The competitive ability of a species is assumed to be determined by a function of one trait of the species, and I call this function the environmental filtering function. I show that information on local species abundances in a network of plots, together with trait data for each species, enables the inference of both the immigration rate and the environmental filtering function in each plot. I further study how the diversity patterns produced by this model deviate from the neutral predictions, and how this deviation depends on the characteristics of the environmental filtering function. I show that this inference framework is more powerful at detecting trait-based environmental filtering than existing statistical approaches based on trait distributions, and discuss how the predictions of this model could be used to assess environmental heterogeneity in a plot, to detect functionally meaningful trade-offs among species traits, and to test the assumption that there exists a simple relationship between species traits and local competitive ability.     

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.     

A stochastic model of the dynamics of host-pathogen systems with mutation

In this paper a stochastic model of the dynamics of host-pathogen systems with mutation is constructed. In previous works deterministic models of host-pathogen systems with no mutation were considered. The evolution of the pathogen population in any generation of the host is formulated as a multidimensional birth and death process, while the evolution of genotypic frequencies in successive generations of the host is described by a solution of a nonlinear vector difference equation. A general solution of the differential equations of the multidimensional birth and death process is presented and expressions for the stationary distribution, whenever it exists, and the mean time to extinction, when absorbing states are present, are derived. Some answers to questions raised in the discussion of a previous paper (Mode, 1962) are also contained in this paper. The research reported in this paper was supported by the United States Atomic Energy Comission, Division of Biology and Medicine Project AT(45-1)-1729.     

A stochastic model of evolutionary dynamics with deterministic large-population asymptotics

An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents’ positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents’ individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.     

Mathematical model of interphase cell death. Biophysical justification and generalization

The authors propose a biophysical justification of a radiation-induced injury and interphase death of cells. The injury to certain units of the microtrabecular network and cytoskeleton is considered to be a primary biological effect of radiation on cells. The role of these structural changes in the development of the specific radiation response is discussed. It is found possible to describe formally, by the defined parameters of the proposed model, the survival curves for not only interphase but also reproductive cell death.     

The intercellular interactions in the interphase death of irradiated thymocytes. A study of the influence of different cells on thymocyte interphase death]

The influence of different cells on death and pycnosis of thymocyte nuclei after in vitro irradiation has been investigated. It has been shown that the removal from the thymocyte suspension of cells, having the activity of natural killers, medullar thymocytes, and macrophages, does not influence the radiation-induced damage to cortical thymocytes. The injury of exposed thymocytes decreases, however, after incubation them with nonirradiated thymocytes or cultured cells, the efficiency of the latter being dependent on the type of cells. The data obtained may indicate that the exposed thymocytes interact with each other and exchange some factors that promote their injury.     

The interphase death of dividing cells. The relation of interphase death to cell energy requirements

In experiments with irradiated cells of Chinese hamster and Ehrlich ascites tumor a study was made of the influence of energy provision on their interphase death rate. The presence of the uncoupler of respiration and oxidative phosphorylation--carbonyl cyanide-3-chlorophenylhydrazone--in a medium without glucose was shown to drastically increase the interphase death rate of cells of both types, whereas this effect was not observed in a medium with glucose.     

Microtubule dynamics in interphase cells

The sites of microtubule growth and the kinetics of elongation have been studied in vivo by microinjection of biotin-labeled tubulin and subsequent visualization with immunocytochemical probes. Immunofluorescence and immunoelectron microscopy demonstrate that injected biotin-labeled subunits are incorporated into new segments of growth which are contiguous with unlabeled microtubules. Rapid incorporation occurs by elongation of existing microtubules and new nucleation off the centrosome. The growth rate is 3.6 micron/min and is independent of the concentration of injected labeled tubulin. This rate of incorporation together with turnover of existing microtubules leads to approximately 80% exchange in 15 min. The observed kinetics and pattern of microtubule turnover allow for an evaluation of the relevance of several in vitro models for steady-state dynamics to the in vivo situation. We have also observed a substantial population of quasi-stable microtubules that does not exchange subunits as rapidly as the majority of microtubules and may have specialized functions in the cell.     

Testing a simple stochastic model for the dynamics of waterfowl aggregations

We consider a simple stochastic model for the dynamics of mixed-species waterfowl aggregations and describe two methods for assessing the fit of this model to field data. The model does not incorporate species-specific behavior. It assumes that all birds act independently and incorrectly predicts an exponential distribution for inter-event times. We reject this model, show that 29% of the birds move in groups of two or more birds, and demonstrate that the distribution of inter-event times between the movements of groups of birds is exponential. We find no difference in movement rates or group sizes between seasons, and no difference between groups arriving into or departing from the observed aggregations. An analysis of group composition suggests that species at low abundance behave differently than species at high abundance: birds with few conspecifics are more likely to move in mixed-species groups than birds with many conspecifics. We suggest that simple stochastic models provide a useful way to explore the dynamics of animal behavior.     

Structure and dynamics of interphase chromosomes

During interphase chromosomes decondense, but fluorescent in situ hybridization experiments reveal the existence of distinct territories occupied by individual chromosomes inside the nuclei of most eukaryotic cells. We use computer simulations to show that the existence and stability of territories is a kinetic effect that can be explained without invoking an underlying nuclear scaffold or protein-mediated interactions between DNA sequences. In particular, we show that the experimentally observed territory shapes and spatial distances between marked chromosome sites for human, Drosophila, and budding yeast chromosomes can be reproduced by a parameter-free minimal model of decondensing chromosomes. Our results suggest that the observed interphase structure and dynamics are due to generic polymer effects: confined Brownian motion conserving the local topological state of long chain molecules and segregation of mutually unentangled chains due to topological constraints.     

Prostaglandins and interphase death of irradiated cells

The contribution of the post-irradiation changes in prostaglandin transformation to the biochemical mechanism of interphase death of irradiated cells is estimated. It is supposed that prostaglandins are secondary trigger-effectors which initiate the development of primary biochemical reactions giving rise to radiation sickness. It is suggested that the biochemical mechanism of interphase death is complex and involves several concurrent trigger mechanisms including prostaglandin regulation system.     

Pro-oxidant-induced proteolysis in the postradiation interphase death of thymocytes

Activity of intracellular alkaline proteinases increased and that of the trypsin-like proteinase inhibitors decreased in thymocytes at early times following whole-body X-irradiation of rats with a dose of 4 Gy. Pro-oxidant mechanisms of intracellular proteolysis activation are discussed.     

A plea for stochastic population dynamics

It is argued that biological populations are finite and consisting of individuals with varying life span and reproduction, and that they should be thus modelled. Modern probability theory provides tools for this.     

Modification of the interphase death of thymocytes by using colcemid

The pretreatment of thymocytes by colcemid (0.02 to 0.5 mu g/ml) induces a change in the plasma membrane state, registered by a pyrene fluorescent probe, and a decrease in the interphase cell death after 4 Gy X-irradiation. The authors discuss the role of the cell surface as a trigger initiating death program in irradiated lymphoid cells.     

A two-backbone polymer model for interphase chromosome geometry

A polymer model for the overall geometric structure of a human chromosome during the G0/G1 portion of cell-cycle interphase is constructed, based on fluorescencein situ hybridization data on distances between defined genomic sequences. The model consists of flexible giant loops, averaging about 6 million base pairs, with two random-walk backbones; it involves essentially three parameters. Numerical results based on properly selected values of parameters fit the data well.