Kinetics of Aggregate Formation in Social Insects

A model for the kinetics of aggregation in social insects which accounts for stochastic effects arising from individual variability and covers both the early and the mature stages of the process is developed. Different aggregation scenarios are studied, depending on the degree of cooperativity and the mean population density. It is shown that under certain conditions, the system evolves slowly to a single cluster incorporating all individuals, or to two coexisting clusters of similar sizes. Present address: Department of Zoology, University of Oxford, OX1 3PS Oxford, UK.     

Dynamics of infection with multiple transmission mechanisms in unmanaged/managed animal populations

Deterministic and stochastic models motivated by Salmonella transmission in unmanaged/managed populations are studied. The SIRS models incorporate three routes of transmission (direct, vertical and indirect via free-living infectious units in the environment). With deterministic models we are able to understand the effects of different routes of transmission and other epidemiological factors on infection dynamics. In particular, vertical transmission has little influence on this dynamics, whereas the higher the indirect (direct) transmission rate the greater the tendency to persistent oscillation (stable endemic states). We show that the sustained cycles are also prone to demographic effect, i.e., persistent oscillation becomes impossible in the managed case (in the sense of balanced recruitment and death rates) by comparing with results in unmanaged populations (exponential population dynamics). Further, approximations of quasi-stationary distributions are derived for stochastic versions of the proposed models based on a diffusion approximation to the infection process. The effect of transmission parameters on the ratio of mean to standard deviation of the approximating distribution, used to judge the validity of the approximations and the expected time until fade out of infection, is further discussed. We conclude that strengthening any route of transmission may or may not reduce the expected time to fade out of infection, depending on the population dynamics.     

Self-organization vs Watchmaker: stochastic gene expression and cell differentiation

Cell differentiation and organism development are traditionally described in deterministic terms of program and design, echoing a conventional clockwork perception of the cell on another scale. However, the current experimental reality of stochastic gene expression and cell plasticity is poorly consistent with the ideas of design, purpose and determinism, suggesting that the habit of classico-mechanistic interpretation of life phenomena may handicap our ability to adequately comprehend and model biological systems. An alternative conceptualization of cell differentiation and development is proposed where the developing organism is viewed as a dynamic self-organizing system of adaptive interacting agents. This alternative interpretation appears to be more consistent with the probabilistic nature of gene expression and the phenomena of cell plasticity, and is coterminous with the novel emerging image of the cell as a self-organizing molecular system. I suggest that stochasticity, as a principle of differentiation and adaptation, and self-organization, as a concept of emergence, have the potential to provide an interpretational framework that unites phenomena across different scales of biological organization, from molecules to societies.Edited by R.J. Sommer     

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.     

The importance of sampling scale in the assessment of intraspecific life-history differences in plains killifish,Fundulus zebrinus,populations (Pisces: Cyprinodontidae)

Synopsis The purpose of this study was to determine the effects of unpredictable environmental fluctuations on the demographic and genetic structure of Fundulus zebrinus populations. Collections of F. zebrinus were taken from three rivers in the Arkansas River basin: the Arkansas, Chikaskia, and Ninnescah. Fish were sampled from three sites on each river on nine collection dates throughout 1984 and 1985. Totals of 2100 fish and 6000 fish were included in electrophoretic and demographic analyses, respectively. The results of the study indicate that within a limited geographic region (i.e. within rivers) spatial differences and temporal changes in both demographic and genetic population characteristics occur frequently and are primarily stochastic. However, on a larger spatial scale (i.e. across rivers), general trends emerge for demographic and especially for genetic population characteristics. These results illustrate the importance of sampling scale for conclusions of life-history evolution in fluctuating environments. In addition, it was found that regulation of Fundulus zebrinus populations includes an important density-independent component. Stochastic demographic differences across space and changes through time and spatially and temporally heterogeneous allele frequencies, are both indicative of density-independent regulation. Variation in population parameters, both demographic and genetic, was observed between populations sampled from each river. These population differences were attributed to differences between the rivers themselves.     

Effects of variation in individual growth on plant species coexistence

Abstract. Both size structure and variability (spatial heterogeneity, disturbance, stochasticity, variation in species attributes, etc.) are regarded as regulatory mechanisms of species coexistence. However, none of the models so far proposed consider both size structure and variability simultaneously. A size-structured variation model for plant-community dynamics is proposed, which is based on the diffusion model for growth dynamics of plant populations. This model has four functions: (1) mean growth rate of individuals of size x at time t, G(t, x) (species-specific mean traits, e.g. competitive ability); (2) variance in growth rate of individuals of size x at time t, D(t, x) (stochastic factors due to genetic variation, environmental heterogeneity, spatial variation of individuals, etc.); (3) mortality rate of individuals of size x at time t, M(t, x); and (4) recruitment rate at time t, R(t), as a boundary condition. The interference function for individuals of size x at time t, C(t, x), is introduced, which expresses the degree of interactions between individuals and hence averaged effects of local neighbourhood competition; the G(t, x), D(t, x), M(t, x) and R(t) functions are given in terms of C(t, x). These four functions describe the growth dynamics of individuals of each species in the plant community. Effects of the G(t, x), D(t, x), M(t, x) and R(t) functions on species coexistence in plant communities were evaluated by simulation and the relative importance of the D(t, x) function as well as size structure was shown for species coexistence especially in plant communities where competition among species is non-transitive or niche limitation does not work.     

Self-organization versus watchmaker: molecular motors and protein translocation

Generation of directional movement at the molecular scale is a phenomenon crucial for biological organization and dynamics. It is traditionally described in mechanistic terms, in consistency with the conventional machine-like image of the cell. The designated and highly specialized protein machines and molecular motors are presumed to bring about most of cellular motion. A review of experimental data suggests, however, that uncritical adherence to mechanistic interpretations may limit the ability of researchers to comprehend and model biology. Specifically, this article illustrates that the interpretation of molecular motors and protein translocation in terms of stochasticity and self-organization appears to provide a more adequate and fruitful conceptual framework for understanding of biological organization at the molecular scale.     

A mathematical and computational approach for integrating the major sources of cell population heterogeneity

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking.In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level.The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.