A stochastic difference equation was build to represent a metapopulation of annual plants suffering from a variable environment. The annual plants were allowed to spread their risk by either an escape in space (dispersal) or in time (delayed germination). Optimal germination and dispersal fractions were calculated for different levels of environmental fluctuations, different size and connectivity in the metapopulation, and for different values of mortality during dispersal and delaying germination. In Klinkhamer et. al. (1987) we focused on the case of r- selection (maximum growth rate). Later research also focused on density dependent selection (ESS) (unpublished so far). The parameter subset providing an optimum where both dispersal and delayed germination are present is much larger in the case of K-selection than in the case of r-selection.
Proliferation of plant cells in liquid medium is influenced by the composition of that medium. A stochastic model for cell division has been approximated with a deterministic model in which a cell is subdivided in compartments having different biochemical properties. Population dynamics is modeled with a set of partial differential equations (Metz & Diekmann 1986). Using Linear Chain Trickery, this set is transformed to a set of delay differential equations. Monte-Carlo studies and non-linear curve fitting gave rise to a close match with experimental data. See http://www.johnval.nl/biology/thesis for the online publication.
Plant cells are able to reduce oxygen via two main pathways. Besides the common eucaryotic cytochrome respiratory pathway, plant cells have the possibility to reduce oxygen in a cyanide resistant pathway. Processes involved in respiration are: the energy requirements of the cell (mol ATP per unit time), respiration itself, and sugar consumption. A model is put forward including both pathways and the two other processes. In the literature there are two negative feedback processes proposed. One in which ATP inhibits the respiratory chain directly, and one in which ATP inhibits glycolysis, i.e the influx of reducing equivalents to the respiratory pathways. We examined which of these regulatory mechanisms could be in favor, by fitting the highly non-linear equations to the data. Although regulation via glycolysis has certain advantages, our experimental data are not able to give evidence for one or the other regulatory mechanism. See http://www.johnval.nl/biology/thesis for the online publication.
Individuals live in a intrinsic non-homogeneous environment. In this project a landscape is divided in patches, suitable for habitation by some species, and non-habitat, in which habitation by this species is impossible. Models developed for this system are compared to models in which the spatial component is less or more pronounced.
An individual based deterministic model is evaluated for species for which the local density can be high and which individuals have a high probability for dispersal. The landscape exist out of an infinite number of patches. Next to common individual mortality, disasters occur which wipe out the total or a part of the local population. The resulting models are non-linear partial differential equations. It appears that non-spatial models are as good in predicting metapopulation existence. However, those models still have a need for understanding of process at the spatial and individual level, since the parameters in the simple models are combinations of parameters from the spatial model. The simple models are less suitable for determination of the equilibria and dynamics of the spatial system, but still can be of use for examining the boundaries of population behavior. These results are supplemented with results form models with a landscape consisting of a finite number of patches. Metapopulation extinction happens with probability 1, but mean lifetime of a population can tend to infinity. Monte-Carlo simulations give rise to distributions for time till extinction of the metapopulation.
A paper on this metapopulation model can be found at http://www.johnval.nl/biology/mpop
In recent years an understanding of the molecular mechanisms for the budding yeast cell cycle has rapidly increased. There are still many questions to be resolve experimentally but we started modeling of the cell cycle to bring about an understanding of the connection between the various molecular mechanisms, and more over an understanding of the coupling form the chemical model to the observed population behavior of yeast cultures. We try to build models which are as simple as possible, and still will be able to explain many of the kinetics of mutant cell lines.
An Kinetic Analysis of a Molecular Model of the Budding Yeast Cell Cycle can be found here.
A description of the model for the population dynamics of budding yeast can be found at http://www.johnval.nl/biology/sizedist