Abstracts:  NVTB - Meeting  2000

I will describe an ongoing attempt to develop spatially realistic models of interactions between organisms that can make sense of observed patterns of ``facilitation'', where fitness can be enhanced by the presence of neighbors. I will present preliminary models of two mechanisms of facilitation in plants. In the first, plants decrease the amount of valuable resources (competition), but also decrease the degree of environmental stress (facilitation). In the second, facilitation is mediated through the foraging behavior of herbivores that might be deterred indirectly by the defenses of neighbors. By explicitly describing the resources that determine fitness, I hope to make specific predictions about the types of environments that facilitate facilitation.

Abstract not available.

MHC polymorphism: a result of host-pathogen coevolution Major histocompatibility (MHC) molecules are involved in pathogen presentation to the immune system, and are characterised by an extremely high degree of polymorphism. Despite their high population diversity, the mutation rate of MHC genes does not differ from that of other genes. The mechanisms behind the selection for MHC polymorphism have been debated for over three decades. A commonly held view is that MHC polymorphism is due to selection favouring heterozygosity. As MHC genes are codominantly expressed, individuals that are heterozygous at MHC loci have a selective advantage, because they can present a larger fraction of pathogens than homozygous individuals can. Alternatively, it has been proposed that the polymorphism of the MHC is maintained by selection for rare MHC molecules, because pathogens are expected to evolve towards evading presentation by the most common MHC molecules.

Although both views have been modelled extensively, a direct comparison of both theories is lacking. Here we use a genetic algorithm to simulate the coevolution of hosts and pathogens. Our model allows us to directly compare the effects of selection for heterozygosity and frequency-dependent selection on the polymorphism of MHC molecules. Starting from a population diversity of only one MHC molecule, we show that a diverse set of functionally different MHC molecules is obtained. Our analysis demonstrates that selection involving coevolution of pathogens can account for a much larger MHC diversity than selection for heterozygosity alone can.

Molecular analysis of fertilisation genes has revealed a remarkable pattern of molecular evolution in several marine free-spawning organisms (abalones, sea urchins). In these species, fertilisation is mediated by gamete recognition proteins that interact species-specifically during fertilisation. It appears that these gamete recognition proteins have evolved very rapidly. Using an individual-based simulation model I will explain how this pattern of molecular evolution is tied up with sexual selection and speciation.

Hypotheses about the origin of vegetation pattern formation in semi-arid areas around the world almost all include a common feature of these semi-arid areas: the presence of a positive feedback between plant density and water infiltration. However most of these hypotheses include many other factors as well.

The analysis of a model consisting of partial differential equations reveals that pattern formation can occur given only this positive feedback coupled with the spatial redistribution of run-off water. Bifuraction analysis of the model reveal the effects of herbivory, rainfall, plant properties and soil properties on vegetation pattern formation.

Several hunderd independent germinal centers (GCs) form in lymphoid tissue after infection. In about three weeks, B-cells in GCs evolve to a much higher affinity, and emerge as memory cells or secondary antibody producers. Most interpretations of the role of GCs have focussed on affinity-maturation, but we stress another functional demand on the set of B-cells emerging form GCs: Diversity. The need for diversity arises because the short-term success of a B-clone during affinity maturation within a GC does not guarantee its long-term success, namely protecting the host from re-infection, especially if the pathogen has even slightly mutated its dominant epitope in the mean time. We first estimate that a diversity of one to several dozen clones is required for reasonably reliable protection. The main question then becomes how to maintain this diversity despite the loss of diversity within each GC, due to the strong selection required for fast affinity-maturation. Using stochastic model-analysis and simulations, we compute how the output-diversity of a set of parallel GCs depends on the system parameters, i.e. the primary-response diversity, the number of cells seeding each GC, and the number of parallel GCs used. We find that tens to hundreds of independent GCs must be used, and that each must be seeded by only very few primary-response B cells. Finally, we argue that affinity-maturation can occur at least as well in parallel GCs as in one globally coupled system.

Upon starvation, solitary amoebae of Dictyostelium discoideum aggregate and form migrating multicellular slugs. A slug migrates towards the soil surface, where migration halts and the whole process culminates in the formation of a fruiting body consisting of a globule of spores on a slender stalk. The cell movement during culmination is likened to a ``fountain running backward'', in which prestalk cells from the upper part form a stalk that moves downwards to anchor to the soil, while prespore cells from the lower part move upwards to form the spore head. However, no chemical gradient nor any specific chemotactic response is yet found which could guide this straight downward motion of the stalk. It is also not clear what kind of process displaces the stalk, since the stalk cells themselves very quickly loose their motility. To gain some insight in the process of culmination we have modelled it using a hybrid cellular automata/partial differential equation model. In our model, individual amoebae are represented as a group of connected automata. It also describes slime layers with their accompanying stickiness and stiffness, as well as ongoing induction and production processes. Using our model we were able to reproduce some main features which occur during culmination, such as the straight downward motion of the stalk, the anchoring to the soil and the formation of a long slender stalk with a globule of spores on top. We postulate that the process is mainly organized by once again re-using the cAMP signalling system in a roundabout way. Note, that many complicated processes are taking place, such as differential adhesion, chemotaxis, differentiation, induction, and production of specific components. However, the culmination process is still only composed of responses of individual amoebae to the local circumstances. The collective behaviour of fruiting body formation emerges from these interactions.

Abstract not available.

I shall define a fitness concept applicable to structured metapopulations consisting of infinitely many equally coupled patches, and provide means for calculating its numerical value. In addition I shall introduce a more easily calculated quantity Rm that relates to fitness in the same manner as Ro relates to fitness in ordinary population dynamics: Rm of a mutant is only defined when the resident population dynamics converges to an equilibrium, and Rm is larger (smaller) than one 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. As an example of the usefulness of these concepts I shall calculate the ES conditional dispersal strategy for individuals that can account for the local population density in their dispersal decisions.

I will analyse the consequences of intraguild predation (IGP, a special case of omnivory) and stage- or size structure for the possible composition of a three-species community consisting of resource, consumer and predator. Two model approaches are discussed: (1) a simple ODE model, with and without stage structure for the consumer and the predator, and (2) a physiologically structured population model, where both the consumer and the predator populations are size-structured.

In the ODE model, IGP induces two major differences with traditional linear food chain models: (1) The potential for the occurrence of alternative equilibria: Convergence to either one of two stable equilibria is possible at intermediate levels of resource productivity. (2) Extinction of the consumer at high productivities. At low productivities the consumer dominates, while at intermediate productivities predator and consumer can coexist. The qualitative behavior of the model is robust against addition of an invulnerable size class for the consumer population and against addition of a juvenile, non-predatory class for the predator population. These results indicate that, over a range of environmental productivities, elimination of the intermediate species by the top species is more likely than coexistence. This is in agreement with the classical view that omnivory should be rare. The physiologically structured model shows both differences and similarities to the ODE model.

When predators overexploit local prey populations (as seems to occur, for instance, in many acarine predator-prey systems), the frequency at which predators arrive in patches with prey will influence the evolution of prey-exploitation strategies. Analogous to the evolution of virulence were multiple infection acts in favour of virulent pathogens, we expect selection for efficient predators in systems were predator invasion rates are high. In contrast, when local populations of predators are generally founded by only one or a few individuals, selection may favour those predator types that exploit their resource more prudently.

An individual based metapopulation model was used to investigate under what conditions prudent prey-exploitation strategies can evolve. Evolutionary variables included per capita predator dispersal rate from patches with prey (so-called Milker-Killer Dilemma), and per capita predator attack rate. Evolutionary dynamics were examined by looking at the mutual invasibility of resident populations and by evaluating the resident's persistency in competition experiments with mutants. In addition, we tried to relate the outcomes of the invasion and exclusion experiments to maxima or minima in the system's statistics.

It appeared that the degree of isolation of (groups of) patches plays an important role in the evolution of prey-exploitation strategies. Only in systems where most patches are inhabited just by prey can prudent predator types invade, and exclude, more efficient predator residents. Furthermore it followed that the over-all prey density is a reliable statistic for predicting the evolutionary dynamics, and hence for framing adaptive landscapes.

Original SSF process utilising grain particle to cultivate fungi offers promising novel food product and ingredients, i.e., enzymes. To have a clearly defineo d process, it is important to bridge the gap between the macroscopic fermentor-scale work and microscopic fungal growth at individual hyphae. Active hyphae migrates in the substrate mat; the grain particle, as its natural growth mechanism. At the same time, enzyme excretion to hydrolyse polymeric substrate and diffusion of these compounds occur.

Objective of this project is to provide predictions of macroscopic respiration kinetics (oxygen fluxes) based on microscopic predictions of mycelium elongation and branching, and diffusion of substrates and intermediate products. Later on, the knowledge obtained should provide predictions of variables that are important for product quality, such as enzyme concentrations and the degrees of polymer hydrolysis.

A model system is used to study the respiration kinetics instead of real grain particles and Aspergillus oryzae is used. Colony expansion rate is measured in time and oxygen consumption rate together with carbon dioxide production rate is followed on line. The colony expansion rate is expected to have certain correlation to the oxygen consumption rate. Oxygen seems to be the first limiting factor due to the layer formed by fungal mat.

Preliminary results show good agreement between the colony expansion rate and oxygen consumption rate. A system that can resemble more closely to the grain particle needs to be set up.

The consequences of size-dependent competition among individuals of a consumer population are investigated by analyzing the stability and dynamic properties of a physiologically structured population model. Only 2 size-classes of individuals are distinguished: juveniles and adults. Juveniles and adults both feed on a shared resource and hence interact by means of exploitation competition. In line with results that we previously obtained in size-structured consumer-resource models, unstable dynamics primarily occur when either juveniles or adults have a distinct competitive advantage. When adults are more competitive than juveniles, population oscillations occur that are primarily induced by the fact that the juvenile period changes with changing food conditions. When juvenile are competitively superior, two different types of population fluctuations can occur: (1) rapid, low-amplitude flucutations having a period of half the juvenile delay and (2) slow, large-amplitude fluctuations characterised by a period length of slightly more than the juvenile delay. By considering a few limiting cases of the model the mechanisms responsible for the fluctuations are identified.

Competition theory predicts that, at equilibrium, the number of coexisting species cannot exceed the number of limiting resources. In contrast to this prediction, in natural waters dozens of phytoplankton species coexist, although only a handful of resources are potentially limiting. Here we offer a surprisingly simple solution to this 'paradox of the plankton'. First, we show that, in contrast to common opinion, the textbook models for resource competition do often not lead to a stationary outcome. In fact, competition for three or more limiting resources can easily generate oscillations and chaos. Second, we show that such fluctuations in species abundances allow the coexistence of many species on a small number of resources, even for quite realistic parameter combinations.

A number of bacterial species form patterns of concentric rings or spots under conditions of oxidative stress. These patterns evolve through chemotaxis towards a self-excreted attractant [1,2]. The mechanism underlying the pattern formation behaviour has been analysed on the basis of different theoretical assumptions [1,4,5,7]. The assumptions of some of these assumptions are now outdated by experimental evidence; none of the current analyses is able to reproduce all occurring patterns by changing the appropriate parameters.

We study the pattern formation behaviour of Escherichia coli and Salmonella typhimurium. Each species is capable of producing a number of strikingly different patterns. We present a Keller-Segel type PDE model [3] which we analyze numerically to explain both differences and similarities in the large-scale patterns made by these colonies. Within species, the variety in pattern formation behaviour can be explained by differences in the amount of nutrients available. Differences between E. coli and S. typhimurium can be shown to arise from a species-specific difference in the relative rate of food depletion.

The cooperative behaviour of these bacterial species might represent a substrate which facilitated the development of more involved cooperative behaviour, as in Dictyostelium discoideum [3,6]. By elucidating the mechanism that leads to this behaviour, our modelling work may contribute towards understanding some of the evolutionary possibilities and constraints relevant in the development of multi-cellularity.

1. D.E. Woodward et al., (1995): Spatio-Temporal Patterns generated by Salmonella typhimurium Biophysical Journal 68: 2181-2189
2. H.C. Berg and E.O. Budrene, (1995): Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature (1995) 49-53
3. E.F. Keller and L. A. Segel, (1975): Travelling bands of chemotactic bacteria: a theoretical analysis. Journal of Theoretical Biology 30, 235-248 (1975)
4. L. Tsimring et al., (1995): Aggregation Patterns in Stressed Bacteria. Physical Review Letters 75(9) 1859-1862(o.a. Ben-Jacob)
5. M.P. Brenner, L.S. Levitov and E.O. Budrene, (1998): Physical Mechanisms for Chemotactic Pattern Formation by Bacteria. Biophysical Journal 74(4): 1677-1693
6. N. J. Savill and P. Hogeweg, (1997): Modeling Morphogenisis: from Single Cells to Crawling Slugs. Journal of Theoretical Biology 184:229-235
7. E. Ben-Jacob et al., (1995), Complex bacterial patterns. Nature 373: 566-567