Samenvattingen voordrachten

Paul Doucet, v/h VU     The H-response: a satiation-driven functional response

The standard way to explain the shape of functional responses is based on the notion of handling time. Although satiation is commonly recognised to be a more plausible driving principle, its adoption has always been hampered by the resulting mathematical complexity. This can be overcome by a near-perfect approximation in the form of a family of non-orthogonal hyperbolas, with the following properties.

1. The family has one extra parameter, which represents prey size
2. It covers both the Type 1 response and Holling's disk equation, and a range of intermediate forms.
3. Food preference is built-in, allowing a natural extension to multi-prey situations.

André M. de Roos, UvA     How prey change the size distribution of their predators and promote their own persistence

Current theory does not account for the influence of population composition, like age- or size-structure, on community properties. Changes in population composition may especially be important when species undergo ontogenetic niche shifts during life history, as such shifts introduce a population subdivision into distinct stages that play different ecological roles. We investigate the influence of population composition on community properties using a model of predators, consumers and two resource populations. Predators and consumers are both size structured and have exclusive resources to forage on, while predators with larger body sizes prey in a size-dependent manner on consumers. At low productivities of consumer-exclusive resource, population abundance effects determine community structure. Apparent competition with the predator-exclusive resource may drive consumers to extinction. At high productivities of consumer-exclusive resource, population size-structure effects strongly influence community properties. Alternative stable communities states occur commonly, but coexistence of predators and consumers is most likely when the predator population has a wide-spread size-distribution and consists of high density of small individuals and low density of very large and fecund individuals. Predator recruitment to large size classes is limited by a juvenile bottleneck that is induced intraspecifically. Coexistence in this community state occurs under a significantly larger range of conditions than is expected on the basis of numerical abundance of the populations alone, underlining the importance of population structure for community persistence.

Max Rietkerk, UU     Self-organized patchiness and catastrophic shifts in ecosystems

Unexpected sudden catastrophic shifts may occur in ecosystems, with concomitant losses or gains of ecological and economic resources. Such shifts have been theoretically attributed to positive feedback and bistability of ecosystem states. However, verifications and predictive power with respect to catastrophic responses to a changing environment are lacking for spatially extensive ecosystems. This situation impedes management and recovery strategies for such ecosystems. I will present a theoretical framework linking self-organized patchiness and catastrophic shifts in ecosystems by a resource concentration mechanism. This framework serves as an hypothesis of our VIDI research program, and will be further developed and tested for arid and peatland ecosystems by the PhD projects of Sonia Kèfi and Maarten Eppinga respectively.

Maarten Eppinga, UU     Evolution of metabolic organization

Peatlands occupy less than 2% of the world's land surface yet contain about 30% of the global carbon pool. Paleoecological data suggests that gradual changes in climate have caused major and sudden shifts in peatlands in the past, and concern has risen that under current climate change these systems may switch from sinks to sources of atmospheric carbon. Self-organized vegetation patterns consisting of mosses and vascular plants are a common feature of these ecosystems. Because of the ecosystem engineering capacities of both mosses and vascular plants, several positive feedbacks may play an important role in peatlands. The possible role of these feedbacks in creating bistability and self-organized pattern formation will be discussed.

Sonia Kèfi, UU     Discontinuous transitions in arid ecosystems and desertification

Arid ecosystems cover 40 per cent of the land surface of the globe and are home to nearly 20 per cent of the world population. A high proportion of the dryland area is already affected by desertification and its degradation is proceeding at accelerating rates. However, no synthetic approach to address the desertification question is actually available. The framework of pair approximation has been used to derive an analytical model describing the spatial dynamic of the vegetation of arid ecosystems. Spatial self-organization of the vegetation arises as a result of an interplay between local facilitation and global competition. The vegetation of the system may be lost through continuous or discontinuous transitions because the system can be bistable. Spatially explicit simulations have been used to link the two possible types of transitions to a desert state to the vegetation patterning.

Karen van de Wolfshaar, UvA     Life history omnivory in size-structured populations; effects on community structure

Life history omnivory and food dependent development are two important and commonly found processes in nature. Two populations, an omnivorous top predator and an intermediate consumer are modeled using a physiologically structured population model.The top predator is allowed to forage on different resources, besides the shared resource and the intermediate consumer there is an exclusive resource available for the top predator. The effects of different diet compositions of the top predator on the community structure are studied. Surprisingly, the use of a size structured model does not allow for coexistence when predators do not have access to the exclusive resource. With this diet composition the system corresponds to an intraguild predation system (IGP) but the equilibria found do not resemble the ones found in unstructured or stage structured IGP models. However, when the exclusive resource for the top predator is included in its diet the pattern of equilibria shows a far better resemblance with the community patterns predicted by stage structured models, which are also found in field data. In this setting life history omnivory promotes coexistence in size structured populations and allows for more diverse patterns in community structure.

Hans Metz, UL     Een eenvoudige fitness proxy voor gestructureerde populaties met continue kenmerken

Een bekende "fitness proxy" voor leeftijdsafhankelijke populaties in populatie-dynamisch evenwicht is R₀ - 1, with R₀ de verwachte nakomelingschap over het hele leven: $R_0 - 1 > 0 \Leftrightarrow r > 0$ met r de (invasie) fitness, dwz. de asymptotische (aanvangs-) per capita groeisnelheid van een (mutant) populatie. Deze proxy kan worden afgeleid door de karakteristieke vergelijking te evalueren bij 1 (in discrete tijd, 0 in continue tijd; ik beperk me hier tot het discrete tijd geval). Als iedereen gelijk wordt geboren is het ook voor meer algemene modellen meest tamelijk eenvoudig om deze proxy expliciet uit te rekenen, omdat in constante omgevingen dan een equivalente leeftijdsrepresentatie mogelijk is. In het algemeen moeten wel R₀ interpreteren als de dominante eigenwaarde van de volgende-generatie-operator. De aanname dat iedereen gelijk wordt geboren is equivalent met het een-dimensionaal zijn van het bereik van deze operator. Wanneer dat bereik hoger dimensionaal is vervalt de eenvoud van R₀ - 1 als fitness proxy. Mijn stelling is dat, mits de demografische parameters continu zijn in de kenmerken en we met een verbonden kenmerk-ruimte van doen hebben, we altijd het karakteristiek polynoom (functie) van de volgende-generatie-operator bij 1 kunnen gebruiken als fitness proxy voor ESS berekeningen, mits we het karakteristieke polynoom zo schrijven dat $\lambda \rightarrow \infty$ als , Y de mutant, X de resident: X is oninvadeerbaar als Y≠X : P_Y(1 ) > 0 en kan worden geïnvadeerd als er een Y bestaat zdd. P_Y(1 ) < 0. Zonder continuïteit of verbondenheid is het mogelijk om gevallen te construeren met voor alle Y≠X : P_Y(1) > 0 terwijl toch X geinvadeerd kan worden.

Ellen Evers, UU     Evolutionary branching and in-phase cycles in an algae zooplankton system

My starting point will be the multi-clone model of an algae zooplankton system published by Yoshida et al. (2003), where a number of algae types differ in a certain parameter which describes a trade-off between predation and growth. An interesting phenomenon in this system is the occurrence of predator-prey population cycles which are almost out of phase. This happens when the total algae population consists of some subpopulations with quite different trade-off parameters.

Extending the model with prey that are evolving this trade-off parameter we investigate whether on an evolutionary time scale this behaviour would be expected. Starting with one algae type gradual evolution drives the trade-off parameter to an optimal value. Under appropriate conditions the algae population can indeed split up into two types which then each follow an opposed strategy.

Michel Durinx, UL     Analysing adaptive dynamics models

Adaptive dynamics studies which rare mutants can establish themselves in an environment inhabited by a large equilibrium population of residents closely resembling the mutant, which of these invasions will lead to the demise of the original residents, and what the evolutionary outcome will be of a series of such substitution events.

As such, evolution is modelled as proceeding through gradual, heritable changes in the strategies (i.e. the life history parameters) of individuals. There is an approximation for the rate of change in the strategies, the so-called canonical equation. This approximation does however fail in the close proximity of evolutionary singularities, which are basicly the interesting points in the strategy set, as they include the possible evolutionary endpoints and points where diversification takes place. It can be shown that near such singularities, all physiologically structured models behave approximately like Lotka-Volterra models.

In this talk I will show how the two approximations, away from and near to singularities, can be linked up and where the problems reside. That way, these rather theoretical results can be practically applied: since structured population models form such a broad class -- continuous or discrete time, ODE or delay equation, Leslie model or multiple birth state model -- the presentation will show how a general adaptive dynamics research program can be applied to everybody's favourite model.

Pleuni Pennings, Ludwig-Maximilians-University Munich     The role of standing genetic variation in adaptation

Imagine a population that has to adapt to a new environment. What happens is roughly this: Selection will fix the alleles that were already present in the population but that were neutral or slightly deleterious and now have become beneficial. At the same time new mutations will arise and some of them will be favourable and may become fixed as well. So we can see the adaptation of the population as a process consisting of two waves of fixation events (that overlap in time): in the first wave old mutations are fixed and in the second wave new mutations. New mutations that sweep through the population are known to leave a molecular footprint due to the hitchhiking effect. Therefore people search for this footprint (regions with low variation) hoping to find genes that are important for adaptation. The questions that I will address in my talk are: Is the first wave or the second wave of fixation events more important for adaptation? When looking for so-called sweep regions will we find fixation events from the second wave of fixation events only? Is it possible to use variation data to look for events from the first wave?

George van Voorn, VU     Predators can stimulate prey by indirect syntrophy

Traditionally predators are considered a burden for consumers (prey) in ecosystems; however, this judgement is the result of a very simple view on the interaction between the predator and the consumer. Recycling in a closed nutrient-producer-consumer-predator system points in a totally different direction; one in which predators interact symbiotically with consumers. We regard a model with negligible nutrient input and three classes of consumers: healthy and reproducing consumers, weak and post-reproductive consumers, and dead consumers. Bifurcation analysis shows that the preferences of the predator greatly affect the long-term dynamics of the system. Apart from the direct interactions, the predators stimulate nutrient recycling and eliminate competition for the healthy, reproducing consumers by feeding preferentially on the weak.

Anne Willem Omta, VU     The impact of geophysical turbulence on three-dimensional plankton distribution patterns

It has been well-established that phytoplankton in the ocean's upper layer binds carbon dioxide from the atmosphere and hence reduces the greenhouse effect. By transporting nutrients and plankton itself, turbulent 'stirring' of the ocean is thought to have a large influence on plankton growth and dispersal patterns. Unfortunately, this influence is not yet quantified or even well understood. Hence, our aim is to investigate and quantify the impact of ocean eddies on plankton growth and dispersal by means of computer simulations. This project is still in its preliminary stage and suggestions regarding our work are appreciated.

Jorn Bruggeman, VU     Trait-based models for functional groups

The concept of organism traits is well-established, in particular in (theoretical) evolutionary biology. Here, traits are looked upon as quantifiable species-bound entities. In this presentation, I will explore a means to describe a large variety of species with a generic multiple-trait population model. This bare-bone model incorporates Marr-Pirt kinetics in combination with multiple-substrate growth. Traits are added as trade-off relationships: they enhance nutrient affinity, but also increase costs for maintenance and growth. The spectra of trait values are assumed to be broad and continuous, implying infinite biodiversity. To account for this, the system is set-up with a grid of many populations, each population with a unique combination of trait values. The transient behavior of the trait value distributions may be interpreted as the rise and fall of species and functional groups. As a test case, I apply the approach to describe plankton-based functional groups and ecosystems in the ocean water column.

Remko Holtkamp, UU, S.C. Dekker and P.C. de Ruiter     Soils in Transition: modeling patterns and soil processes of former agricultural ecosystems

Conversion of arable land into grasslands is one of the major practice for restoring natural ecosystems in the Netherlands. The process, however, can take up to several decades. In this project we study underlying processes that cause that long period and study practices to shorten the transition time. Besides an empirical study for collecting data, we want to analyze this with a theoretical point of view. A first simple model with the first tropic levels (substrate and microbes) is evaluated. Since some important parameters in the model are unknown we need to develop a calibration routine for calibrating these parameters with the measurements we collected. After calibration we want to simulate the fungi and bacteria biomass during transition before we expand the model to the entire soil food web.

Otto Cordero, UU     Mutational Dynamics and the Structure of Gene Regulatory Networks

We study the evolution of networks of regulatory networks at different organizational levels such as degree distribution, modularity and local interconnections, by means of a null model that allows us to focus on the consequences of mutational dynamics on network organization. We are able to reproduce and explain important aspects of these networks such as the presence of regulatory hubs, the distribution of binding sites and the over-representation of some particular network motifs. Our results and insights are mainly compared and validated against the yeast regulatory network.

Nobuto Takeuchi, UU     Phenotypic error threshold; additivity and epistasis in RNA evolution

BACKGROUND: The error threshold puts a limit on the amount of information maintainable in Darwinian evolution. The error threshold was first formulated in terms of genotypes. However, if a genotype-phenotype map involves redundancy (``mutational neutrality''), the error threshold should be formulated in terms of phenotypes since there is no unique fittest genotype. A previous study formulated the error threshold in terms of phenotypes, and their results showed that a rather low degree of mutational neutrality can increase the error threshold unlimitedly. RESULTS: We obtain an analytical formulation of the phenotypic error threshold by considering the ``additive assumption'', in which base substitutions do not influence each other (no epistasis). Our formulation shows that an increase of the error threshold due to mutational neutrality is limited. Computer simulations of RNA evolution are conducted to verify our formulation, and the results show a good agreement between the analytical prediction and the simulations. The comparison with the previous formulation illustrates that it is important for the prediction of the error threshold to consider that the number of base substitutions per replication is rather large near the error threshold. To examine the additive assumption, a detailed analysis of additivity and epistasis in RNA folding of a particular sequence is performed. The results show a high degree of epistasis in RNA folding; furthermore, the analysis also elucidates the reason of the success of the additive assumption. CONCLUSIONS: We conclude that an increase of the error threshold by mutational neutrality is limited, and that the additive assumption achieves a good prediction of the error threshold in spite of a high degree of epistasis in RNA folding because the average number of base substitutions of sequences retaining the phenotype per replication is sufficiently small to avoid of the effect of epistasis.
Literature: BMC Evol Biol. 2005 Feb 3;5(1):9

Veronica Albers Grieneisen, UU     Modelling Tumour Growth Dynamics

We explore quantitatively, through both experiments and computer simulations, how the relationship between tumour structure, cell phenotype and cell cycle regulation brings forth feedback mechanisms that determine growth and invasiveness of cancer lineages. It is well established that, on a phenomenological level, some populational growth models can be adjusted with much success to experimental growth curves of tumour cells. For example, the Gompertz model is widely used to fit experimental data and obtain parameters that describe different tumour lineages. However, a physical or biological interpretation of the parameters is lacking. Measuring and analyzing both the growth curve and the phenotypical characteristics of six different tumour lineages, we were able to establish a novel interpretation of these growth parameters in the light of phenotypical characteristics of the individual cells that constitute the tumour. This part of the study strongly suggested that especially cell deformation can be closely linked to tumour cell growth. To verify the predictions and theoretically understand the implications of such a dependency, we incorporate the experimentally obtained cell phenotype regulation mechanism hypothesis in simulations using the Cellular Potts Model. Because cells exist on a mesoscopic level within this model, cell adhesions and cohesions with substratum naturally bring forth differentiated cell spreading and cell forms. By postulating an intrinsic cell shape dependent mitosis mechanism, we demonstrate that a variation in cell form can indeed regulate population growth as a result of the emergent topology of the tumour. Thus, we are finally able to link adhesion, cohesion and mitosis regulation properties with global characteristics of a tumour, such as growth rates and degree of malignancy. On a higher level, this work shows how the evolution of a tumour generates certain distributions of cell phenotypes within the tumour, which, influenced by intrinsic properties of the cells, also determines the topology of the tumour itself. The manner in which cell division is controlled in the light of these morphological signals makes one of the differences between normal cells and altered cells.

Dejan Milutinovic, UU     Stochastic evolution of drug resistance in HIV-1: What is the impact of recombination?

This talk will be about stochastic models exploited to analyze T-Cell-APC interaction. We found that ODE models of cells population interaction have limitation in explaining experimental data. In order to develop more realistic models of the population we propose stochastic modeling approach which is based on the individual cells behavior. We expect that stochastic models provide better insight into experimental data and the individual cell dynamics.

Christian Althaus, UU     Stochastic evolution of drug resistance in HIV-1: What is the impact of recombination?

The emergence of drug resistance mutations in HIV has been a major setback in the treatment of infected patients. Beside the enormous mutations rate, recombination has been conjectured to have an important impact on acquiring drug resistance mutations. In population genetic theory, recombination may be beneficial in combining beneficial mutations in finite population sizes. Over the last years, several studies estimated the effective population size (N_e) of HIV-1 in vivo to be very small, close to 1'000. We expand a previously described deterministic population genetic model of HIV replication that incorporates the stochastic processes in finite populations of infected cells. We use several parameters from literature to simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquiring beneficial mutations for drug-resistant viral strains for small effective population sizes. Viral strains seem to fix beneficial mutations sequentially rather than combine them from different strains through recombination. Furthermore, a reduction in population size caused by drug therapy can be overcome by higher viral mutagenesis following a faster evolution of drug resistance. We conclude that it is rather unlikely that recombination significantly speeds up the evolution of drug resistance in HIV if effective population sizes are small. However, under certain circumstances, recombination can lead to a substantial acceleration of drug resistance.

Hans Heesterbeek, UU     Interaction between different scales in the dynamics of infectious diseases

The application of mathematical reasoning to the field of infectious disease epidemiology and control has a long and rich history, going back to the 17th century. In the past two decades there has been enormous interest in epidemic theory, reflected in the large increase in scientific papers, in the 'reality content' of the topics addressed and in the broadening of methods that are applied. In this lecture I aim to give some of the flavour of the topics that are studied presently and the biological and mathematical questions that they raise. For example, the study of networks of contacts and contact tracing, emergence of resistant strains and strain diversity, and newly emerging disease agents.

I will especially pay attention to, what I call, interaction between different scales. Recently we have seen resilient outbreaks of foot-and-mouth disease and avian influenza, re-emerging malaria, spread of resistance to antiviral (HIV), antibacterial (tuberculosis, MRSA, VRE,) and ruminant nematode treatment, endemic infections that remain elusive to eradication and the surprisingly rapid spread of SARS. These examples have a population phenomenon in common: there is an additional dimension involved beyond spread in an individual or a community. All examples show interaction at different scales of biological integration:

a.

Interaction of within-host dynamics and between-host transmission ('the population dynamics of immunity')

b.

Interaction of within-community transmission and between-community spread ('the metapopulation dynamics of disease'