Abstracts:  NVTB - Meeting  1999

I will discuss the consequences of population interactions on the evolution of emergent properties in plant communities. I will demonstrate this in three case studies: recovery in a Dutch heathland, spatiotemporal dynamics of an annual plant community in the Negev, and postglacial vegetation change in North America.

Steady-state levels of HIV-1 viremia in the plasma can vary more than a thousand-fold between HIV+ patients, and have been shown to be of paramount importance for the prognosis of the infection. It has previously been shown that the level of viremia is negatively correlated with the frequency of CTLs specific for HIV-1 antigens. It is also known however that the viremia level, and the rate of disease progression, is correlated with the supply of target cells, and with characteristics of the virus such as the co-receptor usage.

Analyzing a set of mathematical models we show that such correlations between steady values provide little information on the mechanisms by which the virus is controlled. The correlations between steady state levels in mathematical models depend too crucially on the precise form of the model. Because mathematical models are always based upon simplifications, such as the number of variables taken into consideration, the correlations predicted by mathematical models are not generic. Clinically observed correlations therefore provide little information on the contribution of the different factors controlling the infection.

We here develop a ``lumped parameter approach'' which is insensitive to the precise form of the mathematical model. We show that several generic parameters can be estimated from published steady state values. Importantly, these parameter values are independent of the precise form of the underlying mathematical model. Establishing the variation in the realized lumped parameter values in a group of HIV-1 patients, we proceed by discussing the underlying processes that may be responsible for this variation. This provides more parsimonious explanations for the previously observed correlations.

Cannibals and their victims often share common resources and thus potentially compete. Smaller individuals are usually competitively superior, while larger ones may use cannibalism to counter this competition. We study the interplay between cannibalism and competition using a size-structured population model, in which all individuals consume a shared resource, but larger ones may cannibalize smaller conspecifics. In the model, intercohort competition causes single-cohort cycles when cannibalism is absent. Moderate levels of cannibalism reduces intercohort competition, enabling coexistence of many cohorts. More voracious cannibalism, in combination with competition, produces large-amplitude cycles and a bimodal population size-distribution with many small and few giant individuals. These coexisting ``dwarfs'' and ``giants'' have very different life histories, resulting from a reversal in importance of cannibalism and competition. The population structure at time of birth determines whether individuals suffer severe cannibalism with the few survivors reaching giant sizes, or suffer intense intracohort competition, with all individuals remaining small. These model results agree remarkably well with empirical data on perch population dynamics, suggesting that the induction of cannibalistic giants in piscivorous fish is a population dynamic, emergent phenomenon that requires a combination of size-dependent cannibalism and competition.

Because habitat fragmentation is generally considered to be detrimental to the persistence of natural populations, nature management tends to prefer few large nature reserves over many small nature reserves having equal total area. This presentation examines whether this preference is warranted in the Levins metapopulation model with circular reserves (patches) by formulating the dependence of metapopulation persistence on the size and number of reserves, which both depend on reserve radius if the total area is kept constant. Two measures of metapopulation persistence are used: Ro, the number of patches colonized by an occupied patch during its lifetime as an occupied patch, and Te, the time to extinction, which is only defined in the Levins model if Ro < 1. These two measures are functions of the extinction and colonization rates of the Levins model, and therefore several mechanisms for the extinction and colonization processes are formulated from which the dependence of these rates on reserve radius is calculated. It turns out that Te generally increases with reserve radius for all mechanisms, which supports the preference of few large reserves; however, Ro only supports this preference for some special, rather unrealistic, mechanisms. In many other, more realistic, cases an intermediate reserve size exists for which metapopulation persistence measured by Ro is optimal. The exact value of this optimal reserve size depends on the species under consideration and the total amount of reserve area. These results seem to remain valid qualitatively when some of the constraints due to the asumptions of the Levins model are relaxed.

In a finite population a single locus with a pair of alleles A and a is considered. Under the influence of selection and genetic drift, the allele A will become extinct or fixed in a finite time. In this paper we study the expected extinction and fixation times using a diffusion approximation. Though exact expressions are available for these exit times, they are not very transparent. For large populations, though, it is possible to derive asymptotic approximations that are more informative. We obtain our solutions by asymptotically solving the backward Fokker-Planck equations for these exit times. In particular we study the case where the fitness of the heterozygote Aa is in between the fitnesses of the homozygotes AA and aa.

With the eutrophication of many freshwaters and coastal environments, phytoplankton blooms have become a common phenomenon. This paper uses a reaction-diffusion model to investigate implications of vertical mixing processes for the dynamics and species composition of phytoplankton blooms. The model reveals that there are two fundamentally different mechanisms for bloom development. One mechanism works in well-mixed environments, and corresponds to the classical ``critical-depth'' theory. The other mechanism is based on the rate of turbulent mixing. If turbulent mixing is less than a ``critical turbulence'', phytoplankton growth rates exceed vertical mixing rates, and a bloom develops irrespective of the depth of the upper water column. Interestingly, these two different mechanisms select for different species traits, and hence for a different species composition of the phytoplankton bloom as well.

Adaptive dynamics considers phenotypic trait evolution as a process which proceeds in many small steps, each step initiated by the occurrence of mutants in a resident community. Aim of a bifurcation analysis for adaptive dynamics is to explain how this process depends on parameters of the underlying population dynamics. As a toy model to study this dependence we analyse phenotypic trait evolution in case the population dynamics is given by a Lotka-Volterra competition model. The Lotka-Volterra model serves to introduce several ideas of adaptive dynamics that go beyond the limitations of the model under consideration. Only by simplifying can we grasp the complex process of phenotypic trait evolution. The usual interaction coefficients in the Lotka-Volterra model are obtained from an interaction function. This function has the phenotypic trait values of the competing species as its variables, and in addition depends on several parameters. From the interaction function the invasion function is derived. The invasion function plays an essential role in adaptive dynamics. It is a tool to express the initial fate of mutants after their emergence from a resident population, in terms of the phenotypic traits of residents and mutants. First we discuss phenotypic trait evolution in case a second degree polynomial is used to describe the interaction. This polynomial should be interpreted as a local second order Taylor expansion of a more general smooth interaction function. For many regions of the corresponding parameter space of the second degree polynomial the properties of trait evolution will be stable, i.e. the properties do not change under a small change of the parameter values. For certain parameter values however properties can become unstable. By taking into account higher order terms of the interaction function we unfold the several possibilities for phenotypic trait evolution at these initially unstable parameter values, i.e., we study how these higher order terms discriminate between evolutionary scenarios that can not be distinguished when only the second order polynomial is considered. Restricting ourselves to scalar trait values and to two competing populations, we can represent trait evolution in a so-called Pairwise Invasibility Plot, shortly denoted by PIP, which is a sign plot of the invasion function. By making use of PIP's the bifurcation analysis gets a geometric component, which can guide the intuition in finding patterns in the evolutionary process.

Tijdens een uitbraak van Klassieke Varkenspest, zoals in 1997-1998 in Nederland, is het tijdens bestrijding zaak de Basic Reproduction Ratio Ro onder de 1 te brengen. Omdat elk besmet bedrijf wordt geruimd, is vooral de Ro tussen bedrijven van belang, de Rh. Bedrijven kunnen alleen voor detectie infectieus zijn naar andere bedrijven, en om het risico van een bedrijf te kunnen inschatten, is het van belang een idee te hebben over hoe de infectie zich binnen een bedrijf ontwikkelt. In dat geval zou je (a) het infectie moment kunnen schatten en (b) het verwachte aantal bedrijven kunnen schatten, dat door het gedetecteerde bedrijf geïnfecteerd is. Bovendien zou je (c) vooraf kunnen inschatten hoe snel je een besmet bedrijf zou moeten detecteren om deze verwachtingswaarde zo laag mogelijk te houden. Zelf ben ik voornamelijk geïnteresseerd in toepassing (c). Ik zal beginnen met uiteen te zetten wat er volgens mij in een model moet zitten voor een dergelijke toepassing. Daarna zal ik twee modellen bespreken (Laevens et al., 1998; Stegeman et al., in press), die ontwikkeld zijn voor toepassing (a) en bediscussiëren in hoeverre die voor toepassing (c) bruikbaar zijn. Tenslotte zal ik het hebben over een eventueel nieuwe opzet, afhankelijk van hoever ik dan gevorderd ben.

The Barn owl is a common species in Western Europe that has shown a strong decline in numbers in many areas of its range. Conservation actions have resulted in an increase in nesting facilities (considered to be a bottleneck), but numbers are still low compared to former times. Food now seems to be the limiting factor. The influence of fluctuating vole numbers (the most important food species) on the equilibrium density of Barn owls has been assessed with mathematical models. Preliminary results indicate that especially the vole densities in low vole years have a high impact on the equilibrium owl density.

The evolutionary literature is still heavily biased towards the allopatric speciation scenario. Contrary to the past situation, it is now relatively easy to produce working models for sympatric and parapatric speciation. Sympatric speciation is also making a comeback in the experimental literature.

Oddly enough it are now the models for allopatric speciation which are relatively underdeveloped: there is a lot of handwaving but little hard mathematics or computer simulations. Yet there is also considerable field evidence for allopatric speciation, including seemingly contingent, or non-adaptive, speciation, i.e., speciation occurring without any obvious connection to differences among local selective regimes. To study one set of conditions for contingent speciation we devised a simulation model which combines a simple genotype, consisting of a number of two-state loci, with a simple model for stabilising selection on the resulting phenotype with the slight twist that we let the optimum phenotype undergo fluctuations in time but not in space. Environmental tracking is made possible by the continual but infrequent occurrence of mutations. If the population is temporarily split into two, the two populations diverge genotypically, producing two distinguishable clouds in genotype space, but not phenotypically. Next we remove the barrier. For an additive genotype to phenotype map the two genotypic clouds speedily merge. But for random genotype to phenotype maps we occasionally keep two clearly distinct clouds after the barrier has been partially lifted.

We analyze simple evolutionary population dynamics using a mathematical frame work derived from methods used in the theory of statistical mechanics.

A model is presented that shows under which circumstances genetic redundancy can evolve. It incorporates not only developmental errors, but also costs of producing enzymes, which is a major omission in a number of existing models. Apart from the general results we present a classification of all qualitatively different parameter combinations. One of the important results is that, contrary to general belief, redundancy can evolve in temporally stable environments. As this is a work in progress, the model can still be improved a bit, so any comments are welcome !

We discuss the problem of building of a realistic electrophysiological model of the human atria. From the Institut für Mathematik und Datenverarbeitung in der Medizin, Hamburg, Germany, we obtained voxel data of the atria, which was generated by segmenting the slice data available from the Visible Human Project. Using the marching cubes algorithm, we constructed the atrial surface as a three-dimensional triangular mesh. Methods for the numerical solution of reaction-diffusion equations on this mesh are designed and evaluated.

De overgang van een eindig communicatie-systeem naar de ``oneindige'' taal van mensen wordt gezien als een van de 'major transitions' in de evolutie. Een heftig debat woedt over de vraag of die overgang genetisch is gecodeerd en onder welke selectie-druk zij is ontstaan. Wij bestuderen het ontstaan van grammaticale taal in een computermodel, waarin een kleine, evoluerende groep agents met elkaar communiceert. De agents produceren en begrijpen korte strings van symbolen met behulp van hun eigen ``herschrijf-grammatica'' en de scores die zij daarvoor ontvangen bepalen de reproduktie-kansen. De resultaten van de eerste serie simulaties laten zien dat met een bepaald gemengd scoringsschema zowel grammatica's kunnen ontstaan die een kleine, eindige taal opleveren, als grammatica's die een krachtige, oneindige taal opleveren. Uit experimenten met 5 simpelere scoring-schema's concluderen we dat een selectie-druk op ontvangst en verwerking van informatie wel, maar een druk op informatie-uitwisseling, intimidatie of manipulatie niet zulke krachtige talen oplevert.