Abstracts:  NVTB - Meeting  2002

How much of its resources should an individual allocate to a costly immune system? In this presentation I apply an evolutionarily stable strategy (ESS) analysis to an epidemic model to answer this question. On the one hand, an investment in immune function confers protection to infectious agents. On the other hand, an immune system is costly, and it may reduce the host's fertility or survival. Using a reproductive value approach, we derive a number of 'evolutionary currency translations' that express the value of a decrease or increase in fertility in terms of an increase or decrease in the ability to cope with the pathogen. The currency translations determine the Evolutionarily Stable (ES) level of immunity. The analysis shows that only under special circumstances does the ES investment in immune function increase as the lifespan of the host increases. For other scenarios the ES investment in immunity may decrease with increasing lifespan, or it may even be dependent on the initial population strategy.

A major impediment of cellular automata (CA) derives from the difficulty of utilizing their complex behavior to perform useful computations. In this project, we employ non-uniform CA to implement drug treatment of HIV infection, in which each computational domain might contain a different CA rule, in the comparison with normal uniform CA model. R.M. Zorzenon dos Santos et al. (2001) reported a cellular automata approach to simulated three phase patterns of HIV infection (primary response, clinical latency and onset of AIDS), while ordinary (or partial) differential equations models have obstacles to describe the two time scales (weeks and years). In the base of this model, we introduced nonuniform rule to simulate drug therapy of HIV infection, which includes four phase patterns (primary response, clinical latency, clinical drug treatment and onset of AIDS). Preliminary results indicate that both simulations (with and without treatments) evolve to the same steady state (characteristic of class II behavior). The new model for prediction of the temporal behavior of immune system to drug therapy qualitatively correspond to clinical data.

Individuals are assumed to be vulnerable to cannibalism in some size window and to practise cannibalism in some window of larger sizes, where they do not yet reproduce. Therefore cannibalism has a negative effect on the survival of the small and, via increased growth, a positive effect on the survival of the bigger individuals. The aim is to analyse when the positive effect exceeds the negative effect.

Following the failure of a recent study [1] and the small numbers of animals yet screened for infection, it remains uncertain whether bovine spongiform encephalopathy (BSE) was transmitted to sheep in the past via feed supplements and whether it is still present. Mathematical and statistical models are therefore essential to integrate the limited and disparate data, to explore uncertainty, and to define data-collection priorities. We analysed the implications of different scenarios of BSE spread in sheep for relative human exposure levels and variant Creutzfeldt-Jakob disease (vCJD) incidence. We show that, if BSE entered the sheep population and a degree of transmission occurred, then ongoing public health risks in Britain from ovine BSE are likely to be greater than those from cattle, but that any such risk could be reduced by up to 90% through additional restrictions on sheep products entering the food supply.

[1] Frankish, H. Samples blunder renders sheep-BSE study useless. Lancet 358, 1436 (2001).

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A three-dimensional model of diffusion limited coral growth is introduced. In contrast to previous models, in this model we take a ``polyp oriented'' approach. Here, coral morphogenesis is the result of the collective behaviour of the individual coral polyps. In the polyp oriented model, branching occurs spontaneously, as opposed to previous models in which an explicit rule was responsible for branching. We discuss the mechanism of branching in our model. Also, the effects of polyp spacing on the coral morphology are studied.

Drastic changes in ecosystems such as collapses of exploited fish stocks and abrupt shifts in overall ecosystem functioning are presently discussed in terms of catastrophic behavior of these systems. Because of their threshold behavior, the presence of catastrophic events has immense implications for our understanding of the dynamics of ecological systems as well as for their management. We show that two basic individual level traits found in many species food dependent individual growth and individual mortality decreases with body size - lead to that the possibility of catastrophic population collapses is expected to be common in natural systems. Our analysis is based on a size-structured, individual-based model and shows that the interplay between these individual-level processes causes the positive density dependence that is characteristic for the depensatory growth mechanisms and catastrophic behavior in ecological systems.

The primary framework for classical life-history models is that of fitness maximization. The basic underlying assumption is that useful fitness measures can be determined a priori. However, in recent years there is an increasing awareness that adaptational studies should be done in terms of an invasion analysis. For this end one should model the outcome of an selection process with the hypothetical average growth rate of a rare mutant type in a population of a resident type (dominant Lyapunov exponent rho). This verbal definition brings out immediately that rho necessarily depends both on the mutant and the resident type. The requirement of resident stationarity implies that we have to include density dependence explicitly in the calculation of rho. I present a model for the evolution of reproductive effort in simple life-histories. I show that, depending on the exact form of density dependence, different evolutionary outcomes are possible. Beside pure and mixed ESS's, the coexistence of two pure strategies becomes possible. Furthermore, I show that polymorphisms can emerge in the course of evolution due to evolutionary branching. I discuss how the exact mechanism of density dependence and the shape of the trade-off between survival and fecundity determine the evolutionary outcome.

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Abstract not available yet.

We compare responses to enrichment of model food chains (with plants, herbivores and carnivores) in the case that both plants and herbivores have, alternatively, inducible defences, permanent defences or no defences. We investigate two basic phenomena; how enrichment affects the stability of the system, and how it affects the levels of biomasses of the three trophic levels, the latter for both stable and unstable equilibria. Our analysis shows that inducible defences lead to a major region in parameter space in which the paradox of enrichment does not hold. In this area, enrichment does not cause a transition from a stable equilibrium to population cycles. Instead, a stable equilibrium is maintained under enrichment, and a simultaneous increase in biomass densities of all trophic levels is observed. This is in contrast with the enrichment response of 'classical' model food chains with prey- dependent functional responses that assume either permanent defences or no defences. In those cases only plants and carnivores increase in biomass with enrichment, whereas the equilibrium density of herbivores remains constant. Interestingly, inducible defences may promote population persistence in the unstable region of parameter space. They do so because the minimum densities of cycling populations remain relatively high, which decreases the risk of extinctions.

The statistical testing of mechanistic models to observed time series of infectious disease cases has been problematic because the dynamics of susceptible hosts is incompletely observed. A method is presented for reconstructing the dynamics of numbers of susceptible hosts from information on case reports and serological data. It is shown how mechanistic transmission models can be tested against the reconstructed time series of infections and susceptible hosts. The proposed method is applied to data on measles outbreaks in a highly vaccinated human host population. The most parsimonious transmission model is identified, and the values of several parameters of interest are estimated, such as the basic reproduction ratio.