Bob W. Kooi

INDUCIBLE DEFENSES AND TROPHIC STRUCTURE

Resource edibility is a crucial factor in ecological theory on the relative importance of bottom-up and top-down control. Current theory explains trophic structure in terms of the relative abundance and succession of edible and inedible species across gradients of primary productivity. We argue that this explanation is incomplete owing to its focus on inedibility and the assumption that plants and herbivores have fixed defense levels. Consumer-induced defenses are an important source of variation in the vulnerability of prey and are prevalent in natural communities. Such induced defenses decrease per capita consumption rates of consumers but hardly ever result in complete inedibility. When defenses are inducible a prey population may consist of both undefended and defended individuals. Here we use food chain models with realistic parameter values to show that variation in consumption rates on different prey types causes a gradual instead of stepwise increase in the biomass of all trophic levels in response to enrichment. Such all-level responses have been observed in both aquatic and terrestrial ecosystems and in microbial food chains in the laboratory. We stress that, in addition to the known food web effects of interspecific variation in edibility, intraspecific variation in edibility is another form of within-trophic-level heterogeneity that also has such effects. We conclude that inducible defenses increase the relative importance of bottom-up control.

The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis.

In many countries in Asia and South-America dengue fever (DF) and dengue hemorrhagic fever (DHF) has become a substantial public health concern leading to serious social-economic costs. Mathematical models describing the transmission of dengue viruses have focussed on the so-called antibody-dependent enhancement (ADE) effect and temporary cross-immunity trying to explain the irregular behavior of dengue epidemics by analyzing available data. However, no systematic investigation of the possible dynamical structures has been performed so far. Our study focuses on a seasonally forced (non-autonomous) model with temporary cross-immunity and possible secondary infection, motivated by dengue fever epidemiology. The notion of at least two different strains is needed in a minimalistic model to describe differences between primary infections, often asymptomatic, and secondary infection, associated with the severe form of the disease. We extend the previously studied non-seasonal (autonomous) model by adding seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of dengue fever epidemics. A comparative study between three different scenarios (non-seasonal, low seasonal and high seasonal with a low import of infected individuals) is performed. The extended models show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. We discuss the role of seasonal forcing and the import of infected individuals in such systems, the biological relevance and its implications for the analysis of the available dengue data. At the moment only such minimalistic models have a chance to be qualitatively understood well and eventually tested against existing data. The simplicity of the model (low number of parameters and state variables) offer a promising perspective on parameter values inference from the DHF case notifications.

DYNAMIC ENERGY BUDGET REPRESENTATIONS OF STOICHIOMETRIC CONSTRAINTS ON POPULATION DYNAMICS

Metabolism, and thus population dynamics, can be limited by energy, carbon, nitrogen, and/or other nutrients. This is due to homeostasis, the relatively constant composition of biomass. Yet growth-rate-dependent changes in the composition of biomass do exist. The dynamic energy budget (DEB) theory provides the framework to deal with these simultaneous limitations and stoichiometric restrictions. We illustrate the application with three examples. First, we discuss simple single-species growth of a chemolithoautotroph to illustrate the interactions between nutrients and substrates in growth. We show how the macrochemical reaction equation with variable yield coefficients can be decomposed in a number of subprocesses with constant yield coefficients. We then discuss a simple predator– prey system, where nutrients are accumulated in the prey, which no longer have a constant composition of biomass. The implication is a varying conversion efficiency from prey to predator, with consequences for qualitative aspec...

Ecological Specialization of Mixotrophic Plankton in a Mixed Water Column

In recent years, the population dynamics of plankton in light‐ or nutrient‐limited environments have been studied extensively. Their evolutionary dynamics, however, have received much less attention. Here, we used a modeling approach to study the evolutionary behavior of a population of plankton living in a mixed water column. Initially, the organisms are mixotrophic and thus have both autotrophic and heterotrophic abilities. Through evolution of their trophic preferences, however, they can specialize into separate autotrophs and heterotrophs. It was found that the light intensity gradient enables evolutionary branching and thus may result in the ecological specialization of the mixotrophs. By affecting the gradient, other environmental properties also acquire influence on this evolutionary process. Intermediate mixing intensities, large mixing depths, and high nutrient densities were found to facilitate evolutionary branching and thus specialization. Later results may explain why mixotrophs are often more dominant in oligotrophic systems while specialist strategies are associated with eutrophic systems.

Omnivory and food web dynamics

Abstract Intraguild predation is a trophic interaction in which two consumers compete for one resource and where one of the consumer species may also feed on its competitor. The intraguild predator’s diet follows from the relative strength of its interactions with its potential prey. Current view holds that weak interactions between species promote the stability of food webs. To the contrary, nutrient enrichment is predicted to destabilize ecosystems. We present a theoretical analysis of the interplay between intraguild predation and nutrient enrichment in a Marr-Pirt chemostat model of a microbial food web. We perform a two-dimensional bifurcation analysis along a gradient of allochtonous nutrient levels and a gradient of one out of two biologically plausible strategies to explore the spectrum of the intraguild predator’s foraging interactions. Both strategies show that intraguild predation may • stabilize food chains; • eliminate chaos, predicted by food chain models; • give rise to multiple stable states; • be favored in systems with low turn-over rates, where the intraguild predator has a low interaction strength and a low yield on the basal resource.

Joint evolution of predator body size and prey-size preference

We studied the joint evolution of predator body size and prey-size preference based on dynamic energy budget theory. The predators’ demography and their functional response are based on general eco-physiological principles involving the size of both predator and prey. While our model can account for qualitatively different predator types by adjusting parameter values, we mainly focused on ‘true’ predators that kill their prey. The resulting model explains various empirical observations, such as the triangular distribution of predator–prey size combinations, the island rule, and the difference in predator–prey size ratios between filter feeders and raptorial feeders. The model also reveals key factors for the evolution of predator–prey size ratios. Capture mechanisms turned out to have a large effect on this ratio, while prey-size availability and competition for resources only help explain variation in predator size, not variation in predator–prey size ratio. Predation among predators is identified as an important factor for deviations from the optimal predator–prey size ratio.

Multiparametric bifurcation analysis of a basic two-stage population model

In this paper we investigate long-term dynamics of the most basic model for stage-structured populations, in which the per capita transition from the juvenile into the adult class is density dependent. The model is represented by an autonomous system of two nonlinear differential equations with four parameters for a single population. We find that the interaction of intra-adult competition and intra-juvenile competition gives rise to multiple attractors, one of which can be oscillatory. A detailed numerical study reveals a rich bifurcation structure for this two-dimensional system, originating from a degenerate Bogdanov--Takens (BT) bifurcation point when one parameter is kept constant. Depending on the value of this fixed parameter, the corresponding triple critical equilibrium has either an elliptic sector or it is a topological focus, which is demonstrated by the numerical normal form analysis. It is shown that the canonical unfolding of the codimension-three BT point reveals the underlying dynamics of...

Dynamic noise, chaos and parameter estimation in population biology

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models such as multi-strain dynamics to describe the virus–host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

Quantitative steps in symbiogenesis and the evolution of homeostasis.

The merging of two independent populations of heterotrophs and autotrophs into a single population of mixotrophs has occurred frequently in evolutionary history. It is an example of a wide class of related phenomena, known as symbiogenesis. The physiological basis is almost always (reciprocal) syntrophy, where each species uses the products of the other species. Symbiogenesis can repeat itself after specialization on particular assimilatory substrates. We discuss quantitative aspects and delineate eight steps from two free‐living interacting populations to a single fully integrated endosymbiotic one. The whole process of gradual interlocking of the two populations could be mimicked by incremental changes of particular parameter values. The role of products gradually changes from an ecological to a physiological one. We found conditions where the free‐living, epibiotic and endobiotic populations of symbionts can co‐exist, as well as conditions where the endobiotic symbionts outcompete other symbionts. Our population dynamical analyses give new insights into the evolution of cellular homeostasis. We show how structural biomass with a constant chemical composition can evolve in a chemically varying environment if the parameters for the formation of products satisfy simple constraints. No additional regulation mechanisms are required for homeostasis within the context of the dynamic energy budget (DEB) theory for the uptake and use of substrates by organisms. The DEB model appears to be closed under endosymbiosis. This means that when each free‐living partner follows DEB rules for substrate uptake and use, and they become engaged in an endosymbiotic relationship, a gradual transition to a single fully integrated system is possible that again follows DEB rules for substrate uptake and use.

Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ade and temporary cross immunity.

We analyse an epidemiological model of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, is known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra, has to be applied in comparison to get further insight into such dynamical structures. Here we present for the first time multi-parameter studies in a range of biologically plausible values for dengue. The multi-strain interaction with the immune system is expected to have implications for the epidemiology of other diseases also.