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This is the joint group meeting of the research groups in Applied and Theoretical Systems Science. We discuss new results, bounce off new ideas, practice talks, and do journals clubs - just to mention a few of our activities.

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Archive: Previous research groups meetings

Summer Semester 2015

Abstracts of selected talks

Eduardo Liz, Departamento de Matemática Aplicada II, Universidad de Vigo (España)

Logistic population models revisited

The logistic equation is one of the best known models of population growth. The original ODE proposed by Verhulst inspired other related models which exhibit rich dynamics; for example, the discrete logistic equation (quadratic map) became a paradigm of chaos after the seminal papers of May.

In this talk, we consider logistic models of exploited populations, focusing on the changes in the dynamics as the harvesting effort is increased. In this way, we discuss the global dynamics and highlight the link among different logistic equations usually employed in population models.

Daniel Ritterskamp and Bernd Blasius (ICBM, University of Oldenburg)

Evolutionary Dynamics in Food Webs:  Influence of Interaction Range, Resource Distribution and Space

Food webs encode feeding interactions in ecological communities, originating from an interplay of evolutionary and ecological processes. Here we develop an evolutionary food web model in which feeding interactions between species are related to the relative distance of their adaptive traits in niche space. We present three model variants, which are analyzed using numerical simulations in combination with adaptive theory.

First, considering a single trait (bodysize), we uncover novel evolutionary dynamics, characterized by oscillations of bodysize within whole trophic guilds. Next, we study a system driven by two basal resources at different niche positions. For certain resource configurations this can lead to a dynamic instability of the food web, because the predators can not optimize their trait position towards both resources. This results into tight coupling of ecological and evolutionary dynamics, giving rise to biomass oscillations and intermittence in the population dynamic. Finally, we embed the model into a two dimensional niche space, where the additional niche axis might describe a spatial coordinate. The model is able to produce a wide range of static and dynamic food webs, depending on the width of the interaction kernel.

The structure of these food webs has common features with empirical data (e.g. intervality) that other models lack to describe. We conclude that the interaction of ecological and evolutionary dynamics can give rise to complex behaviour, such as sustained oscillations, intermittency, and ongoing evolution. Combined with spatial considerations, our studies have the potential to predict evolutionary behaviour in real food webs.

Fanny Groll, University of Cologne

Chaotic attractor in 2-prey-1-predator-system originates from interplay of limit cycles

We investigate the appearance of chaos in communities promoting coexistence. Our paradigm is an aquatic microbial food web comprising two prey and a predator species. We show that even in this small system a regime of chaotic population dynamics is formed over a wide range of intermediate dilution strengths. Specifically, the numerical simulation of the system reveals the presence of a chaotic attractor in the intermediate parameter window between two regimes of periodic coexistence (stable limit cycles). The intermediate structure provides the basis for the stable coexistence of all three species: environmental perturbations may result in huge fluctuations in species abundances, however, the system at large tolerates those perturbations in the sense that the population abundances quickly fall back onto the chaotic attractor manifold and the system remains. This mechanism explains how chaos helps the system to persist and stabilize against migration. The model is in agreement with laboratory studies. 

Virgile Baudrot, Antoine Perasso, Clémentine Fritsch and Francis Raoul

Laboratoire Chrono-environnement – UMR 6249, Université de Franche-Comté / CNRS, 16 route de Gray, 25000 Besançon (France)

The foraging behavior on trophically transmitted parasites

Small mammal populations display fluctuating patterns of densities in many ecosystems worldwide, leading their predators to adapt their foraging strategy (the multi-species functional response, MSFR). The predator-preys relationship is the route of transmission of a large number of zoonotic parasites with a complex life cycle (infecting different hosts during their life), like the cestode Echinococcus multilocularis (Em). This parasite is widely distributed in the Northern Hemisphere and is the causative agent of the emerging zoonosis alveolar echinococcosis in humans. The red fox Vulpes vulpes is a typical definitive host (DH) of Em, with, in eastern France, the rodents Microtus arvalis and Arvicola scherman as intermediate hosts.

We described this eco-epidemiological system with ODEs and we computed the basic reproductive number R₀, i.e., the number of secondary infections caused by a single primary infection into an otherwise susceptible population. We developed a general approach to model MSFR including accessibility to resources and switching of prey preference by predator. In this framework, we investigated the importance of MSFR and intermediate host diversity on the transmission patterns of Em. Few works have coupled adaptive predator-prey interactions with parasite transmissions, and the inclusion of switching behavior is a first attempt to feed hot topics linking adaptive foraging behavior and IHs diversity. We showed that switching of prey preference may have a dilution or amplification effect, that is a decrease, resp. increase, of the disease risk with an increase of IHs diversity.

Zepeng Sun (University of Amsterdam)

What can we learn from seasonal reproduction?

Seasonal reproduction is common among mammals at all latitudes, even in the deep tropics (Bronson, 2009). The timing of one species’ reproduction, which can be influenced by environmental changes, significantly affects the interactions with other species. As a consequence, this timing plays quite an important role in the consumer population, in particular, when the development and maturation of juveniles, as well as the reproduction of adults, are resource-dependent. The effects of seasonal reproduction are studied using semi-discrete population models and the theory of adaptive dynamics. The results show that seasonal reproduction does not qualitatively affect the occurrence of bistability observed in continuous-time models. However, seasonal reproduction results in some surprising dynamics, for example, Allee effect. To investigate how adults time their reproduction coping with environmental changes, the evolution of reproduction schedule is studied. The results show that in fluctuating environments seasonal reproduction schedules will evolve, and the starting time and duration of the reproductive season are determined by different patterns of environmental changes.

Gunnar Petter (University of Göttingen)

Simulating the long-term dynamics of tropical forests using functional-structural tree models

Gunnar Petter, Juliano Sarmento Cabral, Yongzhi Ong, Holger Kreft

In tropical forest systems, many different tree species compete for resources such as water, nutrients and light. The ability to establish and grow in response to the resource availability can differ largely among tree species. While some shade-tolerant species are able to grow under low-light conditions in the understory, pioneer species require high-light conditions for successful establishment and survival. Leaves as fundamental functional units of photosynthesis play a central role for the growth behavior of trees and it has been shown that a universal spectrum of leaf economics consisting of key functional traits exists (Wright et al. 2004). This spectrum runs from quick to slow return on biomass and nutrient investments in leaves and, in addition, a correlation between the leaf economics spectrum and the photosynthetic light response has been found (Marino, Aqil & Shipley 2010). On this basis, we hypothesized that the leaf economics spectrum captures many aspects of the observed differences in whole-tree growth behaviors among species.

To test this, we integrated the leaf economics spectrum in a functional-structural tree model (FSTM). In FSTMs, trees consist of interconnected tree components (e.g. trunks, branches, leaves) which are arranged in 3D space and respond to their local environment. FSTMs thus allow simulating the feedback between leaf growth and the within-canopy light distribution, which is regarded as important mechanism affecting the tree crown development. In addition, we integrated the FSTM into a demographic forest model to simulate and analyse the long-term forest dynamics.
Our FSTM successfully reproduced the growth behavior of different tree species. Species at the one side of the leaf economics spectrum showed fast growth rates, but their maximum height and life span, both emergent properties of the model, was rather short. This pattern corresponds well with pioneer species. In contrast, species at the other side of the spectrum were slow-growing, but their maximum height and life span was increased, what complies with the typical pattern of shade-tolerant emergent tree species. When integrated in a forest model, many stand parameter (e.g. basal area, above-ground biomass or number of trees per ha), rates (e.g. net primary production or carbon turnover per ha), and detailed pattern (e.g. the vertical leaf area distribution) were well reproduced. In addition, the simulated forests reached quasi-stationary states after about 100 years, which agrees with our understanding of long-term forest dynamics.

Our modelling study demonstrates a link between the leaf economics spectrum and whole-tree growth, indicating that differences in leaf traits among tree species explain a substantial part of their growth behavior. In addition, we show that functional-structural tree models are suitable tools for detailed simulations and analyses, both at single-tree scale and at the forest scale.

References
Marino G., Aqil M. & Shipley B. (2010) The leaf economics spectrum and the prediction of photosynthetic light-response curves. Functional Ecology 24, 263–272.
Wright I.J., Reich P.B., Westoby M., Ackerly D.D., Baruch Z., Bongers F., et al. (2004) The worldwide leaf economics spectrum. Nature 428, 821–827.

Veronika Bernhauerova (Masaryk University)

Evolution of male-killing in horizontally transmitted parasites

Male-killing bacteria are maternally transmitted endosymbiotic parasites which manipulate the host reproduction by killing male offspring who inherit them. Male-killing, however, brings about a fitness benefit to the surviving female and uninfected male offspring in terms of reduced competition between siblings, enhanced resource availability through consumption of their dead brothers or reduced rates of inbreeding. The incidence and prevalence of male-killing bacteria in natural systems have been well documented, however characteristics actually allowing originally virulent, horizontally transmitted non-male-killing parasite to evolve the male-killing trait awaits research. We introduce an evolutionary model to study the dynamics of a potential male-killing bacterium whose ancestral agent is a virulent parasite transmitted both vertically and horizontally. We show that horizontal transmission is a key mechanism actually enabling a vertically transmitted male-killer to evolve from a predominantly horizontally transmitted non-male-killing. This is observed for a wide range of ecological settings, thus strongly supporting the empirical evidence on current male-killers, explaining their high efficacy in killing infected males, their variability across and within the insect taxa, and supporting the idea that they may have evolved independently in phenotypically distinct species.

Matthew W. Adamson (U. Leicester)

Cyclic competition, virus evolution and structural sensitivity

In this talk, I will present three different areas of my research. Firstly, I'll talk about spatial modelling of three cyclically competing species - in which competitive dominance follows the ordering of the game "rock-paper-scissors". We shall consider how the mobility of each species affects their coexistence, and the types of spatiotemporal dynamics they show. Secondly, I'll discuss an investigation into the evolution of a disease infecting the prey species in a predator-prey system. We'll see how the short term ecoepidemic dynamics and the long term evolutionary dynamics interact - sometimes with disastrous ecological consequences. Finally, I'll talk about ways to detect and quantify structural sensitivity in biological models. A model is structurally sensitive if a small change in the model functions can totally change the model dynamics. This is a particular problem in environmental modelling, since the processes involved are often too complex to justify representing them by any particular equation.

Eric Siero (Leiden University, NL)

Resilience of banded vegetation on slopes

Observations of banded or striped vegetation patterns are widespread. We study banded vegetation formation and the breakup of these bands in a simple arid ecosystem model. The relation between banded vegetation resilience and terrain slope (advection) is presented. If time permits, we also look into effects of grazing on vegetation patterns.

Jane Ndunge (U. Twente, NL)

Synergy in system modeling, field measurements, and remote sensing

Management decisions that are based on scientific findings have potential assurance of utilization of natural resources by future generation. Enough scientific data are required in order to provide sound understanding of the functions and services of ecosystems. However, conventional data acquisition is expensive and often leads to losses to the already constrained resources. A synergy between modeling, remote sensing and field measurements can reduce the costs of data acquisition. A case study will be presented to show how the integration of the modeling, remote sensing and field measurements can be used in water quality studies in lakes ecosystems. The study was carried out in Lake Naivasha, Kenya.

Lake Naivasha is a shallow endorheic fresh water lake situated on the floor of the Eastern Rift Valley in Kenya at 1885m above sea level. Amalgamation of physical and biological processes that result from a myriad of environmental perturbations in Lake Naivasha’s ecosystem transformed the lake from a clear to muddy eutrophic turbid state, which resulted in a decline in ecological quality, impacting heavily on fish population and tourism. Cases of fish kills have been observed which may be attributed to deterioration of the quality of the water, turbidity being one of the factors contributing significantly towards it. The study demonstrates the strength in integrating modeling, remote sensing and field measurements in enhancing the understanding of the status water quality in the lake.