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Agent-based models (ABMs) are widely used to predict how populations respond to changing environments. As the availability of food varies in space and time, individuals should have their own energy budgets, but there is no consensus as to how these should be modelled. Here, we use knowledge of physiological ecology to identify major issues confronting the modeller and to make recommendations about how energy budgets for use in ABMs should be constructed. Our proposal is that modelled animals forage as necessary to supply their energy needs for maintenance, growth and reproduction. If there is sufficient energy intake, an animal allocates the energy obtained in the order: maintenance, growth, reproduction, energy storage, until its energy stores reach an optimal level. If there is a shortfall, the priorities for maintenance and growth/reproduction remain the same until reserves fall to a critical threshold below which all are allocated to maintenance. Rates of ingestion and allocation depend on body mass and temperature. We make suggestions for how each of these processes should be modelled mathematically. Mortality rates vary with body mass and temperature according to known relationships, and these can be used to obtain estimates of background mortality rate. If parameter values cannot be obtained directly, then values may provisionally be obtained by parameter borrowing, pattern-oriented modelling, artificial evolution or from allometric equations. The development of ABMs incorporating individual energy budgets is essential for realistic modelling of populations affected by food availability. Such ABMs are already being used to guide conservation planning of nature reserves and shell fisheries, to assess environmental impacts of building proposals including wind farms and highways and to assess the effects on nontarget organisms of chemicals for the control of agricultural pests.
This is a publication-based dissertation comprising three original research stud-ies (one published, one submitted and one ready for submission; status March 2019). The dissertation introduces a generic computer model as a tool to investigate the behaviour and population dynamics of animals in cyclic environments. The model is further employed for analysing how migratory birds respond to various scenarios of altered food supply under global change. Here, ecological and evolutionary time-scales are considered, as well as the biological constraints and trade-offs the individual faces, which ultimately shape response dynamics at the population level. Further, the effect of fine-scale temporal patterns in re-source supply are studied, which is challenging to achieve experimentally. My findings predict population declines, altered behavioural timing and negative carry-over effects arising in migratory birds under global change. They thus stress the need for intensified research on how ecological mechanisms are affected by global change and for effective conservation measures for migratory birds. The open-source modelling software created for this dissertation can now be used for other taxa and related research questions. Overall, this thesis improves our mechanistic understanding of the impacts of global change on migratory birds as one prerequisite to comprehend ongoing global biodiversity loss. The research results are discussed in a broader ecological and scientific context in a concluding synthesis chapter.
Estimating parameters from multiple time series of population dynamics using bayesian inference
(2019)
Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.
Background
In Europe, bank voles (Myodes glareolus) are widely distributed and can transmit Puumala virus (PUUV) to humans, which causes a mild to moderate form of haemorrhagic fever with renal syndrome, called nephropathia epidemica. Uncovering the link between host and virus dynamics can help to prevent human PUUV infections in the future. Bank voles were live trapped three times a year in 2010–2013 in three woodland plots in each of four regions in Germany. Bank vole population density was estimated and blood samples collected to detect PUUV specific antibodies.
Results
We demonstrated that fluctuation of PUUV seroprevalence is dependent not only on multi-annual but also on seasonal dynamics of rodent host abundance. Moreover, PUUV infection might affect host fitness, because seropositive individuals survived better from spring to summer than uninfected bank voles. Individual space use was independent of PUUV infections.
Conclusions
Our study provides robust estimations of relevant patterns and processes of the dynamics of PUUV and its rodent host in Central Europe, which are highly important for the future development of predictive models for human hantavirus infection risk.
Hantaviren in Deutschland
(2018)
Hantaviren sind Kleinsäuger-assoziierte Krankheitserreger, die vor allem in Nagetieren, aber auch in Spitzmäusen, Maulwürfen und Fledermäusen vorkommen. Ziel dieser Arbeit ist es, einen aktuellen Überblick zur Epidemiologie und Ökologie der Hantaviren in Deutschland zu geben und Modelle zur Vorhersage von Virusausbrüchen zu diskutieren. In Deutschland werden die meisten humanen Erkrankungsfälle beim Menschen durch das von der Rötelmaus (Myodes glareolus) übertragene Puumalavirus (PUUV) verursacht. PUUV ist mit der westlichen evolutionären Linie der Rötelmaus assoziiert und fehlt im östlichen und nördlichen Teil Deutschlands. Ein zweites humanpathogenes Hantavirus ist das Dobrava-Belgrad-Virus (DOBV), Genotyp Kurkino, dessen Reservoir die vor allem im östlichen Teil Deutschlands vorkommende Brandmaus (Apodemus agrarius) ist. Ein PUUV-verwandtes Hantavirus ist das selten humanpathogene Tulavirus (TULV), das mit der Feldmaus (Microtus arvalis) assoziiert ist. Darüber hinaus wurden mit dem Seewis-, Asikkala- und Brugesvirus Spitzmaus- und Maulwurf-assoziierte Hantaviren mit noch unklarer Humanpathogenität gefunden.
Die humanen Erkrankungen sind jeweils mit den verschiedenen Hantaviren in deren regionaler Verteilung assoziiert und können mild bis schwer, aber auch subklinisch verlaufen. Das Auftreten von Häufungen humaner, durch PUUV verursachter Erkrankungen in den Jahren 2007, 2010, 2012, 2015 und 2017 korreliert mit dem Auftreten einer starken Fruktifikation der Buche („Buchenmast“) im jeweiligen Vorjahr. Auf der Basis von Wetterparametern sind Modelle zur Vorhersage von PUUV-Erkrankungshäufungen entwickelt worden, die zukünftig validiert und optimiert werden müssen. Neben dem Ausmaß des Virusvorkommens im Reservoir wird das Risiko humaner Infektionen durch das Expositionsverhalten des Menschen beeinflusst. Durch die Anwendung von Prognosemodellen soll der öffentliche Gesundheitsdienst in die Lage versetzt werden, räumlich und zeitlich gezielte und sachgerechte Präventionsempfehlungen für die Bevölkerung abzugeben.
Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.
Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.
The intrinsic predictability of ecological time series and its potential to guide forecasting
(2019)
The life of microorganisms is characterized by two main tasks, rapid growth under conditions permitting growth and survival under stressful conditions. The environments, in which microorganisms dwell, vary in space and time. The microorganisms innovate diverse strategies to readily adapt to the regularly fluctuating environments. Phenotypic heterogeneity is one such strategy, where an isogenic population splits into subpopulations that respond differently under identical environments. Bacterial persistence is a prime example of such phenotypic heterogeneity, whereby a population survives under an antibiotic attack, by keeping a fraction of population in a drug tolerant state, the persister state. Specifically, persister cells grow more slowly than normal cells under growth conditions, but survive longer under stress conditions such as the antibiotic administrations. Bacterial persistence is identified experimentally by examining the population survival upon an antibiotic treatment and the population resuscitation in a growth medium. The underlying population dynamics is explained with a two state model for reversible phenotype switching in a cell within the population. We study this existing model with a new theoretical approach and present analytical expressions for the time scale observed in population growth and resuscitation, that can be easily used to extract underlying model parameters of bacterial persistence. In addition, we recapitulate previously known results on the evolution of such structured population under periodically fluctuating environment using our simple approximation method. Using our analysis, we determine model parameters for Staphylococcus aureus population under several antibiotics and interpret the outcome of cross-drug treatment. Next, we consider the expansion of a population exhibiting phenotype switching in a spatially structured environment consisting of two growth permitting patches separated by an antibiotic patch. The dynamic interplay of growth, death and migration of cells in different patches leads to distinct regimes in population propagation speed as a function of migration rate. We map out the region in parameter space of phenotype switching and migration rate to observe the condition under which persistence is beneficial. Furthermore, we present an extended model that allows mutation from the two phenotypic states to a resistant state. We find that the presence of persister cells may enhance the probability of resistant mutation in a population. Using this model, we explain the experimental results showing the emergence of antibiotic resistance in a Staphylococcus aureus population upon tobramycin treatment. In summary, we identify several roles of bacterial persistence, such as help in spatial expansion, development of multidrug tolerance and emergence of antibiotic resistance. Our study provides a theoretical perspective on the dynamics of bacterial persistence in different environmental conditions. These results can be utilized to design further experiments, and to develop novel strategies to eradicate persistent infections.
Complex transient dynamics of stage-structured populations in response to environmental changes
(2013)
Stage structures of populations can have a profound influence on their dynamics. However, not much is known about the transient dynamics that follow a disturbance in such systems. Here we combined chemostat experiments with dynamical modeling to study the response of the phytoplankton species Chlorella vulgaris to press perturbations. From an initially stable steady state, we altered either the concentration or dilution rate of a growth-limiting resource. This disturbance induced a complex transient response-characterized by the possible onset of oscillations-before population numbers relaxed to a new steady state. Thus, cell numbers could initially change in the opposite direction of the long-term change. We present quantitative indexes to characterize the transients and to show that the dynamic response is dependent on the degree of synchronization among life stages, which itself depends on the state of the population before perturbation. That is, we show how identical future steady states can be approached via different transients depending on the initial population structure. Our experimental results are supported by a size-structured model that accounts for interplay between cell-cycle and population-level processes and that includes resource-dependent variability in cell size. Our results should be relevant to other populations with a stage structure including organisms of higher order.