Populations and communities are complex systems whose properties result from the interplay between non-linear feedbacks that are intrinsic to the system (e.g., biotic interactions that lead to density- and frequency-dependence) and external inputs (e.g., abiotic factors) that are outside the feedback structure of the system. Understanding this interplay requires that we understand the mechanisms by which the effects of external inputs on lower levels of the system (e.g., traits of organisms) influence properties at higher levels (e.g., population viability, species diversity). Using temperature as the axis of abiotic variation, I develop a mechanistic theoretical framework for elucidating how abiotic effects on traits translate into population dynamics and species interactions, and how these ecological dynamics in turn feedback into the trait response, causing trait evolution. I test model predictions with data on insects. The integration of theory and data paves the way for making testable predictions about the effects of climate warming on population viability, biodiversity and the control of invasive species.
Classical models for dispersal and invasion typically assume that the underlying environment is fixed in size, shape, and location. They also typically focus on a single species or a pair of interacting species, with fixed attributes and interactions. In the presence of climate change and other anthropogenic changes to the environment those assumptions often will not be valid. In a changing climate the structure and properties of the underlying environment will change with time, which by itself poses modeling challenges. Climate change could shift the timing of events such as flowering, migration, or emergence from hibernation in different ways for different species, thus changing the interactions experienced by any particular focal species. To account for that models would have to explicitly include parameters describing the timing of events. Climate change could also shift the ranges of species in space, which could also change species interactions and could cause niches to open up because the species occupying a particular niche has shifted its range and left that niche empty in some locations. To account for that, models would have to include multiple species. Finally, both climate change and the invasion process itself may impose novel selection pressures, so the attributes of a species invading a new region while the climate is changing are not likely to remain fixed. To address that would seem to require building some evolutionary processes into invasion models. This talk will discuss those issues and suggest some modeling approaches and ideas that might be relevant to addressing them
We have developed a network-patch model for the spread of mosquito-borne pathogens, including chikungunya, dengue, and West Nile virus. The model accounts for the movement of individual people through mosquito habitats that respond to environmental factors, such as rainfall and temperature. Our approach extends the capabilities of existing agent-based models for human movement developed to predict the spread of directly transmitted pathogens in human populations. These agent-based models are combined with differential equations representing clouds of mosquitoes in geographic patches that account for heterogeneity in mosquito density, mosquito emergence rates, and the extrinsic incubation period of the pathogen. I will illustrate the importance of heterogeneity in both human and mosquito populations on disease spread. The new hybrid agent-based/differential equation model can help quantify the importance of heterogeneity in predicting the spread and invasion of mosquito-borne pathogens and extend the capabilities of existing agent-based models to include vector-borne diseases. This research is in collaboration with Carrie Manore, Kyle Hickmann, Ivo Foppa, Dawn Wesson, Chris Mores, and Sara Del Valle.
For successful ecosystem management and biodiversity conservation, in addition to ecological and evolutionary processes, we need to consider social and economic influences on the management target. Here, we introduce several theoretical models that address economic and social aspects of human society that are closely related to ecosystem management.
The first model analyzes coupled socio-economical and ecological dynamics for lake water pollution. Players choose between cooperative (but costly) option and economical option, and their decision is affected by the fraction of cooperators in the community and by the importance of water pollution problem. When an opportunity for choice arrives, players take the option with the higher utility. This social dynamics is coupled with the dynamics of lake water pollution. First, oscillation of large amplitude is generated if social change occurs faster than ecosystem responses. Second, the model can show "paradox of nutrient removal". If phosphorus is removed more effectively either from the inflow or from the lake water, the pollution level may increase (rather than decrease) due to the decline in people's willingness to cooperate.
The second model discusses how activities that promote social concern about biodiversity help to maintain public support for biodiversity conservation. We study the optimal investment in the trade-off between activities that increase social concern and those that maintain and improve the conservation target.
The third model analyzes punishment as a mechanism to maintain cooperative behavior in a social group. We discuss the efficiency of a graduated punishment system, in which the severity of the punishment applied to deviators increases with the amount of harm caused by the selfish action, which field research has shown to be essential for successful resource management. We conclude that graduated punishment is the most efficient way to ensure cooperation when evaluation errors are unavoidable and when the social group is heterogeneous with respect to the sensitivity of its members to utility difference.
In current modeling practice for complex systems, including agent-based and network-based simulations, the best available descriptions of a system often come at a fine level (atomistic, stochastic, individual-based) while the questions asked and the tasks required by the modeler (parametric analysis, optimization, control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by deriving macroscopic evolution equations from the microscopic models. I will review a mathematically inspired, systems-based computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly in an input-output mode. This "equation-free" approach circumvents the step of obtaining accurate macroscopic descriptions. I will discuss applications of this approach and its linking with recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".
Most observational data sets in ecological research have a spatial component, but analysis of spatial data is challenging. Observations that are made in nearby locations are often similar and consequently the data points are not independent of each other. The presence of spatial autocorrelation can be considered as trouble, as simple statistical tests assuming independence are not valid, or as an opportunity of learning about the biological processes creating a given level of autocorrelation. One point in case is research on animal movement. Consecutive locations in an animal track are necessarily correlated, invalidating e.g. the assumption of independence in models of habitat use. I discuss how this problem can be avoided by analyzing animal movement data either with state-space models or with randomization tests. I also discuss how the level of autocorrelation (or persistence in direction) as well as long-term movement behavior can be summarized for a wide family a models with two parameters only: the characteristic spatial and temporal scales of movement. I then move to species distribution modeling, which I extend to community-level models in two different ways. First, I describe a multivariate regression model that can be used to ask if some species combinations occur more or less often together than by expected by random. This approach is suited for cases where there are much data on few species. Second, for the opposite case of few data on many species, I describe how statistical inference can be improved by gluing the species-specific models together with a higher-level community model.
Complex systems subject to changing external conditions can undergo unexpected rapid transitions from one stable state to another, a phenomenon known as "tipping". The well established tipping mechanism is a traditional bifurcation, where the stable state disappears or destabilises at some critical level of external conditions. I will describe a different tipping mechanism termed the "rate-induced tipping". Here, the stable state exists continuously for all fixed levels of external conditions and never bifurcates. When external conditions vary in time, the position of the stable state changes and the system tries to keep pace with the changes. However, some systems fail to adapt to the changing stable state and tip if the external conditions are changed too fast.
Scientists often find rate-induced tipping counter-intuitive because there is no obvious loss of stability and no obvious tipping threshold. On the other hand, these non-autonomous instabilities cannot be captured by classical bifurcation theory and remain fairly unexplored. I will present an approach based on geometrical singular perturbation theory to study critical rates of change and non-obvious tipping thresholds. I will also discuss repercussions for climate change policy making which currently focuses on critical levels of the atmospheric temperature whereas the critical factor may be the rate of warming rather than the temperature itself.
The virtual ecologist is an intuitive and widely used approach which includes simulating artificial species or ecosystem data, an observer that collects data according to a specific sampling protocol, the statistical analysis or modelling of the collected data and subsequent evaluation of the results against known (virtual) truth. In my talk, I will briefly review the concept and existing examples. For example, in global change research this approach holds great potential for rigorous testing of different modelling methods under controlled and changing conditions and with controlled sampling bias. Specifically, I want to emphasize the merit of using complex dynamic simulation models for simulating data and observers. This ingredient takes the virtual ecologist approach beyond simple proof of concept making it a truly integrative and rigorous framework not only for testing sampling protocols or modelling and analysis tools but for theory development and testing more generally.
Pike populations have been suffering from eutrophication, water pollution and habitat loss since the fifties of the previous century. In view of its role as a top predator in aquatic ecosystems and its recreational value, there has been an increasing number of rehabilitation and restoration programs in Europe and North America, but these programs had only limited success. In order to set up more effective restoration programs in the future, it is important to gain insight into the spatio-temporal dynamics of pike. Even though the availability of data on the spatio-temporal spread of pike is growing, no efforts have been spent to develop a spatially explicit model that enables a better understanding of the observed patterns of movement, and which might be parameterized using observed data. Therefore, and actually as a first step towards an integrated spatially explicit model for describing pike dynamics, a model mimicking the movement of pike in the river Yser, Belgium, is proposed.
The traditional epidemiological approach to characterize transmission of infectious disease consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and vectors into susceptible, exposed and infected (SEI), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). Compartmentalized models are based on a series of simplifying assumptions and have been successfully used to study a broad range of disease transmission dynamics. These paradigm is challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: An infection can include the simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus an individual might belong to multiple compartments simultaneously. This precludes the traditional calculation of the basic reproductive number. (ii) Antigenic diversity and variation: Antigenic diversity, defined as antigenic differences between pathogens in a population, and antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the host immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission. This work explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics upon environmental transmission. A basic propagation number is calculated that could guide public health policy.
Forest disturbances maintain diversity within a community by providing an environment suitable to early successional species, which, in the absence of disturbance, are marginalized by late successional species. We model the forest landscape as a metacommunity of patches connected via seed dispersal and subject to random disturbance. Within a patch, we implement a mathematically and computationally tractable model, the Perfect Plasticity Approximation, which employs height-structured competition for light. Lichstein and Pacala (2011) solved for the landscape-scale equilibrium of this model when disturbance is catastrophic. We propose a method to solve for the landscape-scale equilibrium of this model when some portion of early successional species biomass survives disturbance.
When we construct mathematical models to represent a given real-world system, there is always a degree of uncertainty with regards to the model specification - whether with respect to the choice of parameters or to the choice of formulation of model functions. This can become a real problem in some cases, where choosing two different functions with close shapes in a model can result in substantially different model predictions. This phenomenon is known in the literature as structural sensitivity, and is a significant obstacle to improving the predictive power of biological models. In this poster, the definition of structural sensitivity is revisited and its relation to the property of structural (in)stability is addressed. A general approach to reveal structural sensitivity is proposed which is a far more powerful technique than the conventional approach consisting of fixing a particular functional form and varying its parameters. In particular, a rigorous method is suggested to unearth sensitivity with respect to the local stability of a system's equilibrium points. This method is implemented to explore sensitivity in several well-known multicomponent ecological models. The existence of structural sensitivity in these models is demonstrated and it is shown that conventional methods based on variation of parameters alone would often miss such sensitivity. Furthermore it is shown that structural sensitivity may allow models to represent far more complex dynamics than the dimension of the state-space may suggest, and that in a structurally sensitive model, the concept of a 'concrete' bifurcation structure may no longer be relevant.
Evolutionary computation lets us create an agent-based model without specifying the rules governing agent behavior. Instead we specify the kinds of information an agent uses and the actions available. These inputs define the rule 'search space' for a learning classifier system (LCS). The LCS searches that space using an algorithm that mimics Darwinian evolution, continually and uniquely, modifying agent rules as the agent's environment and knowledge change. The search space can be very large and intractable; it is narrowed considerably by using a decision approach that partitions the problem into a spatial/temporal hierarchy, e.g., very local and short term; broad scale and slow moving. This makes the problem tractable but creates large path dependent costs in the form of agent ignorance about those parts of the domain not searched. This ignorance strongly affects the choice of actions by individual agents. Agents search their domain through costly autonomous search or through costly communications with other agents. In each case the cost is best described as the loss of knowledge about places not searched. The relative value of these two costs determines whether agents are motivated to cooperate and form persistent social structure. We apply the approach to the Maine lobster, urchin and groundfish fisheries. In the lobster fishery the circumstances of search lead to cooperation and persistent social structure which are necessary for collective action. In the urchin and groundfisheries the nature of the search problem leads to secrecy, close to no social structure and no collective action.
Due to their ability to grow in complex environments, fungi are present in most natural ecosystems. Their central role in nutrient cycles allows the redistribution and reutilization of nutrients over long distances. Besides, they are the primary decomposers of litter in forests. For these reasons much effort has been spent to fully comprehend the processes steering fungal growth and the mathematics behind it in order to build fungal growth models. Most of these models, however, are unable to fully grasp the dynamics underlying the growth of fungi. In addition growth is often confined to a lattice in these models, and therefore they do not best represent the irregular aspects of fungi. This work presents a lattice-free 3D model of fungal growth, one that explicitly accounts for nutrient uptake, translocation, anastomosis, apical growth and irregular branching. Highly versatile, the model is able to simulate growth in both three and two dimensions, to produce realistic simulations of different fungal species and to replicate the results of some problem-specific models already established. As such, it offers a serious comparative advantage which will undoubtedly open new doors for understanding fungal growth and its consequences.