Mathematical Biology Graduate Seminar

The Mathematical Biology Graduate Student Seminar is a seminar organized by John Fricks and Tim Reluga. The goals are learn about mathematical modelling of biological systems (including statistical and computational models), and to give graduate students more practice presenting their research projects. The seminar participants are students and researchers who know a bit about modelling in general and are very interested in learning more about biology and your particular approach to describing the biology. Presenters should expect frequent interruptions and plan accordingly.

When: Spring Semester, 2012, 2:00 pm - 3:00 pm, Thursdays (sporadically)

Where: 327 Thomas Hall

Students interested in this seminar may find these books interesting.

Those interested cal also look at a list of the talks from Fall, 2011

Schedule

Date: Thursday, February 9, 2012

Speaker: Adam David Miller, Department of Biology, PSU

Title: How Interacting Aspects of Disturbance Influence Community Diversity

Abstract: Understanding the relationship between disturbance regimes and species diversity has been of central interest to ecologists for decades. For example, the intermediate disturbance hypothesis (IDH) proposes that diversity will be highest at intermediate levels of disturbance. While peaked and unimodal diversity-disturbance relationships (DDR) have been documented in nature, increasing, decreasing and U-shaped DDRs have been reported as well. Our results are an attempt to theoretically unify these diverse empirical findings by showing how simple models can generate several different DDRs within the same system, depending on the aspect of disturbance that is considered. I will present several models of plant communities, which illustrate how different aspects of disturbance (including frequency, intensity, extent, timing, autocorrelation) can influence species coexistence and competitive exclusion. Our framework for quantifying mechanisms of coexistence based upon species’ life-history traits and disturbance regime parameters can potentially be applied to a variety of communities, and also has applications for conservation and management.

Date: Thursday, February 16, 2012

Speaker: Nicole Mideo

Title: Causes of variation in malaria infection dynamics: insights from data and theory

Abstract: Despite a wealth of biomedical research into infectious diseases, very little is known about the basic biology of their causitive agents. For many parasites, there are no satisfying answers to important ecological and evolutionary questions like: what is it specifically about the interaction between hosts and parasites that results in disease symptoms? How do these interactions differ between closely related parasite strains or species? Finding the answers to these questions demands a multi-faceted approach, and one that integrates model building with experimental tests is the most powerful way to progress. The mouse model for malaria offers an excellent opportunity for reciprocal feedback between data and theory, since there is a wealth of replicated and controlled data on within-host disease dynamics already available with which to inform models, and experimental perturbations for testing model inferences are possible. Using this iterative approach, my research reveals the factors that underlie the patterns and outcomes of disease (and variation thereof) observed in this rodent malaria system.

Date: Thursday, February 23, 2012

No Talk. Instead, we suggest everybody attend Colin Campbell's dissertation defense.

When: 2:45 pm

Where: 339 Davey

Title: Complex dynamics of biological systems

Summary: The analysis of complex systems has become intertwined with, and driven by, network theory: the study of a system within the context of discrete, interacting components. A network-based investigation of a complex system enables analysis of its structure, function, and dynamics, even in the face of noisy or otherwise incomplete data. This is particularly relevant to the biological sciences, as recent advances in data-collection techniques have made a systems-level study of biological systems feasible. Here, I present applications and advancements of network theory within the context of three biological systems that range in scale from cellular to ecological.

First, the dynamic “tug of war” between the human immune system and cancer of the brain, bones, and pancreas is studied with a model of coupled ordinary differential equations, with the ultimate goal of directing researchers towards curative therapies. Known qualitative and quantitative time-course data are replicated, and several predictions of the model are experimentally validated. Second, a set of topological network measures are proposed and applied to a network representation of the immune response to attack by respiratory bacteria and allergen. The measures elucidate the functioning of the network, and along with analysis of the small-scale structure of the network, identify key regulators in the immune system response to the joint attack. Finally, a novel, dynamic model of the formation of ecological communities consisting of plants and their pollinators is proposed and shown to replicate expected ecological behavior. The model is used as the basis for a study of the stability of the communities in the face of species extinctions, and successfully identifies key properties in critical species and communities susceptible to significant damage from the loss of a single species.

In this dissertation, mathematical models are developed, networks are formed, network topologies are analyzed, and both discrete- and continuous-time dynamics are studied. Novel measures and models are proposed and discussed. Thus, in addition to offering significant insight into each of the studied biological systems, this dissertation constitutes an advancement of the techniques by which complex systems are studied.

Date: Thursday, March 15, 2012

Speaker: Megan A Greischar

Title: Modeling synchronization of within-host malaria dynamics

Abstract: Periodic bouts of fever are classically associated with malaria, and often thought to be caused by synchronized waves of parasites invading red blood cells, multiplying, and bursting out. There is evidence for intense competition among parasites for red blood cells, and synchronous behavior should serve to maximize that competition, which begs the question of what malaria parasites gain by synchronizing their life cycles. Other species—including periodical cicadas—utilize synchronized reproduction as a strategy to overwhelm predators, with any individuals who break synchrony subject to intense predation. We use a modeling framework to investigate both when malaria parasites may benefit from synchronous growth as a means of overwhelming host defenses and when immunity may cull the parasite population so as to maintain synchrony through time.

Date: Thursday, March 22, 2012

Speaker: Colin Campbell

Title: Network science as a tool for studying complex systems

Abstract: Understanding the structure and function of a complex system, such as the human immune system, can be extremely challenging. One powerful approach is to represent the system as a network, i.e. as a set of discrete components and their interactions. The topology of the network may be studied to yield insight into how the various components interact, and the network structure forms a framework upon which dynamic processes may be studied. In this talk I will discuss some technical challenges (and solutions) that arise when studying both the topology and dynamics of network representations of complex systems. I will frame the discussion with examples from the human immune system as well as ecological plant-pollinator communities.

Date: Thursday, March 29th, 2012

Speaker: Lindsay Beck-Johnson

Title: Temperature dependence in mosquito populations and the potential for malaria transmission

Abstract: Temperature has the potential to alter disease transmission and intensity, a fact exemplified in vector borne diseases such as malaria. The link between malaria and temperature results in large part from the close association between the parasites and the mosquito vector. Mosquitoes are highly sensitive to ambient temperature conditions throughout their life cycle, with temperature determining the rates of life history processes as well as the development rate of malaria parasites. Temperature has nonlinear and differential impacts on mosquito versus parasite development. Consequently, the effect of temperature on vector populations is complex but essential to our understanding of malaria transmission. We have developed a modeling framework that allows for the exploration of the temperature driven mosquito population dynamics and accounts for the highly structured nature of mosquito populations. Incorporating the relevant biology and temperature dependence in population models leads to a better understanding of the potential for mosquito populations to vector malaria parasites both currently and in the future.

Date: Thursday, April 5th, 2012

Speaker: Allison K. Shaw, Princeton University

Title: Modeling Motives for Movement: Theory for Why Animals Migrate

Abstract: Migration (the round-trip movement of organisms, usually on an annual cycle) is a widely used strategy for dealing with a seasonally variable environment. Most discussion of migration tends to be taxonomically restricted (e.g. “bird migration”, “fish migration”), while less work has been done to draw comparisons across taxonomic groups. As a result, broad questions such as 'what types of conditions generally favor the evolution of migration?' have gone unanswered. In this talk I will present some of my dissertation research, in which I use a combination of analytic models and individual-based simulations to study migration as an adaptive behavior and to understand what ecological conditions select for migration. I will describe the types of motivation drive migration and how these combine into different round-trip migration patterns. I'll use the example of partial migration to discuss why understanding migration motivation matters. Finally I'll show how the spatial distribution of resources and information availability can influence the evolution of migration under different motivations. I will discuss these theoretical results in the context of observed empirical patterns of animal migration across various taxonomic groups.

Date: Thursday, April 19th, 2012

Speaker: Russell deForest

Title: Pattern Formation and Transport in Evolutionary Games

Abstract: