Mathematical Biology

Optimizing Biogas Generation Using Anaerobic Digestion

Speaker:

Gail Wolkowicz

Date:

Tue, Nov 27, 2018

Location:

PIMS, University of Manitoba

Conference:

PIMS-UManitoba Distinguished Lecture

Abstract:

Anaerobic digestion is a complex, naturally occurring process during which organic matter is broken down into biogas and various byproducts in an oxygen-free environment. It is used for bioremediation and the production of methane which can be used to produce energy from animal waste. A system of differential equations modelling the interaction of microbial populations in a chemostat is used to describe three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis. To examine the effects of the various interactions and inhibitions, we study both an inhibition-free model and a model with inhibition.

A case study illustrates the importance of including inhibition on the regions of stability. Implications for optimizing biogas production are then explored. In particular, which control parameters and changes in initial conditions the model predicts can move the system to, or from, the optimal state are then considered. An even more simplified model proposed in Bornh\”{o}ft, Hanke-Rauschenback, and Sundmacher [Nonlinear Dynamics 73, 535-549 (2013)], claimed to capture most of the qualitative dynamics of the process is then analyzed. The proof requires considering growth in the chemostat in the case of a general class of response functions including non-monotone functions when the species death rate is included.

Class:

Scientific

Subject:

Mathematics

Mathematical Biology

The Mathematics of Social Evolution

Speaker:

Troy Day

Dave McLeod

Date:

Thu, Mar 22, 2018

Location:

PIMS, University of Manitoba

Conference:

PIMS-UManitoba Distinguished Lecture

Abstract:

How social traits evolve remains an open question in evolutionary biology. Two traits of particular interest are altruism (where an individual incurs a cost to help others) and spite (where an individual incurs a cost to harm others). Both traits should be evolutionarily disadvantageous because any benefits arising from these behaviours are also available to “cheaters” who do not pay the cost of displaying altruism or spite themselves. In this talk I will show how stochasticity can sometimes reverse the direction of evolution and drive the emergence of these behaviours. I will start with an individual-based evolutionary model and then approximate it using a system of stochastic differential equations (SDEs). These SDEs are then be reduced to a single SDE on a “slow manifold” governing the evolutionary dynamics. A rather complete analysis of this SDE is then possible, showing exactly when and how stochasticity can drive the evolution of altruism and spite.

Biography:

Tryo Day is a Professor and former CRC in the Department of Mathematics and Statistics at Queen’s University. His research interests involve evolutionary theory, including the evolution of pathogen virulence, drug resistance, social traits, and epigenetic inheritance.

Dr. Day is coauthor (with James Stewart) of the textbooks “Biocalculus: Calculus, Probability and Statistics for the Life Sciences”, and (with Sarah P. Otto) “A Biologist’s Guide to Mathematical Modeling”. He is an Elected Fellow of the Royal Society of Canada and the AAAS, and is the recipient of a Killam Research Fellowship, a Steacie Fellowship, the CAIMS Research Prize, and the Steacie Prize.

Class:

Scientific

Subject:

Mathematics

Mathematical Biology

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The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems

Speaker:

Linda Petzold

Date:

Fri, Mar 28, 2014

Location:

PIMS, University of British Columbia

Conference:

PIMS/UBC Distinguished Colloquium

Abstract:

In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes. Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or “stochastic focusing". Numerous cellular systems rely on spatial stochastic noise for robust performance. We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.

Class:

Subject: