Atlantic Mathematical Biology Workshop Schedule

All talks are in Singer Hall Room 361. Enter the building through the main doors (uphill side) and go up the stairs.

Abstracts

Joseph Apaloo

Evolutionary Game Theory: ESS, Convergence Stability, and NIS

Ever since Maynard Smith and Price's (1973) pioneering work, evolutionary game theory has advanced from matrix to continuous games, from single to multiple species, from scalar to vector-valued strategies, and from static analyses to adaptive dynamics. Essentially three related stability concepts underlie the theory for predicting the outcomes of natural selection: ESS, convergence stability and NIS. Here, we use the fitness generating function concept (G -function) and adaptive landscapes to illustrate these stability concepts. Explicit consideration of population dynamics and strategy dynamics permits a clear appreciation for each stability concept in terms of ecology (population dynamics) and evolution (strategy dynamics). We conclude by tabulating how most of the evolutionary stability acronyms, definitions and terminologies reduce to one or several aspects of ESS, convergence stability and NIS

Gerda de Vries

Quantitative Analysis of Single Particle Tracking Experiments: Applying Ecological Methods in Cell Biology

A commonly used experimental technique to study the movement of biomolecules in the cell membrane is Single Particle Tracking (SPT). SPT involves tagging biomolecules with a fluorescent label and observing and recording their trajectories over time. A diffusion coefficient then can be extracted from the data from mean square displacement calculations. Although the diffusion coefficient provides an overall measure of mobility, it does not provide insight into the underlying heterogeneity of the membrane environment.

Since the method of data collection from individual biomolecules is analogous to that from individual animals, we propose to use methods from ecology to provide spatial insight. Ecologists regularly quantify animal movement using the concepts of correlated random walk, net squared displacement, and first-passage time. In this talk, we will demonstrate the applicability of these methods in the context of cell biology. In particular, we will show how we can distinguish biomolecule trajectories undergoing a correlated random walk from those that do not, and how we can identify the presence of transient confinement zones in molecular diffusion.

Abba Gumel

Mathematics of the Transmission Dynamics of Chlamydia Trachomatis

Chlamydia trachomatis is a sexually-transmitted disease that continues to inflict major public health and socio-economic burden around the world. The talk will address the problem of the design and analysis of appropriate models for the transmission dynamics of Chlamydia in a heterosexual population. The effect of risk of acquiring or transmitting infection will be assessed.

Jeff Picka

Random Trajectories in Biological Systems

To model the changes in a complex biological system over time, a dynamical system is often used to model the interactions among many individual cells, plants, or animals. To validate any model of this kind, it is necessary to incorporate into the model any uncertainties about the exact mechanism of interactions and about environmental conditions. The conditions required to achieve different degrees of validation will be discussed.

Lisa Kanary¹, Andrea Locke², James Watmough¹, Joël Chassé² and Daniel Bourque²

1 University of New Brunswick, P.O. Box 4400, Fredericton, NB, E3B 5A3;
2 Gulf Fisheries Centre, Fisheries and Oceans Canada, P.O. Box 5030, Moncton, NB, E1C 9B6

Model of the Invasive Tunicate Population Spread in Hillsborough Bay, PEI

Invasive tunicates have been a problem for mussel farmers in Prince Edward Island since 1997. In this presentation we develop a model to ascertain the conditions necessary for an infestation to spread within Hillsborough Bay from Charlettetown Harbour to Nine Mile Creek. Nine Mile Creek where the majority of mussel seed production and distribution is based.

A system of partial differential equations models the tunicate population spread, taking into consideration parameters based on larval mortality, reproductive and settling rates. Our main result is a study of the conditions necessary for the persistence and spread of tunicates based on the spacing of intermediate settlement substrate. Advection (ocean current) data provided by the Department of Fisheries and Oceans and conditions derived from previous analysis are incorporated into a numerical simulation of the PDE system to demonstrate how the varying amounts of intermediate substrate affect the persistence of a tunicate invasion.

Majid Jaberi-Douraki

Dynamics of a honeybee model on regulation of work distribution

In this talk, we study age-related activities of honeybees (Apis mellifera L.) first by illustrating the life cycle of honeybee which exhibits a combination of individual traits and social cooperation, and then by constructing an age structured model given by a system of difference equations as follows

David Drolet and Myriam A Barbeau

Effects of climate warming on metapopulation dynamics of the intertidal amphipod Corophium volutator in the upper Bay of Fundy

We are developing population models to investigate the impact of rising temperature on the dominant invertebrate on mudflats of the Bay of Fundy, the amphipod Corophium volutator. We are using stage-based matrix models using transition probabilities obtained from the literature. The transition probabilities are temperature-dependant and affected by a variety of factors known to influence C. volutator. Single population models will be tested against time series of densities of the different stages at 10 different sites that are currently being sampled, with parameters representing local conditions. Sensitivity analysis will be performed to assess the relative importance of the parameters at the different sites. The models will then be used to evaluate population responses to predicted temperature changes in the area. Finally, the models for the different sites will be integrated by allowing dispersal between mudflats (based on a study that is presently conducted) and the effect of increasing temperature on metapopulation dynamics will be examined.

Humberto Muñoz

Department of Mathematics

Eduardo Martinez-Ceballos

Department of Biological Sciences

Southern University and A&M College

Novel Polypeptides for the Hydrogel-Based Encapsulation of Mouse ES Cells

This work proposes the creation of new polypeptides for the hydrogel-based encapsulation of mouse embryonic stem cells (ES cells). The design of these novel polypeptides will be based on relevant domains of proteins with known ES differentiating activities. The polypeptide-containing hydrogels will be characterized based on their physicochemical properties and their effect on the directed differentiation of ES cells along the three specific cell lineages: ectoderm, mesoderm, and endoderm. Encapsulation conditions will be optimized by applying mathematical algorithms based on biological responses and the physicochemical properties of the hydrogels. The data analysis involves nonlinear optimization and regression analysis methods.

Richard Karsten, Holger Teismann, Rebecca Hammond, Jeff Franklin, Mike Hardman

Determining an appropriate Model for Mites on Apple Trees

Holger Teismann, Richard Karsten, Angela Vogels

Shengqiang Liu

Olga Vasilyeva

University of Ottawa

Population dynamics in rivers: steady states and competition

We study diffusion-reaction-advection models describing population dynamics of logistically growing aquatic organisms subject to a constant downsteam drift, with reflecting upstream and outflow downstream boundary conditions. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady state solutions, and we analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and and analytical techniques, we describe the effect of advection on competition outcomes.

Huaichun Wang

Department of Mathematics and Statistics

Dalhousie University

An improved /w/ statistics for covarion and heterotachy tests

The /w/ statistics is a quantity that compares amino acid substitution patterns between two monophyletic groups of protein sequences. It is defined as the difference between the fraction of varied sites in both groups and the fraction of varied sites in each group. The /w/ test has been used to distinguish a covarion process from equal rates and rates variation across sites processes. Using simulation we show that the /w/ test is effective only for small datasets and for datasets that have small substitution rates in the groups. Using site entropy as a measure of variability of the sequence site we generalize the /w/ statistics by assigning those sites that are varied in both groups but have a large entropy difference to those sites that are varied only in one group, thus modifying the fractions of varied sites in each group and in both groups. We show that the /w/’ test has more power to detect heterotachy processes (covarion, bivariate rate shift and branch length mixture) in large and variable data. We also show that the difference in correlation coefficient of the site entropies between the two groups can be used for separating the heterotachy models and the rate-across-sites model.

Yijun Lou

Yu Jin