Math 151 - Fall 2006

References Cited for Lectures

August 23, 2006 lecture: Intro to Statistics

Swimming Paramecium in magnetically simulated enhanced, reduced, and inverted gravity environments
by Karine Guevorkian and James M. Valles Jr.
Full paper as a PDF file - Proc. Natl. Acad. Sci. 103:13051-13056. (Aug. 29, 2006)

Comments: This paper illustrates and models the movements of single-cell organisms as they are affected by simulated gravity. Gravity has a variety of effects at cellular level on multicellular organisms, including humans, and the methodology derived in this paper may be useful in controlling gravity effects on groups of cells to evaluate their response. The observations of Paramecium illustrate how these cells can orient to a gravity field, how their swimming speed is modified as the field changes, and how they can "stall" out. In addition the use of algebraic equations to model this system, histograms are used to describe the speed distributions. The author has posted some movies of these experiments

Containing Pandemic Influenza at the Source
by Ira M. Longini, Jr., Azhar Nizam, Shufu Xu, Kumnuan Ungchusak, Wanna Hanshaoworakul, Derek A. T. Cummings, and M. Elizabeth Halloran
Full paper as a PDF file - Science 309: 1083-1087 (12 Aug 2005)

Comments: This paper uses a probability model to analyze the potential spread of "bird flu" among humans. The objective is to compare the potential effectiveness of alternative control methods to limit the spread of the pandemic at its initial source, using targeted drugs (antivirals), quarantine, and early vaccination. The resulting effectiveness depends upon the underlying reproductive number (how many secondary infections would arise from a single infected individual if no control were applied). They show that a mixture of these possible control methods could control the spread of the disease up to a reproductive number of 2.1 and they obtain results as to how much of a stockpile of antiviral drugs would be needed.

August 28, 2006 lecture: Bar Charts and categorical data

Evolution and Development of Sex Differences in Cooperative Behavior in Meerkats
by T. H. Clutton-Brock, A. F. Russell, L. L. Sharpe, A. J. Young, Z. Balmforth,3 G. M. McIlrath
Full paper as a PDF file - Science July 12 2002 297: 253-256

Comments: This article focuses on the issue of whether males or females devote more effort to caring for young, contrasting cooperatively breeding birds with meerkats. Female meerkats are more likley to breed and remain in their natal group than males, and the authors found that female meerkat helpers were more likely to contribute to rearing than males. They argue this is because females are more likely to derive genetic benefits (through helping more closely related individuals rear their young) than males in meerkat groups. The authors make use of extensive histograms, arranged by gender or experimental regime, to illustrate their points.

August 28, 2006 lecture: Bar Charts and Histograms

An Experimental Study of Search in Global Social Networks
by Peter Sheridan Dodds, Roby Muhamad, Duncan J. Watts
Full paper as a PDF file - Science Aug 8 2003 301: 827-829

Comments: Experiment to determine how many contacts are necessary, using email, to reach a specific target individual about which the location, name and occupation are provided to the initial email sender. Histograms show the length of an email chain necessary to reach the target.

September 6, 2006 lecture: Correlations

The Neural Basis of Economic Decision-Making in the Ultimatum Game
by Alan G. Sanfey, James K. Rilling, Jessica A. Aronson, Leigh E. Nystrom, Jonathan D. Cohen
Full paper as a PDF file - Science June 13 2002 300: 1755-1758

Comments: Individuals were observed using functional magnetic resonance imaging (fMRI) while playing an economic game with other humans, and with a computer. The intent was to determine if the "non-rational" response of humans to this game was reflected in the activity of certain areas of the brain, as measurable using the fMRI. The results indicate there is a correlation between activity in one area (anterior insula) and the acceptance of what could be perceived as an unfair offer in the game. This is an example of the work in the new area of neuroeconomics, which attempts to ascertain a biological basis for human economic decisionmaking.

Sept. 11, 2006 lecture: Exponential and logarithmic plots

Effect of trace metal availability on coccolithophorid calcification
Full paper as a PDF file - Nature August 5 2004 430: 673-676

Comments: This paper analyzes the growth rate of one of the most prominant microalgae in the oceans, as it is affected by trace minerals (particularly zinc) that enter the ocean in part through deposition of atmospheric dust. They relate the results to carbon production in the oceans which impacts the partitioning of CO2 between the oceans and atmosphere and therefore changes in dust deposition can affect the global C cycle.

September 11, 2006 lecture: Allometry

Global Allocation Rules for Patterns of Biomass Partitioning in Seed Plants
by Brian J. Enquist and Karl J. Niklas
Full paper as a PDF file - Science February 22 2002 295: 1517-1520

Comments: This paper shows numerous allometric relationships that arise both within and between species for plant parts.

September 20, 2006 lecture: Land Use Change and Markov Chains

Developing a science of land change: Challenges and methodological issues
by Ronald R. Rindfuss, Stephen J. Walsh, B. L. Turner II, Jefferson Fox, and Vinod Mishra
Full paper as a PDF file - PNAS Sept. 28, 2004, 101:13976-13981

Comments: This paper presents a summary of the modern science of land-use change and focuses on how this involves an integration of infor,mation science, geography and economics. They also discuss the basic techniques in geographic information systems appropriate to land use change analysis.

September 27, 2006 lecture: Matrix algebra

Mathematical models of RNA silencing: Unidirectional amplification limits accidental self-directed reactions
by Carl T. Bergstrom, Erin McKittrick, and Rustom Antia
Full paper as a PDF file - PNAS September 12, 2003, 100:11511- 11516

Comments: This paper presents a mathematical model to anaylze the "silencing" of genes in which aberrent genes are not expressed - this essentially is a method by which a mutant is suppressed by a rapid response of RNA transcription. It is a form of gene repair. They argue that current models do not explain how silencing doesn't also impact "good" genes which are not damaged, and produce two new mathematical models for silencing. One of these models uses a matrix formulation in which the components of the matrix symbolically represent the rates at which different types of silencing RNAs change from one type to another.

September 27, 2006 lecture: Matrix Algebra

Recovery and Management Options for Spring/Summer Chinook Salmon in the Columbia River Basin
by Peter Kareiva, Michelle Marvier, and Michelle McClure
Full paper as a PDF file - Science November 3, 2000, 290:977-979

Comments: This paper applies a matrix model for the demographics of salmon to issues associated with the effects of dams on the Snake river. One focus is on how the population might respond given different dam mitigation scenarios. They point out that the limitations on population growth and recovery of the salmon may not be related to further improvements in the ability of salmon to negotiate around the dams, but rather to mortality in other life stages.

October 4, 2006 lecture: Leslie Matrices and Population Projection

Human Population: The Next Half Century
by Joel E. Cohen
Full paper as a PDF file - 14 Nov 2003 Science 302:1172-1175

Comments: This paper reviews the history of human population on our planet focusing on the dynamics of the size of the population as well as its growth rates. The author points out how rapidly the human population has been growing, at an increasing rate. Thus the doubling time of the population has changed from 50 years in 1927 to 25 years in 1974. What is greatly significant is that the yearly population growth rate has declined over the past 3 decades from 2.1% to 1.2%, associated with a large reduction in the fertility rate (from over 5 to less than 3 children per woman per lifespan). The author uses mathematical models to project the changes in population structure (age) through the next 50 years.

October 9, 2006 lecture: Transfer matrices and compartment models

Human evolution: Pedigrees for all humanity
News article as a PDF file - Nature September 30, 2004, 431:518-519

Comments: This is a news and views article that summarizes the below paper by Rohde et al. on the time to the common ancestor of all living humans.
see also
Modelling the recent common ancestry of all living humans
Full paper as a PDF file - Nature September 30, 2004, 431:562-566

Comments: This paper uses a mathematical model and a simulation model to estimate how many generations in the past you would have to go to find an individual who was an ancestor to all human beings currently alive (the most recent common ancestor - MRCA). They compare results from a simple model that assumes random mating between all humans to a model that assumes the world is broken down into sub-regions with transfers of humans regularly occuring between these regions, in the same way a transfer matrix describes the movement of something between various components. Their results indicate that the MRCA lived in the relatively recent past (a few thousand years ago), and going back a few thousand more years (to about 7,000 years ago) we would get to the IA point where each present-day human has exactly the same set of ancestors.

October 18, 2006 lecture: Chance and Biology

Monkeys reject unequal pay
Full paper as a PDF file - Nature September 18, 2003, 425:297-299

Comments: This paper describes experiments in which capuchin monkeys interacted with human experimenters who offered them a more valuable food (grapes) or a less favored one (cucumber) when they returned an item to the human. The monkeys generally, but not always, refused to participate in an exchange of items for food when they saw that other monkeys got a better food item and they did not. The monkeys thus had a tendency to refuse to participate if they saw another monkey get a better reward for no effort, but there was a random component to this - it did not happen all the time and the sample size of monkeys used was very small - only 5 monkeys. It was therefore not possible to predict exactly what any particular monkey would do.

October 25, 2006 lecture: Probabilities and epidemics

Forecast and control of epidemics in a globalized world
by L. Hufnagel, D. Brockmann, and T. Geisel
Full paper as a PDF file - Proc. Natl. Acad. Sci. October 19, 2004, 101: 15148-15153

Comments: This paper describes, using SARS (severe acute respiratory syndrome) as an example, how to model the global spread of an epidemic. In addition to using the standard epidemiological model (susceptibles who become infected and then can infect others) in a local region served by an airport, they analyze global spread using data on movements of aircraft between airports. The probability of movement of individuals between airports is obtained from looking at the number of air passenmgers between different cities. This gives them a Markov chain (it is large - they used 500 airports giving a 500x500 matrix) to characterize movements between airports. They link this with local epidemic models to indicate how one infected individual can lead to a global epidemic and compare it to data from SARS.

November 1, 2006 lecture: Bayes Theorem and epidemics

Bayesian analysis of botanical epidemics using stochastic compartmental models
by G. J. Gibson, A. Kleczkowski, and C. A. Gilligan
Full paper as a PDF file - Proc. Natl. Acad. Sci. August 17, 2004, 101: 12120-12124

Comments: This paper combines several aspects of the material we have covered in this course: compartment models similar to matrix models with susceptible, exposed (or latent), and infected infected individuals; a probability framework built around an extension of the Markov chain type of models we have seen; and they use a Bayesian method to analyze experimental data and make inferences about the impact of the experiments. In this case, they analyze data on a fungal disease of radish plants in the presence and absence of another fungal species which is used to biologically control the harmful fungus. They conclude from their analysis that the biological control fungus is effective at reducing the rate of infection from the soil of the radish by the harmful fungus (primary infection) but not at limiting the spread of the disease from secondary (e.g. from other infected plants) infection.

November 8, 2006 lecture: Population genetics models

Genetic diversity and reproductive success in mandrills (Mandrillus sphinx)
by M. Charpentier, J. M. Setchell, F. Prugnolle, L. A. Knapp, E. J. Wickings, P. Peignot and M. Hossaert-McKey
Full paper as a PDF file - Proc. Natl. Acad. Sci. November 7, 2005, 102: 16723-16728

Comments: This paper analyzes the effects of heterozygosity on a variety of measures of individual fitness for a population of mandrills. They found that for both males and females higher heterozygosity was correlated with higher numbers of offspring, but this correlation in males only held for the alpha males. Achieving alpha status for males was not correlated with heterozygosity though the length of tenure as an alpha male was correlated with heterozygosity. They also found that the effects of heterozygosity on reproductive success was multi-locus, not due to a small number of loci with strong effects.

November 8, 2006 lecture: Population genetics models

Genetic Structure of Human Populations
by Noah A. Rosenberg, Jonathan K. Pritchard, James L. Weber, Howard M. Cann, Kenneth K. Kidd, Lev A. Zhivotovsky, and Marcus W. Feldman
Full paper as a PDF file - Science December 20, 2002, 298:2381-2385

Comments: This paper analyzes data on the genetic structure of human populations by analyzing information from over 1000 individuals in more than 50 locations. They looked at more than 300 genetic loci and found that the vast majority of genetic variation in humans is accounted for by variation within populations, and only a small amount (3-5%) is due to genetic differences between populations. Nevertheless, the data do indicate that there are distinct human populations, defined by the genetics, but correlating with geographically separate populations as well.

November 27, 2005 lecture: Difference Equation Models

Lattice Effects Observed in Chaotic Dynamics of Experimental Populations
by Shandelle M. Henson, R. F. Costantino, J. M. Cushing, Robert A. Desharnais, Brian Dennis, and Aaron A. King
Full paper as a PDF file - Science October 19, 2001, 294: 602-605

Comments: This paper analyzes both a discrete model in which organisms are counted as integers, and a continuous model in which the population size can take on non-integer values. Both of these models are discrete in time - that is they are difference equations. They apply their results to data from an experimental organism, the flour beetle Tribolium, and point out how chaotic dynamics can arise.
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