Math 151 - Fall 2004

References Cited for Lectures

August 18, 2004 lecture: Intro to Statistics

Optimal neural population coding of an auditory spatial cue
by Nicol S. Harper and David McAlpine
Full paper as a PDF file - Nature 430: 682 - 686 (05 Aug 2004)

Comments: This paper contrasts responses to sounds for animals of different head sizes based upon how much longer it takes for sound to reach one ear versus the other. They show how differences between gerbils, barn owls, cats and humans regarding ear placement affect the ITD (interaural time difference) in neural firing response to pure (sinusoidal) audio tones. They argue that the auditory signals an animal normally encounters, and ear location, can be used to assess the "optimal" frequency of sounds as measured by neural firing rates.

August 23, 2004 lecture: 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.

August 23, 2004 lecture: Linear regression and tree graphs

Phylogenetics and the Cohesion of Bacterial Genomes
by Vincent Daubin, Nancy A. Moran, and Howard Ochman
Full paper as a PDF file - Science Aug 8 2003 301: 829-832
see also
Passages Found Through Labyrinth of Bacterial Evolution
by Elizabeth Pennisi
News article as a PDF file - Science Aug 8 2003 301:745-746

Comments: In determining the phylogeny, or evolutionary relationship, between different bacteria, it has been hypothesized that the difficulty in determining these relationships is due to lateral gene transfers (LGT). LGT refer to the possibility that genes "jump" between species, arising since bacteria can absorb DNA from the environment or by engulfing other bacteria. Bacteria may therefore not have clear ancestries - so a branching tree for their evolutionary history would not be an adequate description. The authors use a regression to illustrate the relationship between length of the branches in the phylogenetic tree and the frequency at which a branching structure was not an adequate description. Using this, they argue that the history of bacterial lineages may be represented by traditional phylogenetic trees.

August 23, 2004 lecture: Histograms 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 brred 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 25, 2004 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. 1, 2004 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 1, 2004 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 15, 2004 lecture: Introduction to Matrices

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 15, 2004 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.

September 22, 2004 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.

October 4, 2004 lecture: Networks and Matrix Algebra

Social Insect Networks
by Jennifer H. Fewell
Full paper as a PDF file - Science September 26, 2003, 301:1867-1870

Comments: This paper illustrates how social systems may be viewed as networks with information transfer being used, for example, to transfer data about pollen foraging between individuals carrying out differing roles in the colony. Just as the matrices we have described for transfering individuals from one age class to another or matter from one compartment to another are used to summarize information in the conceptual graph of our models, matrices are used to summarize information on how behaviors of individuals affect the group dynamics. In general, even without quantitative values included in the matrix (e.g. if we just have a matrix of connections with values 0 or 1), mathematical methods can inform us about the behavior of the full system sometimes.

October 6, 2004 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 13, 2004 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, 2004 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, the 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, 2004 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 pinfected plants) infection.

November 3, 2004 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 17, 2004 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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