Description
Evolution by Substitution
In this module students relate DNA changes and resulting amino acid substitutions to evolution. Students analyze the various pathways of change which could occur in a single amino acid position and, facilitated by the use of transition matrices, develop a powerful model for explaining and predicting long-term mutation probabilities. Math Topics: synonymous and non-synonymous substitutions, probability, matrices and Markov chains; Biology Topics: evolution, DNA and amino acids. Read more...
Imperfect TestingThis module uses an interrupted case study approach to answer the following two questions: What do the results of an imperfect medical test actually mean? How does this information affect public policy or personal decision making? The students are presented with the case of an adult female who learns her mammography test is positive. They then discuss the possible implications or outcomes of a positive test result given the properties of the test, including its sensitivity and specificity, and explore the predictive value of a test for a single individual. Math Topics: probability, conditional probability, ratios, probability trees, Bayes’ Rule; Biology Topics: imperfect testing, cancer, genetic testing, genetic variation, pharmacogenetics, ethical choices, decision making based on data interpretation, taking perspectives, and gold standards. Read more...
Genetic InversionsIn this module students explore the basic concepts of DNA and chromosomal inversions. The module starts with a game that introduces the idea of gene rearrangements, and then gradually leads the students through a series of improved algorithms designed to rearrange one genome into another in the least number of steps. Math Topics: algorithmic thinking, problem solving, optimization; Biology Topics: genetic mutations, inversions, evolution, phylogenetic trees. Read more...
Spider SilkThis module invites students to pose and answer the fundamental question: "What alignment of two sequences is biologically most meaningful?" Students explore the rapidly emerging field of bioinformatics by developing the basic mathematical principles that underlie computer programs used to align nucleotide and peptide sequences. As students become researchers, they begin to understand how mathematical modeling, computing, and biology can work together to answer important scientific questions. Students work through the ideas of mutation and selection, gene and protein sequences and homology, alignment, dynamic programming and iteration.
Array of HopeThis module is written as seen through the eyes of a doctor. This doctor has a patient who is diagnosed with melanoma. To find the best treatment for this patient a microarray is done. The doctor wants to know more so he begins to educate himself on the topic of microarrays. He begins by learning how a microarray is done. He becomes very interested so he visits a friend from med school, who now works in a research lab specializing in microarrays. The doctor learns not only how to run a microarray, but how to read a microarray and analyze the individual results mathematically taking into consideration variability of tests and standard deviation. This doctor's exploration causes him to look at larger data sets of many patients to see if different genes could be involved in different forms of the same disease. Ultimately, he understands which variation his patient has and which treatment is most likely to be successful. Math Topics: dot plot, interpolate, mean, median, standard deviation, variance; Biology Topics: microarray, DNA, protein, gene, mutation, control, qualitative vs. quantitative data.
Help! I’m Surrounded by Squirrels: Habitat SelectionUnderstanding and predicting species abundance is of fundamental concern to nearly every aspect of population ecology. Whether trying to preserve habitat for endangered species, or trying to engineer control strategies for invasive pests, it is important to understand the impact of habitat preference on species abundance. This module has students develop a mathematical method to infer habitat preferences based upon species abundance measures and uses this method to predict changes in population distributions as land use changes over time. In the process students learn about biotic and abiotic factors, niche, data categorization, dependent and independent variables, and line of best fit. Math Topics: dependent/independent variable, graphs, descriptive modeling, interpolate, line of best fit, scatter plot, slope intercept, trendline; Biology Topics: habitat selection, biotic/abiotic factors, niche, ecosystem.
Food WebsFood webs are abstract representations of feeding relationships in communities and use a series of arrows from one species to another where the first is a source of food for the second. Discrete mathematics provides a model for a food web using a directed graph (digraph) whose vertices are the species and an arc goes from a to b if a is food for b. Digraphs representing food webs make understanding predator prey relationships easier and various properties of digraphs provide insight into properties of the food web and the species contained within. Keystone species, species trophic levels, status, dominance, etc. can all be recognized from the digraph. Math Topics: graph theory, path lengths, mathematical modeling; Biology Topics: food webs, keystone species, predator/prey dynamics, energy transfer.
What’s My Ecological Impact?This module helps students see themselves and humans in general as intimately connected to the environment. In order to better understand humans' impact on the environment, basic mathematics is used to quantify aspects of their ecological impact. Ecological footprinting is developed as a tool for assessing humans' impact and as a decision- making tool. This module enables students to be more aware of humans' roles in threats to the environment and enables them to make more informed decisions about behaviors that have an impact on the environment. Students will gain a foundation in mathematical modeling that will inform any future work with creating or using other mathematical models. Math topics: ratios & proportions (in particular the equivalent ratios used in conversions), dimensional analysis, and writing, using, & interpreting simple formulas; Biology topics: human impact on the environment, carrying capacity, resources, ecology.
Drawing Lines: Spatial Arrangements of Biological PhenomenaOne of the fundamental needs of any organism is space in which to exist. Depending on how organisms engage in vital activities, such as finding shelter, foraging for food, courtship, and reproduction, the spatial needs of different species can vary and interact. Some animals range over many hundreds of square miles while foraging, while others never leave the small pond in which they were born. Many animals, regardless of their sizes or the scale of their habitats, are very territorial. These territories can be formed both within and between species. In addition, there are many other scales at which the biological organization of space is important. For example, at the cellular level, some cells interact with their neighboring cells, and at the ecosystem level all of the plants that comprise a forest structure the space in which they grow. The organization of space, at scales ranging from microns to kilometers, both affects and is affected by various biological phenomena. This module examines a single underlying principle governing the partitioning of a space in a wide range of biological contexts. Students will come to understand how the minimization of energy expenditure results in a widely applicable “nearest-neighbor” dynamic that helps us model and understand biological phenomena with Voronoi diagrams. Students will choose to examine the use of these diagrams in one of several different contexts. The heart of this module is student group work on one of four different case studies; student groups will create posters and share their work on their chosen case study in a mini science conference. Math topics: Nearest-neighbor Principle, Voronoi diagrams, perpendicular bisectors & equations for them, spatial patterns; Biology topics: animal behavior and the implications of different uses of space using case studies.
Home Range AnalysisHow do researchers determine the home range of a particular species? How does the home range of a species connect to its habitat? This module explores how data is collected and analyzed to determine the home range of a number of species. Students are provided with actual data for prairie dogs, black footed ferrets, pronghorn antelopes, and curlews. They determine the home range of these animals, including the size and breadth of the home range, and how one would create a buffer zone for the home range. They are encouraged to draw conclusions about the relationships among the species as they compare their data to other student’s data. They consider the usability and effectiveness of different tracking techniques in data collection. This module is appropriate for use in a variety of biology classes, algebra 1 and geometry. Math topics: unit conversions, graphing, estimation, area, convex and concave polygons, similar polygons, and the Pythagorean Theorem. Biology topics: home range, habitat, trophic levels, buffers, human impact, corridors, tracking methods, and other areas of conservation biology
Pass it on! Disease CompetitionThis module examines infectious diseases from the perspective of evolutionary biology on a basic level. Students gain an understanding of how different methods of pathogen reproduction can greatly affect the fitness of a disease. After learning to compute simple and conditional probabilities, students calculate probable levels of exposure to a disease in a population, probabilities of infection given exposure, and expected rates of disease incidence. Students practice rounding real numbers to integers, and converting among fractions, decimal representations and percentages while discussing methods of disease transmission, fitness, natural selection, and competition. Math Topics: probability, practice switching among multiplying fractions, decimals, and percentages; single- and multi-stage probability events; disjoint and independent events; Biology Topics: disease transmission, infection, epidemiology, fitness, natural selection, adaptation, and competition.
Computer Modeling of Disease OutbreaksThis module uses two hypothetical infectious disease outbreaks, which students simulate, to introduce and develop mathematical models for disease spread. As models are constructed the students have the opportunity to interactively see how changes in the parameters of the model change the pattern of the disease outbreak, thereby investigating how effective various intervention strategies can be, and witnessing how powerful a good model can be. Topics covered include arithmetic, state graphs, viruses, bacteria and the diseases they cause; vaccination, transmission routes and spread of disease.
Genetic Epidemiology: Finding Disease Susceptibility Alleles in Presence of Population StratificationPersonalized medicine based on known risk factors, including genetic risk factors, is a major focus of research. In order to include genetic risk factors in these predictions, the genetic risk factors need to be identified. This is a major focus of genetic epidemiology. The frequencies of genetic polymorphisms vary across different race and ethnic groups. These differences can be both helpful and problematic for those trying to identify genetic risk factors for diseases like cancer, diabetes and heart disease. This module explores the potential for falsely identifying a genetic factor as increasing risk of disease when the individuals chosen for study are not genetically homogeneous. This can happen even if individuals self-identify as being from the same race and ethnicity (note that even in Finland, there is potential for this "population stratification"). After identifying the problem, potential solutions are introduced, including using patterns of allele frequencies to re-classify individuals into genetically homogeneous groups. Students will use two web tools to explore concrete examples of genetic factors that have been associated with different traits such as Alzheimer Disease and response to beta-blocker drugs. In addition they will investigate some of the frequency differences of genetic risk factors across world-wide populations. Math Topics: simple probability, simple to complex distance measures, including Hamming Distance; Biology Topics: types of genetic polymorphisms (e.g. repeat, SNPs, insertions/deletions, copy number), mutation, haplotypes, genetic drift, evolutionary ancestry, study design - eliminating confounders, International HapMap Project.
CrIME: Criminal Investigations Through Mathematical ExaminationThis module uses the forensics of fingerprint analysis to introduce students to some of the basic mathematical concepts in the areas of graph theory, matrices, and the biological concept of individual identification and its underlying genetic mechanisms. Identification has applications in ecology and conservation biology that include such areas as dispersal of population, measuring extinction rates, migration, demographics, and effective population sizes. The module begins with an activity in which the students are given a scenario in which they discuss how one investigates fingerprint evidence that is found at a crime scene. This is followed by a series of activities in which the students are introduced to terminology and procedures used in fingerprint analysis, mathematical procedures used in fingerprint identification, and its application to identification. Graph theory terminology and techniques are thoroughly explained so that students with no prior graph theory experience will understand the basic concepts. The anatomy of the skin and the genetics associated with uniqueness are presented so that students familiar with basic genetics will understand these concepts. Math Topics: graph theory, adjacency matrices; Biology Topics: skin, individuality, fingerprints, penetrance, expressivity, epigenetics.