Probability and Betweenness of Points The Genetic Ruler

Probability and Betweenness of Points: The Genetic Ruler Kevin De. Vizia & Mark Nebzydoski Delaware Valley High School Milford, PA

The Delaware Valley Program • scientists vs. lab assistants • student-initiated research vs. canned experiments • link math and science • scheduling • www. dvsd. org/honorsmathsci

NCTM’s Connections Standard l Instructional programs from prekindergarten through grade 12 should enable all students to: – recognize and use connections among mathematical ideas; – understand how mathematical ideas interconnect and build on one another to produce a coherent whole; – recognize and apply mathematics in contexts outside of mathematics.

The Delaware Valley Program l 9 th grade: Biology / Geometry l 10 th grade: Chemistry / Algebra 2 l 11 th grade: Physics / Precalculus l Statistics taught throughout

Some Biology/Geometry Links Statistical Inference & Experimental Design l Similarity/Proportion & Anatomical Morphology l Sequences/Recursion & Population Ecology l Probability/Combinatorics & Genetics l

Mapping Points l Given a set of points and the distances shown, sketch a map of how the points might appear in the plane and describe the geometry of the shape they form. Justify your response in each case: – – 1. 2. 3. 4. AB = 5, BC = 5, AC = 5 AB = 3, BC = 4, AC = 5 AB = 2, BC = 3, AC = 4 AB = 2, BC = 3, AC = 5

More Problems in Placing Points Sometimes an atlas will show a set of distances between pairs of cities in a chart like this…

More Problems in Placing Points l Try mapping the points designated in this chart; justify the geometry involved.

More Problems in Placing Points l Try mapping the points designated in this chart… Hint: these points are collinear.

Gene Mapping l An ordered list of genetic loci along a particular chromosome l First done by Thomas Hunt Morgan and later used in the Human Genome Project

Linked Genes • Genes located on the same chromosome, linked genes, tend to be inherited together because the chromosome is passed along as a unit. • Results of crosses with linked genes deviate from those expected according to independent assortment.

First Use of Gene Mapping Thomas Hunt Morgan observed this linkage and its deviations when he followed the inheritance of characters for body color and wing size. l The wild-type body color is gray (b+) and the mutant black (b). l The wild-type wing size is normal (vg+) and the mutant has vestigial wings (vg). l

Copyright © 2002 Pearson Education, Inc. , publishing as Benjamin Cummings

b+b vg+vg X b b vg vg (Assuming independent assortment) (Genes on different chromosomes) b+vg+ b+vg b vg+ b vg b+b vg+vg b+b vg vg b b vg+vg b b vg vg b+b vg+vg b+b vg vg b b vg+vg b b vg vg

A Gene Mapping Problem l Consider genes X, Y, and Z. If the percent recombination between X and Y is 10, – between X and Z is 4, – between Z and Y is 6, – l then what is the order of the genes on the chromosome?

A Gene Mapping Problem l mah=mahogany eyes, h=hairy body, se=sepia eyes, e=ebony body mah 0 h 10 0 se 3. 5 6. 5 0 e 19. 5 16 0 mah h se e

A Gene Mapping Problem (with a twist) l Ye=yellow body, Ve=Vermillion eyes, MW=miniature wings, Wh=white eyes Ye 0 Wh 1 0 Ve 32. 2 30 0 MW 35. 5 32. 7 3 0 Ye Wh Ve MW

An Explanation of the Twist l Using multiple crosses of this type with different genes percentages of recombination can be generated. l b – cn = 9% l cn – vg = 9. 5% l b – vg = 17%

An Explanation of the Twist Fig. 15. 6 Copyright © 2002 Pearson Education, Inc.

For More Information… l www. dvsd. org/honorsmathsci