Probability and Betweenness of Points: The Genetic Ruler Kevin DeVizia & Mark Nebzydoski Delaware...

Probability and Betweenness of Points: The Genetic Ruler

Kevin DeVizia & Mark NebzydoskiDelaware 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

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

9th grade: Biology / Geometry10th grade: Chemistry / Algebra 211th grade: Physics / PrecalculusStatistics taught throughout

Some Biology/Geometry Links

Statistical Inference & Experimental Design Similarity/Proportion & Anatomical

Morphology Sequences/Recursion & Population Ecology Probability/Combinatorics & Genetics

Mapping Points

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. AB = 5, BC = 5, AC = 5– 2. AB = 3, BC = 4, AC = 5– 3. AB = 2, BC = 3, AC = 4– 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…


Try mapping the points designated in this chart; justify the geometry involved.


Try mapping the points designated in this chart… Hint: these points are collinear.

Gene Mapping

An ordered list of genetic loci along a particular chromosome

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.

The wild-type body color is gray (b+) and the mutant black (b).

The wild-type wing size is normal (vg+) and the mutant has vestigial wings (vg).

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 vg b+b vg+vg b+b vg vg b b vg+vg b b vg vg




A Gene Mapping Problem

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,

then what is the order of the genes on the chromosome?

A Gene Mapping Problem

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 9.5 16 0

mah h se e

A Gene Mapping Problem(with a twist)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

Using multiple crosses of this type with different genes percentages of recombination can be generated.

b – cn = 9%cn – vg = 9.5%b – vg = 17%


Fig. 15.6

An Explanation of the Twist

For More Information…

www.dvsd.org/honorsmathsci

Probability and Betweenness of Points: The Genetic Ruler Kevin DeVizia & Mark Nebzydoski Delaware...

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