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GENETICS CHAPTER 5
Part 2
A smart undergrad…
and an excellent mentor
• T. H. Morgan and A. H. Sturtevant:
– Cross over frequency is proportional to
distance between loci
– Recombination frequency (RF) can be used
to determine distance between genes located
on the same chromosome and construct a
genetic map

• 1% RF = 1 map unit (m.u.)
= 1 centimorgan (cM)
Genes follow linear sequence
Example from last time…..

Final Step: Draw the Map
You can then draw a map showing the distance between
the two genes
19 cM

P

L

This is Two Point Linkage Analyses
Limitations of the two-point cross
approach

• Difficult to determine gene order if two
genes are very close together (small
differences could be result of sampling
error)
– Requires examination of large progeny
– Needs statistical analyses

• Actual distances do not always add up
5.3 Three-Point Test-Cross Analysis Maps Genes
• A two-point test cross is not the most effective way
to build genetic maps
• By performing three-point test-cross analysis,
geneticists can efficiently map three linked genes
simultaneously

www.mun.ca
Determining gene order by threepoint crosses
• If genes w, y, and m
are in line, then one of
them must be in the
middle flanked by the
other two

• Greatest genetic
distance (y-m)
separates two genes
on the outside [third
gene (w) must be in
the middle]
Three-point crosses
• Allows positioning of
three genes in
relation to each other
using just one set of
crosses
• Allows correction for
double crossovers
(DCOs), which result
in double exchanges
of genetic material
A Three-Point Testcross Can Be Used to
Map Three Linked Genes
• Constructing a Genetic Map with the Three-Point Testcross
Finding the Relative Order of Genes by ThreePoint Mapping
• In a cross between a trihybrid individual
and one homozygous recessive for all
three genes, the gene configuration need
not be known in advance
• Incomplete linkage produces eight different
gamete genotypes, with unequal
frequencies if the genes are linked
• Parental types will be observed most
frequently, the recombinant types less
frequently
Three Point Mapping Criteria
• Wild-type organism producing crossover
gametes must be heterozygous at all three
loci
• Progeny phenotypes must reflect the
genotypes of the parental gametes (No
epistasis! No altered penetrance! Etc.)
• Number of offspring must be large enough to
facilitate recovery of all potential recombinants
(double crossovers!)
Example: a b c / a b c  a b c / a b c
(Test Cross 1)

• Parental gametes are
produced when there is no
crossing over between the
genes: a b c and a b c
• A single crossover
between a and b produces:
a b c and a b c
• A single crossover
between b and b produces:
a b c and a b c

• A double crossover (in
both intervals) produces:
a b c and a b c
Example: a b c / a b c  a b c / a b c
(Test Cross 2)

• Parental gametes are
produced when there is no
crossing over between the
genes: a b c and a b c
• A single crossover
between a and b produces:
a b c and a b c
• A single crossover
between b and c produces:
a b c and a b c
• A double crossover (in
both intervals) produces:
a b c and a b c
• NOTE! In trihybrid
cross, parental
phenotypes are not
necessarily all wild-type!
Frequencies of Gamete Classes
• When three genes are linked, each of the six recombinant gamete classes
are produced at frequencies significantly lower than that predicted by
chance
• Within each crossover class (e.g., single crossover between genes a and
b) both gamete types that result are equally frequent
• Double crossover classes are the least frequent because both crossover
events must occur to produce these

Least number →

Most number →
Constructing a Three-Point
Recombination Map
• Rollins Emerson (1935) mapped three
genes in maize: one for green (V-) or
yellow seedling (vv); one for rough
leaf (Gl-) or glossy leaf (gl gl); and
one for normal fertility (Va-) or
variable fertility (va va)
• He made trihybrids of genotype V Gl
Va/v gl va and crossed these to v gl
va/v gl va

• He analyzed the progeny to map the
genes
Great organism to study!
Double cross-overs: yellow, rough variable (v Gl va/v gl
va) & green, glossy, normal (V gl VA / v gl va)
Analysis of Data – Five Questions
1. Are the data consistent with the proposal of
genetic linkage?
2. What are the alleles on the parental
chromosomes?
3. What is the gene order on the chromosome?
4. What are the recombination frequencies of the
gene pairs?
5. Is the frequency of the double crossovers
consistent with independence of the single
crossovers?

•

Each of these questions is answered in
analyzing the three-point test-cross data
1. Are the Data Consistent with the Proposal of
Genetic Linkage?
• Under independent assortment,
eight genetically distinct gametes
would be produced with equal
frequency: 1/8  726  90.75 for
each class
• The chi-square value from the data
in Table 5.3 is over 800, with df  7
and a p value of  0.005

• This is consistent with genetic
linkage; parental gametes are
more frequent and recombinant
gametes less frequent than
predicted
2. What Are the Alleles on Parental
Chromosomes?
• The genotypes of original parents are
known in this case, so the alleles on
the parental chromosomes are V Gl Va
and v gl va
• The frequencies of the F2 progeny also
show this, as these are the most
abundant F2 phenotypes. So if we
didn’t know this already, we can
determine it from the data!

V Gl Va: 235!
v gl va: 270!
3. What Is the Gene Order on the Chromosome?
• The double recombinants, or double crossover
progeny, can be used to determine the gene order

• To determine the order, genes can be listed in each
of three possible orders and the resulting double
crossover progeny determined (trial and error)
• Alternatively when parental alleles and the
double crossover genotypes are compared, only
one allele will differ; this is the gene in the
middle of the three (the ‘odd one out’)
Determining the Gene Order on the
Chromosome by Trial and Error

Double cross-overs:
yellow, rough, variable (v Gl va/v gl va) &
green, glossy, normal (V gl VA / v gl va)

•
normal, yellow, rough
variable, green, glossy

• Result: double-crossover gametes from this order
are not those predicted from the data
•
green, variable, rough
yellow, normal, glossy

• Result: double-crossover gametes from this order
are not those predicted from the data
The Correct Gene Order on the Chromosome
•
green, glossy, normal
yellow, rough, variable
Double cross-overs:
yellow, rough variable (v Gl va/v gl va) &
green, glossy, normal (V gl VA / v gl va)

• Result: double-crossover gametes from this order are those
predicted from the data
• Conclusion: this predicted gene order is the correct one! 

• NOTE: glossy/rough is the odd one out! This is the
middle!
Map in progress……..

V

Gl

va
4. What Are the Recombination Frequencies of
the Gene Pairs? (Start with the two small ones!)
• Count the number of crossovers that occurred between the two members
of each gene pair, including the double crossover classes
• For V-Gl the frequency, r, is 60  62  4  7/726  0.183 or 18.3 cM
•

So NOT yellow, glossy OR green, rough; count yellow, rough & green, glossy

• For Gl-Va the frequency, r, is 48  40  4  7/726  0.136 or 13.6 cM
The Recombination Frequencies of the Largest
of the Three Distances
• Count the number of crossovers that occurred between the two most distant
genes, including the double crossover classes

• So, V-Va (from order we determined!) has frequency r  60  62  48  m 40  4
 7  4  7/726  0.320 or 32.0 cM
•

NOT green, normal OR yellow, variable, but everything else!

• For the larger distance, the double crossover progeny are added twice because
each represents two crossovers between V and Va

X
X

26
OUR MAP! 

18.3 cm

V

13.6 cm

Gl
32.0 cm

va
5. Is the Frequency of Double Crossovers
Consistent with Independence of the Single
Crossovers?
• In most experiments the number of observed double
crossovers is less than expected
• This is caused by an effect called interference (I)

• In Emerson’s data, the expected double crossovers would be
the product of the two single-crossover frequencies
(0.183)(0.136) = 0.025 (2.5%)  726  18.2
• But we only have 11!

• Observed double crossovers/Expected double crossovers 
the coefficient of coincidence, c.
Interference
c = Observed double crossovers/Expected double crossovers
In Emerson’s experiment, c  11/18.2  0.60

• I  1  c, or 0.40
• Interference identifies the double crossovers
expected but not produced (ie. How many are
missing?)
• Crossover in one chromosomal region inhibits
second crossover nearby
• In cases where I  0, negative interference has produced
more double crossovers than predicted
The relationship between
recombination frequency
and physical distance
between genes
-Recombination frequency
measured in organisms
underestimates the distance
between genes
Interference
Interference (I): the presence of a crossover interferes
with the formation of another crossover in the area

I=1-

Observed double crossover frequency
0.015
Expected double crossover frequency

A-B-Caabbcc
A-B-cc
aabbCA-bbCaaB-cc
aaB-CA-bbcc

379

354
94
80
42
36
8
7

25.2 cM
9.3 cM

18.9 cM

B

A

C

b

a

c

f (D.C.O) = (8 + 7) / 1000 = 0.015
Interference
Interference (I): the presence of a crossover interferes
with the formation of another crossover in the area

0.015

I=1-

0.166

Expected double crossover frequency
0.018

25.2 cM
9.3 cM
B

18.9 cM
A

9.3% = .093

C

18.9% = .189

0.093 x 0.189 = 0.018

Interference
IS happening!
Interference
Observed double crossover frequency

I=1Expected double crossover frequency

What does it mean?
If I > 0

Observed D.C. < Expected; 1 crossover decreases the
chance of a second crossover

If I = 0

Observed D.C. = Expected; No interference

If I < 0

Observed D.C. > Expected; 1 crossover increases the
chance of a second crossover
= rare
18.3 cm

V

13.6 cm

Gl

va

32.0 cm

We come across a map, what can we do with it?
Determining Gamete Frequencies from Genetic
Maps
• The relationship between recombination frequency
and map distance can be used to predict
frequencies of recombinant gametes based on map
distances

We can predict
what the next
generation will
look like!

http://fromdahliastodoxies.blogspot.com
Gamete Frequencies from Genetic Maps
• Both recombinant
gametes (A b and a B)
should be observed
equally frequently, ½
(0.10)  0.05, or 5% each
• The parental gametes will
be observed when there
is no crossover between
the genes, or 100% 
10%  90% of the time
• The two gametes, A B
and a b, will be seen in
equal proportion, in this
case ½ (0.90)  0.45, or
45% each
Whew, that can be a little confusing when done on slides….

LET’S DO A PROBLEM
TOGETHER! 
Scales: Green (Y) or Yellow (y)
Eyes: Tan (B) or blue (b)
Scales: Smooth (R) or rough (r)

Phenotype

Offspring Number

Green, Tan, Smooth

1

Green, Blue, Rough

61

Yellow, Tan, Rough

88

Green, Blue, Smooth

96

Yellow, Blue, Smooth

367

Yellow, Blue, Rough

3

Yellow, Tan, Smooth

46

Green, Tan, Rough

338
Analysis of Data – Five Questions
1. Are the data consistent with the proposal of
genetic linkage?
2. What are the alleles on the parental
chromosomes?
3. What is the gene order on the chromosome?
4. What are the recombination frequencies of the
gene pairs?
5. Is the frequency of the double crossovers
consistent with independence of the single
crossovers?

•

Each of these questions is answered in
analyzing the three-point test-cross data
Practice Problems!
• Chapter 5: 7 & 13
• Chapter 5: 26 (answer in back of book!)
• There are LOTs of appropriate practice
problems for chapter 5! 
Biological Factors Affecting Accuracy of Genetic
Maps
• Age, environment, and sex may
affect recombination frequency

• In female fruit flies, increased
age decreases recombination
frequency
• Fruit flies grown at temperatures
above or below the optimal 22°C
experience changes in
recombination frequency
• Levels of dietary calcium and
magnesium also affect rates of
crossover in flies
Influence of Sex on Rates of Recombination
• Recombination rates differ
between males and females for
most animals
• The heterogametic sex generally
has a lower recombination rate
than the homogametic sex
• The differences in recombination
rate are genome-wide, i.e., not
confined to the sex chromosomes
• In male fruit flies, there is no
crossing over at all
How do we map human genes?
• Humans do not do controlled
matings.
• Humans produce small number of
offspring.
• Mid-1980s: Advances in
polymorphic DNA markers and in
gene-mapping software make
human mapping possible.
• Polymorphinc DNA markers:
restriction fragment length variants
(RFLP) and single nucleotide
polymorphisms (SNP)
Linkage Group
• Assigning a disease-causing
gene to a chromosomal
location is a first step toward
the cloning and sequencing of
the gene
• Linkage groups: clusters of
syntenic genes that are linked
to one another
• Linkage groups can be
assigned chromosomal
locations.
• Allelic phase: the arrangement
of alleles of linked genes on
the homologous parent
chromosomes.

When a disease-causing allele
is seen to segregate along with
a known genetic marker, allelic
phase can be determined
Allelic Phase Analysis
D travels with P1!

recombinant

If we don’t know all the markers, we
don’t know how it traveled!
Questions?

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Genetics chapter 5 part 2(1)

  • 2.
  • 3. A smart undergrad… and an excellent mentor • T. H. Morgan and A. H. Sturtevant: – Cross over frequency is proportional to distance between loci – Recombination frequency (RF) can be used to determine distance between genes located on the same chromosome and construct a genetic map • 1% RF = 1 map unit (m.u.) = 1 centimorgan (cM)
  • 5. Example from last time….. Final Step: Draw the Map You can then draw a map showing the distance between the two genes 19 cM P L This is Two Point Linkage Analyses
  • 6. Limitations of the two-point cross approach • Difficult to determine gene order if two genes are very close together (small differences could be result of sampling error) – Requires examination of large progeny – Needs statistical analyses • Actual distances do not always add up
  • 7. 5.3 Three-Point Test-Cross Analysis Maps Genes • A two-point test cross is not the most effective way to build genetic maps • By performing three-point test-cross analysis, geneticists can efficiently map three linked genes simultaneously www.mun.ca
  • 8. Determining gene order by threepoint crosses • If genes w, y, and m are in line, then one of them must be in the middle flanked by the other two • Greatest genetic distance (y-m) separates two genes on the outside [third gene (w) must be in the middle]
  • 9. Three-point crosses • Allows positioning of three genes in relation to each other using just one set of crosses • Allows correction for double crossovers (DCOs), which result in double exchanges of genetic material
  • 10. A Three-Point Testcross Can Be Used to Map Three Linked Genes • Constructing a Genetic Map with the Three-Point Testcross
  • 11. Finding the Relative Order of Genes by ThreePoint Mapping • In a cross between a trihybrid individual and one homozygous recessive for all three genes, the gene configuration need not be known in advance • Incomplete linkage produces eight different gamete genotypes, with unequal frequencies if the genes are linked • Parental types will be observed most frequently, the recombinant types less frequently
  • 12. Three Point Mapping Criteria • Wild-type organism producing crossover gametes must be heterozygous at all three loci • Progeny phenotypes must reflect the genotypes of the parental gametes (No epistasis! No altered penetrance! Etc.) • Number of offspring must be large enough to facilitate recovery of all potential recombinants (double crossovers!)
  • 13. Example: a b c / a b c  a b c / a b c (Test Cross 1) • Parental gametes are produced when there is no crossing over between the genes: a b c and a b c • A single crossover between a and b produces: a b c and a b c • A single crossover between b and b produces: a b c and a b c • A double crossover (in both intervals) produces: a b c and a b c
  • 14. Example: a b c / a b c  a b c / a b c (Test Cross 2) • Parental gametes are produced when there is no crossing over between the genes: a b c and a b c • A single crossover between a and b produces: a b c and a b c • A single crossover between b and c produces: a b c and a b c • A double crossover (in both intervals) produces: a b c and a b c • NOTE! In trihybrid cross, parental phenotypes are not necessarily all wild-type!
  • 15. Frequencies of Gamete Classes • When three genes are linked, each of the six recombinant gamete classes are produced at frequencies significantly lower than that predicted by chance • Within each crossover class (e.g., single crossover between genes a and b) both gamete types that result are equally frequent • Double crossover classes are the least frequent because both crossover events must occur to produce these Least number → Most number →
  • 16. Constructing a Three-Point Recombination Map • Rollins Emerson (1935) mapped three genes in maize: one for green (V-) or yellow seedling (vv); one for rough leaf (Gl-) or glossy leaf (gl gl); and one for normal fertility (Va-) or variable fertility (va va) • He made trihybrids of genotype V Gl Va/v gl va and crossed these to v gl va/v gl va • He analyzed the progeny to map the genes Great organism to study!
  • 17. Double cross-overs: yellow, rough variable (v Gl va/v gl va) & green, glossy, normal (V gl VA / v gl va)
  • 18. Analysis of Data – Five Questions 1. Are the data consistent with the proposal of genetic linkage? 2. What are the alleles on the parental chromosomes? 3. What is the gene order on the chromosome? 4. What are the recombination frequencies of the gene pairs? 5. Is the frequency of the double crossovers consistent with independence of the single crossovers? • Each of these questions is answered in analyzing the three-point test-cross data
  • 19. 1. Are the Data Consistent with the Proposal of Genetic Linkage? • Under independent assortment, eight genetically distinct gametes would be produced with equal frequency: 1/8  726  90.75 for each class • The chi-square value from the data in Table 5.3 is over 800, with df  7 and a p value of  0.005 • This is consistent with genetic linkage; parental gametes are more frequent and recombinant gametes less frequent than predicted
  • 20. 2. What Are the Alleles on Parental Chromosomes? • The genotypes of original parents are known in this case, so the alleles on the parental chromosomes are V Gl Va and v gl va • The frequencies of the F2 progeny also show this, as these are the most abundant F2 phenotypes. So if we didn’t know this already, we can determine it from the data! V Gl Va: 235! v gl va: 270!
  • 21. 3. What Is the Gene Order on the Chromosome? • The double recombinants, or double crossover progeny, can be used to determine the gene order • To determine the order, genes can be listed in each of three possible orders and the resulting double crossover progeny determined (trial and error) • Alternatively when parental alleles and the double crossover genotypes are compared, only one allele will differ; this is the gene in the middle of the three (the ‘odd one out’)
  • 22. Determining the Gene Order on the Chromosome by Trial and Error Double cross-overs: yellow, rough, variable (v Gl va/v gl va) & green, glossy, normal (V gl VA / v gl va) • normal, yellow, rough variable, green, glossy • Result: double-crossover gametes from this order are not those predicted from the data • green, variable, rough yellow, normal, glossy • Result: double-crossover gametes from this order are not those predicted from the data
  • 23. The Correct Gene Order on the Chromosome • green, glossy, normal yellow, rough, variable Double cross-overs: yellow, rough variable (v Gl va/v gl va) & green, glossy, normal (V gl VA / v gl va) • Result: double-crossover gametes from this order are those predicted from the data • Conclusion: this predicted gene order is the correct one!  • NOTE: glossy/rough is the odd one out! This is the middle!
  • 25. 4. What Are the Recombination Frequencies of the Gene Pairs? (Start with the two small ones!) • Count the number of crossovers that occurred between the two members of each gene pair, including the double crossover classes • For V-Gl the frequency, r, is 60  62  4  7/726  0.183 or 18.3 cM • So NOT yellow, glossy OR green, rough; count yellow, rough & green, glossy • For Gl-Va the frequency, r, is 48  40  4  7/726  0.136 or 13.6 cM
  • 26. The Recombination Frequencies of the Largest of the Three Distances • Count the number of crossovers that occurred between the two most distant genes, including the double crossover classes • So, V-Va (from order we determined!) has frequency r  60  62  48  m 40  4  7  4  7/726  0.320 or 32.0 cM • NOT green, normal OR yellow, variable, but everything else! • For the larger distance, the double crossover progeny are added twice because each represents two crossovers between V and Va X X 26
  • 27. OUR MAP!  18.3 cm V 13.6 cm Gl 32.0 cm va
  • 28. 5. Is the Frequency of Double Crossovers Consistent with Independence of the Single Crossovers? • In most experiments the number of observed double crossovers is less than expected • This is caused by an effect called interference (I) • In Emerson’s data, the expected double crossovers would be the product of the two single-crossover frequencies (0.183)(0.136) = 0.025 (2.5%)  726  18.2 • But we only have 11! • Observed double crossovers/Expected double crossovers  the coefficient of coincidence, c.
  • 29. Interference c = Observed double crossovers/Expected double crossovers In Emerson’s experiment, c  11/18.2  0.60 • I  1  c, or 0.40 • Interference identifies the double crossovers expected but not produced (ie. How many are missing?) • Crossover in one chromosomal region inhibits second crossover nearby • In cases where I  0, negative interference has produced more double crossovers than predicted
  • 30. The relationship between recombination frequency and physical distance between genes -Recombination frequency measured in organisms underestimates the distance between genes
  • 31. Interference Interference (I): the presence of a crossover interferes with the formation of another crossover in the area I=1- Observed double crossover frequency 0.015 Expected double crossover frequency A-B-Caabbcc A-B-cc aabbCA-bbCaaB-cc aaB-CA-bbcc 379 354 94 80 42 36 8 7 25.2 cM 9.3 cM 18.9 cM B A C b a c f (D.C.O) = (8 + 7) / 1000 = 0.015
  • 32. Interference Interference (I): the presence of a crossover interferes with the formation of another crossover in the area 0.015 I=1- 0.166 Expected double crossover frequency 0.018 25.2 cM 9.3 cM B 18.9 cM A 9.3% = .093 C 18.9% = .189 0.093 x 0.189 = 0.018 Interference IS happening!
  • 33. Interference Observed double crossover frequency I=1Expected double crossover frequency What does it mean? If I > 0 Observed D.C. < Expected; 1 crossover decreases the chance of a second crossover If I = 0 Observed D.C. = Expected; No interference If I < 0 Observed D.C. > Expected; 1 crossover increases the chance of a second crossover = rare
  • 34. 18.3 cm V 13.6 cm Gl va 32.0 cm We come across a map, what can we do with it?
  • 35. Determining Gamete Frequencies from Genetic Maps • The relationship between recombination frequency and map distance can be used to predict frequencies of recombinant gametes based on map distances We can predict what the next generation will look like! http://fromdahliastodoxies.blogspot.com
  • 36. Gamete Frequencies from Genetic Maps • Both recombinant gametes (A b and a B) should be observed equally frequently, ½ (0.10)  0.05, or 5% each • The parental gametes will be observed when there is no crossover between the genes, or 100%  10%  90% of the time • The two gametes, A B and a b, will be seen in equal proportion, in this case ½ (0.90)  0.45, or 45% each
  • 37. Whew, that can be a little confusing when done on slides…. LET’S DO A PROBLEM TOGETHER! 
  • 38. Scales: Green (Y) or Yellow (y) Eyes: Tan (B) or blue (b) Scales: Smooth (R) or rough (r) Phenotype Offspring Number Green, Tan, Smooth 1 Green, Blue, Rough 61 Yellow, Tan, Rough 88 Green, Blue, Smooth 96 Yellow, Blue, Smooth 367 Yellow, Blue, Rough 3 Yellow, Tan, Smooth 46 Green, Tan, Rough 338
  • 39. Analysis of Data – Five Questions 1. Are the data consistent with the proposal of genetic linkage? 2. What are the alleles on the parental chromosomes? 3. What is the gene order on the chromosome? 4. What are the recombination frequencies of the gene pairs? 5. Is the frequency of the double crossovers consistent with independence of the single crossovers? • Each of these questions is answered in analyzing the three-point test-cross data
  • 40. Practice Problems! • Chapter 5: 7 & 13 • Chapter 5: 26 (answer in back of book!) • There are LOTs of appropriate practice problems for chapter 5! 
  • 41. Biological Factors Affecting Accuracy of Genetic Maps • Age, environment, and sex may affect recombination frequency • In female fruit flies, increased age decreases recombination frequency • Fruit flies grown at temperatures above or below the optimal 22°C experience changes in recombination frequency • Levels of dietary calcium and magnesium also affect rates of crossover in flies
  • 42. Influence of Sex on Rates of Recombination • Recombination rates differ between males and females for most animals • The heterogametic sex generally has a lower recombination rate than the homogametic sex • The differences in recombination rate are genome-wide, i.e., not confined to the sex chromosomes • In male fruit flies, there is no crossing over at all
  • 43.
  • 44. How do we map human genes? • Humans do not do controlled matings. • Humans produce small number of offspring. • Mid-1980s: Advances in polymorphic DNA markers and in gene-mapping software make human mapping possible. • Polymorphinc DNA markers: restriction fragment length variants (RFLP) and single nucleotide polymorphisms (SNP)
  • 45. Linkage Group • Assigning a disease-causing gene to a chromosomal location is a first step toward the cloning and sequencing of the gene • Linkage groups: clusters of syntenic genes that are linked to one another • Linkage groups can be assigned chromosomal locations. • Allelic phase: the arrangement of alleles of linked genes on the homologous parent chromosomes. When a disease-causing allele is seen to segregate along with a known genetic marker, allelic phase can be determined
  • 46. Allelic Phase Analysis D travels with P1! recombinant If we don’t know all the markers, we don’t know how it traveled!

Editor's Notes

  1. NOTE: there are two THEs in this header and in the text book page 157, one is capitalized and one is not. I have left both in lower case here to match other headings in this section.