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MEIOSI
S
GRADE 12
EDITED BY
KHANYISILE
MASIKANE
MEIOSIS
 The form of cell division

by which gametes, with
half the number of
chromosomes also known
as haploid, are produced.

 Diploid (2n)

(n)

→ haploid

 Meiosis is sexual
reproduction.
MEIOSIS
cont..

 Sex cells divide to produce

gametes (sperm or egg).
 Gametes have half the # of
chromosomes.
 Occurs only in gonads (testes or
ovaries).
Male: spermatogenesis
Female: oogenesis

 Meiosis is similar to mitosis with
some chromosomal differences.
Spermatogenesis
n=23

human
sex cell

n=23

sperm

n=23
2n=46
haploid (n)
diploid (2n)

n=23

n=23

n=23
Meiosis I

Meiosis II
Interphase I
 Similar to mitosis Interphase.
 Chromosomes replicate (S phase).
 Each duplicated chromosome consist of two
identical sister chromatids attached at their
centromeres.
centromeres

 Centriole pairs also replicate, INSIDE THE
CENTROSOME
Interphase I
 Nucleus and nucleolus visible.
chromatin

nuclear
membrane

cell membrane
nucleolus
Meiosis I
(four phases)
 Cell division that reduces the

chromosome number by one-half.
a.
b.
c.
d.

Four phases:
phases

Prophase I
Metaphase I
Anaphase I
Telophase I
PROPHASE I
 Longest and most complex phase (90%).
 Chromosomes condense.
 Synapsis occurs: homologous chromosomes come
together to form a BIVALENT TETRAD.
TETRAD

 Tetrad= TWO chromosomes of THREE OR
Tetrad
FOUR chromatids (sister and nonsister chromatids).
 IN THIS PHASE THE PROCESS CROSSING
OVER TAKES PLACE- EXCHANGE OF
GENETIC MATERIAL.
Prophase I - Synapsis
Homologous chromosomes

sister chromatids

Tetrad

sister chromatids
HOMOLOGOUS
CHROMOSOMES
 PaIr Of chrOMOSOMES (MatErnal

and PatErnal) that arE SIMIlar In
ShaPE and SIzE.

 hOMOlOgOuS PaIrS (tEtradS) carry
gEnES cOntrOllIng thE SaME
InhErItEd traItS.

 Each lOcuS (POSItIOn Of a gEnE) IS In
thE SaME POSItIOn On hOMOlOguES.

 huManS havE 23 PaIrS Of

hOMOlOgOuS chrOMOSOMES.
a. 22 PaIrS Of autOSOMES
b. 01 PaIr Of SEx chrOMOSOMES
Homologous Chromosomes
eye color
locus

eye color
locus

hair color
locus

hair color
locus

Paternal

Maternal
Crossing
Over
????????????
Crossing over (variation) may occur between nonsister
chromatids at the chiasmata.
chiasmata
Crossing over: segments of nonsister chromatids break and
over
reattach to the other chromatid.
chromatid
Chiasmata (chiasma) are the sites of crossing over.
over
Crossing Over nonsister chromatids

chiasmata: site
of crossing over

vARIATION
Tetrad

variation
Sex
Chromosomes

XX chromosome - female

XY chromosome - male
Prophase I
spindle fiber

aster
fibers

centrioles
Metaphase I
 Shortest phase
 Tetrads align on the metaphase plate.
plate
 INDEPENDENT ASSORTMENT OCCURS:
1. Orientation of homologous pair to poles is
random.
2. Variation
3. Formula: 2n
Example: 2n = 4
then n = 2
thus 22 = 4 combinations
Metaphase I
OR

metaphase plate

metaphase plate
Anaphase I
Homologous chromosomes
separate and move towards the
poles.

Sister chromatids remain
attached at their centromeres.
centromeres
Anaphase I
Telophase I
 Each pole now has haploid set of chromosomes.
chromosomes
 Cytokinesis occurs and two haploid daughter cells
are formed.
Telophase I
Meiosis II

 No Interphase II

(or very short - no more DNA replication)
replication

 Remember: Meiosis II is similar to
Mitosis
Prophase
II
 Same as prophase in mitosis
Metaphase II
 Same as Metaphase in Mitosis

metaphase plate

metaphase plate
Anaphase II
 Same as Anaphase in Mitosis
 Sister chromatids separate
Telophase II
Same as Telophase in Mitosis.
Mitosis
Nuclei form.
Cytokinesis occurs.
Remember: four haploid daughter
cells

produced.

gametes = sperm or egg
Telophase II
Meiosis
sex cell

n=2
sperm

n=2

n=2

2n=4
haploid (n)
diploid (2n)

n=2

n=2

n=2
meiosis I

meiosis II
SUMMARY OF MEIOSIS
Variation

 Important to population as the raw material for
natural selection.

Question: What are the three
sexual sources Of genetic
Answer:

1. Crossing over (Prophase I)
2. Independent assortment (Metaphase
I)
3. Random fertilization

Remember: VaRiAtIoN
iS gOoD!
Fertilization


The fusion of a sperm and egg to
form a zygote.
zygote
A zygote is a fertilized egg
WOW
ALL OF THAT
FOR ME! WOW
6. KARYOTYPE
• A karyotype is an ordered display of
magnified images of an individual’s
chromosomes arranged in pairs.
• Karyotypes allow for the
observation of :
 homologous chromosome
pairs,
 chromosome number, and
 chromosome structure.
© 2012 Pearson Education, Inc.
SCIENTIST OBSERVING A HUMAN
KARYOTYPE
Centromere

Sister
chromatids
Pair of
homologous
chromosomes

Sex chromosomes
7. Alteration in chromosome number

 An extra copy of chromosome 21 causes
Down syndrome or also known as
TRISOMY 21.

 A. Trisomy 21
• involves the inheritance of three copies
of chromosome 21 and

• is the most common human
chromosome abnormality.

© 2012 Pearson Education, Inc.
Down syndrome
 Trisomy 21 produces a characteristic set of
symptoms, which include:

•
•
•
•
•

mental retardation,
characteristic facial features,
short stature,
heart defects,
susceptibility to respiratory infections,
leukemia, and Alzheimer’s disease, and

• shortened life span.
 The incidence increases with the age of the
mother.
B. Accidents during meiosis can alter
chromosome number
 Nondisjunction is the failure of chromosomes or
chromatids to separate normally during meiosis.
This can happen during:

• meiosis I, if both members of a homologous
pair go to one pole or

• meiosis II if both sister chromatids go to one
pole.

 Fertilization after nondisjunction yields zygotes
with altered numbers of chromosomes.
MEIOSIS I

Nondisjunction

MEIOSIS II
Normal
meiosis II

Gametes
Number of
chromosomes

n+ 1

n+ 1

n− 1

Abnormal gametes

n−1
MEIOSIS I

Normal
meiosis I

MEIOSIS II

Nondisjunction

n+ 1

n−1

Abnormal gametes

n

n

Normal gametes
C. Abnormal numbers of sex
chromosomes

 Sex chromosome abnormalities tend
to be less severe, perhaps because of
• the small size of the Y
chromosome or
• X-chromosome inactivation.

© 2012 Pearson Education, Inc.
In general,
general
• a single Y chromosome is enough
to produce “maleness,” even in
“
combination with several X
chromosomes, and

• the absence of a Y chromosome
yields “femaleness.”
© 2012 Pearson Education, Inc.
 THE FOLLOWING TABLE LISTS THE
MOST COMMON HUMAN SEX
CHROMOSOME ABNORMALITIES.

© 2012 Pearson Education, Inc.
D. New species can arise from errors in
cell division

 Errors in mitosis or meiosis may produce
polyploidy species, with more than two
chromosome sets.
.

© 2012 Pearson Education, Inc.
8. Alterations of chromosome structure

 Chromosome breakage can lead to
rearrangements that can produce:

• genetic disorders or,
• If changes occur in somatic cells,
cancer.

© 2012 Pearson Education, Inc.
THESE REARRANGEMENTS MAY
INCLUDE:
• a Deletion, the loss of a chromosome
segment,

• a Duplication, the repeat of a
chromosome segment,

• an Inversion, the reversal of a
chromosome segment, or

• a Translocation, the attachment of a
segment to a non-homologous
chromosome that can be reciprocal.
THESE REARRANGEMENTS MAY
INCLUDE:

Deletion

Inversion

Duplication

Reciprocal translocation

Homologous
chromosomes

© 2012 Pearson Education, Inc.

Nonhomologous
chromosomes
PRESENTED and EDITED BY
KHANYISILE MASIKANE
ACKNOWLEDGEMENTS TO
Hasimah Azit
AND
Janice Williamson
Images taken from:
Campbell, N. Reece, J.2007.
BIOLOGY 8th edition. Pearson
Education.

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Meiosis

  • 2. MEIOSIS  The form of cell division by which gametes, with half the number of chromosomes also known as haploid, are produced.  Diploid (2n) (n) → haploid  Meiosis is sexual reproduction.
  • 3. MEIOSIS cont..  Sex cells divide to produce gametes (sperm or egg).  Gametes have half the # of chromosomes.  Occurs only in gonads (testes or ovaries). Male: spermatogenesis Female: oogenesis  Meiosis is similar to mitosis with some chromosomal differences.
  • 5. Interphase I  Similar to mitosis Interphase.  Chromosomes replicate (S phase).  Each duplicated chromosome consist of two identical sister chromatids attached at their centromeres. centromeres  Centriole pairs also replicate, INSIDE THE CENTROSOME
  • 6. Interphase I  Nucleus and nucleolus visible. chromatin nuclear membrane cell membrane nucleolus
  • 7. Meiosis I (four phases)  Cell division that reduces the chromosome number by one-half. a. b. c. d. Four phases: phases Prophase I Metaphase I Anaphase I Telophase I
  • 8. PROPHASE I  Longest and most complex phase (90%).  Chromosomes condense.  Synapsis occurs: homologous chromosomes come together to form a BIVALENT TETRAD. TETRAD  Tetrad= TWO chromosomes of THREE OR Tetrad FOUR chromatids (sister and nonsister chromatids).  IN THIS PHASE THE PROCESS CROSSING OVER TAKES PLACE- EXCHANGE OF GENETIC MATERIAL.
  • 9. Prophase I - Synapsis Homologous chromosomes sister chromatids Tetrad sister chromatids
  • 10. HOMOLOGOUS CHROMOSOMES  PaIr Of chrOMOSOMES (MatErnal and PatErnal) that arE SIMIlar In ShaPE and SIzE.  hOMOlOgOuS PaIrS (tEtradS) carry gEnES cOntrOllIng thE SaME InhErItEd traItS.  Each lOcuS (POSItIOn Of a gEnE) IS In thE SaME POSItIOn On hOMOlOguES.  huManS havE 23 PaIrS Of hOMOlOgOuS chrOMOSOMES. a. 22 PaIrS Of autOSOMES b. 01 PaIr Of SEx chrOMOSOMES
  • 11. Homologous Chromosomes eye color locus eye color locus hair color locus hair color locus Paternal Maternal
  • 12. Crossing Over ???????????? Crossing over (variation) may occur between nonsister chromatids at the chiasmata. chiasmata Crossing over: segments of nonsister chromatids break and over reattach to the other chromatid. chromatid Chiasmata (chiasma) are the sites of crossing over. over
  • 13. Crossing Over nonsister chromatids chiasmata: site of crossing over vARIATION Tetrad variation
  • 14. Sex Chromosomes XX chromosome - female XY chromosome - male
  • 16. Metaphase I  Shortest phase  Tetrads align on the metaphase plate. plate  INDEPENDENT ASSORTMENT OCCURS: 1. Orientation of homologous pair to poles is random. 2. Variation 3. Formula: 2n Example: 2n = 4 then n = 2 thus 22 = 4 combinations
  • 18. Anaphase I Homologous chromosomes separate and move towards the poles. Sister chromatids remain attached at their centromeres. centromeres
  • 20. Telophase I  Each pole now has haploid set of chromosomes. chromosomes  Cytokinesis occurs and two haploid daughter cells are formed.
  • 22. Meiosis II  No Interphase II (or very short - no more DNA replication) replication  Remember: Meiosis II is similar to Mitosis
  • 23. Prophase II  Same as prophase in mitosis
  • 24. Metaphase II  Same as Metaphase in Mitosis metaphase plate metaphase plate
  • 25. Anaphase II  Same as Anaphase in Mitosis  Sister chromatids separate
  • 26. Telophase II Same as Telophase in Mitosis. Mitosis Nuclei form. Cytokinesis occurs. Remember: four haploid daughter cells produced. gametes = sperm or egg
  • 28. Meiosis sex cell n=2 sperm n=2 n=2 2n=4 haploid (n) diploid (2n) n=2 n=2 n=2 meiosis I meiosis II
  • 30.
  • 31. Variation  Important to population as the raw material for natural selection. Question: What are the three sexual sources Of genetic
  • 32. Answer: 1. Crossing over (Prophase I) 2. Independent assortment (Metaphase I) 3. Random fertilization Remember: VaRiAtIoN iS gOoD!
  • 33. Fertilization  The fusion of a sperm and egg to form a zygote. zygote A zygote is a fertilized egg
  • 35. 6. KARYOTYPE • A karyotype is an ordered display of magnified images of an individual’s chromosomes arranged in pairs. • Karyotypes allow for the observation of :  homologous chromosome pairs,  chromosome number, and  chromosome structure. © 2012 Pearson Education, Inc.
  • 36. SCIENTIST OBSERVING A HUMAN KARYOTYPE
  • 38. 7. Alteration in chromosome number  An extra copy of chromosome 21 causes Down syndrome or also known as TRISOMY 21.  A. Trisomy 21 • involves the inheritance of three copies of chromosome 21 and • is the most common human chromosome abnormality. © 2012 Pearson Education, Inc.
  • 40.  Trisomy 21 produces a characteristic set of symptoms, which include: • • • • • mental retardation, characteristic facial features, short stature, heart defects, susceptibility to respiratory infections, leukemia, and Alzheimer’s disease, and • shortened life span.  The incidence increases with the age of the mother.
  • 41. B. Accidents during meiosis can alter chromosome number  Nondisjunction is the failure of chromosomes or chromatids to separate normally during meiosis. This can happen during: • meiosis I, if both members of a homologous pair go to one pole or • meiosis II if both sister chromatids go to one pole.  Fertilization after nondisjunction yields zygotes with altered numbers of chromosomes.
  • 42. MEIOSIS I Nondisjunction MEIOSIS II Normal meiosis II Gametes Number of chromosomes n+ 1 n+ 1 n− 1 Abnormal gametes n−1
  • 43. MEIOSIS I Normal meiosis I MEIOSIS II Nondisjunction n+ 1 n−1 Abnormal gametes n n Normal gametes
  • 44. C. Abnormal numbers of sex chromosomes  Sex chromosome abnormalities tend to be less severe, perhaps because of • the small size of the Y chromosome or • X-chromosome inactivation. © 2012 Pearson Education, Inc.
  • 45. In general, general • a single Y chromosome is enough to produce “maleness,” even in “ combination with several X chromosomes, and • the absence of a Y chromosome yields “femaleness.” © 2012 Pearson Education, Inc.
  • 46.  THE FOLLOWING TABLE LISTS THE MOST COMMON HUMAN SEX CHROMOSOME ABNORMALITIES. © 2012 Pearson Education, Inc.
  • 47. D. New species can arise from errors in cell division  Errors in mitosis or meiosis may produce polyploidy species, with more than two chromosome sets. . © 2012 Pearson Education, Inc.
  • 48. 8. Alterations of chromosome structure  Chromosome breakage can lead to rearrangements that can produce: • genetic disorders or, • If changes occur in somatic cells, cancer. © 2012 Pearson Education, Inc.
  • 49. THESE REARRANGEMENTS MAY INCLUDE: • a Deletion, the loss of a chromosome segment, • a Duplication, the repeat of a chromosome segment, • an Inversion, the reversal of a chromosome segment, or • a Translocation, the attachment of a segment to a non-homologous chromosome that can be reciprocal.
  • 50. THESE REARRANGEMENTS MAY INCLUDE: Deletion Inversion Duplication Reciprocal translocation Homologous chromosomes © 2012 Pearson Education, Inc. Nonhomologous chromosomes
  • 51. PRESENTED and EDITED BY KHANYISILE MASIKANE ACKNOWLEDGEMENTS TO Hasimah Azit AND Janice Williamson Images taken from: Campbell, N. Reece, J.2007. BIOLOGY 8th edition. Pearson Education.

Notas do Editor

  1. Figure 8.18_s4 Preparation of a karyotype from a blood sample (step 4)
  2. Figure 8.18_s5 Preparation of a karyotype from a blood sample (step 5)
  3. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. If you have several hundred students or more in your class, it is likely that at least one of your students has a sibling with Down syndrome. The authors note that, overall, about one in every 700 babies are born with Down syndrome. 3. The National Down Syndrome Society has a website at www.ndss.org. It is a wonderful resource.
  4. Figure 8.19A A karyotype showing trisomy 21, and an individual with Down syndrome
  5. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. If you have several hundred students or more in your class, it is likely that at least one of your students has a sibling with Down syndrome. The authors note that, overall, about one in every 700 babies are born with Down syndrome. 3. The National Down Syndrome Society has a website at www.ndss.org. It is a wonderful resource.
  6. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Students might be confused by the term nondisjunction. But simply put, it is an error in the sorting of chromosomes during mitosis or meiosis. Figure 8.20 illustrates two types of nondisjunction errors in meiosis.
  7. Figure 8.20A_s3 Nondisjunction in meiosis I (step 3)
  8. Figure 8.20B_s3 Nondisjunction in meiosis II (step 3)
  9. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Some syndromes related to human sexuality are not the result of abnormalities in sex chromosome number. Androgen insensitivity syndrome produces sterile males who possess mostly female sex characteristics. People with this condition are genetically male, but have bodies that fail to respond to male sex hormones. The National Institute of Health web site “Genetics Home Reference” can provide additional details about this and most genetic disorders at http://ghr.nlm.nih.gov/.
  10. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Some syndromes related to human sexuality are not the result of abnormalities in sex chromosome number. Androgen insensitivity syndrome produces sterile males who possess mostly female sex characteristics. People with this condition are genetically male, but have bodies that fail to respond to male sex hormones. The National Institute of Health web site “Genetics Home Reference” can provide additional details about this and most genetic disorders at http://ghr.nlm.nih.gov/.
  11. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Some syndromes related to human sexuality are not the result of abnormalities in sex chromosome number. Androgen insensitivity syndrome produces sterile males who possess mostly female sex characteristics. People with this condition are genetically male, but have bodies that fail to respond to male sex hormones. The National Institute of Health web site “Genetics Home Reference” can provide additional details about this and most genetic disorders at http://ghr.nlm.nih.gov/.
  12. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. In general, flowering plants are more likely to form new species through polyploidy than animals, because unlike most animals, many flowering plants can fertilize themselves. 3. The gray tree frog, which is found over most of the eastern half of the United States, from Florida and Texas to Ontario and Maine, consists of two species Hylachrysoscelis, which is diploid, and Hylaversicolor, which is tetraploid. The two species cannot be distinguished except by the number of chromosomes in their cells. The tetraploid species is thought to have been formed by an error in meiosis, similar to that frequently seen in plants.
  13. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Challenge students to create a simple sentence and then modify that sentence to represent (a) a deletion, (b) a duplication, and (c) an inversion as an analogy to these changes to a chromosome.
  14. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Challenge students to create a simple sentence and then modify that sentence to represent (a) a deletion, (b) a duplication, and (c) an inversion as an analogy to these changes to a chromosome.
  15. Student Misconceptions and Concerns Before addressing karyotyping and nondisjunction events, consider reviewing the general structure and terminology associated with replicated chromosomes and the arrangement of chromosomes during metaphase of mitosis, meiosis I, and meiosis II. Figures 8.3B and 8.14 will be particularly helpful. A firm foundation in chromosome basics is necessary to understand the irregularities discussed in Modules 8.19–8.23. Teaching Tips 1. The Human Genome Website is a tremendous asset for nearly every discussion related to human genetics. It can be accessed at www.genomics.energy.gov. 2. Challenge students to create a simple sentence and then modify that sentence to represent (a) a deletion, (b) a duplication, and (c) an inversion as an analogy to these changes to a chromosome.