WCSU Quantitative Genetics Polygenic Inheritance Lab 9 Calculation Questions Homework assignment is on page 6. Please complete all parts of the questions.

WCSU Quantitative Genetics Polygenic Inheritance Lab 9 Calculation Questions Homework assignment is on page 6. Please complete all parts of the questions.

Any calculations must be submitted with the final assignment back to me.

You must calculate a t-test, mean, variance, and regression coefficient for both data set of height and total ridge. all calculates must be typed out. Formulas are included in the packet.

This assignment includes making a graph on excel, please read requirements on page 5. two graphs have to be made one for height and the other for total ridge. you must calculate heritability and type your calculations.

Last part of the paper requires finding a scientific paper on heritability. Again please refer to page 5 for all requirements and questions that have to be answered. you must attach the paper of your choosing and submit back to be.

Please submit:

All typed calculations. please separate each calculation with a heading. one page should be for all height calculations and another page for total ridge count.

All of question 1.

All of question 2. *** you have to repeat this question twice. I should have to graphs.

All of question 3. answer question and include paper in submission. LABORATORY  9  (week  11)  
Quantitative  Genetics  –  Polygenic  inheritance  
Introduction  
Qualitative  vs.  Quantitative  Traits  
Up  until  now,  we  have  been  exploring  the  inheritance  of  Mendelian  traits,  
traits  that  are  affected  by  one  or  a  few  genes.    These  classical  Mendelian  traits  have  
been  qualitative  in  nature,  i.e.  traits  which  are  easily  classified  into  distinct  
phenotypic  categories.  These  discrete  phenotypes  are  under  the  genetic  control  of  
only  one  or  a  very  few  genes  with  little  or  no  environmental  effects,  which  might  
obscure  the  genetic  effects.    In  contrast  to  this,  the  variability  exhibited  by  many  
biologically  important  traits  does  not  fit  into  separate  phenotypic  classes  
(discontinuous  variability),  but  instead  forms  a  spectrum  of  phenotypes  which  
blend  imperceptivity  from  one  type  to  another  (continuous  variability).  
Economically  important  traits  such  as  body  weight,  plant  height,  egg  or  milk  
production,  yield  of  grain  per  acre,  etc,  are  quantitative  traits  with  continuous  
variability.    The  basic  biological  difference  between  qualitative  and  quantitative  
traits  involves  the  number  of  genes  contributing  to  the  phenotypic  variability  and  
the  degree  to  which  the  phenotype  can  be  modified  by  environmental  factors.  See  
Table  1  for  some  of  the  major  differences  between  quantitative  and  qualitative  
traits.  
1.
2.
3.
4.
5.
Table  1:    Major  differences  between  qualitative  and  quantitative  traits  
Qualitative  Traits  
Quantitative  Traits  
Characters  of  kind  
1.
Characters  of  degree  
Discontinuous  variation;  discrete   2.
Continuous  variation;  phenotypic  
phenotypic  classes  
measurements  form  a  spectrum  
Single  gene  affects  discernible  
3.
Polygenic  control;  effects  of  single  
Concerned  with  individual  
genes  too  sight  to  be  detected  
matings  and  their  progeny  
4.
Concerned  with  a  populations  of  
Analyzed  by  making  counts  and  
organisms  consisting  of  all  
ratios  
possible  kinds  of  matings  
5.
Statistical  analyses  give  estimates  
of  population  parameters  such  as  
mean  and  standard  deviation  
 
Quantitative  traits  may  be  governed  by  many  genes  (perhaps  10-­‐100  or  
more),  each  contributing  a  small  amount  to  the  phenotype  so  that  their  individual  
effects  cannot  be  detected  by  Mendelian  methods.  The  alleles  at  each  gene  locus  lack  
dominance,  and  each  active  allele  has  an  effect  on  the  phenotype  that  is  small  and  
equal  to  that  of  each  of  the  other  alleles  affecting  the  trait.  These  alleles  are  often  
called  additive  because  their  effects  on  phenotype  can  be  added  up.  Phenotype  is  
determined  by  the  sum  of  all  the  active  alleles  present  in  the  individual.  However,  
the  genes  that  contribute  to  continuous  traits  (or  polygenes)  are  not  qualitatively  
different  from  other  genes,  they  regulate  the  production  of  polypeptides  and  they  
segregate  and  independently  assort  according  to  Mendelian  principles.  Their  
inheritance  only  seems  different  because  they  work  together  to  affect  one  trait.    
Statistics  have  been  developed  describe  and  test  hypotheses  regarding  
quantitative  traits  (what  kind  of  statistics  did  we  used  for  qualitative  traits?).    In  
 
1  
LABORATORY  9  (week  11)  
Quantitative  Genetics  –  Polygenic  inheritance  
particular,  populations  can  be  described  by  the  mean  trait  value  as  well  as  the  
variance  around  that  mean  (see  page  7  for  equations).    Once  we  know  these  two  
descriptive  statistics  about  populations,  we  can  test  the  hypotheses  that  two  
populations  have  the  same  mean  trait  value,  using  a  test  called  a  t-­‐test.    T-­‐tests  were  
invented  to  monitor  the  quality  of  Guinness  stout,  so  drink  up!    I  mean,  enjoy  testing  
the  differences  between  two  populations?  
 
Heritability  
Quantitative  traits  are  not  all  t-­‐tests  and  beer,  however.  There  is  more  to  
learn  about  them.  The  phenotypic  variability  expressed  in  most  quantitative  traits  
Table!1.!Fingerprint!data!that!may!be!strongly!suggestive!of!a!diagnosis!for!
has  
a  relatively  large  environmental  component,  and  a  correspondingly  small  
Chromosome!anomalies.!
genetic  
component.  It  is  the  task  of  the  geneticist  to  determine  the  magnitude  of  the  
!
genetic  and  environmental  components  of  the  total  phenotypic  variability  of  each  
Trisomy!21:!trait  in  a  population.    The  proportion  of  the  phenotypic  variability  in  a  
quantitative  
Fingers*primarily*ulnar*loops:*radial*loops*on*fingers*4*and*5.*
quantitative  
trait  that  is  due  to  genetic  influences  is  called  the  heritability.      
*
There  
Trisomy!18:!are  multiple  ways  to  estimate  heritability.    Today  we  will  be  estimating  
heritability  
by  comparing  the  values  of  the  quantitative  trait  in  parents  to  the  values  
Underdeveloped*epidermal*ridges;*high*frequency*of*arches*(average*7[8;*without*
in  at*least*one*arch,*the*diagnosis*is*suspect);*thumbs*lacking*arches*have*radial*loops;*
their  offspring.    We  will  do  this  by  calculating  a  regression  coefficient  for  the  
low*TRC.* between  parental  trait  values  and  offspring  trait  values.  The  regression  
relationship  
*
coefficient  
is  the  slope  of  the  best-­‐fit  line  between  the  x  and  y  values.    
Turner!Syndrome!45,!X:!
The  way  that  heritability  is  calculated  from  the  regression  coefficient  
Increased*TRC*with*no*increase*in*whorls.*
depends  
on  the  data  that  are  available.  If  measurements  for  both  parents  are  
*
available,  
the  average  of  the  two  values  is  plotted  on  the  x-­‐axis.    This  parental  
Relationship!between!average!TRC!and!the!number!of!X!and!Y!Chromosomes!
average  
i
s  
called  the  midparent  value.    T47,*XYY*–*103*
he  offspring  traits  are  plotted  on  the  x-­‐axis.  
45,*X*–*165*
We  
expect  that  the  midparent  value  will  48,*XXYY*–*88*
be  a  good  predictor  of  offspring  values.    
46,*XY*–*145*
This  
i
s  
b
ecause  
o
ffspring,  
o
n  
a
verage,  
w
ill  
exhibit  a  trait  value  that  is  the  average  of  
46,*XX*–*126*
48,*XYYY*–*83*
47,*XXY*–*114*
their  
parents.    In  this  case,  heritability  49,*XXXXX*–*17*(only*two*individuals*
is  simply  the  regression  coefficient  
examined)*
between  offspring  values  and  midparent  
values.  If,  however,  data  are  only  
*
available  for  one  parent,  heritability  is  estimated  as  2*regression  coefficient.  
* is  because  we  expect  the  data  from  one  parent  to  do  a  worse  job  predicting  
This  
*
offspring  values.    How  much  worse?    Exactly  twice  as  bad.  
*
 
 
 
 
*
*
*
 
 
 
*
 
!
  !!!!A:!Arch! !
!
!
!!!!!B:!Loop! !
!
!!!!!!!!!!!C:!Whorl!
*
 
Figure*1.*Examples*of*some*fingerprint*patterns*and*the*TRC*for*each*example.*A:*
 
arch*with*no*tri[radius*and*ridge*count*of*0;*B:*loop*with*one*tri[radius*and*a*ridge*
 
count*of*12;*C:*whorl*with*two*tri[radii*and*a*ridge*count*of*15*(the*higher*of*the*two*
 
possible*counts)*
 
*
II.(Classification(of(Prints(
(
*
*
Fingerprint*patterns*of*dermal*ridges*can*be*classified*into*three*major*
  groups:*arches,*loops,*and*whorls*(see*Figure*1.).*The*arch!is*the*simplest*and*least*
frequent*pattern.*It*may*be*subclassified*as*“plain”*when*the*ridges*rise*slightly*over*
the*middle*of*the*finger*or*“tented”*when*the*ridges*rise*to*a*point.*
2  
LABORATORY  9  (week  11)  
Quantitative  Genetics  –  Polygenic  inheritance  
Today  we  will  be  using  statistics  to  study  two  quantitative  traits,  total  ridge  
count  and  height.  Height  needs  little  introduction,  but  total  ridge  count  does.    In  
1890,  Francis  Galton  suggested  fingerprints  as  a  useful  tool  in  personal  
identification.  One  of  the  features  of  a  fingerprint  is  the  total  ridge  count.  The  
formation  of  the  epidermal  ridge  pattern  and  the  total  ridge  count  are  polygenic,  but  
they  are  also  influenced  by  environmental  factors.  The  embryology  of  epidermal  
ridges  offers  clues  to  prenatal  environmental  influence  on  their  pattern  of  
development.  Fetal  fingertip  pads  are  observable  around  the  sixth  week  of  gestation  
and  reach  their  maximal  size  by  week  12  or  13,  after  which  they  regress,  giving  rise  
to  elevated  dermal  ridges.  The  ridges,  once  formed,  are  very  resistant  to  later  
prenatal  or  postnatal  influences,  making  them  an  ideal  trait  for  genetic  studies  as  
well  as  for  identification  of  individuals.    
 
Classification  of  Finger  Prints  
Fingerprint  patterns  of  dermal  ridges  can  be  classified  into  three  major  
groups:  arches,  loops,  and  whorls  (see  Figure  1).  The  arch  is  the  simplest  and  least  
frequent  pattern.  It  may  be  subclassified  as  “plain”  when  the  ridges  rise  slightly  over  
the  middle  of  the  finger  or  “tented”  when  the  ridges  rise  to  a  point.    
The  loop  pattern  has  a  triradius  and  a  core.  A  triradius  is  a  point  at  which  
three  groups  of  ridges  coming  from  three  directions,  meet  at  angles  of  about  120  
degrees.  The  core  is  essentially  a  ridge  that  is  surrounded  by  fields  of  ridges,  which  
turn  back  on  themselves  at  180  degrees.  Loops  can  be  either  radial  or  ulnar.  A  finger  
possesses  a  radial  loop  if  its  triradius  is  on  the  side  of  the  little  finger  for  the  hand  in  
question  and  the  loop  opens  toward  the  thumb.  A  finger  has  an  ulnar  loop  if  its  
triradius  is  on  the  thumb-­‐side  of  that  hand  and  the  loop  opens  toward  the  little  
finger.  The  whorl  pattern  has  two  tridaii,  with  the  ridges  forming  various  patterns  
inside.  The  frequencies  of  these  fingerprint  pattern  types  in  the  general  population  
are  as  follows:  arch,  5.0%;  radial  loop.  5.4%;  ulnar  loop,  63.5%;  and  whorl,  26.1%.    
   
Ridge  Count    
The  focus  of  this  investigation  is  the  polygenic  or  quantitative  trait  called  the  
total  ridge  count  (TRC),  the  sum  of  the  ridge  counts  for  all  10  fingers.  Ridge  counts  
are  the  number  of  ridges  between  a  tri-­‐radius  of  a  fingerprint  and  the  center  of  the  
loop  or  whirl.    The  average  TRC  for  males  is  145  and  that  for  females  is  126.  For  an  
arch,  the  ridge  count  is  0.  The  ridge  count  on  a  finger  with  a  loop  is  determined  by  
counting  the  number  of  ridges  between  the  triradius  and  the  center  of  the  pattern.  
For  a  whorl,  a  ridge  count  is  higher  of  the  ridge  counts  from  the  two  triradius  to  the  
center  of  the  fingerprint  (Figure  1.).    
Once  everyone  has  prepared  their  own  fingerprints  (see  section  V)  and  
determined  their  own  TRCs  and  individual  fingerprint  patterns,  we  will  examine  
how  the  TRC  data  support  a  polygenic  model  of  inheritance.      
Upon  completing  today’s  lab,  you  should  be  able  to  classify  fingerprints  into  
arches,  radial  and  ulnar  loops,  and  whorls,  construct  histograms,  use  t-­‐tests  to  test  
hypotheses  
 
 
 
3  
LABORATORY  9  (week  11)  
Quantitative  Genetics  –  Polygenic  inheritance  
Methods:    
Class  TRC  Data  Collection  
1.  Rub  a  no.  2  pencil  on  an  index  card  to  make  a  blackened  square  about  3  cm.    
2.  Rub  one  of  your  fingers  on  the  graphite  square,  making  certain  that  you  cover  all  
the  triradii  on  the  finger.  Carefully  place  a  piece  of  transparent  tape  on  the  
graphite  covered  finger  so  that  the  tape  comes  in  contact  with  the  entire  portion  
of  the  finger  that  you  want  to  print.  Roll  the  finger  across  the  tape  in  one  smooth  
motion.  Peel  away  the  tape,  and  affix  it  to  the  appropriate  place  on  your  record  
sheet  (Table  1).    
3.  Repeat  this  process,  preparing  a  print  for  each  of  your  10  fingers.    
4.  Examine  each  print  carefully;  if  a  print  is  incomplete,  prepare  a  new  one.  Use  the  
dissecting  scope  to  help  classify  the  pattern  and  determine  the  ridge  count  for  
each  print.    
5.  Write  your  total  ridge  count  and  sex  in  the  table  on  the  chalkboard,  as  directed  by  
Dr.  Prunier.  Record  all  of  the  class  data.  
 
Analysis  
6.  Use  the  class  data  to  construct  a  histogram  in  which  frequencies  (number  of  
individuals)  are  plotted  against  TRC.  
7.    Calculate  the  mean  and  variance  for  TRC  for  males  and  females  separately  
8.  Use  a  t-­‐test  to  test  the  null  hypothesis  that  males  and  females  do  not  differ  in  total  
ridge  count  
 
Class  Height  Data  Collection  
1.    Remove  your  shoes  and  have  your  partner  measure  your  height  to  the  nearest  .5  
cm.      
2.    Record  both  heights  and  sexes  on  the  board.  
3.    When  all  of  the  section’s  heights  are  on  the  board,  record  all  of  the  individual  
heights  and  sexes.  
 
Analysis  
1.    Draw  a  section  histogram  for  male  and  female  heights.    Bin  by  10  cm  increments  
2.    Calculate  the  mean  and  variance  for  height  for  males  and  females  separately  
3.    Do  a  t-­‐test  to  determine  whether  males  and  females  differ  significantly  in  height.  
 
Heritability:  Triradius  count  and  Height  
1.    You  are  provided  with  TRC  and  height  data  from  parents  and  offspring  
2.    Calculate  the  regression  coefficients  for  each  set  of  data  
3.    Use  this  to  calculate  the  heritability  of  these  two  traits  (see  bolded  section  on  
page  2)  
 
 
 
 
 
 
 
4  
LABORATORY  9  (week  11)  
Quantitative  Genetics  –  Polygenic  inheritance  
Homework  (10  pts)  
1.    Turn  in  the  t-­‐test  results  for  the  cla…
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