Chapter 22 – Quantitative Genetics and Multifactorial Traits
• Most of the traits that we have examined so far have been discontinuous traits.
– Either yellow or green
– Either tall or short
• Each trait was markedly different from one another.
– Single identifiable phenotype observed
• Many traits exhibit a wide range of possible phenotypes.
– Eg. Human birth weight, adult height and number of eggs laid by fruit flies.
• Traits like these are called continuous traits.
– Since these traits are usually described by quantitative measure (eg how tall,
how many etc.), these traits are also know as quantitative traits.
Polygene Hypothesis for Quantitative Inheritance
• A trait may have a range of phenotypes because of environment influence.
– Same genotype may produce range of phenotypes.
– Multiple genotypes may produce same phenotype.
• Work in the early 20th century indicated that both the environment and genotype
influence quantitative traits.
– These are multi-factorial traits.
– Phenotype cannot be explained by a single locus.
• Explanation for these traits is the polygene or multiple-gene hypothesis
for quantitative inheritance.
• Meristic Traits
– Phenotypes described by whole numbers
• Eg. Seeds in a pod or eggs laid by a
• Threshold Traits
– Small number of discrete classes
– Found in number of human diseases
Eg. Type II diabetes
Polygene Hypothesis for Kernel Colour
• The work of Hermann Nilsson-Ehle in 1909.
• Crossed true breeding red kernel to white
– F1all were all the same intermediate
shade between red and white…pink.
– F2kernels were 15 red(all shades) to 1
white. • When he categorized the red shades he found a phenotypic ratio of
• Did not observe 9:3:3:1 ratio, but a 1:4:6:4:1 ratio.
• Alleles here can either be contributing alleles or noncontributing alleles.
– Each contributing allele will allow for the synthesis of some pigment. Kernel
coloration is dependent on the number of R or C alleles (the r and c alleles are
• Eg. RRCC dark red, rrcc white.
• Multiple gene hypothesis fits some observations of quantitative inheritance.
• May be explained by the action and segregation of allelic pairs at a number of different
loci called polygenes.
Each polygene has a small effect on the overall phenotype.
Calculating the Number of Polygenes
• 1/4 = ratio of F 2ndividuals expressing either extreme phenotype
• Eg. 1/4 = 1/16 n
4 = 16
n ln 4 = ln 16
n = (ln 16)/ (ln 4)
n = 2 genes
Stats in Genetics
• Quantitative genetics addresses this question of nature vs nuture, or the relative roles
of genes vs the environment.
• Variation in the phenotype of a population is V P
– The portion of this variation that is genetic variation is V , while the variation
from the environment is V . E
V P V +GV E
• How do we partition the phenotypic and
We need to understand some statistical tools first.
The Variance and Standard Deviation • Variance is a measure of how much the individual measurements spread out around the
– How variable the individuals and their measurements are.
• Two distributions can have the same mean, but have dramatically different distributions
• The sample variance is symbolized as s , is defined as the average squared deviation
from the mean.
• Variance = s = ∑ (x -ix) /n – 1
• Standard Deviation = s = s 2
Some Generalizations to Quantitative Inheritance Studies
• Mean of F 1 is usually intermediate between
means of parents.
• Mean of F i2 usually approximately equal to F . 1
• F2almost always shows more variability around
the mean than F . 1
The extreme values in the F exte2d closer to the two
parental values than do the extreme values of the F . 1
• Proportion of a population’s phenotypic variation that is attributable to genetic factors.
• Important to know genetic contribution of traits.
– Eg In agriculture such as weight gain in cattle, milk production in cows and # of
eggs laid by chickens.
– Eg. In natural populations such as body size, fecundity and developmental rates
can help us understand natural selection and evolution.
• Phenotypic variance (V ) Ps a measure of all variability for a trait.
– Genetic contribution to the phenotypic variance is called genetic variance (V ) G
– Environmental contribution to the phenotypic variance is called environmental
variance (V E
• Includes any nongenetic variation such as temperature, nutrition and
VP= V G V E Covariance (COV )G,E
• 100% of the variation among individuals is accounted for by genetic and environmental
• However, the sum of genetically and environmentally caused variance may not add to
the total phenotypic variance.
– Here the genetically and environmentally caused variance covary.
– Eg. Milking cows known to produce more milk are given greater feed than those
that are poor milking cows.
• Individuals of above average genetic quality receive above average
resources leading to a covariance between genotype and environment.
Genotype-by-Environment Interaction (V GxE)
• Relative effects of genotypes differ among environments.
– Eg. In cold environment AA plants are 40cm tall on average, while aa plants are
– In warm environments AA plants are 50cm, while aa plants are 60cm.
• Both plants grow taller in warm environment so there is an
• There is also a genetic effect with the relative performance of the
genotypes differ in the two temperatures.
– While both genetic and environmental differences contribute to
the phenotypic variance, the effects of the genotype and
environment cannot simply be added together.