Download See these math fitness and selection concepts explained nicely in a

Calculation of Fitness and Selection Coefficient
http://www.radford.edu/~rsheehy/GraphingDemo/fitness1.html
Survival rate = the overall survival rate is the % of individuals born that survive to reproductive age. But often we can only
measure the % that survive over some period of time, e.g. the survival rate of fledglings, the survival rate from one year to
the next, or the survival rate through a winter storm.
Reproductive rate = for any given genotype or phenotype, the average number offspring born per individual.
Relative Fitness (w) is the survival and/or reproductive rate of a genotype (or phenotype) relative to the maximum survival
and/or reproductive rate of other genotypes in the population.
Calculate the Relative Fitness (w) of each genotype by dividing each genotype's survival and/or reproductive rate by the
highest survival and/or reproductive rate among the 3 genotypes. For example:
If only survival rates differ and reproductive rates are all equal, then the fitnesses are simply each survival rate divided by the
highest survival rate. (reminder: taking the simplest situation for learning purposes, genes come in pairs in most organisms,
humans included; hence a pair of chromosomes will have two different genes for the same trait. Traits are anatomy,
physiology and behavioral traits that affect fitness. One of those genes can be dominant (D) and one recessive (d) for a given
trait), so there are three genotypes possible for each person – DD, Dd, and dd.)
DD
Dd
Survival rate
10%
10%
Reproductive rate
4
4
Relative fitness (w) 10/20 = 0.50 10/20 = 0.50
dd
20%
4
20/20 = 1.0
If only reproductive rates differ and the survival rates are all equal, then fitnesses are each reproductive rate divided by the
highest reproductive rate.
Survival rate
Reproductive rate
Relative fitness (w)
DD
10%
8
8/8 = 1.00
Dd
10%
8
8/8 = 1.00
dd
10%
4
4/8 = 0.50
If both survival and reproductive rates vary among the genotypes, then divide each survival X reproductive rate by the
highest survival X reproductive rate.
Survival rate
Reproductive rate
Survival X Repro Rate
Relative fitness (w)
DD
Dd
10%
10%
10
8
0.1 X 10 0.1 X 8 = 0.8*
=1.0*
dd
20%
6
0.20 X 6 =
1.2*
1.0/1.2 = 0.8/1.2 = 0.67 1.2/1.2 = 1.0
0.83
*On average, every DD born produces 1 viable offspring, while a typical Dd newborn produces 0.8 offspring
and dd newborns average 1.2 offspring each.
Interpretation of fitness: wdd = 1.00 means the dd genotype is the most fit, most successful, of the 3 genotypes in that
particular environment at that particular time (even though many may be dying young). The fitnesses of the other
genotypes are some percentage of that highest fitness. For example, wDD = 0.9 means the DD individuals produce
offspring on average at 90% of the rate of individuals with the most successful genotype with w = 1.0.
Selection coefficient is a measure of the relative strength of selection acting against a genotype. Calculate the selection
coefficient (s) by subtracting each fitness value from 1.0 (that is, s = 1-w).
Interpretation of selection coefficient: sdd = 0.0 means genotype dd is not being selected against. That is, although they
are dying, the dd individuals on average are dying less or produce more offspring than the other genotypes in the same
population. sDD = 1.0 is total selection (DD individuals produce no viable offspring. sDD = 0.10 means each generation,
DD individuals produce offspring on average at 90% of the rate of the dd individuals, or in other words, DD individuals on
average have a 10% harder time producing offspring than dd individuals.
----------------------------------------------------------------------------------------------------A concrete example in humans:
The lactose-tolerant allele (gene) in humans spread from very low frequencies to high frequencies in less than 9000
years since farming with an estimated selection coefficient of 0.09-0.19 for a Scandinavian population. Though this
selection coefficient might seem like a very small number, over evolutionary time, the favored alleles accumulate in the
population and become more and more common, potentially reaching fixation. (wikipedia)
Background Information for lactose-tolerance in Humans
NIH National Library of Medicine
Lactose intolerance is an impaired ability to digest lactose, a sugar found in milk and other dairy products. Lactose is
normally broken down by an enzyme called lactase, which is produced by cells in the lining of the small intestine.
Congenital lactase deficiency, also called congenital alactasia, is a disorder in which infants are unable to break down
lactose in breast milk or formula. This form of lactose intolerance results in severe diarrhea. If affected infants are not
given a lactose-free infant formula, they may develop severe dehydration and weight loss.
Lactose intolerance in adulthood is caused by reduced production of lactase after infancy (lactase non-persistence). If
individuals with lactose intolerance consume lactose-containing dairy products, they may experience abdominal pain,
bloating, flatulence, nausea, and diarrhea beginning 30 minutes to 2 hours later.
Most people with lactase non-persistence retain some lactase activity and can include varying amounts of lactose in
their diets without experiencing symptoms. Often, affected individuals have difficulty digesting fresh milk but can eat
certain dairy products such as cheese or yogurt without discomfort. These foods are made using fermentation processes
that break down much of the lactose in milk.
Lactose intolerance in infancy resulting from congenital lactase deficiency is a rare disorder. Its incidence is unknown.
This condition is most common in Finland, where it affects an estimated 1 in 60,000 newborns.
Approximately 65 percent of the human population has a reduced ability to digest lactose after infancy. Lactose
intolerance in adulthood is most prevalent in people of East Asian descent, affecting more than 90 percent of adults in
some of these communities. Lactose intolerance is also very common in people of West African, Arab, Jewish, Greek,
and Italian descent.
The prevalence of lactose intolerance is lowest in populations with a long history of dependence on unfermented milk
products as an important food source. For example, only about 5 percent of people of Northern European descent are
lactose intolerant.
The type of lactose intolerance that occurs in infants (congenital lactase deficiency) is inherited in an autosomal
recessive pattern, which means both copies of the LCT gene in each cell have mutations. The parents of an individual
with an autosomal recessive condition each carry one copy of the mutated gene, but they typically do not show signs
and symptoms of the condition.
The ability to digest lactose into adulthood depends on which variations in the regulatory element within the MCM6 gene
individuals have inherited from their parents. The variations that promote continued lactase production are
considered autosomal dominant, which means one copy of the altered regulatory element in each cell is sufficient to
sustain lactase production. People who have not inherited these variations from either parent will have some degree
of lactose intolerance.
A hypothesis as to how this gene for lactose tolerance evolved involves the idea that drinking milk must have been a
positive fitness factor for us, for example, something happened when we started drinking milk that reduced mortality and
the gene was selected.
See this link below for some detailed thoughts on this. Remember, that cheese and other dairy products have little or no
lactose because the lactose is changed to lactic acid during cheese making.
http://www.npr.org/sections/thesalt/2012/12/27/168144785/an-evolutionary-whodunit-how-did-humans-develop-lactosetolerance