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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