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Population genetics Thinking like a population geneticist ! Thinking like a population geneticist Expectation! The expected value of a random variable, especially the average; a prediction or forecast.! T04_Thinking like a popgen.key - 25 September, 2014 Expectation of being hit by a meteorite? Expectation of being hit by a meteorite? Probably null. Why?! ! ! Expectation of being hit by a meteorite? Expectation of being hit by a meteorite? Barringer Meteor crater, Arizona http://www.barringercrater.com T04_Thinking like a popgen.key - 25 September, 2014 Expectations Expectations in population genetics attempt to predict things like:! You have combined your knowledge of the physical world and your experience to arrive (perhaps unconsciously) at a prediction or an expectation: ! ! meteorite strikes are possible but are so infrequent that the risk of being struck is minuscule. 1) how much genetic variation is present in a population, ! 2) how genetic variation in a population changes over time,! 3) pattern of genetic variation that might be left behind by a given biological process that acts over time or through space First principles FIRST PRINCIPLES T04_Thinking like a popgen.key - 25 September, 2014 Parameters and parameter estimates Parameters and parameter estimates Quantities in population genetics are estimated with error. ! ! ! WHY?! Parameters and parameter estimates Parameters and parameter estimates Parameter A variable or constant appearing in a mathematical expression; a value (usually unknown) used to represent a certain population characteristic; any factor that defines a system and determines or limits its performance.! Parameter: exact value of some measurement ! Parameter estimate: value measured on a sample Estimate An indication of the value of an unknown quantity based on observed data; an approximation of a true score, parameter, or value; a statistical estimate of the value of a parameter.! T04_Thinking like a popgen.key - 25 September, 2014 Example Example p̂ = 0.483 p̂ = 0.474 p̂ = 0.464 p̂ = 0.490 p̂ = 0.498 p̂ = 0.531 p̂ = 0.518 p̂ = 0.483 p̂ = 0.521 p̂ = 0.460 p̂ = 0.483 p̂ = 0.517 SUM 3.980 AVERAGE 0.498 (SUM/ N) SUM 7.896 S.D. 0.0271 (SUM/ N) S.E. 0.0096 (SD/ √ N) p̂ = 0.478 p̂ = 0.489 p̂ = 0.514 p̂ = 0.493 AVERAGE 0.494 (SUM/ N) S.D. 0.0212 (SUM/ N) S.E. 0.0053 (SD/ √ N) S.E.: how far the true population average (a parameter) may be from the sample average (a parameter estimate) by chance. Example p̂ = 0.483 p̂ = 0.474 p̂ = 0.464 p̂ = 0.490 p̂ = 0.498 p̂ = 0.531 p̂ = 0.518 p̂ = 0.483 p̂ = 0.521 p̂ = 0.460 p̂ = 0.483 p̂ = 0.517 p̂ = 0.478 p̂ = 0.489 p̂ = 0.514 p̂ = 0.493 SUM 3.9800 SUM 7.8960 AVERAGE 0.4980 AVERAGE 0.4940 S.D. 0.0271 S.D. 0.0212 S.E. 0.0096 S.E. 0.0053 Inductive and deductive reasoning T04_Thinking like a popgen.key - 25 September, 2014 Inductive and deductive reasoning Inductive and deductive reasoning Inductive Inductive Observation/ Experiment Observation/ Experiment Inductive and deductive reasoning Inductive and deductive reasoning Inductive Inductive Observation/ Experiment Observation/ Experiment Generalizations Generalizations Paradigma / Theory T04_Thinking like a popgen.key - 25 September, 2014 Inductive and deductive reasoning Inductive and deductive reasoning Inductive Inductive Deductive Observation/ Experiment Observation/ Experiment Generalizations Generalizations Paradigma / Theory Paradigma / Theory Deductive Paradigma / Theory Inductive and deductive reasoning Inductive and deductive reasoning Inductive Inductive Deductive Observation/ Experiment Deductive Observation/ Experiment Observation/ Experiment Generalizations Predictions Generalizations Predictions Paradigma / Theory Paradigma / Theory Paradigma / Theory Paradigma / Theory T04_Thinking like a popgen.key - 25 September, 2014 Inductive and deductive reasoning Inductive Observation/ Experiment Observation: Every time I’ve walked by that dog, he hasn’t tried to bite me. ! Generalizations Paradigma / Theory Generalization: the next time I walk by that dog he won’t try to bite me. ! Theory: that dog will not bite me. Inductive and deductive reasoning Inductive Observation/ Experiment Isaac Newton used knowledge of how objects fall to the surface of the Earth as well as knowledge of the movement of planets to arrive at the general principles of gravity. Deductive Theory: All cars have tires Prediction: Therefore, your car has tires Observation/ Experiment Predictions Generalizations If the initial premise is correct, Paradigma / Theory the conclusion is correct… Paradigma / Theory T04_Thinking like a popgen.key - 25 September, 2014 Inductive and deductive reasoning Theory: Every day, I leave for work in my car at eight o’clock. Every day, the drive to work takes 45 minutes I arrive to work on time. Prediction: Therefore, if I leave for work at eight o’clock today, I will be on time. Theory and assumptions Deductive Observation/ Experiment Predictions • What is a theory and what are assumptions?! • How can theories be useful with so many! assumptions?! If the initial premise is correct, the conclusion is correct… Paradigma / Theory allele frequency ! how often a form of a gene appears in a gene pool T04_Thinking like a popgen.key - 25 September, 2014 allopatric speciation ! The formation of a new species as a result of an ancestral population's becoming isolated by a geographic barrier biological species concept ! a species concept defining a species as a population or group thereof whose members potentially interbreed and produce fertile offspring! bell curve ! Bell-shaped curve; typically results from graphing frequency versus distribution for a trait that varies continuously in a population! directional selection ! occurs when natural selection favors one of the extreme variations of a trait! T04_Thinking like a popgen.key - 25 September, 2014 disruptive selection ! natural selection that favors individuals with either extreme of a trait! emigration ! movement of individuals out of a population! gene flow ! exchange of genes between populations! gene pool! combined genetic information of all the members of a particular population! T04_Thinking like a popgen.key - 25 September, 2014 genetic drift ! the gradual changes in gene frequencies in a population due to random events! geographic isolation! form of reproductive isolation in which two populations are separated physically by geographic barriers such as rivers, mountains, or stretches of water! ! gradualism ! the theory that evolution occurs slowly but steadily! Hardy-Weinberg principle ! the principle that states that the frequency of alleles in a population does not change over generations unless outside forces act on the population (mutation, genetic drift, gene flow, natural selection and mate selection) T04_Thinking like a popgen.key - 25 September, 2014 immigration ! movement of individuals into an area occupied by an existing population! ! morphology ! the branch of biology that deals with the structure of animals and plants! microevolution evolution ! resulting from small specific genetic changes that can lead to a new subspecies phenotype ! frequency equal to the number of individuals with a particular phenotype divided by the total number of individuals in the population T04_Thinking like a popgen.key - 25 September, 2014 population genetics ! the study of genetic changes in populations; the science of microevolutionary changes in populations prezygotic isolation ! reproductive isolation that occurs before a zygote can be formed! ! postzygotic isolation ! reproductive isolation that occurs after members of two different species have mated and produced a hybrid offspring. Such hybrids are usually unable to reproduce! punctuated equilibrium ! pattern of evolution in which long stable periods are interrupted by brief periods of more rapid change! T04_Thinking like a popgen.key - 25 September, 2014 reproductive isolation ! separation of species or populations so that they cannot interbreed and produce fertile offspring speciation ! the formation of new species as a result of evolution sexual selection ! a form of natural selection in which individuals with certain inherited characteristics are more likely than other individuals to obtain mates stabilizing selection ! natural selection that favors intermediate variants by acting against extreme phenotypes T04_Thinking like a popgen.key - 25 September, 2014 CONCLUSIONS • General principles and direct measurements taken in actual populations combine to form comprehensive expectations about amounts, patterns, and cause-and-effect relationships in population genetics. • The theory of population genetics is the collection of well-accepted expectations used to articulate a wide array of predictions about the biological processes that shape genetic variation. CONCLUSIONS CONCLUSIONS sympatric speciation ! the formation of new species in populations that live in the same geographic area T04_Thinking like a popgen.key - 25 September, 2014 CONCLUSIONS • Population genetics is not a spectator sport! Direct participation in computer simulation provides the opportunity to see population genetic processes in action. You can learn by trial and error and test your own understanding by making predictions and then comparing them with simulation results. CONCLUSIONS CONCLUSIONS • Parameters are idealized quantities that are exact while parameter estimates wear notational “hats” to remind us that they have statistical uncertainty. • !• ! Population genetics uses both inductive reasoning to generalize from knowledge of specifics and deductive reasoning to build up predictions from general principles that can be applied to specific situations. T04_Thinking like a popgen.key - 25 September, 2014