Consider the information in Exercise 3.28 on page 93. The problem deals with the weight in ounces of the product in a cereal box, with f(x)=2 5, 23.75 x 26.25, (a) Plot the density function. (b) Compute the expected value, or mean weight, in ounces. (c) Are you surprised at your answer in (b)? Explain why or why not.
BSC2010 Exam 3 04/21/2015 ▯ Evolution= the change in biological populations over time Populations evolve, individuals do not o The fossil record o Laboratory experiments o Natural populations ▯ Evolutionary Theory=set of ideas about how evolution takes place Unifying principle of biology Dobzhansky said “nothing in biology makes sense except in the light of evolution” ▯ Evolution is NOT just a theory Well-supported Parsimonious (simplest explanation) Falsifiable Refers to the totality of our understanding, NOT a single hypothesis ▯ Darwin’s grandfather first proposed that species change No evidence Lacked a workable mechanism of evolution ▯ Jean-Baptiste Lamarck French naturalist Attempted to explain the mechanisms of evolution before Darwin was even born Found that unimportant traits become reduced or lost (atrophy) Organisms inherit traits that their parents acquired ▯ Lamarck’s theory of evolution involved required traits, Darwin’s theory of evolution involved heritable traits ▯ Darwin was influenced by Charles Lyell (geology) Thomas Malthus (population dynamics) ▯ Natural Selection The differential reproductive success of certain individuals with more or less desirable traits Only acts on heritable traits Required for natural selection to occur: o Population must exhibit some variation in a trait Variation results from genetic mutation o The trait that exhibits variation must be heritable A trait is heritable when it can be passed on to one’s offspring o The trait must impact an individual’s reproductive success Differential reproductive success means that individuals with more desirable traits will be more likely to pass those traits on to future generations ▯ Gene Pool= sum of all alleles in a population Mutation can introduce a novel allele to the gene pool Mutations are random ▯ Adaptation= beneficial mutation/trait that is favored by natural selection Note that natural selection produces adaptations ▯ Heritability (H^2) H^2=genetic variation/genetic + environmental variation=Vg/Vp Heritability is the fraction of variability that is genetic Not the same as “having a genetic basis” o Nearly all traits have a genetic basis If trait is extremely heritable, then H^2 is 1 o If trait is not heritable, then H^2 is 0 Can be estimated by taking the slope of a parent-offpsring regression line ▯ Reproductive Fitness Fitness refers to the contribution of genotype/phenotype to the next generation o Ex: slow rabbits will get killed by predators, so the average speed of rabbits will slowly increase Breeder’s equation: R= H^2 * S o Allows animal and plant breeders to predict the strength of response when they apply artificial selection ▯ Modes of Selection Stabilizing o Average phenotype is most fit o Mean stays the same o Variation decreases Ex: birth weight Disruptive o Both extremes of phenotype re most fit o Mean becomes bimodal o Variation Ex: island has large seeds and seeds are buried in the ground, so birds with long beaks and short/strong beaks are favored Directional o One extreme of phenotype is most fit o Mean shifts in one direction Could be positive or negative o Variation decreases ▯ Frequency Dependent Selection Positive o Common phenotypes favored Ex: poisonous type of butterfly has certain wing pattern, that poisonous butterfly’s fitness increases as it becomes more common So that birds are aware not to eat that type of butterfly Negative o Rare phenotype o Ex: side-blotched lizards Red(orange)= territorial Blue= maintain only 1 female at a time Yellow= sneaker males o Influenzai The newest/rarest virus that has the best chance of spreading Old viruses (which are more common) do not have a good chance of spreading o Floral parts ▯ Sexual Selection= a type of non-random mating in which an organism’s phenotype impacts its chance of mating Intersexual selection (female choice) Intrasexual selection (male competition) Intersexual Selection Driven by female choice Chosen based on 3 observable traits: o Male may provide female with direct benefits to assist her in survival and reproduction o Indicator of health or longevity (“good genes”) o Sensory bias (looks attractive) Ex: male guppies developed bright orange tails because females noticed them more Risk associated: noticeable traits may attract predators o Ex: big feathered peacocks are noticeable to lions ▯ Intrasexual Selection Male competition o Males may become physical for access to females (ex: fight each other) o Sneaker males Males remain small so they can avoid larger males ▯ Genetic Drift= unpredictable, random fluctuations in allele frequencies from one generation to another because of a population’s small size Bottleneck effect o Occurs when a large portion of a population becomes wiped out o Typically from natural disaster o Surviving population is no longer genetically representative of the original population Founder effect o Genetic drift that occurs when a few individuals become isolated from the rest of the population ▯ Gene Flow Another word for migration Exchange of genes from one population to another Increases genetic variation Decreases differences between both populations ▯ Hardy Weinberg Assumptions o Random mating o No mutations o No gene flow (migration) o Population size must be very large (infinite in size-no drift) o No selection (natural, artificial, etc.) ▯ Genotype frequency # of individuals with the genotype of interest/# of individuals in the population smaller # over total ▯ Allele Frequency # of copies of a particular allele in a population/ number of copies of all alleles in the population smaller # over total ▯ HW Theorem p^2 +2pq+q^2=1 o p^2= homozygous dominant o 2pq= heterozygote o q^2= homozygous recessive NO evolution when the equation equals 1 ▯ Create and Maintain Variation Mutation Migration (gene flow) Disruptive or negative frequency-dependent selection Heterozygote advantage ▯ Nucleotide Substitution Synonymous substitution Nonsynonymous substitution ▯ Neutral Theory Explains that most molecular variations in most populations are selectively neutral (don’t convey a selective advantage or disadvantage) M=2Nu(1/2N) o Ex: gene pool 1/2N=1/2(20)=1/40 o Rate of fixation of neutral mutations is independent of population size (because 2N cancels out) o Rate of fixation of neutral mutations=mutation rate ▯ Purifying (Negative Selection) Synonymous mutations>Nonsynonymous mutations (more to less) o Nature has been removing mutations (most likely deleterious) o No real change is happening to amino acid sequence (stabilizing selection) ▯ Directional (Positive Selection) Nonsynonymous mutations>Synonymous mutations (more to less) o Nature is keeping non-neutral mutations o Changes amino acid sequence ▯ Sexual Reproduction Advantages o Recombination- increases variation in offspring o Repairs damaged DNA (you have 2 copies) o Defense against diseases Disadvantages o Recombination breaks up good genes o Reduced rate of reproduction ▯ Asexual Reproduction Advantages o Higher reproductive rate o No need for physical contact to reproduce Disadvantages o No variation o Muller’s ratchet Cant get rid of a bad mutation ▯ Lateral Gene Transfer Swapping DNA from one cell to another o Transduction Virus inputs DNA into host o Transformation Prokaryotic cells take up DNA from environment o Conjugaion Two cells link up and exchange DNA o Hybridization Exchange of genes between 2 different species ▯ Species Concepts Morphological (Linneaus) o Based on observable characteristics o Species are groups that look familiar o Limitations: Members of the same species may not look alike (look different) Ex: male and female wood ducks look different Members of different species may look similar Ex: cryptic species Biological (Mayr) o Species are groups that can actually or potentially mate with each other o Limitations: Asexual organisms can’t mate Extinct species/fossils can’t mate Hybrids (ex. Horse+donkey=mule, but horses and donkeys are not the same species) Ring species Lineage (Simpson) o Species are groups that share a branch on the tree of life o We create phylogenies based on relationships between species o Relies a lot on DNA sequencing o Limitations: 2 species that look the same and interbreed may differ in only neutral mutations ▯ Dobzhansky-Muller Model= explains how a single lineage can split into 2 reproductively isolated species Applies to major chromosomal rearrangements ▯ ▯