Gene350 Animal Genetics Lecture 11 18 August 2009

Last Time Genetic structure of animal populations Hardy-Weinberg Equilibrium Genetic variation in space and time Variation in animal populations, Wright’s Fixation Index (Fst)

Today Forces that change gene frequencies Non-random mating Migration Selection Random genetic drift

Forces that change gene frequencies: Natural populations harbor enormous amounts of genetic variation. If population is in Hardy-Weinberg equilibrium (large, random mating, free from mutation, migration, and natural selection) allele frequencies remain constant. Many, if not most populations, do not meet Hardy-Weinberg equilibrium conditions, allele frequencies change, and the population’s gene pool evolves. Four evolutionary processes responsible for such changes: Mutation Genetic drift Migration Natural selection

Mutation: Heritable changes within DNA . Source of all new genetic variation. Raw material for evolution. Mutation rate varies between loci and among species: ~10-4 to 10-8 mutations/gene/generation. Mutation rate is abbreviated . Some mutations are neutral (no effect on reproductive fitness). Others are detrimental or lethal (depends on environment). If population size is large, effects of mutation act slowly (i.e., compared to selection).

Irreversible mutation: Allele A is fixed (p =1.0) and mutates A  a at rate of  = 10-4: Hartl & Clark (1997) Principles of Population Genetics

Mutation: Reversible mutation: Allele A is fixed (p =1.0) and mutates A  a at rate of  = 10-4; but allele a mutates a  A at a rate of  = 10-5. Hartl & Clark (1997) Principles of Population Genetics

Probability of fixation of a new neutral mutation: Ne = effective population size requires and average of 4N generations. Time between successive fixations = 1/ generations. Hartl & Clark (1997) Principles of Population Genetics

Mutation: Fixation of a new favorable mutation: May occur rapidly, depends on strength of selection and effective population size. Selective sweep = process by which a favorable mutation becomes fixed in a population due to force of positive selection. Tightly-linked neutral alleles can hitchhike during a selective sweep (i.e., genetic draft). Linked regions of DNA around the favorable allele are overrepresented in the population; leads to excess of rare alleles at linked loci.

Genetic drift: Chance alone may result in changes in allele frequency, including fixation and extinction. Genetic drift is analogous to sampling effect. Genetic drift has important consequences for small populations. Example: Island population of 10 heads of cattle; 5 with black coat colour (BB) and 5 with red (bb); f(B) = 0.5, f(b) = 0.5. Typhoon devastates the island; 5 head with black coat colour (BB) die. Allelic frequency of b , f(b) = 1.0; chance events have radically changed the allele frequencies and the population evolves. Now imagine the same scenario for an island of 10,000 head of cattle.

Genetic drift: Chance deviations from expected ratios of gametes and zygotes also produce genetic drift. Cross Aa x aa  expect 50% Aa and 50% aa, but not all of the time insofar that sampling is limited (sampling error). Sampling variance: sp2 = pq/2N *N = number of individuals in the population. Variance is large for small populations, and small for large populations. Sampling occurs naturally: Which gametes fertilizes the egg? What proportion of offspring survive? What proportion of offspring contribute gametes to the next generation?

Effective population size: Not all individuals contribute gametes to the next generation. Effective population size (Ne) = equivalent number of adults contributing gametes to the next generation. If sexes are equal in number and all individuals have an equal probability of reproducing, Ne = N. Otherwise: Ne = (4 x Nf x Nm )/ (Nf + Nm ) * Nf and Nm = numbers of breeding females and males. Sampling variance: sp2 = pq/2Ne Standard error: sp = √(pq/2Ne) 95% confidence limit = p  2sp e.g., Ne = ~8 for a population with 70 breeding females and 2 males. Other factors that reduce reduce Ne: Differential production of offspring Fluctuating population size Overlapping generations

Fluctuations in effective population size: Population sizes change over time. Average effective population size (Ne) is a harmonic mean: 1/Ne = 1/t (1/N0 + 1/N1 + … 1/Nt-1) Harmonic mean = reciprocal of the average of the reciprocals. Important consequence---one short period of small population size (i.e., bottleneck) can dramatically reduce Ne, and it takes a long time for Ne to recover.

Bottleneck and founder effects: “Sampling effects” occurs in natural populations: Genetic drift can be pronounced when population size remains small over many generations, especially when subpopulations are isolated. Genetic drift also arises from founder effects = a population is initially established by a small number of breeding individuals. Chance plays a significant role in determining which genes are present among the founders. Bottleneck effect = effects of genetic drift when a population is dramatically reduced in size. Migration and gene flow in populations increase Ne and reduce effects of genetic drift. Fluctuating population size through time may results in complex patterns, as will interaction of drift and selection.

Balance between mutation and genetic drift: Mutation adds genetic variation/genetic drift removes variation. Infinite alleles model predicts that mutation and drift balance each other to result in a steady state of heterozygosity. Assumptions of the infinite alleles model: Each mutation is assumed to generate a novel allele never observed (and the probability that two mutations will generate the same mutation is infinitely small). Genetic drift operates as normal. Heterozygosity: H = (4 Ne )/ (1 + 4 Ne ) Neutral parameter  = 4 Ne  *describes balance between mutation and drift (if Ne doubles and  is halved  H remains the same).

Fig. 24.14, Relationship between  = 4 Ne  and expected heterozygosity.

Hartl & Clark (1997) Principles of Population Genetics

Migration: Migration in genetic terms equates to gene flow - movement of genes from one population to another. Two major effects: Introduces and spreads unique alleles to new populations. If allelic frequencies of migrants and recipient populations differ, gene flow changes allele frequencies of the recipient population. Fig. 24.15, Effect of migration on a recipient gene pool.

Change in allele frequency with one-way migration (m = 0.01) Hartl & Clark (1997) Principles of Population Genetics

Migration (cont.): Increases the effective size of a population. Prevents allelic fixation. Migration rate (m) >> mutation rate rate of (). Especially important to conservation of wild animals because habitat fragmentation can prevent gene flow, and thus reduce effective population size of isolated populations.

Natural selection (and process of adaptation): Populations growth occurs exponentially; more individuals are produced than can be supported by available resources resulting in a struggle for existence (e.g., Malthus). No two individuals are the same, natural populations display enormous variation, and variation is heritable. Survival is not random, but depends in part on the hereditary makeup of offspring. Over generations, this process leads to gradual change of populations and evolution of new species.

Natural selection (and adaptation): Natural selection equates to the differential survival of genotypes. Darwinian fitness (W) = relative reproductive ability of a genotype Calculate the # of viable offspring relative to other genotypes. Selection coefficient (s) = 1 - W Contribution of each genotype to the next generation: AA Aa aa Initial genotypic frequencies p2 2pq q2 Fitness WAA WAa Waa Frequency after selection p2 WAA 2pq WAa q2 Waa Relative frequency after selection p2 WAA/WMEAN 2pq WAa /WMEAN q2 Waa /WMEAN

Natural selection (and adaptation): Some conclusions: WAA = WAa = Waa: no natural selection WAA = WAa < 1.0 and Waa = 1.0: natural selection and recessive allele operate against a dominant allele. WAA = WAa = 1.0 and Waa < 1.0: natural selection and complete dominance operate against a recessive allele. WAA < WAa < 1.0 and Waa = 1.0: heterozygote shows intermediate fitness; natural selection operates without effects of complete dominance. WAA and Waa < 1.0 and WAa = 1.0: heterozygote has the highest fitness; natural selection/codominance favor the heterozygote (also called overdominance or heterosis). WAa < WAA and Waa = 1.0: heterozygote has lowest fitness; natural selection favors either homozygote.

Natural selection (and adaptation): Selection against recessive alleles: Recessive traits often result in reduced fitness. If so, there is selection against homozygous recessives, thus reducing the frequency of the recessive allele. Recessive allele is not eliminated; rare, lethal recessive alleles occur in the heterozygote (protected polymorphism). Fig. 24.20, Selection against a recessive lethal genotype.

Heterozygote superiority: If a heterozygote has higher fitness than the homozygotes, both alleles are maintained in the population because both are favored by the heterozygote genotype (e.g., sickle cell trait). Also known as: heterosis or overdominance Fig. 24.22, Distribution of malaria and Hb-S allele.

Balance between mutation and selection: When an allele becomes rare, changes in frequency due to natural selection are small. Mutation occurs at the same time and produces new rare alleles. Balance between mutation and selection results in evolution. For a complete recessive allele at equilibrium: q = √ (/s) If homozygote is lethal (s = 1) then q = √ 

Important related topics: Assortative mating Individuals do not mate randomly but prefer one phenotype to another. Affects allele frequencies. Assortative mating may be positive or negative. Inbreeding Preferential mating of close relatives. Small populations may show this effect even with no tendency to select close relatives. Acts on allele frequencies like genetic drift (heterozygosity decreases and homozygosity increases). Self-fertilization is the most extreme example.

Summary of effects of evolutionary forces: Mutation Occurs at low rate, creates small changes, and increases genetic variation; balanced with natural selection and drift. Genetic drift Decreases variation due to loss of alleles, produces divergence and substantial changes in small populations. Migration Rates and types of migration vary, increases effective population size and decreases divergence by encouraging gene flow (and reduces drift), but also creates major changes in allele frequencies. Natural selection Increases or decreases genetic variation depending on the environment, increases or decreases divergence, and continues to act after equilibrium has been achieved; also balances with other forces, e.g., mutation and drift. Non-random mating Inbreeding decreases variation and fitness, and contributes to the effects of other processes by decreasing effective population size.

Conservation of genetic diversity = conservation of biodiversity: Maintaining large interbreeding populations typically requires large non-fragmented habitats. Earth’s animal species and most species-rich habitats are being exterminated by humanity at rates ~1,000-fold greater than historical background extinction rates. Currently experiencing the most massive extinction episode in 65 million years. Mutations that give rise to variation accumulate slowly over many generations. Habitat loss and extinction occur much faster. Existent animal biodiversity is the result of a legacy of 4-5 billion years of genetic information.

Hardy-Weinberg Equilibrium (HWE) Can calculate whether the allele frequencies of a given population of organisms deviates from those frequencies predicted by HWE In other words, are allele frequencies being affected by some evolutionary force E.g. Gene flow (emigration, immigration), Natural selection

Hypothesis Testing Develop a null hypothesis and determine the level of experimental error (Type 1 statistical error; rejecting null when it is actually correct) that we are willing to accept while not rejecting the null i.e. Populations of animals are in Hardy-Weinberg equilibrium using a confidence level of 0.95 In other words, we want to be 95% certain that populations under consideration are in HWE; willing to allow 5% (p=0.05) error in our data while still failing to reject the null hypothesis

Hypothesis Testing Find the probability distribution for the event of interest Calculate the observed p-value Compare observed p-value to the preselected level of Type 1 statistical error, or p= 0.05 If observed p-value is less than 0.05, we reject our null hypothesis If observed p-value is greater than 0.05, we fail to reject our null hypothesis

Hardy-Weinberg Equilibrium (HWE) Simplest method for testing for deviations from HWE Chi-square Goodness-of-fit Test O = observed number of individuals of a given genotype E = expected number of individuals of a given genotype if population is at HWE degrees of freedom (df) = k – number of estimated parameters – 1 DF determines the maximum observed chi-square value you can obtain while still failing to reject the null hypothesis (i.e. p < 0.05)

Example Is this population in Hardy-Weinberg equilibrium? Genotype Observed Number A1A1 5000 A1A2 3000 A2A2 2000

Example