1 Random Genetic Drift

2 Conditions for maintaining Hardy-Weinberg equilibrium: 1. random mating 2. no migration 3. no mutation 4. no selection 5.infinite population size √

3 2 mathematical approaches to studying genetic changes in populations: Deterministic models Stochastic models

4 Drift Allele frequency changes can occur by chance, in which case the changes are not directional but random. An important factor in producing changes in allele frequencies is the random sampling of gametes during reproduction.

5 Niche capacity = 10 plants

6 A simple idealized model: All the individuals in the population have the same fitness (selection does not operate). The generations are nonoverlapping. Adult population size is finite and does not change from generation to generation. Gamete population size is approximately infinite. The population is diploid (N individuals, 2N alleles). One locus with two alleles, A 1 and A 2, with frequencies p and q = 1 – p, respectively.

7 Adult population = 2 diploid individuals Gamete population = ∞ The gamete population has exactly the same allele frequencies as the adult population from which it is derived. Generation 1 Generation 2 Generation 3 The gamete population is sampled randomly to derived the next adult population.

8 When 2N gametes are sampled from the infinite gamete pool, the probability, P i, that the sample contains exactly i alleles of type A 1 is given by the binomial probability function: Since P i is always greater than 0 for populations in which the two alleles coexist (i.e., 0 < p < 1), the allele frequencies may change from generation to generation without the aid of selection.

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10 The process of change in allele frequency due solely to chance effects is called random genetic drift.

11 Fixation

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13 Magnitude of fluctuations depends on population size. Large population = Small fluctuations. Small population = Large fluctuations. Mean time to fixation or loss depends on population size. Large population = Long time. Small population = Short time.

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15 yet

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17 Fixation by Drift on an Y-Linked Trait* in a Small Population *Family names!

Founders of Pitcairn Island population in males 12 family names

: Descendants 1930 males 1 family name Adams

20 Random Genetic Drift = Markov Process A random process whose probabilities at each stage are determined by the values of its preceding stage, i.e., a process with very short historical memory.

21 An important property of random genetic drift is its cumulative behavior; i.e., from generation to generation, the frequency of an allele will tend to deviate more and more from its initial frequency.

22 In mathematical terms, the mean and variance of the frequency of allele A 1 at generation t are given by: Mean frequency does not change with time. Variance increases with time.

23 With each passing generation the allele frequencies will tend to deviate further and further from their initial values, however the change in allele frequencies will NOT be systematic in its direction.

24 Change in probability of not deviating from initial frequencies with time

25 Random genetic drift is an important evolutionary force

26 may not change Selection may not change allele frequencies. may change Allele frequencies may change without selection. A summary:

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28 Effectivepopulationsize

29 Population size = the total number of individuals in a population. From an evolutionary point of view, however, the relevant size consists of only those individuals that actively participate in the reproductive process. This part is called the effective population size and is denoted by N e.

30 Why isn’t the census size satisfactory? Some individuals may contribute little to the reproductive potential of a population

31 Sewall Wright (1931) introduced the concept of effective population size, which he rigorously defined as the size of an idealized population that would have the same effect of random sampling on allele frequencies as that of the actual population.

32 In mathematical terms, the mean and variance of the frequency of allele A 1 at generation t are given by: Mean frequency does not change with time. Variance increases with time.

33 Assume a population with census size = N and frequency of allele A 1 at generation t = p. If the number of individuals taking part in reproduction = N, then the variance of the frequency of allele A 1 in the next generation, p t+1, may be obtained from the variance equation by setting t = 1.

34 In practice, since not all individuals in the population take part in the reproductive process, the variance will be larger than that predicted by: The effective population size is the value that is substituted for N in order to satisfy the above equation:

35 effective population size (N e ) number of individuals in an ideal population which has the same magnitude of genetic drift as the actual population.

36 N e is usually much smaller than N Various factors contribute to this difference: overlapping generations. variation in the number of offspring among individuals. number of males involved in reproduction is different from the number of females. long-term variations in population size. bottlenecks

37 Effects of inequality between numbers of males and numbers of females on effective population size Examples: Polygamy: social mammals, territorial birds. Nonreproductive castes: social bees, ants, termites, naked mole rats.

38 Heterocephalus glaber Formicoidea Isoptera Naked mole rat

39 If a population consists of N m males and N f females (N = N m + N f ), then N e is given by:

40 What is the effective population size of a honeybee hive? N ≈ 100,000 N f = 1 N m >> 1 N e = 4

41 A B The effective population size of A is larger than that of B despite the fact that the census size is exactly the same. The effective population size has a historical memory.

42 If a population goes through a bottleneck, the long-term effective population size is greatly reduced even if the population has long regained its pre- bottleneck census size.

43 Long-term (~2 million years) effective population size N e = 10,000 Historicalhumanpopulationsizes