Genetic Drift and Natural Selection:

Transcription

1 llele Overview Genetic Drift and Natural Selection: n Exploration of llele Frequencies Within a Population Harvey Mudd College Math 164: Scientific Computing 29 pril 2008

2 llele Overview Presentation Outline Definition of an allele Modeling genetic drift Trends in genetic drift Modeling natural selection Future work

3 llele Overview What is an allele? given population often contains many versions of the same gene. n allele is one version of a gene at a given location, or locus, along a chromosome. Each person inherits two alleles for each gene one allele from each parent.

4 llele Overview What is an allele? Leslie Fred Mary

5 Genetic Drift llele Overview Force that acts to change allele frequency ased on sampling error during mating

6 Genetic Drift llele Overview Force that acts to change allele frequency ased on sampling error during mating ssumptions Population size remains constant

7 Genetic Drift llele Overview Force that acts to change allele frequency ased on sampling error during mating ssumptions Population size remains constant Mating is random

8 Genetic Drift llele Overview Force that acts to change allele frequency ased on sampling error during mating ssumptions Population size remains constant Mating is random ll individuals survive to reproductive age and reproduce with the same frequency

9 Genetic Drift llele Overview Force that acts to change allele frequency ased on sampling error during mating ssumptions Population size remains constant Mating is random ll individuals survive to reproductive age and reproduce with the same frequency There are no occurrences of migration or genetic mutation

10 Genetic Drift llele Overview Force that acts to change allele frequency ased on sampling error during mating ssumptions Population size remains constant Mating is random ll individuals survive to reproductive age and reproduce with the same frequency There are no occurrences of migration or genetic mutation The population contains only two types of the allele of interest

11 llele Overview n Example of Genetic Drift Generation 1 10, 10 Generation 2?,?

12 llele Overview n Example of Genetic Drift Generation 2 8, 12 Generation 1 10, 10

13 llele Overview Genetic Drift Over Several Generations 1 Genetic Drift 1 Iteration, Population Size N = Frequency of llele Generation

14 llele Overview Genetic Drift Over Several Generations 1 Genetic Drift 10 Iterations, Population Size N = Frequency of llele Generation

15 llele Overview Two Ways to Model Genetic Drift rute Force Method Directly simulates random picking of gametes from a gene pool Create a vector of alleles Random real numbers on the unit interval If less than frequency of allele, reset number to 1 Otherwise, reset number to 0 Summing the components and dividing by the number of alleles gives the new frequency of allele

16 llele Overview Two Ways to Model Genetic Drift inomial Distribution Method Uses MTL s binornd(n,p) function to generate random numbers from the binomial distribution sample size = number of gametes probability = frequency of allele in the previous generation The output of the function gives the allele frequency of the subsequent generation

17 llele Overview Visual Comparison of the Two Techniques Genetic Drift Genetic Drift rute Force Method inomial Distribution Method 10 Iterations, Population Size N =10 10 Iterations, Population Size N = Frequency of llele Frequency of llele Generation Generation

18 llele Overview Comparison of Runtimes Run Time veraged Over 100 Runs Run Time (seconds) Trial rute Force Method inomial Distribu>on Method

19 llele Overview Effects of Population Size Genetic Drift inomial Distribution Method 10 Iterations, Population Size N = Genetic Drift inomial Distribution Method 10 Iterations, Population Size N = Frequency of llele Frequency of llele Generation Generation 1 Genetic Drift inomial Distribution Method 10 Iterations, Population Size N = Frequency of llele Generation

20 llele Overview Effects of Population Size verage Number of Genera&ons Un&l Dele&on (1,000 Runs, Ini&al Frequency 0.5) Genera&ons Popula&on Size rute Force Method inomial Distribu>on Method

21 llele Overview Effects of Changing Initial Frequency Number of Dele/ons and Fixa/ons in 1,000 Runs rute Force Method Number of Runs Ini/al llele Frequency Dele0on Fixa0on

22 llele Overview Natural Selection nother force that acts to change allele frequency ased on differences in reproductive success, or fitness

23 llele Overview Natural Selection nother force that acts to change allele frequency ased on differences in reproductive success, or fitness ssumptions Mating is random

24 llele Overview Natural Selection nother force that acts to change allele frequency ased on differences in reproductive success, or fitness ssumptions Mating is random There are no occurrences of migration or genetic mutation

25 llele Overview Natural Selection nother force that acts to change allele frequency ased on differences in reproductive success, or fitness ssumptions Mating is random There are no occurrences of migration or genetic mutation The population contains only two types of the allele of interest

26 llele Overview Natural Selection nother force that acts to change allele frequency ased on differences in reproductive success, or fitness ssumptions Mating is random There are no occurrences of migration or genetic mutation The population contains only two types of the allele of interest n individual s fitness depends only on his genes not on the environment

27 llele Overview Natural Selection What happens when individuals with a particular allele always reproduce and individuals without it reproduce less often? 1 Natural Selection Initial Frequency =0.001 Fitness =1, Fitness =1, Fitness = Frequency of llele Generation

28 llele Overview Natural Selection and Genetic Drift When both genetic drift and natural selection are at work... 1 Natural Selection with Genetic Drift Initial Frequency =0.001, Population Size =1000 Fitness =1, Fitness =1, Fitness = Frequency of llele Generation

29 llele Overview Natural Selection Extensively explore the effect of changing fitness levels and initial allele frequency