Population Subdivision Activity

Overview

This section will focus on estimating the measures of genetic distance and genetic structure. The lecture content for this topic is here.

The Data

library( gstudio )
data( arapat )

The data for this activity is included in the gstudio library and represents a set of nuclear co-dominant loci (named LTRS, WNT, EN, EF, ZMP, AML, ATPS, MP20) assayed for 363 individuals and partitioned into 3 partitions.

summary( arapat )

      Species      Cluster      Population        ID         Latitude    
 Cape     : 75   CBP-C :150   32     : 19   101_10A:  1   Min.   :23.08  
 Mainland : 36   NBP-C : 84   75     : 11   101_1A :  1   1st Qu.:24.59  
 Peninsula:252   SBP-C : 18   Const  : 11   101_2A :  1   Median :26.25  
                 SCBP-A: 75   12     : 10   101_3A :  1   Mean   :26.25  
                 SON-B : 36   153    : 10   101_4A :  1   3rd Qu.:27.53  
                              157    : 10   101_5A :  1   Max.   :29.33  
                              (Other):292   (Other):357                  
   Longitude          LTRS          WNT            EN           EF     
 Min.   :-114.3   01:01 :147   03:03  :108   01:01  :225   01:01 :219  
 1st Qu.:-113.0   01:02 : 86   01:01  : 82   01:02  : 52   01:02 : 52  
 Median :-111.5   02:02 :130   01:03  : 77   02:02  : 38   02:02 : 90  
 Mean   :-111.7                02:02  : 62   03:03  : 22   NA's  :  2  
 3rd Qu.:-110.5                03:04  :  8   01:03  :  7               
 Max.   :-109.1                (Other): 15   (Other): 16               
                               NA's   : 11   NA's   :  3               
     ZMP           AML           ATPS          MP20    
 01:01 : 46   08:08  : 51   05:05  :155   05:07  : 64  
 01:02 : 51   07:07  : 42   03:03  : 69   07:07  : 53  
 02:02 :233   07:08  : 42   09:09  : 66   18:18  : 52  
 NA's  : 33   04:04  : 41   02:02  : 30   05:05  : 48  
              07:09  : 22   07:09  : 14   05:06  : 22  
              (Other):142   08:08  :  9   (Other):119  
              NA's   : 23   (Other): 20   NA's   :  5  

1. Copy over the function island_frequencies() created in the slides ( here ). If the mainland population frequency was \(p=1.0\) and the island frequency started at \(p=0.32\), how many generations does it take for a migration rate of \(m=0.10\) with the underlying model of unidirectional migration as depicted in the \(N-Island\) diagram?

2. Consider the simple demographic population model with three populations (Pop-X, Pop-Y, and Pop-Z) all connected by symmetric migration (as shown here). If the initial allele frequencies at a simple 2-allele locus are \(p_X = 0.25\), \(p_Y = 0.50\), and \(p_Z = 0.75\), what are the allele frequency for this network of populations at equilibrium if migration is:

   • \(m = 0.0\),
   • \(m = 0.01\),
   • \(m = 0.1\)

3. Isolation by physical distance (classically called IBD) is a relationship between physical separation of populations and some measure of genetic differences. For the the arapat data set, estimate inter-population genetic distance using Nei’s metric and then plot that against inter-population physical distance. Overlay a trendline. Interpret the results, do genetic differences have a relationship with physical separation?

4. Does your interpretation of the IBD relationship change if you only use individuals whose Species == Peninsula?

5. Is there more structure (\(\Phi_{ST}\)) among Species, Clusters, or Populations in the arapat data set? And how would you suggest analyzing these data after seeing these differences?