Calculating F-Statistics

F = The Inbreeding Coefficient, or Fixation Index.

The system: Drosophila melanogaster populations in the Caucasus Mountains in the former Soviet Union. The frequency of the Adh-F allele was estimated for 7 populations using gel electrophoresis (below, assume a 2 allele locus). Three hundred individuals were examined per population. The populations can be grouped into three regions, defined relative to elevation: Plains, Foothills, and Mountain.

Hierarchical Structure in Drosophila melanogaster
 

Subpopulations

Regions

Total

Region

Observed Allele Frequency

Expected

Hetero-zygosity

Mean

Allele Frequency

Expected

Hetero-zygosity

Mean

Allele Frequency

Expected

Hetero-zygosity

Plain

0.082

0.1506

        
 

0.088

0.1605

        
 

0.035

0.0676

0.068

0.1273

    
             

Foothill

0.131

0.2277

        
 

0.109

0.1942

0.120

0.2112

    
             

Mountain

0.321

0.4359

        
 

0.226

0.3498

0.274

0.3974

0.142

0.2433
   

HP=0.2266

  

HR=0.2285

  

HT=0.2433

HP = The average expected heterozygosity among organisms within subpopulations. In the example above, we estimated the heterozygosity of the subpopulations from the measured allele frequencies in those populations (ie: 2pq). HP was calculated by simply averaging all the subpopulations together.

HR= The average heterozygosity among organisms within regions. This is calculated by calculating the average allele frequency in the regions, then using 2pq to estimate the expected heterozygosity of the region, and then finally taking the average of all the expected regional heterozygosities, weighted by the number of populations. Thus, above, HR= ((2*0.3974)+(2*0.2112)+ (3*0.1273)) / 7=0.2285. In effect, this is the expected heterozygosity if all the subpopulations in each region constituted a single, panmictic population.

HT= The average heterozygosity among organisms within the total area considered. This is calculated by taking the average of all the frequencies of the Adh-F allele, and then using 2pq to calculate an expected Total Heterozygosity. In effect, this is the heterozygosity expected if all the individuals in all the subpopulations in all the regions were one happy panmictic unit.