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n Example Calculation

The basic calculation of relatedness, developed by David Queller and Keith Goodnight, has the following form:



where,

P is the population frequency of the allele present at the current locus and allelic position,

Px is thefrequency of the current allele in the current individual (i.e. 0.5 or 1 depending on whether the individual is a heterozygote or homozygote),

and

Py is the frequency of the current allele in the current individual's "partners."

Here is an example:

Colony 1 Pbe492AAT Pbe411AAT
Wasp 1 156,156 166,166
Wasp 2 156,168 166,166
Wasp 3 165,168 166,169
Colony 2      
Wasp 1 162,165 169,172
Wasp 2 162,165 166,172
Wasp 3 168,180 163,166



Population allele frequencies for loci Pbe492AAT and Pbe411AAT


Pbe492AAT Pbe411AAT
156 .175 163 .05
162 .275 166 .525
165 .325 169 .35
168 .05 172 .025
171 .075 175 .05
174 .025      
177 .05      
180 .025      


[(0.5-0.175) + (1-0.525)]/[(1-0.175) + (1-0.525)]= 0.615

Wasp 1, the current individual, is homozygous at loci Pbe492AAT and Pbe411AAT. In the denominator, therefore, we take the frequency of the 156 allele and subtract it from 1, the frequency of the current allele in Wasp 1:

(1-0.175)

To this, we add 1, the frequency of the 166 allele in Wasp 1, minus the frequency of the 166 allele for loci Pbe411AAT:

(1-0.525)

Wasp 2, the current individual's "partner," has both alleles 156 and 166. Because Wasp 1, the current individual, does not have allele 168, we do not consider it in the calculation. Therefore, in the numerator, we subtract the allelic frequency of 156 from 0.5 since wasp 2 is heterozygous at Pbe492AAT:

(0.5-0.175)

From this, we subtract

(1-0.525)

because Wasp 2 is homozygous for allele 166 at locus Pbe411AAT.

 [(0.25-0.275)+(0.25-0.325)+(0-0.35)+(0.25-0.025)]= -0.220 
 [(0.5-0.275)+(0.5-0.325)+(0.5-0.35)+(0.5-0.025)]

This calculation is more complicated because we are comparing Wasp 1 to two individuals. Wasp 1, in colony 2, exhibits four alleles: 162, 165, 169, 172. The denominator is similar to the above example. In the numerator, however, we must use the combined frequency of each allele for both Wasps 2 and 3. For example, Wasp 2 is heterozygous and displays allele 162. Wasp 3 does not display 162. Therefore, 25% of the allelic positions of Wasps 2 and 3 for Pbe492AAT are 162, giving a frequency of 0.25. Neither Wasp 2 nor Wasp 3 displays allele 169. Therefore, the frequency of 169 is 0.


ackground Population Allele Frequencies

The tables below contain data for the estimation of background population allele frequencies necessary for the estimation of relatednes in Polistes bellicosus and P. carolina. Each individual comes from a different colony in the same population (i.e. within a 10 hectare area).

Polistes bellicosus
Wasp ID 203AAG 492AAT 440AAT 80AAC 411AAT 424AAT 269bAAG
100 134/152 162/171 240/246 170/188 166/169 207/222 145/145
87 170/170 174/180 225/246 179/212 163/166 204/219 145/154
114 143/146 162/171 231/249 188/197 166/166 207/219 151/151
424 143/203 156/165 213/249 179/203 166/166 207/216 145/166
164 155/203 156/165 213/249 179/183 166/166 207/216 145/166
209 155/203 156/165 213/252 179/182 166/166 207/216 145/148
184 179/188 165/165 249/252 179/191 169/175 210/216 163/163
426 179/188 162/162 249/252 179/188 166/169 210/216 145/163
401 176/185 162/162 249/252 179/179 166/169 210/216 145/163
428 179/188 165/165 249/252 182/182 166/169 210/216 145/163
430 137/170 156/168 225/249 179/182 166/169 210/213 142/172
135 149/185 165/165 249/252 179/179 169/172 210/213 163/163
433 149/188 162/162 249/252 169/175 210/216 163/163
150 179/188 165/165 249/252 169/169 210/216 145/163
378 143/203 156/177 213/249 166/169 207/216 145/166
260 152/176 162/162 222/243 169/169 207/210 145/148
436 155/164 168/171 225/240 166/166 210/213 151/169
439 161/161 162/165 225/252 163/166 198/216 151/154
286 155/203 156/165 213/252 166/169 207/216 145/166
444 155/203 156/177 213/252 166/166 207/210 145/148

Polistes carolina
Nest 102ACG Pbe128TAG Pbe203AAG Pbe269bAAG Pbe 411AAT Pbe424AAT Pbe440AAT Pbe492AAT
8 118/118 171/174 159/165 150/156 165/165 172/196 220/226 155/158
15 121/127 168/171 159/180 156/156 165/177 181/193 238/241 155/167
19 118/118 168/171 159/159 150/150 165/177 181/208 238/238 158/167
23 118/130 171/174 165/174 147/147 171/177 181/193 220/238 167/167
26 118/121 171/174 162/165 156/156 165/168 181/181 238/238 167/176
29 118/127 168/174 159/177 147/162 162/165 193/196 220/244 155/158
31 109/112 162/168 156/177 147/162 162/165 193/196 220/238 146/167
33 118/127 168/174 174/177 147/150 162/171 193/196 220/244 155/158
34 112/121 168/168 159/159 150/156 165/177 178/181 223/238 167/170
36 118/121 168/171 159/165 147/162 162/162 181/208 238/238 158/170
42 112/118 168/168 165/165 159/162 165/165 196/202 229/238 167/170
44 112/121 165/171 156/165 156/156 162/177 181/193 226/238 155/167
45 112/121 165/171 156/165 156/156 162/165 181/193 226/238 155/158
46 112/121 165/171 156/165 156/156 162/177 193/196 226/238 155/167
6 118/121 168/171 159/159 150/150 181/214 146/167
12 121/121 165/165 150/150 205/232 161/161
41 118/118 159/159 162/162 181/205 167/167
43 118/118 168/168 165/168 159/165 193/196 155/167
119 121/124 165/165 147/150 181/196 158/176



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