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),
- Py is the frequency of the current allele in the current individual's "partners."
Here is an example:
| Pbe492AAT | Pbe411AAT | |
|---|---|---|
Wasp 1 |
156,156 | 166,166 |
Wasp 2 |
156,168 | 166,166 |
Wasp 3 |
165,168 | 166,169 |
| Pbe492AAT | Pbe411AAT | |
|---|---|---|
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 | ||
Estimation of relatedness of Wasp 1 to Wasp 2 on Colony 1
[(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.
Estimatation relatedness of Wasp 1 to Wasps 2 and 3 on Colony 2
[(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.
Estimate relatedness of Wasp 1 to Wasps 2 and 3 on Colony 1.
- Click here to see the answer.
Estimate relatedness of Wasp 1 to Wasp 3 on Colony 2.
- Click here to see the answer.
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 |
|---|---|---|---|---|
| 8 | 118/118 | 171/174 | 159/165 | 150/156 |
| 15 | 121/127 | 168/171 | 159/180 | 156/156 |
| 19 | 118/118 | 168/171 | 159/159 | 150/150 |
| 23 | 118/130 | 171/174 | 165/174 | 147/147 |
| 26 | 118/121 | 171/174 | 162/165 | 156/156 |
| 29 | 118/127 | 168/174 | 159/177 | 147/162 |
| 31 | 109/112 | 162/168 | 156/177 | 147/162 |
| 33 | 118/127 | 168/174 | 174/177 | 147/150 |
| 34 | 112/121 | 168/168 | 159/159 | 150/156 |
| 36 | 118/121 | 168/171 | 159/165 | 147/162 |
| 42 | 112/118 | 168/168 | 165/165 | 159/162 |
| 44 | 112/121 | 165/171 | 156/165 | 156/156 |
| 45 | 112/121 | 165/171 | 156/165 | 156/156 |
| 46 | 112/121 | 165/171 | 156/165 | 156/156 |
| 6 | 118/121 | 168/171 | 159/159 | 150/150 |
| 12 | 121/121 | 165/165 | 150/150 | |
| 41 | 118/118 | 159/159 | 162/162 | |
| 43 | 118/118 | 168/168 | 165/168 | 159/165 |
| 119 | 121/124 | 165/165 | 147/150 |
| Nest | Pbe 411AAT | Pbe424AAT | Pbe440AAT | Pbe492AAT |
|---|---|---|---|---|
| 8 | 165/165 | 172/196 | 220/226 | 155/158 |
| 15 | 165/177 | 181/193 | 238/241 | 155/167 |
| 19 | 165/177 | 181/208 | 238/238 | 158/167 |
| 23 | 171/177 | 181/193 | 220/238 | 167/167 |
| 26 | 165/168 | 181/181 | 238/238 | 167/176 |
| 29 | 162/165 | 193/196 | 220/244 | 155/158 |
| 31 | 162/165 | 193/196 | 220/238 | 146/167 |
| 33 | 162/171 | 193/196 | 220/244 | 155/158 |
| 34 | 165/177 | 178/181 | 223/238 | 167/170 |
| 36 | 162/162 | 181/208 | 238/238 | 158/170 |
| 42 | 165/165 | 196/202 | 229/238 | 167/170 |
| 44 | 162/177 | 181/193 | 226/238 | 155/167 |
| 45 | 162/165 | 181/193 | 226/238 | 155/158 |
| 46 | 162/177 | 193/196 | 226/238 | 155/167 |
| 6 | 181/214 | 146/167 | ||
| 12 | 205/232 | 161/161 | ||
| 41 | 181/205 | 167/167 | ||
| 43 | 193/196 | 155/167 | ||
| 119 | 181/196 | 158/176 |