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

• 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	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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