Female brood assignment

Maternity assignment

In principle, using genotypes to assign maternity to female brood is relatively simple. The genotype of a potential mother along those of her mate(s) are used to determine if she could have produced the progeny genotype at all loci. If she could not, then this female is excluded as a candidate mother. For example, at a single locus, an AC egg could not have been laid by an AC female mated to a B male, but could have been produced by an AC female mated to an A male. On this basis potential mothers are excluded. If all candidate mothers can be excluded bar one, then the remaining individual can be assigned as the parent. The accuracy of this method relies on all potential mothers being genotyped, or on missing candidate mothers being shown to be sufficiently unlikely to match the brood.

The efficiency of maternity assignment depends on the number of loci used, on the variability of the loci, and on the degree of relatedness between candidate mothers. If candidate mothers are sisters (r = 0.75), then more loci, or more variable loci, will be

Chapter 5. Reproductive skew in Parischnogasteralternata

required for maternity exclusion, than would be needed if they were non-relatives. After the true mother of an egg, the closest adult relative that may be present is her sister (aunt of the egg). In this study individuals were genotyped at up to five microsatellite loci. Using these loci, the probability of misassigning an aunt as the mother of her sisters' offspring was 1 in 5556 (following methods of Field et a l, 1998a). However, this figure was reliant on all candidate mothers, their mates and brood being genotyped at all five loci. Sperm was successfully genotyped only, at loci Pal95 and Pal68 for 44 and 24 females respectively (Section 5.3.1). The paucity of sperm alleles meant that it was possible to exclude all candidate mothers bar on^jonly for all female eggs and small larvae in three nests (nests 33, 40 and 123). Therefore, for the remaining nests a method of maternity assignment was used that involved assigning maternity to brood sibgroups (this method has previously been used by Queller et a l, (2000), Reeve et al. (2000) and Sumner et al.

(2002)). Female brood were grouped into sibgroups using the computer program Kinship 1.5b4 (Goodnight & Queller, 1997). This procedure followed the same method as was used for the kinship analysis of the adult females (please refer to Section 3.2.6 for a detailed description of the method used). Kinship 1.5b4 (Goodnight & Queller, 1997) was used to determine, within colonies, the female brood that were more likely to be sisters (r = 0.75) than aunt-niece (r = 0.375). Only the genotypes of the female brood were used in this analysis. Using all five microsatellite loci, with the type I error rate set at a = 0.05, 9.1% (1-power) of real sisters were likely to have been misassigned as aunt- niece (type II error = 0.091, power = 90.9%). For the two least heterozygous loci (Pa74 & Pal54) the power was 54.2%.

Following the placement of the female brood into sibgroups, maternity was assigned as follows (please refer to Section 3.2.6 for a detailed description of how females were placed into sibgroups). For each locus a sibgroup is composed of a maximum of three alleles, one of which, the paternal allele, is shared in common. This information was used in conjuction with insemination status and census data to further exclude previously unexcluded candidates. Candidates were excluded as mothers of sibgroups if their genotypes along with those of their mate(s) could not have produced the genotypes of the

Chapter 5. Reproductive skew in Parischnogasteralternata

sibgroups at all loci (Queller et al., 2000; Reeve et at., 2000; Sumner et at., 2002).

Females were also excluded as mothers if they were uninseminated. This was because uninseminated females could not have produced any female offspring. Census data were used in conjunction with information on brood development time to determine whether all candidate mothers of the young female brood had been collected. The time it takes for brood to develop in P. alternata is not known. However, brood development time has been investigated in the closely related P. nigricans serrei (Turillazzi, 1985b). In this analysis, P. altemata is assumed to have brood development times similar to P. nigricans

serrei (Turillazzi, 1985b; Please refer to Table 5.2 for information on brood development).

When assigning maternity, census data and brood development times were used as follows. Females that had not been seen on their nests for at least 12 days prior to nest collection, were not considered as potential mothers of eggs (deposition to hatching of an egg takes on average 11.39 days in P. nigricans serrei). Likewise, females that had not been seen for at least 28 days were not considered as potential mothers of larvae (deposition of egg to pupation takes approximately 11.39 + 16.62 = 28.01days in P.

nigricans serrei). Furthermore, uncollected females were excluded as mothers of a

sibgroup if they could potentially have produced the older brood, but not the younger brood in that sibgroup, and likewise if they could have produced the younger but not the older brood. Ovarian development data were not used to aid maternity assignment, as this was not considered to be of good enough quality (Section 3.2.8). Reproductive skew was calculated using the computer program Skew l.l.l(K rieger & Keller, 1997) for those nests where maternity assignment was possible, and where two or more female eggs and small larvae (<20mg) were present (n = 9). The partitioning of reproduction was also investigated within colonies by examining whether or not sibgroups overlapped temporally. For example, if a sibgroup is composed of an egg and a small larva that weighs lOmg, while another sibgroup within the same nest contains a small larva of 6mg and a pupa, then these sibgroups are considered to overlap temporally.

Chapter 5. Reproductive skew in Parischnogasteralternata

Table 5.2. Mean (± 95% confidence limits) developmental times of brood stages for P.

nigricans serrei as recorded by Turillazzi (1985b).

Developmental stage of brood _{Number of days (mean ±} 95% confidence limits)

Number of brood

Egg deposition to egg hatching _{11.39 ± 0 .9} 75

Larval stage _{16.62 ± 0.98} 75

Pupal stage _{17.12 ±0.93} 80

Egg deposition to eclosion of pupa _{44.46 ± 1.29} 75

Maximum likelihood analysis

Maternity of female eggs and small larvae was also investigated using a maximum likelihood analysis. This analysis was performed because the brood samples for which skew indices were calculated were small (between two and eight brood per nest). This meant that for the majority of nests, the observed skews did not differ from those expected under the assumption that reproduction within colonies was performed by group members at random. Therefore, a maximum likelihood analysis was used, to determine for the overall population, the proportion of females likely to be daughters of the individuals assigned as reproductive dominants. Using the genotypes of dominants, subordinates and female brood, the maximum likelihood value L, was sought, of the parameter D, the fraction of females produced by dominants as opposed to subordinates (Arévalo et a l,

1998; Hastings et a l, 1998; Sumner et a l, 2002). For each colony containing two or more young female brood (eggs and small larvae), and for which a reproductive dominant could be determined (nests 33, 40, 50, 62, 70, 83, 123), L was calculated as:

Chapter 5. Reproductive skew in Parischnogasteralternata

L,

K Y \ \ D V \ K Y[(DY\pdi

(1

D)Y\psi

brood \ Toci Ibci

for values of D between zero and one, sampled at 0.1 intervals. is a constant that never has to be calculated because it does not affect which likelihood ratio is the maximum. For each female brood genotype used in the analysis, pdi and psi are the probabilities that these genotypes could have been produced by the dominants and by the subordinates, respectively. Colony specific likelihoods were multiplied together to give an overall population likelihood. In essence, the maximum likelihood analysis consisted of calculating the probabilities that dominants or subordinates could have produced the brood genotypes, assuming mendelian segregation and random reproduction. For example, the probability of a female producing a brood genotype at a single locus will be either 0, 0.5 or 1.0 depending on whether none, one, or both of its alleles match one of the brood alleles. Within nests, for each adult female and each brood, the probabilities were determined at each locus and multiplied together to obtain the probabilities of each female producing each brood. Then for each colony the probability that a given female was the offspring of a subordinate was calculated as the average of the probabilities for each subordinate. The dominant and average subordinate probabilities were then used to determine for the overall population, the most likely proportion of young female brood produced by the dominants.