Electronic Supplementary Material
Potential sources of error on the genetic origin (arrhenotokous, thelytokous or fertilized) and
maternity (queen or worker) of the eggs were estimated as follows.
First, we considered a diploid egg or a new reproductive queen as produced by
thelytokous parthenogenesis when it harboured the same alleles as the mother queen at all 4
loci studied. Because queens may have mated by chance with a male with no diagnostic
alleles (a male harbouring the same alleles as the queen at each locus), we calculated for each
queen and each locus the probability that a male would share one of the queen’s alleles using
allelic frequencies reported by Fournier et al. (2008) on the same population:
P(non-detection) thelytokous = (f1i + f2i), when the queen is heterozygous at the ith locus; where
f1i and f2i are, respectively, the frequency of the first and the second allele at the ith locus in
the studied population, and
P(non-detection)
thelytokous
= (f1i), when the queen is homozygous, that is, the population
frequency of the allele (f1i).
The probability of absence of any diagnostic allele was estimated by multiplying, for
each queen, the values obtained for each of the four loci. This probability ranged from 1.93E10 to 0.0039 across colonies according to the queen’s genotype.
Second, we considered as haploid all the eggs appearing homozygous (in fact, hemizygous) at
all four loci studied.
(i) We estimated the probability of regarding an egg as haploid whereas it was diploid
and fertilized by a male harbouring at each locus the same allele as that received from the
mother :
P(non-detection) haploid = ½ (f1i + f2i), when the queen is heterozygous at the ith locus, and
P(non-detection)
haploid
= (f1i), when the queen is homozygous, that is, the population
frequency of the allele (f1i).
The probability of considering erroneously a diploid egg as haploid was estimated by
multiplying, for each queen, the values obtained for each of the four loci. This probability
ranged from 1.21E-11 to 0.0002 across colonies according to the queen’s genotype.
(ii) Because automictic parthenogenesis increases homozygosity (Pearcy et al. 2006),
we also estimated the probability of regarding an egg as haploid whereas it was produced by
thelytokous parthenogenesis and homozygous at all four loci as follows:
P(non-detection) diploid = Ri, when the queen is heterozygous at the ith locus; where Ri is the
rate of transition to homozygosity of the ith locus (RCcur11= 0.06, RCcur46= 0.33, RCcur58= 0.33
and RCcur63b= 0.17 ; Pearcy et al. 2006), and
P(non-detection) diploid = 1 when the queen is homozygous at the ith locus.
The probability of considering erroneously a diploid egg as haploid was estimated by
multiplying, for each queen, the values obtained for each of the four loci. This probability
ranged from 0.0011 to 0.06 across colonies according to the queen’s genotype.
Finally, we ruled out the possibility that worker reproduction (if any) biased our results.
(i) Haploid eggs laid by workers may carry with equal probability either an allele
derived from the mother or the father of the worker. Any egg that carries a non-queen allele is
a worker's son. We estimated the probability that a worker-laid haploid egg was erroneously
considered as laid by the queen because it harbours a queen allele at all four loci:
P(non-detection) worker-laid haploid egg= 1-(He/2) ; where He is the expected rate of heterozygosity
estimated from allele frequencies.
The overall probability was estimated by multiplying the probability for each of the four
loci. For each haploid egg laid by a worker, there was a probability of P= 0.107 to
erroneously consider that it was laid by the queen. Overall, the probability of non detection
equals (0.107)n if workers contributed n eggs. Thus, the probability that worker reproduction
remained undetected drops below 2% if 2 haploid eggs from our sample were laid by workers.
(ii) Workers may also contribute to the production of diploid eggs through thelytokous
parthenogenesis. Without recombination during parthenogenesis, worker-produced diploid
eggs would not be genetically distinguishable from queen's fertilized eggs. The production of
a diploid egg by the workers will be detected when there is recombination, with transition
from heterozygosity to homozygosity for the paternal allele at at least one locus. We
estimated the probability that a worker-laid diploid egg was erroneously considered as laid by
the queen as:
P(non-detection) worker-laid diploid egg= 1 - He (R/2)
The overall probability was estimated by multiplying the probability for each of the four
loci. For each diploid egg laid by a worker, there was a probability of P= 0.661 to erroneously
consider that it was laid by the queen. Overall, the probability of non detection equals (0.661)n
if workers contributed n eggs. Thus, the probability that worker reproduction remained
undetected drops below 4% if 8 diploid eggs were laid by workers in our sample.
References
Fournier, D., Battaille, G., Timmermans, I. & Aron, S. 2008 Genetic diversity, worker size
polymorphism and division of labour in the polyandrous ant Cataglyphis cursor. Anim.
Behav. 75, 151-158. (DOI 10.1016/j.anbehav.2007.04.023).
Pearcy, M., Hardy, O. & Aron, S. 2006 Thelytokous parthenogenesis and its consequences
on inbreeding in an ant. Heredity 96, 377-382. (DOI 10.1038/sj.hdy.6800813).