Individuals and populations
When using microsatellites for identifying cases of triploidy, not all markers are expected to show three alleles because they (1) could be blind due to homozygosity of the parents or due to mother and father sharing the same alleles or (2) are located at a physical position along the chromosome that gets inherited twice from the same homolog (see “Introduction”). During the regular paternity analysis of 4993 alive birds (we consider them as alive birds if they hatch) and 2999 embryos (including cases where the egg shell broke or the egg was opened before the due date of hatching), 6 birds (3 of which survived to adulthood) and 28 embryos had been identified as being trisomic for at least three chromosomes (range 3–16), and we assumed that these 34 individuals were triploid. In previous studies using single nucleotide polymorphism (SNP) markers spread across the whole genome, a subset of these 34 individuals, namely 8 embryos (n = 1395 SNPs; Forstmeier and Ellegren 2010) and 2 adult birds (n = 2417 SNPs; Girndt et al. 2014). were confirmed as being triploid (trisomic for all 32 chromosomes in the WUSTL v3.2.4 assembly). An additional three embryos were found to be triploid by genotyping the same SNP set as in Girndt et al. (2014) in 115 embryos that had died from natural causes. Thus, in total, we had 37 individuals that were triploid. To determine whether the supernumerary haploid chromosome was inherited from the mother or the father, we included all the parents of the triploid individuals in our study.
The 37 triploid individuals stemmed from three different populations: (1) Our main population held at the Max Planck Institute for Ornithology in Seewiesen (n = 19; study population 18 in Forstmeier et al. 2007), (2) a recently wild-derived population held at the Max Planck Institute for Ornithology in Seewiesen (n = 13; originating from study population 4 in Forstmeier et al. 2007), (3) a population that was produced by crossing individuals from a captive population held in Cracow (study population 11 in Forstmeier et al. 2007) with our main population (n = 5). Since we used differing microsatellite sets for trisomy detection within and between each of the three populations, detection probabilities varied and a comparison of the rate of triploidy between populations is not meaningful. The only unbiased estimate of the rate of triploidy can be obtained from the 115 dead embryos genotyped with 2417 SNPs (Girndt et al. 2014), which yielded three triploids (2.6 %) among naturally dying embryos (with about 25–30 % of all embryos dying naturally during development).
For each of the ten chromosomes with a known centromere location, we designed primers to amplify two microsatellites, one of them located close to the known centromere and the other at the most distant chromosome end. On chromosome Tgu5 and Tgu6, the FISH probes mapping closest to the centromere are located on sequences, whose positions within the chromosomes are not known (chromosomes Tgu5_random and Tgu6_random; Warren et al. 2010). Thus, we designed primers for microsatellites that are positioned on the same Contig as the FISH probes. Yet on chromosome Tgu6_random, the marker appears to be quite far from the centromere, so we designed an additional primer pair for a microsatellite on chromosome Tgu6 which should be located close to the centromere. For the 22 microchromosomes with an unknown centromere location, we designed primers for two microsatellites, one at the start and one at the end of each chromosome (excluding the difficult-to-assemble chromosome Tgu16 which is only 9.9 kb in the current genome assembly but known to be several hundred times larger; Ekblom et al. 2011; Pichugin et al. 2001). Since all chromosomes with an unknown centromere position are acrocentric (Pigozzi 2008). one microsatellite should be located close to the centromere and the other one close to the distal end (see Supplementary Table S1 for detailed information for each primer pair). However, if parts of the chromosome are missing from the assembly, markers could be further away from the centromere or from the distal end (see “Discussion”).
We used the primer pair 3007/3112 for sexing all embryos, which amplifies an intron in the CHD1 gene differing in length on chromosome TguZ and chromosome TguW (Ellegren and Fridolfsson 1997).
DNA extraction and genotyping
DNA was extracted from blood or tissue samples of all triploid individuals and their parents using the NucleoSpin Blood QuickPure Kit (Macherey-Nagel). Both the Type-it Microsatellite PCR Kit (Qiagen) and the Multiplex PCR Kit (Qiagen) were used for genotyping following manufacturer’s instructions (with the exception of an extension step of 60 °C for 30 min instead of 72 °C for 10 min with the Multiplex PCR Kit). Details on the PCR protocol for each multiplex are given in Supplementary Table S1.
Determination of parental origin
We first determined whether the supernumerary haploid chromosome set was inherited from the mother or the father. For that, we considered those markers as being informative which showed the genotype AB in one parent, CD or CC in the other parent and ABC or ABD in the offspring. The parental origin of the additional chromosome set could be determined in 32 out of the 37 individuals with at least two markers per individual being informative (Supplementary Table S2). Of the remaining five individuals, two were found to be tetraploid with one additional chromosome set inherited from the mother and one from the father, and were hence still useful for the current study (2011_180, 2011_251). The other three individuals (K2012/13_125, 2011_289, 2006_584) had to be excluded because they were uninformative at all marker loci or appeared to be a mixture of digynic and diandric origins of the third chromosome set.
Determination of mechanism of origin
Triploidy may arise from the non-disjunction of homologous chromosomes at meiosis I or by non-disjunction of sister chromatids at meiosis II. Since diandric triploidies may also result from dispermy, in which case a half-tetrad cannot be recovered, they are not useful for centromere mapping and were excluded from further analyses and will be described elsewhere (n = 12).
In the remaining 20 digynic triploids and the two tetraploids (2011_180, 2011_251), those markers located close to the known centromeres on the ten largest chromosomes (Tgu1–Tgu8, Tgu1A and TguZ) were used to distinguish between the non-disjunction of homologous chromosomes at meiosis I or non-disjunction of sister chromatids at meiosis II (Fig. 2). For that purpose, we assumed that the centromeric markers were in complete linkage with the centromere. Hence, whenever the mother was heterozygous at a centromeric marker and passed on both her alleles to the triploid offspring, we took it as evidence for an error in the first meiotic division. Each time she passed on only one of her two alleles, it was pointing to an error in meiosis II (see “Introduction” and Fig. 1 for the underlying logic).
Female birds carry one Z and one W chromosome. In zebra finches, the Z and the W chromosome pair during meiosis I (Pigozzi and Solari 1998) and a mandatory recombination event happens in the pseudoautosomal region (PAR) (Pigozzi 2008). Since the PAR is located at one end of chromosome TguZ (minimum range 1,213,256–1,464,488 bp; Stapley et al. 2008) and the centromere is located around 28 Mb, a centromeric marker will always be located on chromosome TguZ and not recombine with chromosome TguW. If non-disjunction happens in meiosis I, females will always inherit a single Z and a single W chromosome. Meiosis II errors should lead to the inheritance of either two Z or two W chromatids with equal probabilities.
Mapping of centromeres
We used the maximum likelihood method in Chakravarti et al. (1989) to estimate the genetic distance of our markers to the centromere under complete interference, i.e. that only a single cross-over between the marker and the centromere is allowed. Complete interference is a reasonable assumption since usually a single cross-over happens per chromosome arm in the zebra finch (Calderón and Pigozzi 2006). However, one should keep in mind that the estimated genetic distances are restricted to 50 cM (if there is one cross-over in any meiosis between two markers then they are 50 cM apart) and may be underestimated because of occasional double or triple cross-overs.
In order to estimate the genetic distance of our markers from the centromere, we define m
1 as being the number of non-reduced triploid individuals and m
2 being the number of reduced triploid individuals at a specific marker resulting from an error in meiosis I and m = m
1 + m
2. Similarly, we define n
1 as being the number of non-reduced triploid individuals and n
2 being the number of reduced triploid individuals at a specific marker resulting from an error in meiosis II and n = n
1 + n
2. Then, we calculated the maximum likelihood estimate of y, the probability of a recombinant meiotic tetrad, by solving the equation (m + n) × y
2 − (3 × (m + n) − (2m
1 + n
2)) × y + 2 × (m
2 + n
1) = 0. The variance in y is given by Var(y) = y × (1 − y) × (2 − y)/(n + (m + n) × (1 − y)) (Chakravarti et al. 1989). By assuming complete cross-over interference, y can be translated into the marker-centromere distance (w; in cM) with w = y/2 × 100 (Chakravarti and Slaugenhaupt 1987). The variance in w is given by Var(w) = Var(y)/4 × 100 (Deka et al. 1990).
The locations of several microsatellite markers were not covered by the published linkage map (Backström et al. 2010). Thus, we inferred the genetic location of those microsatellites by extrapolating linearly from the closest two markers in the linkage map.