Allo-allo-triploid Sphagnum × falcatulum: single individuals contain most of the Holantarctic diversity for ancestrally indicative markers

Abstract

Background and Aims Allopolyploids exhibit both different levels and different patterns of genetic variation than are typical of diploids. However, scant attention has been given to the partitioning of allelic information and diversity in allopolyploids, particularly that among homeologous monoploid components of the hologenome. Sphagnum × falcatulum is a double allopolyploid peat moss that spans a considerable portion of the Holantarctic. With monoploid genomes from three ancestral species, this organism exhibits a complex evolutionary history involving serial inter-subgeneric allopolyploidizations.

Methods Studying populations from three disjunct regions [South Island (New Zealand); Tierra de Fuego archipelago (Chile, Argentina); Tasmania (Australia)], allelic information for five highly stable microsatellite markers that differed among the three (ancestral) monoploid genomes was examined. Using Shannon information and diversity measures, the holoploid information, as well as the information within and among the three component monoploid genomes, was partitioned into separate components for individuals within and among populations and regions, and those information components were then converted into corresponding diversity measures.

Key Results The majority (76 %) of alleles detected across these five markers are most likely to have been captured by hybridization, but the information within each of the three monoploid genomes varied, suggesting a history of recurrent allopolyploidization between ancestral species containing different levels of genetic diversity. Information within individuals, equivalent to the information among monoploid genomes (for this dataset), was relatively stable, and represented 83 % of the grand total information across the Holantarctic, with both inter-regional and inter-population diversification each accounting for about 5 % of the total information.

Conclusions Sphagnum ×falcatulum probably inherited the great majority of its genetic diversity at these markers by reticulation, rather than by subsequent evolutionary radiation. However, some post-hybridization genetic diversification has become fixed in at least one regional population. Methodology allowing statistical analysis of any ploidy level is presented.

INTRODUCTION

Allopolyploids exhibit both different levels and different patterns of genetic variation than are typical of diploids, with accentuated differences in higher order allopolyploids such as Triticum × aestivum L. (bread wheat, Marcussen et al., 2014), Elymus × repens (L.) Gould (quackgrass or couchgrass, Mason-Gamer 2008), and the peat mosses Sphagnum × falcatulum Besch. (Karlin et al., 2009; Karlin, 2014) and S. × planifolium Müll. Hal. (Karlin et al., 2014), all of which have nuclear genomes from three ancestral species. The holoploid genome (entire chromosome complement) of an allopolyploid gametophyte consists of two or more homeologous monoploid genomes (Greilhuber et al., 2005), with potentially variable genetic diversity among the ancestral genomes. Gain or loss of homeologous chromosomes arising from meiotic or mitotic aberrations may lead to changes in the structure of a holoploid genome (Chester et al., 2012, 2015), with the balance between disomic and polysomic inheritance across homeologous chromosomes playing a key role in this regard. Thus, the holoploid genome of an allopolyploid may vary considerably across individuals and populations of the derivative organism (Chester et al., 2012, 2015). In marked contrast to the gametophytes of diploid vascular species and haploid bryophyte species, allopolyploid gametophytes harbour considerable internal genetic diversity, and that difference is particularly significant for bryophytes, whose gametophytes are the dominant phase of the life cycle. However, scant attention has been given to the partitioning of allelic information and diversity in allopolyploids, particularly that among monoploid components of the hologenome.

The origin of any allopolyploid lineage is associated with an extreme founder effect. In the case of monoicous bryophytes (with hermaphroditic gametophytes), it is possible for a single meiotically unreduced spore from a hybrid sporophyte to give rise to both the first gametophytic generation of a novel allopolyploid lineage and the first sporophytic generation, via intra-gametophytic selfing (Såstad, 2005). In all such cases, the genetic diversity included within the founding gametophyte, as well as that within individuals of the first generation of sporophytes, would represent the allelic divergence between the component homeologous monoploid genomes. Barring meiotic aberrations or mutation itself, all spores produced by such first-generation sporophytes would be genetically identical to the founding gametophyte, as well as to each other. Thus, the founding genotype of such allopolyploids would initially be maintained by both vegetative and sexual reproduction, with spore production allowing for a rapid and long-distance distribution of that lineage. Subsequent genetic novelty may arise via new mutation, recombination (including inter-genomic transfers) and change in hologenomic structure caused by gain or loss of homeologous chromosomes, so additional genetic diversity may augment that acquired by the initial reticulation (hybridization) event (Feldman et al., 2012). Sexual reproduction between different allopolyploid lineages, resulting from recurrent allopolyploidy, could augment genetic diversity among individuals (Soltis et al., 2010; Symonds et al., 2010).

Genetic markers with a unique allele from each homeologous genome in an individual are useful in the study of allopolyploid genomes, particularly for the assessment of allelic diversity within and among the component monoploid genomes. In addition, allopolyploid bryophyte gametophytes are good model organisms for such studies, because the assignment of alleles to monoploid genomes is facilitated by the absence of homologous chromosome pairs.

Objectives

Here, we use an existing microsatellite (simple sequence repeat, SSR) data set to explore the application of recently articulated Shannon information and diversity measures (cf. Jost, 2006, 2007; Sherwin et al., 2006; Sherwin, 2010; Smouse et al., 2015) to genetically allo-allo-triploid gametophytes in S. × falcatulum, as those manifest across levels of geographical organization, ranging from that within single individuals, representing the monoploid ancestral species (of the haplo-triploid), to that among extant individuals, spread across three Holantarctic regional populations, namely NZ: South Island, New Zealand; TdF: Tierra Del Fuego (Chile and Argentina); and Tas: Australian state of Tasmania (Macquarie Island and Tasmania). For comparison, we also examined the patterns of genetic information and diversity within the two immediate progenitor taxa.

We compared the relative contributions of allelic diversity captured by ancestral hybridization events with those emerging subsequently, addressing four specific questions: (1) How much of the total allelic information and diversity in S. × falcatulum was ‘captured’ from the progenitors? (2) How does allelic information and diversity vary among the three monoploid genomes? (3) To what extent has change in hologenomic structure occurred within S. × falcatulum? (4) How does the partitioning of allelic information and diversity vary across the Holantarctic geographical range of S. × falcatulum?

MATERIALS AND METHODS

The species

The genus Sphagnum (peat mosses) occurs on all continents except Antarctica and contains some 250–400 species (Shaw et al., 2016). Based on multigene phylogenetic analyses, Shaw et al. (2010) recognized five subgenera within the genus. The double allopolyploid S. × falcatulum (Fig. 1) is gametophytically allo-allo-triploid, with homeologous monoploid genomes (R, S and T), each captured from a different ancestral species; the evolutionary history involves both inter-subgeneric and serial inter-ploidal hybridization (Karlin et al., 2009, 2011, 2013; Karlin, 2014). The immediate progenitors are the gametophytically haploid S. cuspidatum Ehrh. ex Hoffm (subgen. Cuspidata), which contributed monoploid genome T, and the gametophytically allodiploid S. × irritans Warnst., an inter-subgeneric hybrid that contributed homeologous genomes R (associated with an unknown subgen. Cuspidata species) and S (associated with an unknown subgen. Subsecunda species) (Fig. 2; Karlin et al., 2009, 2011, 2013; Karlin, 2014; Karlin and Robinson, 2016). The genetic diversity within S. × falcatulum thus represents the initial tripling of evolutionary potential, via double reticulation, followed by subsequent innovation (mutations, changes in hologenomic structure, genetic recombination). With its history of inter-subgeneric hybridization, divergence among S. × falcatulum’s monoploid genomes is thought to be among the highest in Sphagnum allopolyploids (Karlin, 2014; Karlin et al., 2014). Based on nuclear nucleotide sequences, divergence between inter-subgenomic sequences in S. × falcatulum (S vs. R; S vs. T) was about twice as high as that between intra-subgeneric sequences (R vs. T) (Karlin, 2014).

Fig. 1.

The peat moss Sphagnum × falcatulum on South Island, New Zealand, with both allo-allo-triploid (3n) gametophytes and young, putatively allo-allo-hexaploid (6n) sporophytes (small brown spheres on plants near the centre of the picture) being present. Photo taken by E. F. Karlin.

Fig. 2.

Putative evolutionary pathways for the allopolyploids S. × falcatulum and S. × irritans. The maternal parent of each hybridization event is indicated by ‘♀’. The gametophytic ploidy level is indicated on the left side of the diagram. Text in red is in the sporophytic phase. WGD, whole genome duplication. Adapted from Karlin et al. (2014).

Although a relatively young species (estimated origin = 23·5–116 kyr BP), putatively unisexual (dioecous) S. × falcatulum is the most widespread peat moss in the Holantarctic (Fig. 2; Karlin et al., 2013). Genetically documented populations occur in New Zealand (both North and South Islands), the Tierra del Fuego archipelago (Chile and Argentina), and the Australian states of Victoria and Tasmania (Karlin et al., 2013; Karlin and Robinson, 2016). Its precise geographical extent is unclear, by virtue of strong morphological overlap and sympatry with its immediate progenitors (Karlin et al., 2009, 2011; Karlin and Robinson, 2016). Separation of the three taxa at the macroscopic level is sometimes difficult, and they form a cryptic species complex in the Holantarctic (Karlin et al., 2013; Karlin and Robinson, 2016). Karlin et al. (2013) concluded that S. × falcatulum probably evolved in New Zealand, with subsequent colonization of Macquarie Island, Tierra del Fuego and possibly Tasmania, each via a single propagule or (at most) a small number of closely related individuals. Sexual reproduction is known to occur in S. × falcatulum, so genetic recombination plays at least some role in its evolution and population structure, but sexual assortment is absent from at least some isolated populations, both locally and regionally. Although common on South Island, sexual reproduction appears to be rare in Tasmania and lacking in both Tierra del Fuego and Macquarie Island (Karlin et al., 2013). Occasional sexuality aside, vegetative reproduction is ubiquitous in Sphagnum, so populations are typically composed of one to several gametophytic clones.

The allodiploid maternal ancestor (S. × irritans) of S. × falcatulum has been genetically documented only from two New Zealand islands: South Island (where it is sympatric with S. × falcatulum) and Chatham Island (Karlin et al., 2009; Karlin and Robinson, 2016). Sphagnum × irritans had been treated as a heterotypic synonym of S. × falcatulum (Andrews, 1949; Fife, 1996), but Karlin and Robinson (2016) found the type to be associated with allo-diploid plants instead. Thus, S. × irritans has been removed from the synonymy of allo-allo-triploid S. × falcatulum and is now recognized as a proper species. The paternal ancestor, S. cuspidatum (monoploid), was considered to be a Holarctic species with disjunct populations in Australia and New Zealand by Warnstorf (1911). It was subsequently excluded from Australasia by Andrews (1949), Sainsbury (1955), Scott et al. (1976), Catcheside (1980), Beever et al. (1992), Fife (1996) and Seppelt (2012). Recent genetic analyses, however, have documented its presence at two sites in Queensland, Australia, and S. cuspidatum is now reported for all continents except Antarctica (Karlin et al., 2011).

Taxon sampling

The SSR genotypes deployed for this study have been described by Karlin et al. (2009, 2011, 2013) and Karlin and Robinson (2016), and involved 138 individuals of S. × falcatulum gametophytes collected from South Island (New Zealand), Tierra del Fuego archipelago (Chile, Argentina) and the Australian state of Tasmania (Supplementary Data, Table S1). The most complete coverage was for South Island (NZ), with 97 individuals collected from 11 sites (= populations). The Tierra del Fuego archipelago (TdF) was represented by 24 individuals collected from 16 sites across eight islands and one mainland location. Eight of these sites were each represented by one individual and eight sites were represented by two individuals each. The state of Tasmania (Tas) was represented by one site on Macquarie Island (with 15 individuals) and two sites on Tasmania (with one individual each). To allow for Shannon analysis among and within regions, TdF and Tas were each divided into ‘super populations’ (i.e. sub-regions). TdF had three ‘super populations’: (1) Isla Grande de la Tierra del Fuego and one mainland site (eight individuals from six sites); (2) sites occurring south of Isla Grande de la Tierra del Fuego and north of 55·6°S (seven individuals from five sites across three islands); and (3) sites south of 55·6°S (nine individuals from five sites across four islands). There were two ‘super populations’ for Tas: Macquarie Island (15 individuals from one site) and Tasmania (two individuals from two sites). The SSR assay battery also included data for 17 individuals of S. × irritans (from four South Island sites) and 11 individuals of S. cuspidatum (from two Queensland, Australia, sites).

Microsatellite genotypes

DNA was extracted from one gametophyte stem selected from each specimen. DNA extractions were accomplished with the protocols described by Shaw et al. (2003). All samples were assayed across 14 SSR markers. Protocols for microsatellite (SSR) amplification and scoring are presented in Karlin et al. (2008). Fragments of different sizes (nucleotide pairs) were coded as alleles.

Here, we have used just five of these markers. They were selected because each had alleles (within any single individual) that could be unambiguously assigned to their respective monoploid genomes. Thus, these ‘ancestrally indicative’ markers allowed for a study of the allelic diversity among and within the three monoploid genomes present in S. × falcatulum. The markers were 1, 12, 18, 19 and 22 (numbered as in Shaw et al., 2008). Each of the other nine SSR markers, although easily assayed and reliable, had some, even many, alleles that could not be assigned to ancestral genomes.

The allelic data for the individuals are listed in Supplementary Data (Table S2). All five markers exhibited stable homeologous alleles, most of which occurred both within S. × falcatulum and within at least one of the three ancestral linages. Each individual would thus be expected to contain one allele from each of the three homeologous ‘loci’, so the five markers collectively present five ‘trios’ of homeologous alleles within each individual: (1R, 1S, 1T), (12R, 12S, 12T), (18R, 18S, 18T), (19R, 19S, 19T) and (22R, 22S, 22T). These five trios permit comparison of allelic diversity captured by the initial hybridization events (Fig. 3) with that emerging post-hybridization within S. × falcatulum itself.

Fig. 3.

Map showing the location of the three study regions: South Island, New Zealand (NZ), Tierra del Fuego (TdF; Chile, Argentina) and the State of Tasmania, Australia (Tas), which includes Macquaire Island (MI) and Tasmania (Tas).

Allelic information and diversity

To characterize the patterns of holoploid (triploid) allelic diversity within S. × falcatulum, we computed estimates of (allelic) Shannon information. Briefly, consider a single SSR marker (say the marker A), represented in the collective (S. × falcatulum) sample (of N) individuals by a series of alleles (say A₁, … , A_K). The kth allele (k = 1, … , K) is present in that collective sample with a relative frequency (in the N trios) of P_k = (X_k/3N). The total (within-species) Shannon information (H_WS) for marker A is defined as

$$0\le {\mathrm{H}}_{\mathrm{ws}}=-{\sum }_{k=1}^K{p}_k.\ln (p_k)\le \ln (3N),$$ (1)

which is bounded below by ‘0’ and above by ln (3N). The lower bound is achieved when all 3N of the alleles are of the same type (monomorphic marker); the upper bound is achieved when all 3N alleles are different and appear once each. To convert from Shannon (allelic) information to allelic diversity, we exponentiate. The total holoploid within-species diversity (σ_WS) for this A-locus is thus defined as

$$1\le {\sigma }_{\mathrm{ws}}=\text{exp}\hspace{0.17em}\{{\mathrm{H}}_{\mathrm{ws}}\}\le 3N,$$ (2)

obviously bounded below by 1 (= a single, monomorphic allele) and above by 3N (= all alleles different and equally frequent). Both information and diversity increase with the number of different alleles, and for any particular number of alleles, both information and diversity increase with ‘evenness’ of their frequencies. Computation of allelic diversity for each homeologous monoploid genome was the same, but with the upper bound set at N and the relative frequency of each allele being P_k = (X_k/N).

Our targets for allo-triploid Sphagnum gametophytes are the diversity components themselves, but Shannon information values are conveniently additive (see below), so we can partition information among and within regions (H_AR and H_WR), among and within populations (H_AP and H_WP) for single regions, as well as among and within allotriploid individuals (H_AI and H_WI) for single populations, for each of the five loci separately. We then average the assayed information values for the five marker loci. For a single region (say NZ), we compute the information and diversity within that stratum, as in eqn (1), but with 3N now defined as the theoretical maximum number of alleles within that region (H_WR-NZ). Using a weighted average within-region information value for the three regions (H_WR), we then compute the among-regions information component (H_AR = H_WS – H_WR). We extract average within-population (H_WP) and average within-(triploid)-individual (H_WI) information values in similar fashion, and calculate the among-population (H_AP = H_WR – H_WP) and among-individual (H_AI = H_WP – H_WI) values. We compute the information partition, marker by marker, and then average. The information value is then exponentiated to obtain the diversity values, all measured in ‘effective number of ‘equi-frequent’ units. The total layout takes the following form:

Information analysis is similar to traditional analysis of variance (cf. Smouse and Ward, 1978; Smouse et al., 2015). Information is additive:

$$H_{\mathrm{WG}}=H_{AS}+H_{WS},$$ (3)

$$H_{WS}=(H_{AR}+H_{WR})=H_{AR}+(H_{AP}+H_{WP})=H_{AR}+H_{AP}+(H_{AI}+H_{WI}),$$ (4)

but the diversity components are multiplicative (cf. Tuomisto, 2010):

$${\gamma }_{\mathrm{WG}}={\mathrm{\theta }}_{\mathrm{AS}}\mathrm{.}{\sigma }_{\mathrm{WS}},$$ (5)

$${\sigma }_{\mathrm{WS}}=({\mathrm{\delta }}_{\mathrm{AR}}·{\mathrm{\rho }}_{\mathrm{WR}})={\mathrm{\delta }}_{\mathrm{AR}}·({\mathrm{\beta }}_{\mathrm{AP}}·{\mathrm{\alpha }}_{\mathrm{WP}})={\mathrm{\delta }}_{\mathrm{AR}}·{\mathrm{\beta }}_{\mathrm{AP}}·({\mathrm{\lambda }}_{\mathrm{AI}}·{\mathrm{\mu }}_{\mathrm{WI}}).$$ (6)

Allelic diversity within groups (γ_WG, σ_WS, ρ_WR, α_WP, μ_WI) is interpreted as effective numbers of alleles per marker within a group. Allelic diversity among groups (γ_AS, δ_AR, β_AP, λ_AI) is interpreted as effective numbers of non-overlapping allele sets, or ‘compositional units’, among strata per marker (Tuomisto, 2010). Information and diversity among groups measure the divergence (differentiation, distinctness) among the groups (strata) in question (Whittaker, 1977; Sherwin et al., 2006; Jost, 2010; Sherwin, 2010; Tuomisto, 2010; Smouse et al., 2015). For this dataset, allelic diversity within individuals (μ_WI) is equivalent to the divergence among monoploid genomes. Thus, μ_WI can be interpreted as being both the effective numbers of alleles (within an individual) and the effective number of non-overlapping allelic sets, or monoploid genomes (within an individual).

We used GenAlEx 6.5 (http://biology.anu.edu.au/GenAlEx/; Peakall and Smouse, 2006, 2012) to construct the analyses reported here. For each individual, data were arranged in three consecutive rows (one per ancestral monotype), with each of the five trios represented by a single column. This slight shift in GenAlEx data format allowed haplo-triplo data to be analysed as needed here. Shannon analysis was carried out using the ‘Partition’ option, with each individual defined as a ‘population’ of three sub-samples, with each sub-sample represented by one row of data. This approach was elaborated here to deal with additional regions across the Holantarctic, and could easily be extended to other ploidy levels. An example data sheet and a results sheet for triploid analysis are provided in Supplementary Data (Tables S3 and S4).

Three of the five markers typically had three different alleles per marker per individual in S. × falcatulum, with one allele from each monoploid genome; two markers had only a pair of alleles per individual (because of allelic overlap between R and T). These patterns appear to represent those directly inherited from the ancestor and thus allow for the calculation of the ‘founding’ (or original) H_WI and μ_WI for S. × falcatulum. Averaging across the five markers yields a mean ‘founding’ information and diversity of [H_WI = 0·914 ↔ μ_WI = 2·49]. For S. × irritans, which has (1) no allelic overlap between its two monoploid genomes (R′ and S′) at these markers, and (2) each marker typically has two alleles per individual, mean ‘founding’ information and diversity are [H_WI = 0·693 ↔ μ_WI = 2·00]. For both allopolyploid species, a change in hologenomic structure manifests as a change in the within-individual components (H_WI ↔ μ_WI). A tally of the H_WI associated with each individual sampled was made to examine the extent of variation in H_WI.

RESULTS

Monoploid genomes

A total of 26 different alleles were detected across the three monoploid genomes assayed with the five markers, with two monomorphic alleles (12R ≡ 12T) and (18R ≡ 18T) being shared by the (co-subgeneric) ancestral monoploid genomes R and T (Table 1). Nineteen of the alleles (76 %) co-occurred in the immediate progenitors, and we will refer to such alleles as ‘ancestral’. For each monoploid genome, one ancestral allele had a frequency ≥0·60 at each homeologous locus, and with a single exception (18S), these ‘most frequent’ alleles were also predominant in the immediate progenitors (Table 1). The six (of 19) ancestral alleles having a lower frequency in S. × falcatulum were also lower frequency polymorphs in the immediate ancestors. Moreover, only two of the seven putative ‘de novo’ (new) alleles detected in S. × falcatulum (i.e. not yet found in the progenitors) had frequencies ≥0·05 in the respective monoploid genomes. The ‘de novo’ alleles in S. × falcatulum were assigned to a homeologous genome, based on similarity in size to the ancestral alleles associated with that homeologous genome or if the ancestral alleles for the other two homeologues were also present in an individual. The mean total combined frequency of de novo alleles across the five markers was <0·01 in genomes T and R and ∼0·06 in S. The mean number of alleles per marker with frequency ≥0·05 and the mean number of alleles per marker shared with the two immediate progenitors were all lowest in T, highest in S and intermediate in R (Table 2). The numbers of monoploid haplotypes (across 15 homeologous loci) detected for R, S and T were seven, 13 and three, respectively, with the most common haplotypes having frequencies of 0·69, 0·46 and 0·98 for R, S and T, respectively. We infer that the ancestral alleles were captured by hybridization and that the de novo alleles have probably developed within S. × falcatulum, subsequent to formation. Most of the genetic information and diversity contained within these five markers for S. × falcatulum were inherited from the progenitors.

Table 1.

Frequency of the most common allele (F-MCA) per monoploid genome, the combined frequencies of all ‘ancestral alleles’ (CF-Ancestral) in each monoploid genome, and the total number of ‘ancestral alleles’ present in each monoploid genome/marker (given in square brackets) across three regional populations of Sphagnum × falcatulum, based on five ancestrally indicative markers

Ancestral marker	Monoploid genome	F-MCA	CF-Ancestral
Marker - 1	R	0·89 (0·88)	1·00 [2]
	S	1·00 (1·0)	1·00 [1]
	T	0·98 (1·00)	0·98 [1]
Marker - 12	R	1·00 (1·0)*	1·00 [1]
	S	0·90 (0·71)	1·00 [2]
	T	1·00 (1·0)*	1·00 [1]
Marker - 18	R	1·00 (1·0)*	1·00 [1]
	S	0·64 (0·29)	0·83 [3]
	T	1·00 (1·0)*	1·00 [1]
Marker - 19	R	0·96 (0·82)	0·99 [2]
	S	1·00 (1·0)	1·00 [1]
	T	1·00 (1·0)	1·00 [1]
Marker - 22	R	0·99 (1·0)	0·99 [1]
	S	0·84 (0·59)	0·88 [3]
	T	1·00 (1·0)	1·00 [1]
Mean ± s.e.	R	0·97 ± 0·02	1·00 ± 0·00
	S	0·87 ± 0·07	0·94 ± 0·04
	T	1·00 ± 0·00	1·00 ± 0·00

The frequency in the immediate ancestors for the MCA in each monoploid genome is given in parentheses. An asterisk (*) indicates that the same allele occurred in the R and T monoploid genomes.

Table 2.

Allelic sample composition for the holoploid and three monoploid genomes (R, S, T) across three regional populations of S. × falcatulum, as well as those from the ancestral species S. × irritans (R′, S′) and S. cuspidatum (T): number of individuals (N), number of alleles (N_a), number of polymorphic alleles (N_a ≥ 5 %), number of alleles inherited from ancestor (N_i), number of unique (private) alleles (N_u) and effective number of alleles (N_e), based on five ancestrally indicative markers

Genome	N	Na	Na ≥ 5 %	Ni	Nu	Ne
Sphagnum × falcatulum
R	133·2	1·8	1·2	1·4	0·4	1·12
S	137·0	2·4	1·8	1·8	0·6	1·47
T	138·0	1·4	1·0	1·0	0·4	1·02
R,S	270·2	4·2	2·8	3·2	1·0	2·58
R,S,T	408·2	5·2	3·0	3·8	1·2	2·97
Sphagnum × irritans
R′	16·8	1·4	1·4	–	0·0	1·18
S′	17·0	2·2	2·2	–	0·4	1·71
R′,S′	33·8	3·6	3·4	–	0·4	2·84
Sphagnum cuspidatum
T′	11·0	1·0	1·0	–	0·0	1·00

Allelic information and diversity.

Considerable divergence was detected among all three monoploid genomes based on the five markers. Allelic information and diversity between S (subgen. Subsecunda) and each of the two subgen. Cuspidata monoploid genomes R and T were [H_AS = 0·693 ↔ θ_AS = 2·00]. Information and allelic diversity between R and T were [H_AS= 0·415 ↔ θ_AS = 1·51]. A detailed partition of allelic information and diversity for each monoploid genome is presented in Table 3. Total allelic information and diversity (H_WS ↔ σ_WS) across the three regions differed among the three monoploid genomes, with H_WS(S) > H_WS(R) > H_WS(T). This ranking held for all other partitions, except for that within individuals, where [H_WI = 0·000 ↔μ_WI = 1·00] for each of the three monoploid genomes (Table 3). Total allelic diversity ranged from σ_WS(S) = 1·47 to σ_WS(T) = 1·02. For each monoploid genome, allelic diversity among individuals within populations (λ_AI) was slightly higher than that detected among populations (β_AP) and that among regions (δ_AR); H_AI represented between 40 and 58 % of the respective H_WS values.

Table 3.

Shannon diversity analysis of five ancestrally indicative markers for Sphagnum × falcatulum, both as separate monoploid (R, S, T) genomes, and combined as a holoploid (triploid) genome, across three regions (New Zealand, Tasmania, Tierra del Fuego); the R genome was based on four markers (see text for explanation)

Information and diversity	Monoploid (R)	Monoploid (S)	Monoploid (T)	Holoploid (R, S, T)
Within species (S. × falcatulum)
Information (HWS)	0·131	0·385	0·024	1·089
Diversity (σWS)	1·14	1·47	1·02	2·97
Among regions (NZ, Tas, TdF) within species
Information (HAR)	0·014	0·121	0·002	0·054
Diversity (δAR)	1·01	1·13	1·00	1·06
Within regions
Information (HWR)	0·117	0·264	0·022	1·035
Diversity (ρWR)	1·12	1·30	1·02	2·82
Among populations (within regions)
Information (HAP)	0·047	0·111	0·009	0·054
Diversity (βAP)	1·05	1·12	1·01	1·06
Within populations
Information (HWP)	0·071	0·153	0·014	0·981
Diversity (αWP)	1·07	1·17	1·01	2·67
Among individuals (within populations)
Information (HAI)	0·071	0·153	0·014	0·079
Diversity (λAI)	1·07	1·17	1·01	1·08
Within individuals
Information (HWI)	0·000	0·000	0·000	0·901
Diversity (μWI)	1·00	1·00	1·00	2·46

All Shannon analyses were based on the five markers, with one exception. Because the TdF population lacked the (22R) allele, just four markers were used to determine the partitioning of information and diversity within and among regions for R. However, by treating all individuals as one population, a second value for just H_WS(R) was calculated using all five markers. Based on five markers, [H_WS(R)= 0·115 and ρ_WS(R) = 1·12], which were comparable to, but slightly lower than, the H_WS(R) and ρ_WS(R) based on four markers (Table 3). With either approach, H_WS(R) and ρ_WS(R) were intermediate between the corresponding values for T and S.

Holoploid genomes

Among-region allelic information and diversity.

A detailed partition of the holopoloid allelic information and diversity is presented in Table 3. Based on Shannon analysis of the holoploid genome (as triploid data) for the five markers, the grand total information for S. × falcatulum across the three regions was H_WS(R,S,T) = 1·089, translating into an (effective number) diversity equivalent of σ_WS(R,S,T) ∼ 2·97 alleles per trio. By far the majority of allelic diversity was present within each individual, with μ_WI = 2·46 alleles per trio (marker). As this diversity also represents divergence among the monoploid genomes, it shows that the effective number of monoploid genomes present is 2·46. Allelic information within individuals H_WI(R,S,T) = 0·901 represented ∼83 % of H_WS(R,S,T). This is in stark contrast to the monoploid analysis, where for each monoploid genome, μ_WI = 1·00 and H_WI represented 0·0 % of H_WS. The next highest diversity among partitions was λ_AI(R,S,T) = 1·08, with H_AI(R,S,T) representing ∼7 % of H_WS(R,S,T). β_AP(R,S,T) and δ_AR(R,S,T) were comparable, with H_AR(R,S,T) and H_AP(R,S,T) each representing ∼5 % of H_WS(R,S,T). Thus, ∼95 % of H_WS(R,S,T) was resident within regions and ∼ 90 % was resident within populations. For S. × falcatulum, ancestry is (almost) everything!

Within region allelic information and diversity.

New Zealand. A detailed partition of the holoploid allelic information and diversity for NZ is presented in Table 4 and Fig. 4. Shannon analysis of the holoploid genome within NZ yielded a pattern of diversity among partitions similar to the pattern detected for the analysis across the three regions, albeit with slightly higher allelic information and diversity values at all levels (Tables 3 and 4). Total information for New Zealand was H_WR(NZ) = 1·097, translating into a diversity equivalent of 3·00 alleles per trio (marker). H_WI(NZ) represented 83 % of H_WR(NZ), H_AP(NZ) represented 7 % and H_AI(NZ) accounted for 10 %. Thus, some 93 % H_WR(NZ) was resident within populations, and most of that was the ancestral diversity resident within any single individual.

Table 4.

Shannon information and diversity analyses of the holoploid (R,S,T) genomes for each of the regional collections: Tierra del Fuego (TdF), Tasmania (Tas), New Zealand (NZ), along with the average analyses, based on five ancestrally indicative markers

Information and diversity	Separate within-region averages			Overall average
	TdF	Tas	NZ
Within regions
Information (HWR)	0·833	0·914	1·097	1·035
Diversity (ρWR)	2·30	2·49	3·00	2·82
Among populations (within regions)
Information (HAP)	0·000	0·000	0·076	0·054
Diversity (βAP)	1·00	1·00	1·08	1·06
Within populations
Information (HWP)	0·833	0·914	1·021	0·981
Diversity (αWP)	2·30	2·49	2·78	2·67
Among individuals (within populations)
Information (HAI)	0·000	0·000	0·111	0·079
Diversity (λAI)	1·00	1·00	1·12	1·08
Within individuals
Information (HWI)	0·833	0·914	0·911	0·901
Diversity (μWI)	2·30	2·49	2·49	2·46

Fig. 4.

Partitioning of Shannon Information: (A) the two monoploid genomes (R′, S′) and the holoploid genome of S. × irritans (across four sites); and (B) the three monoploid genomes (R, S, T) and the holoploid genome of Sphagnum × falcatulum (across 11 sites) on South Island, New Zealand. The total height of each column represents the total information (H_WR) for the respective genome (or holoploid genome) on South Island. Based on five ‘ancestrally indicative’ microsatellite markers: green for information within individuals (H_WI); red for information among individuals within populations (H_AI); blue for information among populations (H_AP).

Tasmania and Tierra del Fuego. Shannon analysis of the holoploid genome for both these regions showed a starkly different partitioning of allelic information and diversity among levels than that detected for NZ (Table 4). For both regions, 100 % of holoploid H_WR was associated with H_WI; no information was present in any of the other components. Consequently, allelic information and diversity in these two regions was much lower than that detected for NZ, with ρ_WR(Tas) = 2·49 and ρ_WR(TdF) = 2·30. H_WI differed among the three regions, being highest in Tas and lowest in TdF.

Changes in hologenomic structure.

The large majority (109/138) of the S. × falcatulum individuals in this study, including all of the Tasmanian (15) and 92 (out of 97) NZ individuals, had [H_WI(R,S,T) = 0·914 ↔ μ_WI(R,S,T)_I = 2·49 alleles] per average trio. As this value represents the holoploid ‘founding’ H_WI, there appears to have been no change in allotriploid hologenomic structure in these individuals, at least for these markers. The remaining 29 individuals sampled in this study, representing all of the TdF individuals and the remaining five NZ individuals, had [H_WI(R,S,T) = 0·833 ↔ μ_WI′(R,S,T) = 2·30], indicative of a change in hologenomic structure. All 24 of the TdF individuals lacked the (22R) allele, and four of the five South Island individuals, all ramets of one clonal lineage, lacked the (22S) allele instead. The fifth South Island individual (EK498) lacked (12S). These changes for markers (22 and 12) reflect post-hybridization evolution in the hologenomic structure of S. × falcatulum over evolutionary time and geographical space. It is also possible that the change in hologenomic structure occurred in S. × irritans and was directly inherited by S.× falcatulum via one of its multiple origins.

Allelic information and diversity in the immediate ancestors

Allelic information and diversity in the two immediate progenitors of S. × falcatulum, the South Island population of S. × irritans (R′ and S′) and the Queensland population of S. cuspidatum (T′) revealed three major points. (a) Total information and diversity within each of the homeologues (R′, S′, T′) were comparable to those detected within S. × falcatulum (R, S, T) (Table 2). We find [H_WS(T′) ↔ σ_WS(T′)] < [H_WS(R′) ↔ σ_WS(R′)] < [H_WS(S′) ↔ σ_WS(S′)], so the pattern we see today in S. × falcatulum was probably established via the initial hybridization event(s). (b) There were no R′ alleles for these five markers in S. × irritans or T′ alleles in S. cuspidatum that were not also present in S. × falcatulum, but there were two S′ alleles in S. × irritans that have not been detected within S. × falcatulum. (c) Divergence between each monoploid genome in S. × falcatulum and its ancestral progenitor was slight (Table 5). Collectively, the data suggest that the majority of the allelic information and diversity associated with the markers in the two immediate progenitor species was captured by S. × falcatulum, almost certainly via repeated hybridization. In addition, [H_WI = 0·689 ↔ μ_WI = 1·99] in S. × irritans, representing 66 % of H_WS. All (but one) individuals of S. × irritans had the ‘founding’ H_WI = 2·00 at these markers. The one exception lacked the allele for (1R) and had [H_WI = 0·555 ↔ μ_WI = 1·74].

Component	Information	Diversity	Effective number units
Within genus	HWG	γWG = exp{HWG}	Alleles per genus
Among species	HAS	θAS = exp{HAS}	Species per genus
Within species	HWS	σWS = exp{HWS}	Alleles per species
Among regions	HAR	δAR = esp{HAR}	Regions per species
Within regions	HWR	ρWR =exp{HWR}	Alleles per region
Among populations	HAP	βAP = exp{HAP}	Populations per region
Within populations	HWP	αWP =exp{HWP}	Alleles per population
Among individuals	HAI	λΑΙ = exp{HAI}	Individuals per population
Within individuals	HWI	μWI = exp{HWI}	Alleles per individual

Table 5.

Within-species information (H_WS) and diversity (σ_WS) for Sphagnum × falcatulum (R,S,T) monoploid genomes, and of its ancestral (allo-diploid) S. × irritans (R′,S′) and (haploid) S. cuspidatum (T′) progenitors, in addition to the among-species components (H_AS and θ_AS), based on five ancestrally indicative markers

Information and diversity	Ancestral species	Derivative species	Ancestral vs. derivative
S. × irritans → S. × falcatulum
HWS (R or R′) =	0·169	0·131	0·005 = HAS (R′ vs. R)
σWS (R or R′) =	1·20	1·14	1·01 = θAS (R′ vs. R)
S. × irritans → S. × falcatulum
HWS (S or S′) =	0·534	0·385	0·048 = HAS (S′ vs. S)
σWS (S or S′) =	1·70	1·47	1·05 = θAS (S′ vs. S)
S. cuspidatum → S. × falcatulum
HWS (T′ or T) =	0·000	0·024	0·053 = HAS (T′ vs. T)
σWS (T′ or T) =	1·00	1·02	1·05 = θAS (T′ vs. T)

A comparison of the partition of information in the New Zealand regional collections of S. × falcatulum and S. × irritans is shown in Fig. 4. Total holoploid information H_WR(R,S,T) in S. × falcatulum was slightly higher than H_WI(R′S′) in S. × irritans. However, H_WI(R,S,T) in S. × falcatulum was much greater than H_WI(R′,S′) in S. × irritans, while holoploid H_AP and H_AI contributed a much larger portion of the total information in S. × irritans than in S. × falcatulum.

DISCUSSION

Allelic information and diversity capture from progenitors

There is considerable diversity (divergence) among the monoploid genomes contributing to S. × falcatulum, as captured subsequently in its current information and diversity. For these five markers, divergence among monoploid genomes (represented by H_WI and μ_WI here) was by far the major source of allelic diversity in S. × falcatulum. Large differences in allelic information and diversity within the (R,S,T) homeologues are emblematic of the fact that multiple origins and ploidy-level changes have played a large role in the evolution of S. × falcatulum. Recurrent hybridization has evidently increased allelic diversity within both R and S homeologues, but it has not increased the allelic novelty within T. These patterns suggest recurrent hybridization between a genetically depauperate haploid T′ progenitor (S. cuspidatum) and an allodiploid R′ and S′ progenitor (S. × irritans), containing genetically diverse monoploid genomes. The pattern of allelic information and diversity detected in the two latter species supports this hypothesis.

In turn, the large difference in allelic diversity between the R genomes and the S genomes in S. × irritans strongly suggests recurrent hybridization between S. × irritan’s (monoploid) ancestors, with the ancestor contributing genome S′ harbouring greater internal genetic diversity than the ancestor contributing R′. Our results show that the frequency of hybridization between divergent progenitors, plus the diversity within each of the participants, can be expected to influence both the monoploid and the holoploid allelic diversity within allopolyploid derivative species, with diverse ancestors leaving separable signatures. In the case of S. × falcatulum, the addition of monoploid genome T increased holoploid μ_WI, but decreased holoploid β_AP and λ_ΑΙ.

We conclude that the large majority of genetic information and diversity contained within these five markers in S. × falcatulum were ‘captured’ directly from the ancestral progenitors, via serial and recurrent hybridization. Clearly, a trio of monoploid ancestors introduced novelty into S. × falcatulum, with monoploid S contributing the most diversity and T the least. A small number of subsequent mutations and changes in hologenomic structure have also contributed to genetic diversification within S. × falcatulum. Given its relatively recent origin (Karlin et al., 2013), the current genetic information and diversity within each of the three homeologous genomes in S. × falcatulum largely reflects the intense filtering of alleles associated with two serial rounds of recurrent reticulation, the first round giving rise to S. × irritans and the second yielding S. × falcatulum. However, our data show only slight subsequent divergence between S. × falcatulum and its two immediate progenitors.

Post-reticulate innovation

De novo alleles.

As the data sets for each progenitor species were small, separating ancestral from de novo alleles was inevitably a bit tentative. We note, however, that the numbers of de novo alleles per locus (within S. × falcatulum) were comparable among the three monoploid genomes (Table 2), suggesting the appearance of (post-hybridization) allelic novelty, rather than representing alleles captured via hybridization. It is possible, of course, that at least some of these putative de novo alleles, not currently detectable in immediate progenitors, were introduced via hybridization. While more elaborate sampling of the progenitors may eventually provide additional evidence for or against this interpretation, the data in hand argue for post-establishment generation of at least some genetic novelty.

Change in hologenomic structure.

The hologenomic structure in S. × falcatulum based on these five markers has been relatively stable, both within and across regions, and there appears to have been little change in the balance among monoploid genomes, in spite of multiple origins. But some hologenomic change has occurred, either in S. × irritans (subsequently inherited by S. × falcatulum) or post-origin, within S. × falcatulum. The clonal nature of gametophytic Sphagnum allows such changes to replicate with fidelity and to persist for extensive periods of time (Karlin et al., 2012). If a single individual exhibits loss of a particular allele, that might represent no more than a non-amplifying (null) allele in that individual. But when several individuals from a single clonal lineage (or an entire population) lack the allele, absence probably represents a change in holoploid genomic structure. The strongest evidence of hologenomic loss was associated with the TdF population. The evidence for hologenomic change in S.× irritans was ambiguous, as all individuals but one had the ‘founding’ H_WI(R′,S′) = 0·693.

Regional vs. subregional diversification

Based on five ancestrally indicative markers, allelic divergence for S. × falcatulum was slight among these three highly disjunct Holantarctic regions, and also low among populations within those regions. Indeed, divergence among individuals within populations (H_AI) exceeded divergence among regions (H_AR). However, in spite of the low regional divergence, markedly different patterns of holoploid allelic information and diversity occurred among individuals within NZ [H_AP(NZ) + H_AI(NZ)] compared with those in Tas and TdF. The lack of information among individuals within the five sets of three homeologous trios for each of the Tas and TdF regions clearly indicates that their respective histories differ greatly from that associated with NZ. Given the stability of the alleles at these five markers, H_AI(NZ) > 0 indicates that at least two genets are present in at least some NZ populations. Likewise, H_AP(NZ) > 0 indicates that there are at least frequency differences among genets for different NZ populations. In stark contrast, our data show no evidence supporting the occurrence of more than one genet in either Tas or TdF. This possibility is supported by the frequent occurrence of sexual reproduction in NZ, and its virtual absence from TdF and from Macquarie Island (Karlin et al., 2013). The occurrence of a sporophyte on only one Tasmanian herbarium specimen suggests that there may be more than one genet present on that island, but we see no evidence of that in our limited Tas samples. Additional study is required to fully explore this question. Our data indicate that NZ was the probable source region and that TdF and Tas represent later colonizations by one or a few propagules each. Sphagnum × falcatulum’s capacity for long-distance dispersal, its unisexuality and its clonal nature allow for the development of populations, even at the regional level, within which there is no divergence among individuals, based on these five markers. Although a young species, S. × falcatulum has managed to span much of the Holantarctic, more or less clonally.

Appropriate statistical analysis for allopolyploids

With two or more homeologous loci per marker, allopolyploids have a greater genetic potential than that found in diploids (or haploids in the case of bryophytes). Based on the five markers used in this study, the majority of this genetic potential in both S. × falcatulum and S. × irritans, and probably other allopolyploids having highly divergent monoploid genomes, occurs within individuals, and not among individuals. Thus, it becomes important to consider H_WI in the context of (a) how much genetic novelty is present within the species, (b) where it is localized and (c) how it is bundled. Finally, changes in H_WI may signal changes in hologenomic structure. We conclude that it is particularly valuable to elucidate H_WI (and μ_WI) when studying allopolyploids.

Meirmans and Van Tienderen (2013) note that subgenomes (homeologous monoploid genomes) should be analysed as separate loci when strict disomic inheritance occurs in allopolyploids. That approach was utilized by the first author in two previous studies of Sphagnum allopolyploids, one on the allo-diploid S. × palustre (Karlin et al., 2012) and one on S. × falcatulum (Karlin et al., 2013). However, focusing solely on allelic information and diversity among alleles for the constituent homeologous loci misses the larger and perhaps more important story. Although accommodating ‘among-individual’ comparisons, the ‘separate loci’ approach ignores the fact that allelic diversity among homeologous loci (represented by H_WI and μ_WI in S. × falcatulum and S. × irritans) may represent the bulk of allelic information and diversity resident within many allopolyploid species.

CONCLUDING THOUGHTS

As shown here, Shannon information and diversity measures provide a powerful and effective approach to the study of allelic diversity at many levels (Sherwin et al., 2006). Even when applied to a genetically complex species, Shannon analysis yields an interconnected and seamless link from the allelic diversity within individuals to that present within and among regions.

This study focused on five markers that facilitated comparison of allelic diversity captured from multiple origins with that emerging from post-hybridization within S. × falcatulum itself. Although such stable markers are often overlooked by studies focused on one species, we show that they can be quite informative about the evolutionary history of allopolyploids. SSR markers which are evolutionarily more labile, and thus unsuitable for this study, would be expected to provide a different perspective on the allelic information and diversity in S. × falcatulum, notably the recent history of these same populations and regions. Analyses of the nine other SSR markers that have been sampled from this same material are currently underway. It will prove challenging (but nevertheless informative) to compare the information and diversity of those more labile markers with those found for the highly stable markers used here, and we expect to ‘flesh out the story’.

SUPPLEMENTARY DATA

Supplementary data are available online at https://academic.oup.com/aob and consist of the following. Table S1: voucher data for Sphagnum × falcatulum, S. ×irritans and S. cuspidatum. Table S2: allelic data for Sphagnum × falcatulum, S. × irritans and S. cuspidatum at five ancestrally indicative markers. Table S3: data sheet showing format for triploid analysis of the Tasmanian hologenomic data in GenAlEx. Table S4: results of Shannon analysis of the Tasmanian triploid data using the ‘Partition’ option.