Asexual reproduction through clonal seed (apomixis) offers reproductive assurance to isolated individuals1 and is often associated with colonising species that have wider geographic distributions than their sexual counterparts2. Apomixis is widespread among angiosperm families3, but occurs more frequently in the Asteraceae, Poaceae and Rosaceae4,5, where it is associated with polyploidy6. Many apomicts are also pseudogamous, which means that they require pollen to develop functional endosperm for the maturation of their otherwise clonal seed. For species with a pseudogamous apomictic (PA) breeding system, the requirement for pollination may limit seed set just as it often does in sexual species7.

In the Rosaceae, many polyploid pseudogamous apomicts are self-compatible8, which enables seed set through autogamous (within flower) or geitonogamous (within individual) pollen transfer. Curiously, however, some PA species in the Rosaceae are self-incompatible (SI)9, which means that they require heterospecific pollination by congeners. SI-PA species possess a breeding system that seemingly exposes them to the pressures of pollen-limitation without conferring any obvious adaptive benefits. We investigated the performance of this perplexing breeding system in a woodland community of a rare member of the Rosaceae, a putatively self-incompatible triploid Sorbus species.

Pollen-limited seed set can have various causes related to the quantity and quality of pollen available to females10. Factors that limit the quantity of pollen delivered to stigmas include flowering asynchrony between males and females and inadequate service from pollen vectors (insects or wind). Pollen quality limits seed set when too much of the pollen that reaches a female’s stigmas is incompatible. SI-PA species are therefore vulnerable to seed limitation by both the quality and quantity of pollen available to females caused by spatial isolation from compatible congeners. The degree of limitation can be measured by the increase in seed produced when pollen is added to the stigma by hand11, but the ecology of pollen-limited seed set in PA species has rarely been investigated.

The focal species for the present study is a member of the genus Sorbus L., which comprises small and medium-sized trees that produce corymbs of showy, hermaphrodite flowers during late spring and early summer. In common with many other members of the Rosaceae12,13, the floral architecture in Sorbus is entomophilous and its flowers attract generalist flower-visiting insects, mainly bees14. Diploid Sorbus species are typically self-incompatible out-crossers13,15, but Sorbus also contains apomictic polyploids derived from hybridisation3,16. Recent speciation is evident in Sorbus17,18,19 and was likely favoured by breeding systems where apomixis is facultative and possibly coupled with triploid self-incompatibility9. This infrequent sexual route for gene exchange among otherwise clonal species provides the raw variation for adaptation20, whilst apomixis maintains the new gene combinations and enables sympatric speciation4. However, although SI-PA breeding systems may be responsible for diversification in Sorbus, for the species concerned the proximity of suitable mates in both space and time may threaten population sustainability by constraining seed production.

In Sorbus, many polyploid species have small population sizes and a high degree of endemism, which are both features of conservation priority species21. Threats to the persistence of rare Sorbus species arise principally from changing land use, browsing by herbivores (which also prevent recruitment) and competition from invasive non-native plant species16. Conserving this evolutionarily dynamic group relies on understanding the factors that affect population viability, which include the influence of pollination on seed production. In order to measure the extent to which pollen limitation constrains seed production in a threatened PA species in Sorbus, we investigated the pollination and breeding system of the slender whitebeam, Sorbus subcuneata Wilmott, which is putatively self-incompatible.

Sorbus subcuneata is a rare triploid species that is endemic to nine sites in Devon and Somerset (southwestern United Kingdom), where it co-occurs with six closely related tetraploid congeners and the common diploid S. aucuparia L.16,22. Sorbus subcuneata typically occurs at low relative density as an understorey tree, so spatial isolation may be a constraint on seed production. Here, we report an investigation of the breeding system and pollination ecology of S. subcuneata in which we determined: (1) the species’ pollination requirements (i.e. compatibility with conspecific and heterospecific pollen); (2) the extent to which seed set is limited by pollination; and (3) the factors that imposed pollination-limited seed set. Specifically, we evaluated whether pollination limitation arose through either temporal isolation imposed by flowering asynchrony between compatible pollination partners or by spatial isolation of females from suitable male pollen donors.


Breeding system

We confirmed that triploid S. subcuneata is an obligate pseudogamous apomict, because hand-pollinations demonstrated that seed production required pollination (Table 1) and microsatellite analysis revealed that all of the 95 embryos studied had microsatellite phenotypes that were identical to both their maternal tree and the S. subcuneata reference samples shown in Table S1, Supplementary Information.

Table 1 Fruit production at three time intervals after manual pollination with final seed production for four pollination treatments carried out on cultivated specimens of S. subcuneata.

We found that S. subcuneata set seed readily through hand-pollination with congeneric S. admonitor pollen, with a flower-to-seed conversion rate of 65% (Table 1). In contrast, 93 hand self-pollinations failed to produce even a single seed. We calculated the highest rate of flower-to-seed conversion that is statistically consistent with zero seed in a sample size of 93 as 3%. Hand-pollination with diploid S. aucuparia also failed to yield seed and where pollen was removed and excluded, only one seed developed which contained alleles from S. admonitor, so was considered a result of pollen contamination.

Microsatellite analyses of wild-collected seed showed that endosperm formation resulted from heterospecific pollination by S. admonitor in approximately half of the seeds and the other half resulted from self-pollination (Table 2 and Fig. 1). Very rarely (<2% of seeds), the endosperm resulted from pollination by either S. margaretae, which is one of the other tetraploid species on the study site (<10 individuals) or diploid S. aucuparia.

Table 2 Summary of paternity results of microsatellite analysis of seed endosperm from a total of ten maternal S. subcuneata trees over two years.
Figure 1: Distribution map of polyploid Sorbus species at the woodland site.
figure 1

The locations of S. subcuneata maternal seed trees are indicated by pie charts. The sections of the pie charts represent the proportion of seed resulting from pollination (2014 data) by;  = S. subcuneata or  = S. admonitor,  = other.  = S. margaretae,  = S. porrigentiformis. Survey data supplied by Rich and Cann, (2009) ref. 46. (The map was created using ArcGIS Desktop version 10.2.2, ESRI, California, USA, URL:

Causes of pollen-limited seed set

Virtually no seed was produced by 1534 open-pollinated S. subcuneata flowers on three trees (mean flower to seed conversion rate = 0.5%, SD = 0.46, n = 3 trees). Seed production was not limited by the availability of pollen alone because we observed that 88% of two-day old flowers had more than 50 pollen grains on their stigma which had accumulated fairly rapidly over three days (Fig. 2; χ2 = 12.11, d.f. = 1, P < 0.001). Pollen deposition varied between the two trees studied (χ2 = 7.7, d.f. = 1, P = 0.005). This pollen accumulation was probably in part due to the activities of the insect pollinators (Bombus spp., Apis melifera, Diptera and Lepidoptera) that we observed visiting the flowers.

Figure 2: Pollen deposition on the stigmas over the three day life of S. subcuneata flowers.
figure 2

Lines show fitted values (±1 SE) from a negative binomial GLM (square root pollen count = 11.64 [±2.84] + 5.15 [±1.41] *age - 5.47 [±2.06] *tree, where tree 1 is the reference category). Pseudo R2 = 0.102. Tree 1 (upper line): n = 58 flowers; tree 2 (lower line): n = 68.

Seed production in open-pollinated flowers of S. subcuneata was strongly limited by the availability of congeneric pollination because supplementation with pollen from S. admonitor yielded a flower-to-seed conversion rate of between 12% and 16% (Table 3), whereas those flowers that received no congeneric pollen supplementation yielded no seed.

Table 3 Summary of fruit and seed production for two pollination supplementation treatments carried out on two maternal S. subcuneata individuals (S01 and S02).

The lack of congeneric pollination was not the result of asynchrony in blooming of S. subcuneata with S. admonitor. Pollen flow between these species is certainly possible because the mean flowering day (MFD) was similar for both species (9.4 for S. admonitor, n = 6; 11.0 for S. subcuneata, n = 7) and there was no significant difference in F50 (occasion of 50% of flowers open, Wilcoxon test, W = 12; P = 0.23; Fig. 3a and b). Instead, spatial isolation of the maternal trees from compatible pollen donors limited pollen flow between them because the proportion of seed resulting from heterospecific pollination decreased significantly with increasing spatial isolation (i.e. decreasing connectivity) of maternal S. subcuneata seed trees from S. admonitor individuals (Binomial GLM: connectivity likelihood ratio test, χ2 = 4.78, d.f. = 1, P = 0.029; pseudo-R2 = 0.33; Fig. 4).

Figure 3
figure 3

(a) Flowering phenology of individual trees of both species over a 16 day flowering period. Each line indicates the flowering period of an individual tree; dots represent the 50 percentile stage of the cumulative flowering curve; S. subcuneata (•) n = 7 and S. admonitor (o) n = 6. (b) Flowering phenology of both species combined S = S. subcuneata, A = S. admonitor.

Figure 4: Relationship between the connectivity of the maternal S. subcuneata seed trees to S. admonitor and the proportion of seed sampled with S. admonitor as pollinator (2014 data).
figure 4

The line shows the fitted values (±1SE) for a weighted binomial GLM of: logit (proportion of seed) = −119.1 (±60.1) + 0.81 (±0.41)* connectivity. N = 71 seeds from 10 trees.

Despite the substantially greater efficacy of congeneric pollination in producing seed, male contributions from S. admonitor and S. subcuneata were represented fairly equally among endosperms of open-pollinated flowers (Table 2) probably because of the relatively high frequency of geitonogamous pollinations. Specifically, based on the relative flower-to-fruit conversion rates we estimate that the ratio of conspecific: heterospecific pollination is R = 22:1 (see Tables 1 and 2 and equation 1; S = 49.5, Cs = 0.03, A = 48.5, and Ca = 0.65).


We found that S. subcuneata is normally an obligate apomict. The lack of autonomous endosperm development in our hand pollination control group (no pollen added) confirms S. subcuneata as pseudogamous, requiring pollination for successful endosperm formation and seed production in common with other apomictic Sorbus spp.9,23. Thus, the successful pollination of S. subcuneata flowers very rarely affects the genotype of the embryo of resulting seed. Our hand pollination experiments showed that the sympatric tetraploid S. admonitor is by far the most effective pollinator for S. subcuneata on our study site. Indeed, S. subcuneata is strongly dependent on its congener because self-pollen is so poorly compatible.

The most likely explanation for the lack of seed produced by conspecific hand pollination is that S. subcuneata has a system of gametophytic self-incompatibility (GSI), which has been observed in other triploid Sorbus species9. GSI is caused by a disruption of the pollen tube before it reaches the ovules and it is controlled by a multi-allelic S-locus. GSI occurs when the pollen tube has an S-allele in common with the pistil and it is the cause of GSI in diploid Sorbus but appears to break down in polyploids with tetraploids exhibiting self-compatibility24. High prevalence of inviable pollen is an alternative explanation for the widespread failure to set seed by self-pollination, but this is unlikely because the pollen grains from S. subcuneata observed during our study appeared rounded and well-formed and had a higher than average (of triploids tested) stainability25, a proxy for pollen viability. We are unable to exclude the possibility that seed failure after selfing is also due to an imbalance between maternal and paternal genome components (m: p) in the endosperm tissue. The 2 m:1p genome ratio of maternal to paternal contributions to the endosperm in sexual species is considered a prerequisite for successful seed development26. In pseudogamous apomicts, the lack of meiotic division leads to unreduced central cell polar nuclei in the ovary and fertilisation of these results in m:p ratios that greatly exceed 2 m:1p. However, triploid Sorbus such as S. subcuneata can tolerate an unbalanced endosperm, which is an attribute shared with other triploid apomicts in the Rosaceae9,27,28. Thus it seems unlikely that the self-incompatibility that we observed in S. subcuneata is due to unbalanced endosperm and, instead, the lack of seed production by hand conspecific pollination is likely the result of the operation of GSI.

Despite the greater efficacy of pollination from S. admonitor compared to self-pollination, about half of the seeds in open-pollinated flowers arose from conspecific pollination. This finding contrasts to other studies on triploid Sorbus9 and suggests that the GSI system in S. subcuneata is partial, but with a very low rate of success. Self-incompatability can be a quantitive and plastic trait affected by environmental conditions such as temperature at flowering, the composition and density of the pollen load and the internal stylar conditions which change with flower age29. A mentor effect whereby a mix of heterospecific and self pollen on the stigma may reduce heterospecific pollination from plants of different ploidy and promote increased selfing in natural mixed ploidy populations30. Mentor pollination is widely used as a tool to overcome incompatibility in commercial plant breeding31. S. subcuneata stigmas pollinated towards the end of the flower life may show reduced self-incompatibility since pollen/pistil interactions during pollen tube growth change with flower age and can allow successful self pollination as opportunities for cross pollination reduce29. Whilst these mechanisms may be responsible for a relaxation in self-incompatibility, we cannot rule out the possibility that potentially unsampled genotypes in the S. subcuneata population may carry alternative S alleles, conferring pollen/pistil compatability and allowing succesfull pollination, although we were unable to find evidence of genetic variation among both seed embryos and adult trees sampled at the study site. The low rate of seed production despite ample pollen deposition in naturally pollinated flowers, however, suggests self-compatibility is a rare phenomenon in S. subcuneata.

At our study site, the diploid congener, S. aucuparia, was more common than S. admonitor, but it was an ineffectual male parent. S. aucuparia can successfully pollinate other triploid Sorbus16,17, which shows that compatibility is not determined solely by the comparative ploidy of the parents. The relative efficacy of pollination by tetraploid S. admonitor in enabling seed set in closely related triploid S. subcuneata probably reflects a broad gametophytic compatibility that permits the successful growth of pollen tubes.

The most striking feature of reproductive ecology in S. subcuneata is the low frequency of seed set. At our study site, less than one percent of S. subcuneata flowers eventually produced a seed. We observed that open-pollinated flowers of S. subcuneata frequently produced parthenocarpic fruits, which suggests that sufficient resources were available for fructification. Further, the low frequency of seed set that we observed was not attributable to the quantity of pollen received by flowers. The flowers of S. subcuneata each accumulated an average of 191 grains per day on their stigmas and almost all appeared to be well-pollinated during the three-day duration of anthesis. Normally, the arrival of a minimum or four to six pollen grains per ovule are required for maximum seed set32 so there is no evidence that seed set in S. subcuneata is limited by the quantity of pollen on its stigmas. Instead, we conclude that the principal limit to seed set is the quality of the pollen that arrives on the stigmas. Specifically, we argue that seed set was limited by the availability of pollen from its congener, S. admonitor for two reasons. First, controlled hand-pollination with congeneric pollen greatly increased seed set in otherwise open-pollinated flowers. Second, despite congeneric pollen being more than twenty times more likely than conspecific pollen to initiate seed set, only half of the seeds from successfully open-pollinated flowers contained endosperm with congeneric paternity. Consequently, conspecific pollen must predominate numerically on stigmas over congeneric pollen by the corresponding factor of approximately twenty.

Congeneric pollination from S. admonitor was not restricted by asynchronous flowering with S. subcuneata, but instead a major result of our study is to show that the availability of congeneric pollen depended on the relative proximity of Sorbus congeners.

It is likely that much of the pollen on the stigmas of S. subcuneata arrived by insect vectors because we frequently observed bees and flies actively foraging among the entomophilous flowers. Flower-visiting insects tend to make short-distance inter-flower movements when flowers occur in localised patches. Each individual tree of S. subcuneata displays hundreds to thousands of flowers simultaneously in anthesis, which enables insects to forage locally and so promotes geitonogamous (within-display) pollen transfer. Consequently, these insects were probably responsible for the preponderance of conspecific pollen on S. subcuneata stigmas.

At our site, spatial isolation between congeners is compounded by the locally disjunct distributions of S. subcuneata and S. admonitor (Fig. 1). Potentially, insect-mediated pollen transfer can span large distances33,34,35, but understorey Sorbus individuals receive most of their incoming pollen from neighbours. Our study site is less than two kilometres across and potentially pollen could be transported between any two trees15, but the area-restricted movements of flower visitors mean that geitonogamy and short-distance dispersal probably dominated in pollen transfer.

The proportion of seed produced from self-pollination was unrelated to the maternal tree’s proximity to other S. subcuneata trees, which further suggests that the large amounts of Sorbus pollen that accumulated on the flowers of the maternal trees was principally geitonogamous in origin. Moreover, of S. subcuneata and S. admonitor on the study site, the closest extrinsic sources of pollen for maternal S. subcuneata seed trees were normally other individuals of S. subcuneata, not congeners (Fig. 1). Since S. subcuneata is effectively clonal, due to its apomictic mode of reproduction, pollen from these conspecific individuals is likely to be as incompatible as that from the maternal tree itself. Together, these attributes could place additional barriers to heterospecific pollination since high levels of geitonogamous pollination will result in increased competition for space on the stigma from unsuitable self-pollen, or ‘stigma clogging’36,37. Whilst pollen carryover will, to some extent alleviate the effects of geitonogamous pollinator movements38, the normally rapid attenuation of carryover39,40 and localised movements of insect vectors make it inevitable that insect-mediated pollen transfer among large floral displays remains highly restricted in space41.

Our study suggests that seed production is likely to be particularly limited in SI-PA species whose individuals are either spatially isolated from compatible congeners or are dispersed in clusters of identical cytotypes. It is likely that our finding applies to some other Sorbus triploid species in the UK42, which typically exist as small populations sometimes numbering only a few trees43. Consequently, effective strategies of conservation management are critical, which we begin to formulate below.

Low rates of seed production such as we have observed make population sustainability particularly precarious in Sorbus, which is a palatable species in which recruitment from seeds is threatened by browsing from deer16 that exist in large numbers at our study site. When seed production is chronically low, conservation strategies should seek to increase recruitment opportunities to maximise the germination chances of the few seeds currently produced and control herbivore populations. Based on our findings about the reproductive ecology of S. subcuneata, however, we urge conservationists also to consider stewardship strategies that encourage close proximity of compatible congeners, which will mitigate pollination-limitation of seed set.

Serendipitously, a strategy that ensures congeneric proximity for ecological reasons is likely also to help to sustain evolutionary diversity in the Sorbus lineage. The extremely low reproductive output of S. subcuneata in our study population is inherent in its breeding system, which is seemingly maladaptive in a population comprised of a single-cytotype whose individuals have limited access to compatible heterospecific pollen donors. Indeed, although it has been previously predicted on theoretical grounds that SI-PA species should not persist44, we have observed a long-established population of c. 300 such trees at our study site. However, although triploids such as S. subcuneata may be relatively transient over evolutionary timescales, any capacity for occasional sexual reproduction following congeneric cross-pollination (facultative apomixis) means that they may form important evolutionary stages as part of a recurring process of polyploid formation. The products of facultative apomixis will continually diversify the lineage45 because the preponderant involvement of heterospecific pollination in these events increases the frequency of opportunities for hybrid events. In the case of S. subcuneata, for example, the high level of allele sharing between S. subcuneata and S. admonitor suggests recently shared origins from an active process of reticulate evolution by hybridisation. We therefore speculate that a strategy that promotes the proximity of congeners in order to safeguard levels of seed set simultaneously safeguards an evolutionary process in which extinctions of transient microspecies are offset by diversifying hybridisation.

Materials and Methods

Study system and sites

We studied a natural population (c. 300 trees) of triploid Sorbus subcuneata on a woodland site where it occurs with c.100 trees of tetraploid S. admonitor M.C.F. Proctor and abundant diploid S. aucuparia46. We focussed our study on these three species as they are all potential pollen sources for S. subcuneata, although small numbers of three other tetraploid Sorbus species are also found on site: S. porrigentiformis E.F. Warb.; S. margaretae M.C.F. Proctor and Sorbus vexans E.F. Warb. For convenience, pollen compatibility experiments were carried out on two trees held in a collection belonging to the Exmoor Natural History Society (Luckbarrow, West Luccombe, Somerset, UK).

Investigation of the breeding system of Sorbus subcuneata

To determine whether S. subcuneata is a SI-PA species, we tested pollen compatibility and whether pollen is required for apomictic seed production (pseudogamy) as follows: (1) pollen added from the same species to test for conspecific compatibility; (2) pollen added from S. admonitor (4x); (3) pollen added from S. aucuparia (2x); (4) no pollen added to test for autonomous apomixis. All maternal S. subcuneata flowers were emasculated on opening and pollen supplementation was conducted 24 hours later to allow stigma maturation. Twenty inflorescences on each of the two maternal trees were randomly assigned to each of the four pollination treatments. We excluded insect pollinators by placing a mesh bag over both the study and pollen donor inflorescences. To reduce the potential effect of resource limitation on seed set, all other inflorescences were removed from the experimental branches. After the application of pollen, the pollen exclusion bags were then replaced for a week to prevent natural pollination. Successful pollination was measured by the production of at least one seed per fruit and calculated as a flower-to-seed conversion rate. Where there was a failure to produce seed in any treatment, we used the binomial theorem to determine the maximum successful conversion rate that would be statistically consistent with this observation at this sample size. The binomial function can be used to calculate P (x), the probability of x successes in n trials. If the probability of success in a single trial is denoted p, then P(x) is given by:

Thus, given the condition that x = 0, we solved equation (1) for the maximum value of p such that P(x) = 0.05, which identified the greatest success rate at which n flowers producing zero seed is not statistically significant at the conventional level. In effect, we determined the upper 95% confidence interval on p. In addition, we also calculated the overall flower-to-seed conversion rate of naturally pollinated flowers from three trees on the woodland site.

To verify that S. subcuneata is an obligate apomict and determine whether interspecific pollen flow contributes to endosperm fertilisation, we used ten nuclear microsatellites previously used for Sorbus taxa to genotype the embryo and endosperm of wild-collected, naturally-pollinated seed collected from a total of ten trees in two fruiting seasons (2013 and 2014). Seed embryos produced by apomixis will have a genotype identical to that of the maternal tree. Pollen donors were identified through the presence of their unique alleles in a seed’s endosperm and the proportion of seed resulting from pollination by each congener was calculated. All Sorbus species on site were sampled and subjected to genetic analysis to provide reference samples for comparison genotypes. Since polyploid Sorbus species are effectively clonal, microsatellite alleles could only be matched to species, not individuals. DNA extraction of leaf and seed material followed QIAGEN DNeasy Plant Minikit protocol. For microsatellite details and PCR conditions see Supplementary Table S2 and Supplementary Methods and references therein. Only samples that successfully amplified across all loci were included in the endosperm paternity analysis with the exception of locus MS14, which only amplified in S. admonitor, S. subcuneata and S. aucuparia.

To estimate a conspecific: heterospecific pollination ratio of the woodland population we compared the proportion of seed resulting from natural pollination by each congener with the flower-to-seed conversion rates of hand pollinated flowers. The estimated ratio, denoted R, was calculated by:

where S = total proportion of seed sired by S. subcuneata, Cs = flower-to-seed conversion rate for S. subcuneata pollination, A = total proportion of seed sired by S. admonitor, and Ca = flower-to-seed conversion rate for S. admonitor pollination.

Testing pollen limitation of seed set in the natural population

To investigate whether pollen quantity limited seed production in the woodland population of S. subcuneata, we recorded pollen deposition on flower stigmas of two S. subcuneata individuals over six days from the onset of flowering until the peak. To determine the amount of pollen on each stigma, a squash preparation was made by softening each sample in sodium hydroxide (8 M NaOH for 10 mins. at 60 °C) before counting the number of pollen grains at x10 magnification. The accumulation of pollen on the flowers of both trees was modelled using a negative binomial generalised linear model (GLM) with square-root link function, which allowed for over-dispersed data. We tested effect of tree and flower age on pollen counts using likelihood ratio tests. This analysis was implemented in the statistical software R47.

To investigate whether seed production was limited by pollen quality, we tested whether the application of supplementary compatible pollen increased seed production in open-pollinated flowers of woodland S. subcuneata. Based on the outcome of compatibility testing (see Results), we used tetraploid S. admonitor as the most favourable male donor. On two maternal trees of S. subcuneata, ten inflorescences were selected and each was randomly assigned to one of two treatment groups. Group ‘O’ was left to open pollinate naturally whereas group ‘H’ had heterospecific pollen applied from S. admonitor. We assessed the extent of the pollen deficit by comparing the flower-to-seed conversion rate between the H and O treatments.

To investigate whether temporal isolation (asynchronous flowering) could limit pollen flow between maternal trees of S. subcuneata and their congeneric pollinator, S. admonitor, we quantified the flowering periods of six trees of each species, throughout the 17-day flowering period during May. Every two days, we estimated the proportion of flowers in bud, fully open or in senescence, which was evident because the anthers and petals turned visibly brown. To test for flowering asynchrony between S. subcuneata and S. admonitor, the relationship of the cumulative proportion of opened buds on each tree over time was fitted by a sigmoid curve, which we used to estimate the time to 50% of flowers open, denoted F50. Variation in F50 between the two species was analysed using a Wilcoxon Rank-Sum test. For each species, we determined the mean flowering day (MFD), equation (3) 48, in which % Fli is the mean percent of the flowers at anthesis on observation day i and Daysi is the number of days elapsed at dayi from the start of the observation period:

To investigate whether spatial isolation (i.e. spatial separation of maternal trees from compatible pollen donors) could limit seed set in S. subcuneata, we used the genetic paternity data (see microsatellite analysis) and correlated the proportion of seed attributable to S. admonitor with the maternal tree’s ‘connectivity’ to all potential S. admonitor males. The connectivity (Si) for each maternal tree i to every potential paternal tree j was determined by:

where α modulates the effect of distance between trees i and j, denoted di,j, in a negative exponential decay kernel; Ai is the crown size of maternal tree I; Aj is the crown size of pollen donor j; and b and c are exponents that scale the impact of tree size on pollen export and import49. Connectivity analysis was executed using the SI software50. To implement the model, we set α = 0.01 from pollen dispersal patterns measured for S. torminalis15 and assumed that connectivity was unaffected by the size of the maternal tree because female function is typically satisfied by few pollinator visits51 (i.e. c = 0) and that male success saturated with increasing tree size (b = 0.5)15. Distances and crown size were calculated from survey data which had measured location, stem diameter and fruiting for all the polyploid Sorbus species on the study site46. Crown size (area) was derived from the measurements of diameter at breast height (DBH) using the standard forestry relationship for the architecturally similar congener, S. aucuparia52. In the analysis, we included only trees of flowering size (trees > 3 cm DBH for S. admonitor and >2 cm DBH for S. subcuneata).

Using values calculated from equation (4), we tested whether the proportion of seed derived from heterospecific pollen (here S. admonitor) produced by each maternal tree (% of total seed) was explained by the connectivity of the maternal seed trees to all S. admonitor. To test this hypothesis, we used a GLM with a binomial error and logit link function in which the contribution of seed proportion was weighted by the sample size (number of seeds per tree). This analysis was implemented in the statistical software R47. All relevant model assumptions were checked by examining the model deviance residuals and AIC (Akaike information criterion) values were used for model comparisons.

Additional Information

How to cite this article: Hamston, T. J. et al. Breeding system and spatial isolation from congeners strongly constrain seed set in an insect-pollinated apomictic tree: Sorbus subcuneata (Rosaceae). Sci. Rep. 7, 45122; doi: 10.1038/srep45122 (2017).

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