Sex ratios and clonal growth in dioecious Populus euphratica Oliv., Xinjiang Prov., Western China

Sex ratios and clonal growth in dioecious Populus euphratica Oliv., Xinjiang Prov., Western China Anne Petzold, Tanja Pfeiffer, Florian Jansen, Pascal Eusemann & Martin Schnittler Trees Structure and Function ISSN 0931-1890 Trees DOI 10.1007/s00468-012-0828-y

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Author's personal copy Trees DOI 10.1007/s00468-012-0828-y

ORIGINAL PAPER

Sex ratios and clonal growth in dioecious Populus euphratica Oliv., Xinjiang Prov., Western China Anne Petzold • Tanja Pfeiffer • Florian Jansen Pascal Eusemann • Martin Schnittler

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Received: 27 April 2012 / Revised: 21 November 2012 / Accepted: 3 December 2012 Ó Springer-Verlag Berlin Heidelberg 2012

Abstract Using a microsatellite assay, we investigated sex ratios at three levels (apparent, intrinsic, genet) for Populus euphratica stands in Xinjiang, China and possible consequences of sex-specific costs of reproduction in terms of clonal growth and individual growth or mortality. Sex ratios at all levels tended to be male biased (60 % of 3,295 flowering trees were male), although male excess was least pronounced at the genet level (52 % of 850 genets were male). Male clones comprised significantly more (708 vs. 572) trees than female clones. Reproductive investment was measured in terms of carbon (C) and nitrogen (N) contents of male and female reproductive organs: single flowers or fruit capsules, whole inflorescences or infructescences, and whole branches of ca. 2 cm diameter. Male flowers and catkins require less N than female fruits and catkins, but on average only 16 % of female catkins develop into fruits. This changes the measured investment for reproduction at branch level: now male branches spent 3.3 times more N than their female counterparts. This coincides with the annual increment of branches, measured as a possible trade-off for costs of reproduction: female branches needed 2 years less to reach a diameter of 2 cm. We conclude that full fruit set of females would give males a heavy comparative advantage, but frequent abortion of Communicated by A. Franco.

Electronic supplementary material The online version of this article (doi:10.1007/s00468-012-0828-y) contains supplementary material, which is available to authorized users. A. Petzold (&)  T. Pfeiffer  F. Jansen  P. Eusemann  M. Schnittler Institute of Botany and Landscape Ecology, Ernst-Moritz-Arndt-University, Grimmer Str. 88, 17487 Greifswald, Germany e-mail: [email protected]

whole infructescences by females seems to be a powerful mechanism to compensate a higher reproductive effort, thus avoiding a pronounced runaway effect by more vigorous clonal growth of male trees over a long time. Keywords Annual increment  Clonal growth  Microsatellites  Populus euphratica Oliv.  Resource allocation  Sex ratio

Introduction Although dioecious plant species account for just 4 % of all plant species (de Jong and Klinkhamer 2005), dioecious plants received much attention in research. Separated male and female individuals make them well suited to investigate sexual dimorphism in life history traits, which may affect sex ratios, i.e. the proportion of male vs. female individuals or genets within a population. Under natural selection an even seed or ‘primary’ sex ratio (Obeso et al. 1998) should be maintained by negative frequency-dependent selection in growing and mature plant populations (Fisher 1930; Barrett et al. 2010). However, many studies about sex ratios of flowering plants found biased relations of sexes (reviewed in Willson 1983; Delph 1999; Sinclair et al. 2012). From 126 dioecious species, which were nearly all investigated at reproductive stage (reviewed by Barrett et al. 2010), only 33 % exhibited fairly even sex ratios, but 46 % had male biased and 21 % female biased ratios. These results support the common assumption that males benefit from their lower reproductive investment (RI), whereas females suffer higher total costs of reproduction due to the development of seeds and fruits (review in Delph 1999; Leigh et al. 2006). Accordingly, females often show reduced growth and/or have

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lower survival rates (Allen and Antos 1993; Rocheleau and Houle 2001). Furthermore, sensitivity against herbivory is often higher than in males, first flowering occurs at an older age or larger size, flowering is less frequent and vegetative reproduction is often less vigorous than in males (de Jong and Klinkhamer 2002; Obeso 2002 and references therein). However, there are also studies which could not find differences in life history traits (Sakai et al. 2006; Milla et al. 2006; Queenborough et al. 2007). This indicates the existence of compensatory mechanisms for the higher RIs of females (Tuomi et al. 1983). Obeso (2002) gives a detailed overview of the various compensatory responses which may include different timing of vegetative growth and reproduction (Matsuyama and Sakimoto 2008), niche partitioning among sexes (Dudley 2006) and an increased photosynthesis during reproduction (Nicotra et al. 2003). For clonally growing dioecious plants, we have to differentiate between effects on individual performance (slower growth and, ultimately, higher mortality of individual plants, i.e. ramets) and effects on clonal growth (different rates of clonal growth, leading to differences in clone size between the sexes). Consequently, the level at which a bias in sex ratios occurs is important to draw conclusions about the possible reasons of such a bias. Beside the ‘primary’ (seed) sex ratio, Allen and Antos (1993) differentiated three levels for sex ratios in populations of clonal plants: (1) flowering ramet (apparent) sex ratio, (2) ramet (intrinsic) sex ratio and (3) genet (‘secondary’) sex ratio. From these, only the apparent sex ratio is easy to observe, as in virtually all plants sexes can only be recognized in flowering state, although exceptions occur (e.g. Silene alba Mill. with a heterogametic sex determination system, Westergaard 1958). For non-clonal plants with all individuals flowering, the apparent sex ratio equals the genet sex ratio. However, as pointed out by Alliende and Harper (1989), Allen and Antos (1993) and Barrett et al. (2010), most dioecious plants are perennial and capable of clonal growth. Consequently, biased sex ratios may be prevalent at the level of shoots (ramets) but not necessarily at the genet level. Within the Salicaceae as one of the few predominantly dioecious plant families clonal growth can cause highly biased apparent sex ratios (reviewed in Willson 1983; Alliende and Harper 1989; see further Kemperman and Barnes 1976; Douhovnikoff et al. 2005). Examples for the genus Populus are given by Rottenberg (1998, 2000) for P. euphratica Oliv. and by Falinski (1980, 1986) for P. tremula L., who both found unisexual stands or stands with extremely biased sex ratios, presumably the result of clonal growth. Gom and Rood (1999a, b) reported a female biased apparent sex ratio (1.8:1) for mixed stands of P. deltoides Marshall and P. balsamifera L., which changed to an even sex ratio at the genet level. Although clone

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assignment through morphological parameters seems to be applicable in special cases (Barnes 1966; Gom and Rood 1999a), the development of molecular markers, especially microsatellites (SSR—simple sequence repeats), offered a universal and reliable method for clone identification (Arnaud-Haond et al. 2005; Suvanto and Latva-Karjanmaa 2005; Reisch et al. 2007; Eusemann et al. 2009). In this study, we combined SSR genotyping and field observations to carry out a large-scale analysis of sex ratios and clonal growth in P. euphratica in Western China. Our aim was to determine sex ratios at both the ramet (apparent and intrinsic) and the genet (clone) level and to investigate the relationship among sex ratios, clonal growth and costs of reproduction for male and female trees. Consequences of sex-specific resource allocation can be twofold: first, one sex may show lower individual performance (less growth and/or higher mortality of single trees, i.e. ramets). Second, one sex may form larger clones leading to increasingly biased sex ratios at apparent and intrinsic level. In detail, we asked the following questions: 1. Do sex ratios on the three levels, i.e. flowering trees (apparent), all trees (intrinsic) and genets, deviate from an 1:1 ratio? 2. Do male and female trees differ in their investment into sexual reproduction?

Materials and methods Study species Populus euphratica Oliv. (Salicaceae) is a dioecious, obligate phreatophytic riparian tree species (Gries et al. 2005) occurring discontinuously within the continental-arid climate region from North Africa to Central Asia (Browicz 1977; Wang et al. 1996). Along the Tarim River in Xinjiang, China this poplar forms monospecific stands of so-called Tugai forests (Thevs et al. 2008). At the middle reaches of the Tarim P. euphratica flowers from late March to early (mid) April. Flowering of both sexes starts at an age between 10 and 12 years (Wiehle et al. 2009); flower colour of both sexes is usually red (with variations in intensity), but about 6 % (pers. obs.) of all investigated male and female trees had green flowers (see also Wang et al. 1996). Seeds are released in late August to September, which coincides with the annual flood of the Tarim River. The short-lived seeds germinate often already when still floating in water and are deposited at river banks, thereby forming rows of seedlings parallel to the river course. Seedlings survive only near river beds, where the groundwater level remains high for the first years. In older stands, establishment of new trees occurs only through clonally grown root suckers (Sharma et al. 1999); hence root suckering is a highly successful strategy to close gaps

Author's personal copy Trees Fig. 1 a Location of the Tarim Huyanglin Nature Reserve (hatched) c along the middle reaches and the stand Argan (Arg) at the lower reaches of Tarim River, Xinjiang Province, Western China. b Location of the studied P. euphratica stands in the reserve in relation to Tarim River. Plots with open circles were mapped for apparent sex ratios; plots with closed circles include genotyped sections. Triangles denote young stands checked for age at first flowering

between germination rows and form contiguous forests. Clonal growth starts at an age between 11 and 15 years and root suckers grow from lateral roots up to 40 m away from the parent tree (Wiehle et al. 2009). Root suckering ceases if groundwater levels drop below 3–5 m. As river beds are in constant move, stands die off at groundwater levels below 10–13 m; and despite being a pioneer species P. euphratica is never replaced by other trees within later succession (Thevs et al. 2008). Like all Salicaceae P. euphratica lacks definite sex chromosomes (Peto 1938; van Buijtenen and Einspahr 1959; Sharma and Chattopadhyay 1991; Alstro¨m-Rapaport et al. 1997), and sex-linked markers are still unknown (McLetchie and Tuskan 1994; Alstro¨m-Rapaport et al. 1998). Thus, it is not yet possible to sex seeds or nonflowering trees of P. euphratica directly, but the latter can be sexed indirectly through assignment to already sexed clones delineated through genotyping. Study region and sampling design The study was carried out in the Tarim Huyanglin Nature Reserve at the middle reaches of the Tarim River, which is located at the northern fringe of the Taklimakan Desert (Xinjiang Province, Western China, Fig. 1a). The climate is continental-arid with less than 50 mm mean annual precipitation and a mean annual temperature of 11 °C (Liu 1997). Melting waters from the surrounding mountains supply the Tarim River and its tributaries, usually resulting in an annual flood lasting from July (August) to September and replenishing the groundwater reservoirs (Thevs et al. 2008). For apparent sex ratio analyses, we mapped P. euphratica in 19 natural, old-growth plots comprising together 6,761 trees. Only sites without visual impact by agriculture or oil drilling and a negligible influence by former logging were chosen. These 19 plots were arranged into eight stands, uniting all plots in close vicinity to one stand; only the plots FO6, Dune and Arg are geographically isolated (Fig. 1a, b; Table 1). All but one plot is located along the Qayan River, a main tributary of the Tarim River, and around former Tarim River beds 15 and 40 km south of Yengi Bazar (Fig. 1b; Fig. S1 in Supplementary material for exact location of all plots). The last plot (Arg) is located

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ca. 500 km away at the lower reaches of the Tarim River (Fig. 1a). In addition, four young stands at the Tarim River bank were mapped to estimate the age at first flowering (Fig. 1b). All standing trees reaching breast height (ca. 1.4 m, dead or alive) were mapped using a Trimble R3 differential GPS (Trimble Navigation Limited, Sunnyvale, California, USA; horizontal precision 0.1–0.3 m) during the flowering season (late March to mid April) in the years 2005–2007 and 2009. In spring 2011, the data set for the plots Ing8, 10, 11 and YimB was extended; therefore, in Fig. 1b and Table 1, these stands carry the ending ‘ext’ (Table 1; Fig. S1 in Supplementary material for an overview). For all trees diameter at breast height (dbh), sex and flower colour (green, red, light or dark red, reddish brown) were noted. In addition, the often remarkable differences in bud break phenology between the trees of a stand (up to 1 week) were recorded as the relative progress of bud break (stages: leaves still enclosed in bud scales, partially or fully enfolded, extension growth started or not). These context data were used to verify clonal assignment of trees based on microsatellite genotyping (see below). For molecular analyses, three plots for each of the three most intensely studied stands IngII (plots Ing5, 6, 11), IngIII (Ing8, 9, 10) and Yim (plots YimB, E, F) were

chosen; all were easy accessible from our base point Yengi Bazar (Table 2; Fig. 1b). These stands are located at the Qayan River and comprise a total of 3,020 trees. For molecular analyses, fully developed leaves were sampled during repeated visits in late April of the years 2006 and 2009 and dried on silica gel. Microsatellite analyses DNA extraction was carried out using the Invisorb Spin Food Kit II (STRATEC Molecular GmbH, Berlin, Germany) with the following modifications of the manufacturer’s protocol: For lysis, 140 mg dried leaves were grinded with a mixer mill (Retsch, Haan, Germany) and incubated 45 min at 65 °C in 800 ll CTAB-buffer (see Eusemann et al. 2009). RNA was reduced by 30 min incubation at 37 °C with RNase A (AppliChem GmbH, Darmstadt, Germany). DNA was eluted twice with 25 ll of Elution Buffer D. Genotyping was performed with seven nuclear microsatellite (SSR) loci in two multiplex PCRs according to the protocol of Eusemann et al. (2009). PCR products were diluted 1:10 in water. Fragment analysis was carried out with a ABI Prism 310 capillary sequencer and genotyping was performed with the software GeneMapper 3.7 (both

Table 1 Apparent sex ratios and proportions of male trees for eight mapped stands comprising 19 plots of P. euphratica at the middle and lower (Arg) reaches of Tarim River, Xinjiang, China Stand Plot

Ing I Ing1 Ing2

Ing II Ing5 Ing6 Ing11ext

Ing III Ing8ext Ing9 Ing10ext

Yim YimA YimBext YimC–F

FO6 FO6

FO6 II FO6a FO6b

Dune Dune

Arg Arg

Easting (m)

268,857

265,496

266,852

283,482

271,401

268,535

286,162

616,956

Northing (m)

4,559,552

4,560,98

4,570,635

4,579,954

4,523,697

4,548,490

4,569,155

4,442,875

Stand area (ha)

5.5

26.2

8.2

117.9

7.3

10.5

6.2

12.0

R all

194

Mean dbh (m)

0.19

0.46

0.29

0.73

0.40

0.23

0.50

0.33

Trees mapped

609

1,651

1,343

1,566

287

375

170

760

6,761

Dead

369

211

170

557

93

78

3

138

1,619

Living

240

1,440

1,173

1,009

194

297

167

622

5,142

m

79

586

255

536

53

99

77

291

1,976

f

9

403

231

420

37

89

31

99

1,319

451

687

53

104

109

59

232

1,847

nf 152 Flowering male trees (%) Min

32.9

40.7

21.7

53.1*

27.3

33.3

46.1

46.8

38.4

Mean

89.8***

59.3***

52.5

56.1***

58.9

52.7

71.3***

74.6***

60.0***

Max

96.3***

72.0***

80.3***

58.4***

80.9***

70.0***

81.4***

84.1***

74.3***

8.78**

1.45***

1.10

1.28***

1.43

1.11

2.48***

2.94***

1.50***

Apparent sex ratio

Given are plots per stand, geographic position (UTM 45T), stand area, mean diameter at breast height (dbh) and numbers of dead and living trees (m male, f female and nf non-flowering). The mean, minimum and maximum possible proportion of male trees was calculated; the latter two assume that all trees of unknown sex are either female (min) or male (max). Asterisks indicate a significant deviation from a balanced sex ratio (1:1) or a significant excess of male trees (v2 test: * P \ 0.05, *** P \ 0.001)

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Author's personal copy Trees Table 2 Sex ratios and proportions of male trees at three levels (apparent, intrinsic, genet) for three stands comprising nine genotyped plots of P. euphratica

Stand Plot

Ing II Ing5, 6, 11

Ing III Ing8, 9, 10

Yim YimB, E, F

R all

Area (ha)

22

6.35

82

109

Mean dbh (m)

0.43

0.23

0.72

Trees mapped

1,400

899

721

3,020

Dead

182

123

277

582

Living

1,219

776

444

2,439

525

154

229

908

m f

371

152

194

717

nf

322

470

21

813

Min

43.1

19.8

51.6

38.2

Mean Max

58.6*** 69.5

50.3 80.4***

54.1 56.3**

54.4*** 68.8***

1.42***

1.01

1.18

1.20***

By observation

896

306

423

1,625

By genotyping

237

130

2

369

Flowering male trees (%)

Apparent sex ratio Sexed trees

Total

Stands are characterised through stand area, mean diameter at breast height (dbh) and numbers of dead and living trees (m male, f female and nf nonflowering). Proportions of male trees (mean) are given; in addition, we calculated possible ranges assuming that all trees or genets of unknown sex are either female (min) or male (max). Asterisks indicate significant divergence from even sex ratios (1:1) and a significant excess of male trees or genets (v2 test: * P \ 0.05, ** P \ 0.01, *** P \ 0.001) a

Uncertain trees were neither genotyped nor could they assigned to identified clones through matching context criteria (see text). Uncertain trees were not counted for genet sex ratios

1,133

436

425

1,994

m

632

210

230

1,072

f

501

226

195

922

nf (remaining)

86

340

19

445

Min

51.8

27.1

51.8

43.6

Mean

55.8***

48.2

54.1

52.7**

Max

58.9***

70.9***

56.1*

62.0***

1.26***

0.93

1.18

1.12**

Sexed male trees (%)

Intrinsic sex ratio Trees Genotyped

695

616

390

1,701

Assigned

316

8

10

334

Uncertaina

208

152

44

404

Genets (detected)

126

339

385

850

m

68

96

201

365

f

58

101

173

332

nf

0

142

11

153

Min

54.0

28.3

52.2

44.8

Mean

54.0

48.7

53.7

52.1

Max

54.0

70.2***

55.1

59.7***

1.17

0.95

1.16

1.09

Male genets (%)

Genet sex ratio

Applied Biosystems by Life Technologies, Carlsbad, California, USA) resulting in a multi-locus genotype (MLG, Arnaud-Haond et al. 2005) for each analysed tree. In Eusemann et al. (2009), the MLGs based on data from eight SSR loci revealed a high clone resolution with a probability of identity (PID) value of 1.81 9 10-5 over all genets (range: 4.15 9 10-5–1.22 9 10-4). To test for sufficient delimitation between genotypes with only seven

SSR loci in this study, PID was estimated over all genets and plots (IDENTITY 4, Wagner and Sefc 1999). Sex ratios Male to female sex ratios were determined at three levels: (1) apparent sex ratio (all stands) based exclusively on trees observed in bloom, (2) intrinsic sex ratio (genotyped plots)

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based on all trees sexed directly or indirectly by assignment to a clone of known sex and (3) genet sex ratio (genotyped plots) based on all genotypes (clones and singletons). In contrast to the non-symmetrical sex ratio (even at 1, but values can range between 0 and ?), a bias is easier to interpret if the percentage of one sex is calculated. Here, we calculated this symmetrical index (0–100 %) for males. In most plots, trees remained that neither had been genotyped nor could unambiguously be assigned to an identified clone. Therefore, we calculated minimum (min) and maximum (max) scenarios for the proportion of flowering male trees or genets assuming that all trees with unknown sex were either male or female: max ¼

m þ nf  100 % m þ f þ nf

min ¼

m  100 % m þ f þ nf

with m as the number of male, f as the number of female and nf as the number of non-flowering trees (apparent level) or sexed trees (intrinsic level) or genets (genet level). Delimitation of clones and clonal growth Trees with unique MLGs were treated as singletons; a minimum of two trees with identical MLGs constituted a clone. To account for scoring errors or somatic mutations MLGs that differed in one allele were counted as one multi-locus lineage (MLL, Arnaud-Haond et al. 2007), i.e. assigned to the same clone (see Schnittler and Eusemann 2010 for error estimation for a subset of the same dataset). Similar thresholds for clonal identity are employed in other microsatellite studies (Barsoum et al. 2004; De Woody et al. 2009). Clone assignment was verified using the recorded context data (tree position, dbh, sex, flower colour, bud break phenology). Furthermore, we assigned trees which were not genotyped to identified clones if they matched the context data of their putative clone mates. For this, we applied the following criteria: A tree in question must have the (1) same sex, (2) same flower colour, (3) its distance to the putative clone members does not exceed 40 m (the maximum distance where root suckers develop, Wiehle et al. 2009) and (4) bud break phenology of both trees is comparable. In the case of non-flowering trees, the criteria 3 and 4 must be fulfilled and no other possible genotype was allowed to occur within a radius of 40 m. Clonal growth was expressed as an index of clonality, defined as C = 1 - R ranging from 0 in non-clonal to 1 in monoclonal stands. Clonal diversity R was calculated as R = (G - 1)/(N - 1) with G as the number of genotypes found and N as the number of genotyped trees (Dorken and Eckert 2001). Male and female clones were compared in terms of frequency, size (number of trees per clone) and extension. For the latter, we calculated for clones comprising more than two trees ‘convex hulls’ (R package geometry;

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Grasman et al. 2011). A convex hull is the smallest possible area comprising all trees of a clone, which is formed through the linear connection between marginal clone members. To include as well clones with only two members (here, the convex hull would be zero), we additionally calculated the mean Euclidean distance between all trees in a clone. Finally, we compared the total numbers of trees in clones of each sex. Individual performance For the genotyped sections of the stands IngII, IngIII and Yim sex and dbh structure was analysed using six dbh classes of 20 cm assumed to represent young, mature and old growing stages. For each class, the number of male, female and non-flowering trees was determined. Annual increment area of male and female trees was estimated for branches of ca. 2 cm diameter. An initial effort to core trunks failed, as more than 85 % of all trees in the old-growth stands were hollow and rotten inside, and virtually all had trunks deviating from a spherical outline due to strong sectorial growth. Already in larger branches ([10 cm diameter) the heart wood started to decay. One branch each was sampled of 23 female and 27 male trees in spring 2006 and again of 22 female and 28 male trees in spring 2007 in plot YimB, all belonging to different genets. After drying, the stem-bound side of the branches was polished. Tree ring counting and measurements were carried out with the measuring table LintabTM 5 and the software TSAP Win Professional 0.53 (both Rinntech, Heidelberg, Germany). To account for sectorial growth, three radia per branch arranged in angles of 120° were measured and then averaged. As P. euphratica grows actively only during May to July (Gries et al. 2005), the last increment always refers to growth of the previous year. Reproductive investment For both sexes, carbon (C) and nitrogen (N) contents were measured per mg dry mass of inflorescences (i.e. catkins) and fruits (Vario EL III, Elementar Analysensysteme, Hanau, Germany). Based on these data, RI was calculated for three different levels: (i) per single flower and fruit, (ii) per inflorescence and infructescence and (iii) per branch of ca. 2 cm diameter. Catkins from randomly chosen male (n = 44) and female (n = 49) trees were collected from plots Ing6 and YimB 1–2 days before reaching their flowering peaks in the years 2006, 2009 and 2011. Ripe infructescences (shortly before seed release) were collected from 15 fruiting trees from the same plots in late August 2006 and 2009. All samples were dried for 24 h at 60 °C, grinded to powder, and three repeats of each sample were analysed for C and N content. To calculate RI at branch level, we counted the catkins of abundantly flowering

Author's personal copy Trees Table 3 Comparison of male and female clones for three stands comprising nine genotyped plots of P. euphratica Stand Plot

Ing II Ing5, 6, 11

Ing III Ing8, 9, 10

Yim YimB, E, F

Clonality

0.87

0.46

0.04

No. of clones m

R all

94

98

12

204

52

28

10*

90

f

42

33

2

77

nf

0

37

0

37

977

382

28

1,387

m f

552*** 425

133 142

23** 5

708*** 572

nf

0

107

0

107

Trees in clones

Clone size (trees per clone) (mean ± SEM) m

11 ± 2

5±1

2±1

8±1

f

10 ± 2

4±1

3±1

7±1

Inter-tree distance in clones (m) (mean ± SEM) m

27 ± 2

11 ± 1

22 ± 8

21 ± 2

f

21 ± 2

12 ± 1

10 ± 9

16 ± 1

Clone area (m2) (mean ± SEM) m

1,775 ± 388 (n = 38)

182 ± 67 (n = 13)

512 ± 278 (n = 2)

1,239 ± 272

f

1,073 ± 220 (n = 34)

114 ± 36 (n = 18)

1 (n = 1)

705 ± 150

2

* indicate a significant excess of males (v test: * P \ 0.05, ** P \ 0.01, *** P \ 0.001)

branches (ca. 2 cm in diameter, nm = 68; nf = 40) from a total of 61 male and 24 female trees in March 2006 and 2009. In addition, 75 female flowering branches of 31 trees in YimB were marked in 2007; catkins and later in August infructescences were counted. To estimate resource allocation at branch level results of catkins and infructescences were extrapolated following the Gauss rules for error propagation (Gellert et al. 1967). As we noted a very low proportion of fruiting trees in plot YimB in 2007, we counted flowering females at the end of March and fruiting females at the end of August for plots Ing6 and YimB in 2009 and 2010. Statistical analyses All measured or calculated results are given as mean ± standard error of mean (SEM). Deviation from equal proportions of male and female trees or clones was tested with a Chi square (v2) ‘goodness of fit’ test at a 5 % level of significance (a = 0.05). Differences between males and females were tested using a two-tailed, non-parametric Mann–Whitney U test with a 5 % level of significance. The alternative hypothesis was always directed to proof a better performance of the sex with the higher value. All statistical tests were calculated with SPSS software 12.0 (2003 SPSS Inc; Janssen and Laatz 2010).

Results Genotyping Among the seven SSR loci, we found 80 alleles (4–19 per locus, mean 12 ± 5), with loci GCPM 3351 (19 alleles, range: 172–212 bp) and ORPM 023 (15 alleles, range: 191–221 bp) being the most polymorphic. At locus ORPM 1031, we found nine alleles (range: 104–128 bp), for the other four loci allele numbers and allelic ranges were identical to the ones listed in Eusemann et al. (2009). PID values over all genets and loci were sufficiently low (average 5.36 9 10-5, range between plots 1.48 9 10-4– 7.81 9 10-5). The per allele error for genotyping was estimated to be 0.011 (Schnittler and Eusemann 2010). From 2,439 living trees in nine plots 70 % (1,701 trees) were successfully genotyped; 204 of 850 genotypes found represented clones (Table 3; Figs. S2, S3, S4 in Supplementary material). The clone assignment was highly reliable; 95 % of all clones consisted of trees with identical MLGs. In six clones with altogether 13 trees, we found MLGs deviating in a single allele (suggesting a single-repeat insertion or deletion). In all cases, context criteria matched the remaining members of the clone in question; therefore, we assigned those trees to already identified clones. Four other clones comprised trees with identical MLGs but contradicting context

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Author's personal copy Trees b Fig. 2 a Clone size (mean ± SEM) for male (black circles), female (open circles) and non-flowering clones (grey circles) of P. euphratica in dependence from the degree of clonality (index: 0—all trees are singletons to 1—all trees belong to a single clone). Indicated are genotyped sections of the stands Ing II (plots Ing5, 6, 11), Ing III (plots Ing8, 9, 10) and Yim (plots YimB, E, F). b Distribution of clone sizes for male (black circles) and female (open circles) clones. The best fit for an exponential function y = -a ? b/exp(cx) with y = number of clones, and x = trees per clone was obtained for males with a = 1.4, b = 104.9, c = 0.65, ANOVA: P \ 0.001 (continuous line) and females with a = 1.5, b = 53.6, c = 0.51, ANOVA: P \ 0.001 (dashed line). c Differences in spatial extension of male (black circles) and female (open circles) clones. Logarithmic scales for both axes were chosen to visualise differences. The data are fitted best by a linear function log(y) = a * log(x) ? b with y = clone area, and x = trees per clone with a = 1.2, b = 1.7 for males (continuous line, R2 = 0.81) and a = 1.5, b = 1.3 for females (dashed line, R2 = 0.78). The linear regression includes only clones with three or more trees, because clones with one or two trees do not have an extension area

separated [100 m away from the nearest clone member; these were classified as singletons in spite of identical MLGs. Furthermore, one apparent case of a visible somatic mutation was encountered: In Ing11, one large female clone encompassed five trees with green and 14 trees with red flowers, all showing identical MLGs. Another 334 trees could be assigned unambiguously to identified clones using the context criteria (Table 2). In addition to the 1,625 trees directly sexed in the field (Table 2), 369 non-flowering trees were sexed indirectly through matching the MLG and/or context data of an existing clone with known sex. Significantly more of these non-flowering trees were female (55.6 %; P \ 0.05, v2 test). The proportion of young trees among the sexed trees was similar between both sexes: 54.4 % of non-flowering males and 45.6 % of non-flowering females had dbh values B 15 cm (P [ 0.05, v2 test). Sex ratios

criteria: trees were either of opposite sex or separated by an extremely large distance ([100 m). Four trees mapped as male were genetically identical with 16 female trees. As all other context criteria matched, we assigned all trees to a clone counted as female (this translates into a sexing error rate of 0.0023). Three other clones included trees that were

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Sex expression was stable in all but two trees sexed in the field. A single tree of green flower colour had both male and female inflorescences as well as male and female flowers in one catkin. Furthermore, a phenotypically female, green flowering tree developed two red anthers in several female flowers. Both trees were counted as female. Apparent sex ratios of the large-scale stands showed a significant male bias in five of the eight stands (Table 1; total mean ratio 1.50, 60 % males, 3295 flowering trees). For the remaining three stands, the v2 test indicated no significant biases, but an excess of flowering male trees was as well observed. If all non-flowering trees are counted as female to calculate extremes for possible intrinsic sex ratios, only the stand Yim has definitely more male trees.

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Fig. 4 Mean annual increment (DAn ± SEM) for flowering branches of 2 ± 0.2 cm diameter from male (grey bars) and female (white bars) branches of P. euphratica trees from plot YimB over the time period 1995–2006 (male trees: n = 27–55, female trees: n = 22–45, depending on branch age). Significant differences are marked with asterisks (Mann–Whitney U test: *P \ 0.05, **P \ 0.01, ***P \ 0.001)

Genet sex ratios, based on a total of 850 genets did not differ significantly from a 1:1 ratio (Table 2; total mean ratio 1.09, 52 % male genets). Considering all genets with unknown sex also none of the stands showed a significant male bias at genet level. However, in stands IngII and Yim male trees predominate again at all scenarios (Table 2). Clonal growth

Fig. 3 a–c dbh structure of the genotyped sections of the stands Ing II, Ing III and Yim shown in dbh classes of 20 cm diameter for male (black bars), female (white bars) and non-flowering (grey bars) trees. Significant differences are marked with asterisks (v2 test: *P \ 0.05, **P \ 0.01, ***P \ 0.001)

Looking at the genotyped sections of the stands IngII, IngIII and Yim, apparent sex ratios were significantly male biased only for stand IngII (Table 2; total mean ratio 1.20, 54 % males, 1625 flowering trees). For IngIII and Yim, the excess of flowering males was statistically not significant. Intrinsic sex ratios were calculated with a total of 1,994 sexed trees (either directly sexed or indirectly through clone assignment, 82 % of all living trees). A male bias occurred again in stand IngII (Table 2; total mean ratio 1.12, 53 % males). Taking the uncertainty caused by the remaining 445 unsexed trees into account, none of the stands showed a significant male excess. Nevertheless, it has to be mentioned that in stands IngII and Yim male trees predominate at all scenarios (all unsexed trees counted as either male or female, Table 2).

The extent of clonality differed clearly between the three stands (Fig. 2a). Stand IngII included plots with large clones and relatively few singletons. In stand IngIII, clones were smaller and comprised many non-flowering trees. Virtually all trees in stand Yim were singletons (for illustrations see plot and clone maps in Figs. S1, S2, S3 in Supplementary material). Results for the analysed clone parameters are shown in Table 3 and Fig. 2b, c. At all, four fifths (167 clones) of the 204 identified clones could be sexed, i.e. included at least one flowering tree. Male clones outperformed their female counterparts in all investigated parameters, although not all differences were significant. Individual performance Within four stands of young trees at the Tarim River a total of 91 (48 male, 43 female) among 1,039 trees were observed with usually a few flowers in the uppermost crown. The dbh of flowering male and female trees was comparable (17.3 ± 3 vs. 17.5 ± 3, P [ 0.05, v2 test for each stand). The analyses of dbh and sex structure within the genotyped plots (Fig. 3a–c) revealed significantly more male trees in lower dbh classes (\40 cm) of the highly clonal stand IngII; to a lesser extent, this occurred as well in the medium clonal stand IngIII (dbh \ 20 cm). Conversely, in

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2 years older than female branches of the same diameter (7.8 ± 0.5 years); this difference was significant (P \ 0.01, Mann–Whitney U test). Caused by these age differences the sample sizes for mean increment decreased for longer time intervals as some branches were too young to provide data over the entire time interval. From 1995 to 2001, growth was generally slow and did not differ significantly between the sexes. Growth increased considerably after 2001, and females performed better. In the years 2004–2006, female branches grew around 25 % more than male branches (Fig. 4). However, over the whole 10-year increment differences were not significant due to the large fluctuations between the single branches. Reproductive investment

Fig. 5 a Mean numbers (±SEM) of flowers per inflorescence (i.e. catkin) and inflorescences per branch for male (m), female (f) and fruiting (ff) trees of P. euphratica. b, c Mean nitrogen and carbon investment (±SEM) for three levels of reproduction: single flower or fruit capsule, single inflorescence or infructescence and all inflorescences or infructescences of a branch with 2 cm diameter. Values for observed fruit set (ff) and hypothetical full fruit set (fff) were calculated for inflorescences and branches. Asterisks indicate significant differences between males and females and between female flowers and fruits (Mann–Whitney U test: *P \ 0.05, **P \ 0.01, ***P \ 0.001, *1Between female flowers and fruits; white bars with hypothetical calculations were not considered)

the nearly non-clonal stand Yim male trees predominate among the largest, probably oldest trees (dbh \ 300 cm). For measuring increment at branch level in the nonclonal plot YimB, the diameter of sampled male and female branches (all from different genets) was kept constant (1.98 ± 0.03 vs. 2.00 ± 0.03 cm, P [ 0.05, Mann– Whitney U test), hence no reference parameter was needed to compare increment between sexes. Figure 4 shows the annual increment area for the years 1995–2006 of both sexes. With an age of 10.0 ± 0.5 years male branches were

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Male catkins had more flowers, and branches of 2 cm diameter developed nearly twice as many catkins as their female counterparts; both differences were highly significant (Fig. 5a). However, the mean dry mass per flower was comparable between sexes (males: 2.20 ± 0.13 mg, females: 2.29 ± 0.07 mg; P [ 0.05, Mann–Whitney U test). Both C and N contents were comparable for male and female flowers (Fig. 5b, c). Due to divergent numbers of flowers per catkin and catkins per branch, differences occurred at inflorescence and branch level: Male catkins contained 1.4 times more C and N than female ones, and branches invested 3.3 times more C and N than female branches, respectively. A single fruit capsule contained 9.3 times more N and 27 times more C than a male flower (n = 90 fruits; Fig. 5b, c). On average only 12 (54 %) of the 22 flowers of a female catkin developed into fruits (Fig. 5a), but a female infructescence (counting fruits and aborted flowers) required still 4.6 times more N and 12 times more C than a male catkin (Fig. 5b, c). Also the abortion of whole female catkins was frequent: Only 26 % of the monitored female branches (69 were recovered) developed infructescences, corresponding to 16 % of 3,755 counted female catkins (Fig. 5a). This turned the relation: fruiting female branches invested 1.3 times more C, but one-third less N than their flowering male counterparts (Fig. 5b, c). When we considered (hypothetical) full fruit set on inflorescence and branch level (white bars in Fig. 5b, c), RI of females increased considerably. Females would have had to invest 3.6 times more N and 10.3 times more C than males into reproductive structures. The proportion of flowering female trees among all mapped females for the monitored plots YimB and Ing6 ranged between 91 % (YimB, 2009) and 67 % (Ing6, 2010). However, the proportion of trees with infructescences varied between both stands and years (2009 vs. 2010): YimB—58 vs. 17 % and Ing6—18 vs. 61 % of flowering female trees set fruits.

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In addition, for plot YimB, we counted fruiting trees in relation to the distance from the Qayan River, because this plot consisted of three clearly distinguishable germination rows (see Fig. S1 in Supplementary material). The proportion of flowering trees was comparable between the three rows in both years, but the proportion of trees with infructescences decreased in both years with increasing distance to the Qayan River (2010: first row, ca. 10 m distance: 32 % female trees fruited; second row, ca. 240 m distance: 15 % female trees fruited; third row,[460 m distance: 8 % female trees fruited).

Discussion This study shows that a detailed analysis of all three levels of sex ratios—apparent, intrinsic and genet—is important to understand the sexual stand structure in a clonal species like P. euphratica. Especially the intrinsic level, which gives information about flowering behaviour and the intensity of clonal growth, was to our knowledge not yet investigated in other studies about clonal plant species. Due to the combination of a molecular approach (SSR genotyping) with field observations (context data), we could sex 15 % more trees in comparison to mere field observations. Furthermore, context data like sex, tree position, variable bud break phenology and different flower colours offered the opportunity to check for genotyping or sexing errors which lowered the rate of wrong clone assignments to a sufficiently low level (\5 %). Sex ratios Direct sex markers are unknown for the genus Populus; hence there was no way to determine the ‘primary’ (seed) sex ratio in seedling cohorts of P. euphratica. Therefore, we followed the general prediction of de Jong and Klinkhamer (2002) based on the Fisher’s principle (1930) and assumed a seed sex ratio of 1:1. In P. euphratica, germination occurs only along freshly deposited riverbanks. As over time riverbeds moved away from our investigated old-growth stands (Thevs et al. 2008), they do not longer provide suitable conditions for seed germination. Thus, later generative rejuvenation does not influence sex ratios. Remaining factors are (i) sex-specific differences in flowering rates affecting apparent sex ratios, (ii) clonal growth affecting apparent and intrinsic sex ratios and (iii) individual performance in terms of mortality, which may influence sex ratios at all three levels. As in most stands flowering male trees outnumbered flowering females, P. euphratica belongs to the majority of species with a tendency towards a male biased apparent sex ratio (Barrett et al. 2010; Sinclair et al. 2012). These results

coincide with the findings for P. deltoides (Farmer 1964; Kaul and Kaul 1984; Rowland and Johnson 2001) and P. tremuloides (Pauley and Mennel 1957; Einspahr 1960; Lester 1963). An obvious reason is that female trees flower less readily (e.g. Cipollini and Stiles 1991). A genetically determined, sex-specific flowering rate seems to be unlikely, as both numbers and dbh of flowering male and female P. euphratica were comparable for the four young stands at the Tarim River. Furthermore, there was no difference for the number of young male and female trees (dbh \ 15 cm) sexed through clone assignment. If a lower female flowering rate is caused by higher RI of this sex, the apparent sex ratio of all stands suffering from environmental stress like drought should be more heavily male biased. The stands Ing I, FO6, FO6 II, Dune and Arg, all situated around dry river beds, often far from the Tarim main river, and receiving just irregular floods, showed together the highest proportion (69 % of 864) of male trees. Also Rowland and Johnson (2001) invoked environmental stress (water shortage, salinity) to explain a low flowering readiness for P. deltoides. Similarly, Braatne et al. (2007) found a change in apparent male:female sex ratios of P. trichocarpa along a soil water gradient from 1:1 at sites with regular flooding and low soil water deficits to 7:1 at sites with high soil water deficits. Also Comtois et al. (1986) found that male P. balsamifera trees tended to be more common at relatively drier and less fertile sites. Clonal growth As clones are formed by more than one tree the detection of sex-specific deviations in clonal growth requires even larger sample sizes compared to the detection of differences in apparent or intrinsic sex ratios. From this reason, we analysed three plots for each of the most intensely studied stands Ing II, Ing III and Yim. P. euphratica can form large clones: in the southern Taklimakan, Bruelheide et al. (2004), using AFLP genotyping, estimated a clone radius of 100 m which corresponds to an area of approximately 3 ha. Even larger clones were reported for P. tremuloides in eastern North America with 81 ha (Kemperman and Barnes 1976) or 43 ha (‘Pando’-tree, Grant 1993); the latter was also confirmed by microsatellite genotyping. Looking at sex-specific differences in clone parameters, a similar picture like that for sex ratios unravels: male clones are more numerous, cover on average a larger area, the mean distance between clone members is larger, and they comprise more trees. Not all of these differences are significant, but as a whole they point towards more vigorous growth of male clones. This pattern is supported by a male excess in low dbh classes of highly clonal stands (Fig. 3a, b). Results for other species of poplar are

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somewhat contradictory: Comtois et al. (1986) and Mitton and Grant (1996) found for P. tremuloides that male clones had more ramets and a larger extension, but Sakai and Burris (1985) and Sakai and Sharik (1988) found a slightly better performance (size, extension) of female clones of P. tremuloides and P. grandidentata. Individual performance Apart from sex-specific clonal growth, higher mortality of one sex may as well cause biased sex ratios at all three levels. However, increased mortality is usually preceded by less vigorous individual growth. In the case of clonally growing P. euphratica, the analysis of average dbh values does not help: more vigorous male clonal growth will add young male root suckers to the population which masks or even outweighs possible lower individual increments of females. In the non-clonal stand Yim, the average apparent sex ratio is indeed male biased (54.1 % males), and this effect is still visible at the intrinsic (54.1 % males) and genet (53.7 % males) sex ratios (Table 2). This may be interpreted as a sign of lower individual performance and ultimately higher mortality in females, supported by the significantly larger number of probably oldest (i.e. thickest) male trees (Fig. 3c). Nevertheless, as our approaches to measure increment by tree coring failed, only long-term studies like those carried out by Allen and Antos (1993) for Oemleria cerasiformis (lasting 4 years) or by Ward (2007) for Juniperus communis (lasting 23 years) would help to proof a less vigorous individual growth of females. From obvious reasons, mortality studies for long-lived perennials are rare; often studies fail by time limitation (Cipollini and Stiles 1991; Rowland and Johnson 2001), or mortality was not separately investigated for sexes (Worrall et al. 2008). As the second accessible solution, we investigated the increment of branches in stand Yim, where costs of reproduction can be more easily detected than at tree level (Obeso 1997). Individual fluctuations were rather large, especially during the years 2003–2006. The age of the branches harvested at 2 cm diameter varied heavily (for both sexes between 4 and 18 years), and we assume that branches flowered or even fruited not every year. The abrupt increase in average increment since 2003 (Fig. 4) is likely due to a better water supply in the studied plot YimB caused by a different irrigation regime in upstream reservoirs that started in 2001. Westermann et al. (2008) found similar changes at tree level, coring selected trees to test their response to artificial flooding. Against the generally expected lower increments in females, our results suggest that older female branches grow better, indicating a lower RI for females at branch level in the investigated years (Fig. 4, see below). These results do seemingly not fit the pattern of a lower

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individual performance of females, but can be explained by the frequent shedding of female catkins after the flowering period: at a given year, only a small proportion of female trees set fruits (2009: 58 %, 2010: 18 %). A second explanation is the contribution of the green capsules to carbon fixation, which may comparable with that of leaves, supporting as well wood formation. Dioecious plants do not necessarily show significant differences in the growth of male and female shoots: such effects were not found by Milla et al. (2006) for Pistacia lentiscus L. and Bochenek and Erikson (2010) for Fraxinus excelsior L. Reproductive investment As a nutrient that has to be extracted from the soil, N is a good measure for investment into different plant parts (Ashman 1994; Schnittler et al. 2009). At flowering time, the investment of C and N into catkins was significantly higher for male P. euphratica. Flowers of both sexes were still comparable in terms of C and N, but a sexual dimorphism emerged from significantly higher numbers of flowers per catkin and catkins per branch in males. As wind is a relatively uncertain pollen vector, this higher investment should pay off for a wind pollinated tree like P. euphratica, as the amount of produced pollen is usually positively correlated with male reproductive success (Burd and Allen 1988; Bochenek and Erikson 2010; Hesse and Panell 2011). The logical second step is to consider investment in fruit and seeds. Here, the general prediction is that male flowers are ‘cheaper’ than female fruits (see reviews in Delph 1999; Obeso 2002; Dudley 2006; Matsuyama and Sakimoto 2010). For P. euphratica this could be confirmed at the level of single flowers and catkins. In theory, this continues also at the branch level: a fully fruiting branch would have to invest 3.6 times more N and 10.3 times more C than its male counterpart (white bars in Fig. 5b, c). This would give males a huge comparative advantage. However, in nature (grey bars in Fig. 5b, c), a significantly lower proportion of flowers and especially catkins develop into fruits. Due to the high average fruit abortion rate (84 %) fruiting female branches invested only 1.3 times more C and one-third less N than their flowering male counterparts. The amount of C cannot completely be considered as RI, as female inflorescences develop into up to 15-cm-long racemes with green fruit capsules. Until maturation time (3–4 months), the capsules are able to fixate additional carbon, an effect noted as well by other authors (Laport and Delph 1996). We thus must conclude that fruit abortion is likely to be the tipping point for RI, allowing females to compensate a much higher RI in years with high fruit set (cf. ‘compensation hypothesis’ by Tuomi et al. 1983). Similarly, Abe

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(2002) found higher male RI in Aucuba japonica caused by female flower bud abortion. However, although our data on fruit abortion show a very clear tendency, they cannot be interpreted in a quantitative manner, as they rely on observations in 2 years only. Also Wang et al. (1996) noted huge differences in female fruit set, reporting 3,088–60,300 infructescences per female tree. This imposes the question of how fruit abortion can be induced? Preliminary data on seed set per capsule ([60 %) exclude pollen limitation, a phenomenon unlikely to occur in wind pollinated trees (Friedman and Barrett 2009). Microgametophytic competition, which provides a mechanism for female choice in plants (Stephenson and Bertin 1983; Mena-Ali and Rocha 2005), is possible, because through selective abortion a female tree saves valuable resources (Abe 2002) and supports only the fittest embryos. For P. euphratica, the weak point of this argument is the high number of ovules per capsule (ca. 150, Wang et al. 1996) pollinated by wind: it seems unlikely that a pollen cloud is so inhomogeneous that all flowers of one catkin receive either ‘strong’ or ‘weak’ pollen. In contrast to flowering frequencies water stress appears to be a convincing reason for lower fruit set, as females have to support infructescences through the driest time of the year. Evidence came from Freeman and McArthur (1982), who found higher water stress in Atriplex canescens (Pursh) Nuttall during fruit maturation than during flowering. For P. euphratica the possible correlation between water stress and fruit abortion is indicated by the decreasing fruit set in plot YimB with increasing distance to the Qayan River: 32, 15 and 8 % fruit set for the first, second and third row of trees, respectively, although 80 % of all females flowered (see Fig. S1 in Supplementary material for a map). Nevertheless, only a long-term study combined with ground water measurements can answer this question. Better individual growth in spite of higher resource allocation to sexual reproduction has been reported for females of other dioecious plants (Delph 1999; Obeso 2002), including Salix (Turcotte and Houle 2001). In Salix, females with larger reproductive allocation often have a ˚ hman growth rate similar to or even faster than males (A 1997); physiological (Dawson and Bliss 1989) and phenological (Ueno and Seiwa 2003) causative factors have been investigated. Ueno and Seiwa (2003) found that females of S. sachalinensis produce a larger amount of N-rich leaves in the early growing season, when males temporarily pay a greater cost for reproduction due to pollen production. For P. euphratica, we usually observed a delay in leaf bud break of 3–7 days for heavily flowering males. The observed ‘big bang’ flowering (most male trees in a stand shed pollen simultaneously over a period of less than 1 week) can only be realized by depletion of resources of the previous season (Popp and Reinartz 1988),

as P. euphratica flowers about 10 days before bud break. In contrast, female trees flower less abundantly and may use resources saved in the wood parenchyma to achieve an earlier leaf bud break. The longer vegetative period realized by female trees should affect individual performance, as long-term measurements by Gries et al. (2005) demonstrated that trees grow actively for only 3 months (May to July), when ground water from the previous-year flood is still available. In conclusion, our analyses on P. euphratica showed that a female tree has to raise a higher amount of nutrients to carry a significant proportion of catkins to fruit. We estimate that the ‘break even’ (male and female trees invest equally into sexual reproduction) is reached when about 25 % of all flowering female catkins develop into fruit. With frequent water stress during the summer (Gries et al. 2005), abortion of female catkins is certainly frequent and constitutes a powerful compensatory mechanism for female trees in the sense of Tuomi et al. (1983). Nevertheless, over their entire life females may invest more into sexual reproduction, which explains the slightly better performance of males in (i) individual growth, (ii) proportion of flowering trees and (iii) clonal growth. Shedding a part of catkins after flowering, avoids the expected ‘runaway effect’ by more vigorous clonal growth of male trees over a long time, but a tendency to male biased sex ratios, at least at the apparent sex ratio level, is obvious for P. euphratica. Acknowledgments We wish to thank Prof. Nurbay Abdusalih, Xinjiang University, and numerous students of his group, especially Gymanias Saidahmad for logistic help and contributions to field investigations in Xinjiang. We are also indebted to Anja Klahr and Julia Petzold for help with molecular work, Ulrich Mo¨bius and Katrin Bu¨nger for assistance with C/N analyses, and Prof. Martin Wilmking for enabling increment measurements (all Greifswald University). Financial support came from two grants of the Deutsche Forschungsgemeinschaft (DFG, SCHN1080-1/1, SCHN1080-3/1 to MS).

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