Measuring spore settling velocity for an improved assessment of dispersal rates in mosses

Abstract

Background and Aims The settling velocity of diaspores is a key parameter for the measurement of dispersal ability in wind-dispersed plants and one of the most relevant parameters in explicit dispersal models, but remains largely undocumented in bryophytes. The settling velocities of moss spores were measured and it was determined whether settling velocities can be derived from spore diameter using Stokes’ Law or if specific traits of spore ornamentation cause departures from theoretical expectations.

Methods A fall tower design combined with a high-speed camera was used to document spore settling velocities in nine moss species selected to cover the range of spore diameters within the group. Linear mixed effect models were employed to determine whether settling velocity can be predicted from spore diameter, taking specific variation in shape and surface roughness into account.

Key Results Average settling velocity of moss spores ranged from 0·49 to 8·52 cm s^–1. There was a significant positive relationship between spore settling velocity and size, but the inclusion of variables of shape and texture of spores in the best-fit models provides evidence for their role in shaping spore settling velocities.

Conclusions Settling velocities in mosses can significantly depart from expectations derived from Stokes’ Law. We suggest that variation in spore shape and ornamentation affects the balance between density and drag, and results in different dispersal capacities, which may be correlated with different life-history traits or ecological requirements. Further studies on spore ultrastructure would be necessary to determine the role of complex spore ornamentation patterns in the drag-to-mass ratio and ultimately identify what is the still poorly understood function of the striking and highly variable ornamentation patterns of the perine layer on moss spores.

INTRODUCTION

Dispersal, the movement of individuals from where they were born to a breeding or growing site, is a key evolutionary force that determines the survival, growth and reproduction of individuals, the temporal and spatial cycles of colonization and extinction of populations, and, ultimately, the emergence of new species via genetic drift or natural selection (Clobert et al., 2012). In the context of global change, dispersal dynamics are especially important as the long-term survivability of species depends on their ability to shift effectively, and even augment their distributions according to changes in local climatic conditions (Berg et al., 2010; Bellard et al., 2012). For both responses to climate change, dispersal is a central process; it determines the potential spread rate of a population and, as the mechanism by which genes are moved between populations, it influences the rate of adaptation to changing conditions and the potential for evolutionary rescue (Bell and Gonzalez, 2011). Thus, understanding, predicting and managing biodiversity responses to rapid climate change demands a full consideration of species’ dispersal traits (Travis et al., 2013).

Obtaining unbiased estimates of the distribution of dispersal distances in natural unbounded populations has, however, long been known to be problematic (Koenig et al., 1996). Ecologists typically measure long-distance dispersal in two ways. Direct techniques implement descriptions of dispersal kernels from local measurements derived, for instance, from trapping experiments, and then extrapolate the potential for dispersal broadly beyond the scale of measurements, in both time and space (Clark et al., 2001). Indirect techniques are based on inferences from spatial genetic structure (e.g. Vekemans and Hardy, 2004). As compared with direct approaches, indirect techniques do not provide directly measurable dispersal distances for individuals (Cullingham et al., 2008) and tend to overestimate dispersal capacities (Koenig et al., 1996; but see Thompson and Goodman, 1997).

Describing dispersal kernels for very small diaspores, such as spores or vegetative gemmae of bryophytes and ferns, is, however, highly challenging given the problems associated with the identification of those diaspores in the field. For example, data obtained by sampling on sticky microscope slides placed on soil alone are insufficient to characterize the dispersal kernel precisely because of sampling paucity: only a fraction of the released spores is sampled while the fate of the remaining, unsampled spores is unknown (Dam, 2013). In bryophytes, actual dispersal kernels derived from spore-trapping experiments have only been documented in species with highly distinctive diapores (Pohjamo et al., 2006), or in fast-developing, annual species translocated into areas where they do not naturally occur (Lönnell et al., 2012, 2014). Several authors attempted to circumvent this problem by estimating dispersal rates from spatial distribution patterns (Hutsemékers et al., 2008; Sundberg, 2013; Ruete et al., 2014), making, however, restrictive assumptions on the location of diaspore sources.

Alternatively, a common way to approach and predict the potential distance that an airborne particle is able to travel is by evaluating its settling velocity (Seinfeld and Pandis, 1998; Ginoux et al., 2001; Farrell and Sherman, 2015), which may be a useful surrogate for the measurement of dispersal ability in wind-dispersed plants (Andersen, 1992, 1993). This physical property relates to the balance between the gravitational force (which results in the combination of weight and buoyancy) and the drag force, both acting on the particle as it travels through a fluid. For plant dispersal, this key property reflects the maximum velocity of a spore or pollen grain when falling in the air, and, hence, its ability to be dispersed (Matlack, 1987; Niklas, 1985, 1992; Cody and Overton, 1996).

The effect of settling velocity on seed dispersal kernels has been confirmed by empirical measurements (Norros et al., 2014) and is an essential variable in mechanistic dispersal models (Nathan et al., 2011). Small particles disperse further than larger ones due to their lower settling velocity and thus longer expected airborne time (Hall and Walter, 2011). The relationship between settling velocity and diaspore diameter has been experimentally supported (Aylor, 2002; Hussein et al., 2013), so that settling velocities are often approximated in dispersal models from Stokes’ Law, which describes the movement of small spherical particles in a fluid depending on their diameter and density (Tackenberg, 2003; Monteith and Unsworth, 2013; Wilkinson et al., 2012). Sundberg (2010), however, reported settling velocities in Sphagnum spores that were about 48 % slower than expected for spherical particles of the same diameter. In fact, although the impact of seed morphology on density and drag coefficients has been extensively documented (Greene and Johnson, 1990; Matlack, 1987; McGinley and Brigham, 1989; Cody and Overton, 1996), and although ‘numerous hypotheses pertain to the selective aerodynamic advantage of complex morphology such as hollow sacs to reduce density or numerous minute spines to effectively increase the volume’ in pollen (Niklas, 1985), the impact of the shape and ultrastructure of spores on their settling velocity has seldom been taken into account (Roper et al., 2008; Hussein et al., 2013).

In the present study, we used a high-speed camera to report for the first time the settling velocity of the spores in mosses. Moss spores tend to be spherical and range between 10 and 50 μm in diameter with a few outliers up to > 100 μm (Clarke, 1979). Certain genera have spores with prominent, easily observed ornamentations that have received considerable taxonomic attention, but many spores with less obvious ornamentation have been ‘unduly neglected’ (Clarke, 1979). The perine, i.e. the most external layer of the spore formed by sporophyte tissue, is variously ornamented, as revealed by transmitted light microscopy (Boros and Járai-Komlódi, 1975; Brubaker et al., 1998). Scanning electron microscope (SEM) analyses further showed that there is often another order of ornamentation present above the one seen using transmitted light microscopy (Clarke, 1979, and references therein; Medina and Estébanez, 2014). The function of the perine ornamentation is, however, still poorly understood (Mogensen, 1983). Most recently, Medina and Estébanez (2014) suggested that it could affect spore dispersal capacities.

Here, we document the settling velocities in nine moss species selected across a gradient of spore diameters with the ultimate aim of parameterizing explicit dispersal models. We further determine whether settling velocities can be derived from spore diameter using Stokes’ Law or if specific traits of spore ornamentation, as revealed from detailed SEM observations, cause departures from theoretical expectations.

MATERIALS AND METHODS

Species selection and specimen sampling

Nine species, Polytrichum commune Hedw., Bryum capillare Hedw., Dicranum scoparium Hedw., Pohlia nutans (Hedw.) Lindb., Ulota bruchii Hornsch., Philonotis fontana (Hedw.) Brid., Physcomitrium pyriforme (Hedw.) Hampe., Conostomum tetragonum (Hedw.) Lindb. and Encalypta vulgaris Hedw., were selected in order to obtain a representative range of spore diameter across mosses, from around 8 μm for the smallest spores to > 40 μm for the largest ones (Hill et al., 2007). A list of the specimens used for the experiments, kept at the herbarium at the University of Liege (LG), is provided in Supplementary Data Table S1. All specimens were dried in silica gel to homogenize the humidity content and prevent spore clumping. For each species, 3–10 sporophytes were subsequently selected and processed in order to obtain a minimum of ten independent single-spore falling speed measurements per species.

Scanning electron microscopy and analysis of ultrastructure variation

A set of ten fully mature spores from the selected species was collected and processed by SEM in order to document the ultrastructure of spores. A portion of each sample was placed on filter paper (medium filtration rate; particle retention >5 μm) in a sample holder (stainless steel tube) for critical point drying. The holders were subsequently submerged respectively for 30 min in 25 % ammonia, 2 × 20 min in 70 % ethanol, 4 × 30 min in dimethoxymethane and overnight in acetone before the samples were dried out in a critical point dryer (Leica EP CDP 300). The samples were then coated with gold (using argon gas, under 0·05 mbar) for 3 min and 30 s, until a layer of approx. 15 nm was obtained. The SEM was carried out with a JEOL 5800 LV with a tension of 15 kV and working distance of 10–12 mm. Digital SEM images were captured using the Orion V (version 5·22) Image Management System.

Spore ornamentation was described using Brubaker et al.’s (1998) terminology: psilate (none to minute), scabrate (rounded, dense), clavate (elongate, firmly attached to the wall, broadest at the distal end, irregular in shape and density), bacculate (elongate, firmly attached to the wall, irregular shape and density), gemmate (oval to spherical, sometimes fused, loosely attached to the wall, irregular density), verrucate (rounded, broad, irregular shape) and papillate (very elongate, dense, broader at the distal end).

Spore shape and texture were quantified through their roundness and circularity. The roundness parameter (4A/πd², where A is the area and d is the largest diameter) is an index that measures the extent to which the particle departs from perfect circularity. The circularity parameter (4πA/P², where P is the perimeter) accounts for the smoothness of the perimeter, and thus provides a quantitative measure of whether the spore is ornamented. These statistics were calculated with ImageJ 1·50b (Schneider et al., 2012). Average differences in roundness and circularity were sought by analysis of variance (ANOVA) depending on the factor species.

Experimental design

Settling velocity was recorded using a ‘fall tower’ design (Gregory, 1973; Ferrandino and Aylor, 1984; Di-Giovanni et al., 1995; Aylor, 2002; Sundberg, 2010) and applying a high-speed visualization method adapted from Massinon and Lebeau (2012) (Fig. 1). The fall tower was composed of antistatic-treated transparent PVC tubes of 24·5 cm section minimizing air movement within the settling chamber. The release hole was positioned on the top of the fall tower and aligned with the high-speed camera focal point. The vertical distance of 66·5 cm between the release source and the camera axis ensured that the observed falling particles had reached equilibrium and, thus, their terminal velocity. We controlled for that by calculating the relaxation time (i.e. the time required for the particle to attain its steady-state velocity) of the largest spore selected. We obtained this time value using the first-order linear differential equation that describes the sum of forces (drag force, buoyancy and gravity) acting during the fall of a small particle assumed to be spherical. From this relationship, we extracted the time constant τ and multiplied it by five, in order to obtain the required time to reach 99·3 % of the steady-state velocity (Seeler, 2014), as commonly assumed in fluid dynamics.

Fig. 1.

The ‘fall tower’ experimental device employed to measure the setting velocity of moss spores. (1) High-speed camera; (2) LED backlight; (3) PVC transparent tube (=settling chamber); (4) computer; (5) stand; (6) sporophyte (opened capsule); and (7) 53 mm lens flange.

Each selected mature sporophyte was then fixed to a stand with a clamp and the upper part of the capsule was removed using 4·5'' dissection straight scissors. Short vibrations were applied to the seta with a 4·5'' dissection straight forceps to initiate the release of spores from the opened capsule.

Spore settling sedimentation was recorded using a high-speed camera (Y4 CMOS, Integrated Design Tools, Tallahassee, FL, USA) configured with an acquisition frequency of 100 images per second, an exposure time of 25 μs and a + 1 dB sensor gain for an 8 bit pixel depth (giving a 256 greyscale value). A × 12 optical zoom system (Navitar, Rochester, NY, USA) was used to reach a 5·67 μm pixel^–1 spatial resolution, with a depth of field of about 1 mm and a working distance at 172 mm. A calibration target (MIL-STD-150A) was used to calculate the pixel resolution precisely. We applied an LED backlighting (19-LED Constellation, Integrated Design Tools) with a 12·5 ° beam angle on the axis of the camera at 180 mm from the focal point and used it in pulsed mode in order to maximize the light intensity and give more precision to the measurement of spore diameter.

Spore settling velocity measurements

Mean settling velocities were calculated based on a selection from ten to 18 independent spore fall sequences per species. The settling velocity of each spore was estimated from five consecutive images to measure the distance travelled by a spore during a 0·05 s period (Supplementary Data Table S2). We then compared our empirical velocity data with the theoretical settling velocity v_set (m s^–1) as estimated using the Stokes’ Law relationship for the settling velocity of small spherical particles:

$$v_{\mathrm{set}}=(g{d}^{\text{2}}({\rho }_p–{\rho }_f))/\text{18}\mu$$ (1)

where g is the gravitational acceleration, and d and ρ_p represent the observed spore diameter (μm) and the spore density (kg m^–3), respectively. We used the mean spore density of 1·1 g cm^–3 as reviewed in Gregory (1973), which remains close to the value of 1 g cm^–3 typically employed for many biological particles such as pollen grains (Monteith and Unsworth, 2008) and is used in dispersal models such as that described by Wilkinson et al. (2012). The ρ_f and μ parameters account for the fluid density and viscosity and were set to the standard values of 1·225 kg m^–3 and 1·78 × 10^–5 kg m^–3 s^–3, respectively, corresponding to air at 15 °C.

The diameter of each individual spore recorded by the camera, and used in eqn (1), was determined by counting the number of pixels with <80 % of background pixel intensity value (0·8 × I_max). This background value was calculated by random sampling of the background pixel intensity values. Then, to avoid biases due to spore orientation or irregularity of the surface, maximum spore diameter was averaged on a 5–10 image sequence. These measurements, which include the perine protrusions, are coarse because of the 5 μm resolution, but were nonetheless in the range of those reported for the species studied (Table 1).

Table 1.

Spore diameter, average settling velocities (v_set) and corresponding aerodynamic diameter (D_a) (± s.d.), perine ornamentation, spore roundness and circularity for the nine moss species investigated

Species	Spore diameter range (μm)*	Mean spore diameter ± s.d. (μm)†	vset (cm s–1) ± s.d.	Da (μm) ± s.d.	Mean circularity ± s.d.	Mean roundness ± s.d.	Ornamentation
Polytrichum commune	8–12	16 ± 2	0·617 ± 0·232	14·0 ± 2·5	0·239 ± 0·140	0·923 ± 0·001	Proximal side psillate, distal side with scabrate perine elements
Bryum capillare	12–15	14 ± 1	0·495 ± 0·160	12·5 ± 2·3	0·305 ± 0·049	0·893 ± 0·060	Proximal side psillate with gemmate perine elements, distal side with bacculate perine elements
Dicranum scoparium	12–22	21 ± 1	1·440 ± 0·238	21·6 ± 1·9	0·420 ± 0·056	0·869 ± 0·058	Densely covered by clavate, sometimes fused perine elements
Pohlia nutans	18–28	20 ± 1	1·311 ± 0·292	20·5 ± 2·4	0·088 ± 0·071	0·758 ± 0·081	Proximal side psillate, distal side with clavate perine elements
Ulota bruchii	20–26	26 ± 1	2·668 ± 0·265	29·5 ± 1·5	0·191 ± 0·048	0·824 ± 0·049	Verrucate perine elements
Philonotis fontana	26–30	27 ± 1	2·554 ± 0·300	28·8 ± 1·7	0·201 ± 0·091	0·802 ± 0·033	Proximal side scabrate with scattered papillate elements, distal side with dense, sometimes fused papillate elements
Physcomitrium pyriforme	28–36	31 ± 2	2·666 ± 0·398	29·4 ± 2·3	0·115 ± 0·023	0·879 ± 0·074	Densely covered by 2–4 μm long spinula and fused, densely bacculate perine elements
Conostomum tetragonum	40	39 ± 1	3·511 ± 0·358	33·8 ± 1·7	0·234 ± 0·076	0·774 ± 0·072	Verrucate on the distal side, psillate on the proximal side
Encalypta vulgaris	30–45	47 ± 5	8·525 ± 1·586	52·5 ± 4·9	0·232 ± 0·051	0·868 ± 0·059	Proximal side with fused perine elements and gemmate secondary perine elements, distal side with verrucate perine elements and gemmate secondary perine elements

*As documented by Hill et al. (2007).

^†Resulting from the analysis of high-speed camera pictures.

The aerodynamic diameter (D_a) of the spores was then calculated from each observed settling velocity measurement sequence by rearranging eqn (1) to yield:

$$D_{\text{a}}={((\mathrm{18}\mu v_{\mathrm{set}})/(g({\rho }_p–{\rho }_f)))}^{–\text{1}}$$ (2)

This last parameter is defined as the diameter of a spherical particle of standard density (1 g cm^–3) having the same settling velocity as the particle of interest (Hinds, 1999) and is commonly used to characterize the dispersal properties of aerosols of solid particles. We further used D_a estimations and Tukey's tests to quantify the departure of measured speed from the theoretically expected speed.

Statistical analyses

Linear mixed effects models (LMMs) were employed to predict variation in settling velocity depending on spore diameter (fixed effect, as measured for each individual spore as described above) while controlling for variation in other factors potentially affecting this relationship. These factors were: species (nine species), average spore circularity, average spore roundness and sporophyte (from three to ten sporophytes depending on each species). These four variables were included in the random structure. We contrasted the performance of competing models including all the possible combinations of varying intercepts and slopes for the random factors considered (species, sporophyte, spore circularity and spore roundness), using the difference between the Akaike Information Criterion corrected for small sample size (AICc) and the lowest AICc of all models (ΔAICc). All models with a ΔAICc value <2 were considered as having equivalent support (Burnham and Anderson, 2002). LMMs were computed with the ‘lmer’ function in the lme4 library (Bates et al., 2015) in R version 3.1.2 (R Deveopment Core Team, 2015), using restricted maximum likelihood (REML). After finding the best random effect structure, the model including the fixed factor, spore diameter, was obtained using the maximum likelihood (ML) approach in the lm4 library. Comparable R² values (with the same meaning as in simple or multiple linear regression) are not easy to obtain for LMMs (Zuur et al., 2009). We thus used an R² measure that compares the deviance of the LMM with the deviance of a linear intercept-only model (Kvalseth, 1985).

To determine whether the predicted settling velocities departed from expected settling velocities derived from Stokes’ Law for particles with the same size and densities of 1·1 g cm^–3, we employed a one-way ANOVA. The response variable was the difference between observed and expected settling velocities, and the grouping factor was the variable ‘species’. This analysis was followed by Tukey’s post-hoc test to identify species, or groups of species, for which the observations were significantly different. For these analyses, we used the ‘stats’ (Chambers et al., 1992) and ‘multcomp’ packages (Hothorn et al., 2008) in R version 3.1.3 (R Development Core Team, 2015).

RESULTS

Spore ornamentation patterns are described in Fig. 2 and Table 1 (see Supplementary Data Fig. S1 for the complete set of pictures for ten independent spores per species). Average spore roundness and circularity significantly differed among species (ANOVA: F = 8·713, P < 0·001; F = 3·794, P < 0·01; respectively). Spores were either almost spherical (e.g. in Bryum capillare, Fig. 2B) or substantially dissymmetric, with a convex distal side and a flattened proximal side (e.g. in Conostomum tetragonum, Fig. 2H, which exhibited the lowest values of roundness). Ornamentation patterns varied both within spores, often with a marked asymmetry between the distal and proximal side, and among species (Fig. S1; Fig. 2; Table 1). Spores tended to be more conspicuously ornamented on the distal side than on the proximal side. For example, the spores of Polytrichum commune and B. capillare were psillate on the proximal side, whereas the distal side was ornamented by taller scabrate or bacculate perine elements, as shown on the spores in the equatorial position in Fig. 2A and B. Variation in ornamentation patterns was even stronger in species with asymmetrical spores such as C. tetragonum, where the distal side was verrucate, whereas the proximal side was almost smooth, as shown by the spore in equatorial view in Fig. 2H (see also the striking difference in ornamentation in the close-up of Fig. 2h).

Fig. 2.

Scanning electron microscope photographs of the investigated moss spores. (A) Polytrichum commune: spore in equatorial position showing the heterogeneity in the ornamentation pattern between the psillate proximal side (2) and the distal side with dense scabrate perine elements (1); (a) close-up of the proximal side. (B) Bryum capillare: spore in equatorial position showing the heterogeneity in the ornamentation pattern between the psillate proximal side with gemmate perine elements (2) and the distal side with bacculate perine elements (1); (b) close-up showing the difference between the ornamentation of the distal (1) and proximal (2) sides. (C) Dicranum scoparium: spore in equatorial position showing the dense, clavate perine elements (1 in close-up c) that are sometimes fused (2 in close-up c). (D) Pohlia nutans: distal side with clavate perine elements; (d) close-up showing the heterogeneity of the proximal side, with psillate (2) and clavate (1) perine elements. (E) Ulota bruchii: distal side showing verrucate perine elements (close-up in e). (F) Philonotis fontana: spore in equatorial position, with the distal side ornamented with dense, sometimes fused papillate elements; (f) close-up showing the difference in the ornamentation of the distal (1) and proximal (2) sides. (G) Physcomitrium pyriforme: distal side densely covered by 2–4 μm long spinula and fused densely bacculate perine elements (close-up in g). (H) Conostomum tetragonum: spore in equatorial position showing the difference between the verrucate distal (top, see detail in h1) and psillate (bottom, see detail in h2) sides. (I) Encalypta vulgaris: distal side with verrucate perine elements and gemmate secondary perine elements, proximal side (i) with fused perine elements and gemmate secondary perine elements (see Table 1 for a description of spore ultrastructure).

Mean settling velocities and average D_a for each of the nine investigated species are reported in Table 1. Overall inter-specific fall velocities varied from an average of 0·495 cm s^–1, in the case of B. capillare, to 8·525 cm s^–1 for Encalypta vulgaris. According to the LMM approach, the random intercept of ‘sporophyte’ was included in the three competing best-fit models (ΔAICc <2), while either the random slope of ‘circularity’, ‘roundness’ or ‘species’ were also included (Table 2). Using the best random effect structure (ΔAICc = 0), the final selected best-fit model including spore diameter accounted for 98·52 % (R²) of the total variation in settling velocity. The intercept of this final model (see Table 1) was –0·021 and the slope for spore diameter was 0·001.

Table 2.

Factors (species, sporophyte, spore circularity and roundness) included in the random structure controlling for variation in the relationship between settling velocity and spore diameter in nine moss species (linear mixed-effect model analysis)

Random slope				Random intercept				k	AICc	ΔAICW
Species	Sporophyte	Circularity	Roundness	Species	Sporophyte	Circularity	Roundness
	1					1		3	1078·104	0
	1						1	3	1078·1054	4·55E-13
	1			1				3	1078·1064	2·50E-12

Only the best random effect structures (i.e. ΔAICc <2) are shown. A ‘blank field’ indicates that the parameter for a given factor was not included in a given model. The random structure (variables allowed to vary across measurements, see Statistical analyses), the number of parameters in the model (k), AICc, and ΔAICc are given for each model.

Variation in the settling velocity of the spores of the nine investigated species as a function of spore diameter is illustrated in Fig. 3. Whereas settling velocities of spores smaller than 30 μm were within the range of expectations derived from Stokes’ Law for particles of the same size and a density of 1 g cm^–3, spores >30 μm tended to depart from those expectations (Fig. 3). A significant departure of observed and expected settling velocities depending on the factor ‘species’ (ANOVA, F = 69·84, P < 0·001) was thus confirmed in species with spores larger than 30 μm, identifying five groups of species (Fig. 4). The first group included species (B. capillare, Dicranum scoparium, Philonotis fontana, Pohlia nutans and P. commune) with spores smaller than 30 μm and with low ornamentation patterns (Table 1), which exhibited settling velocities in the range of Stokes’ Law expectations. In the other four groups, the settling velocities of the spores, which are variously ornamented (see Fig. 2; Table 1), significantly departed from the observations. In Ulota bruchii and Encalypta vulgaris, the settling velocity of the spores, which are about 20–26 and 30–45 μm in diameter, respectively, was underestimated from Stokes’ Law. These differences are shown by the Tukey’s test groups (b and e in Fig. 3) and also illustrated by the D_a calculated from the observed settling velocities: 28–31 and 47–57 μm, respectively. In the case of Physcomitrium pyriforme and C. tetragonum, the spores, which are variously ornamented and >30 μm in diameter (Table 1), conversely exhibited a settling velocity that was significantly lower than expected, leading to overestimation by Stokes’ Law. Conostomum tetragonum exhibited the strongest departures from theoretical expectations, as also illustrated by its D_a ranging from 32 to 35 μm against an observed diameter of 38–40 μm.

Fig. 3.

Relationship between settling velocity and spore diameter in nine moss species. The regression lines are derived from linear mixed effects models accounting for variation among species, sporophytes and date of experiment. The black and red lines correspond to the regression lines derived from the analysis of the observed values and the those derived from Stokes’ Law for theoretical particles, respectively.

Fig. 4.

Difference between the settling velocities observed for the spores of nine moss species and the expected settling velocity according to Stokes’ Law for particles with a density of 1.1 g cm^–3. Letters indicate the groups of species exhibiting significant differences of settling velocities based on Tukey’s test.

DISCUSSION

In agreement with our primary hypothesis, there was a significant positive relationship between spore settling velocity and size, supporting the notion that settling velocity can be well predicted from spore diameter, at least for globally spherical spores (Aylor, 2002; Hussein et al., 2013). The observed average settling velocity values are comparable with the settling velocities reported in the smallest pollen grains (about 1·7 cm s^–1 for pollen of 16–20 μm and 3·7 cm s^–1 for pollens of 30–35 μm; see Huang et al., 2015), urediospores (0·86 cm s^–1 for spores of about 20 μm) and Lycopodium spores (1·9–2·3 cm s^–1 for spores slightly larger than 30 μm) (Ferrandino and Aylor, 1984), but much lower than larger pollen grains in corn (30 cm s^–1 for grains of 90 μm; Di-Giovanni et al., 1995) and seeds of Asteraceae equipped with a pappus, wherein settling velocities of 27–65 cm s^–1 have been reported (Casseau et al., 2015). These observations support the notion that moss spores are, with their tiny size, well equipped for wind long-distance dispersal. The significant relationship established between spore diameter and settling velocity can further be employed to estimate the settling velocities of any species based on its spore diameter, and be used in explicit dispersal models (Travis et al., 2013).

However, settling velocities in mosses can significantly depart from expectations derived from Stokes’ Law using the density of 1·1 g cm^–3 reported for spores by Gregory (1973). This departure was caused by the different behaviour of spores from a threshold size above 30 μm. While spores below that threshold exhibited settling velocities fitting with the expectations resulting from Stokes’ Law, spores above it displayed more unpredictable settling velocities. Thus, the spores of C. tetragonum had a lower settling velocity than expected. In Sphagnum, Sundberg (2010) similarly found that the spore settling velocity was about 48 % slower than expected for spherical spores with comparable diameters, meaning that Sphagnum spores of 20–45 μm have aerodynamic diameters of spherical-shape smooth spheres of 15–30 μm. Interestingly, the spores of E. vulgaris, with a diameter of approx. 47 μm (see Table 1) exhibited the reverse trend. It therefore appears that the arbitrary threshold diameter of 20 μm between ‘small’ and ‘large’ spores (van Zanten and Pócs, 1981; During, 1992) is not necessarily a good proxy of their dispersal capacities.

Several mechanisms could explain the observed departures of settling velocities from the expectations of Stokes’ Law. First, the density of protoplasm is relatively uniform among plant species, and is roughly equal to that of water, but whole spore or pollen grain densities vary, e.g. 1·175 and 0·987 g cm^–3 for Lycopodium and Pinus, respectively (Niklas, 1985). Variation in spore densities in mosses, which, to our knowledge, have not been documented yet, could offer a straightforward explanation, in particular for the higher than expected settling velocity of the spores of E. vulgaris.

Secondly, the inclusion of spore circularity and spore roundness in the random structure of the best-fit models provides evidence for their role in modulating settling velocities. Departure from a spherical shape could explain the slower than expected settling velocity of the spores of C. tetragonum, which exhibited the lowest values of roundness. Indeed, spherical particles can be dispersed with higher velocity and for longer distances than asymmetrical spores, since there is lower friction force in the former (Ackerman, 2002). In this context, Arredondo-Núñez et al. (2011) observed that pollen grains of introduced species are significantly more spherical than in native species, enhancing their dispersal capacities, and hence, potentially, the invasion potential of the species.

Regarding the impact of spore ornamentation, the variation observed within spores between the distal and proximal sides probably reflects the pressure on the proximal side when the spores are initially clustered together in tetrads, but inter-specific variation in the ornamentation of the distal side could be under selection. In fact, we observed that the settling velocities of spores with low ornamentation patterns were consistent with the expectations of Stokes’ Law, whereas that of spores variously ornamented significantly departed from those expectations. For example, the conspicuously ornamented spores of P. pyriforme and U. bruchii exhibited slower settling velocities than expected. Bolinder et al. (2015) similarly observed that variation in ultrastructure affects pollen settling velocities. In fact, ornamentations of the wall can lead to a substantial reduction of the settling velocity (Schwendemann et al., 2007). In Pinus, for example, the two hollow sacs of the pollen grain decrease the settling velocity by increasing the aerodynamic drag forces acting on the grain (Schwendemann et al., 2007). In this context, it is therefore tempting to interpret the departure of the settling velocities from the expectations of Stokes’ Law reported here as a consequence of spore ornamentation. This could explain, as Medina and Estébanez (2014) suggested based on ultrastructure analyses in the genus Orthotrichum, the selective pressure that is responsible for the spectacular variation of the spore ornamentation in bryophytes. In fact, the function of the perine, which is the outermost layer of the spore and responsible for its ornamentation, is still poorly understood, but was previously interpreted in terms of protection against desiccation or rapid water uptake upon rehydratation (Mogensen, 1983). Andersen (1992) suggested that phenotypic variability in seed morphology reflects different dispersal ‘strategies’ employed by the species, which may be correlated with other life-history traits and with ecological characteristics. Indeed, metapopulation models suggest that, in some landscapes, selection pressures against short-distance dispersal may promote the evolution of seeds with high long-distance capacities, whereas in severely fragmented landscapes, particularly oceanic islands, reverse selection pressure can be found, as seeds that disperse from the safe site can be easily lost (Olivieri et al., 1995; Cody and Overton, 1996; but see Talavera et al., 2012). In bryophytes, one of the most important trade-offs employed to define life strategies concerns the production of a few, large spores or of many, small spores (During, 1992) that control dispersal ability vs. establishment rate, and, hence, dispersal distance and establishment ability (Löbel and Rydin, 2010). Thus, large spores have a low dispersal capacity but better chances of successful establishment (Löbel and Rydin, 2010). They are therefore prominently produced by shuttle species of unstable habitats that persist predictably at a given site, such as E. vulgaris. We expect similar behaviours in the large, strongly ornamented spores of annual species from temporary habitats often characterized by a severe drought season, such as the thalloid liverworts Riccia and Corsinia or the mosses Tortula and Archidium, wherein counter-selection for dispersal is evidenced by the lack of a seta in these thalloid liverwort species, and the frequent lack of a peristome (cleistocarpy) in the latter.

CONCLUSION

Our results suggest that the settling velocities of moss spores can be accurately estimated from their size, allowing their implementation in explicit dispersal models. Significant departures from the expectations of Stokes’ Law were, however, observed for large spores with complex ornamentations of the perine. Although we demonstrated that variation in spore roundness and circularity significantly impact on spore settling velocities, the limited number of species investigated here prevented us from disentangling the individual role of these and other potentially correlated factors such as density. Our observations nonetheless add to the surprisingly very limited literature on the correlated variation in spore ultrastructure and settling velocity, allowing us to formulate the hypothesis that variation in spore ultrastructure modifies their dispersal capacities, and hence is adaptive. In this context, our study opens up a large avenue for research on the still poorly understood function of the striking ornamentations observed in bryophyte spores.

SUPPLEMENTARY DATA

Supplementary data are available online at www.aob.oxfordjournals.org and consist of the following. Table S1: list of specimens used for the experiments and conserved at the herbarium of the University of Liege. Table S2: spore settling velocities (v_set) and sizes estimated from acquired high-speed camera images, and derived theoretical v_set and aerodynamic diameter (D_a) for the selected sporophytes and spores. Figure S1: SEM photographs of ten individual spores per species. Nine video sequences illustrating, for each investigated species, one of the source materials used to build the database (Table S2).