Plants as populations of release sites for seed dispersal: a structural-statistical analysis of the effects of competition on Raphanus raphanistrum

Authors


Correspondence author. E-mail: rcousens@unimelb.edu.au

Summary

  1. Trajectories of dispersing seeds begin at the positions of their fruits on the maternal plant. Mechanistic simulation models usually assume that seed release is restricted to a characteristic, species-specific height. However, real canopies constitute distributed rather than point sources, which may have important consequences for dispersal kernels.
  2. Fruit positions are determined by plant architecture, which is under both genetic control and environmental influence. Competition with other plants has a major modifying influence on canopy structure.
  3. We used quantitative methods to describe the positions of fruits on plants of Raphanus raphanistrum L., examined how fruit spatial distributions change when plants grow under interspecific competition and explored how this is related to changes in the structural geometry and topology of the plant.
  4. Raphanus raphanistrum was grown either as individual plants or in a wheat crop. Branching structures and fruit positions were captured using a three-dimensional digitizer. Propagule locations were also mapped on the ground after dispersal. Fruit distributions pre-dispersal were analysed using various statistical approaches; plant topological and geometrical indices were calculated for the branching structures.
  5. Plants grown under competition were smaller, but the reduced size was because fewer modules were produced rather than because individual branches were in some way different. The distribution of these branches was also different under competition, with more apical dominance resulting in less branching along dominant modules. Under competition, fruits were concentrated in the upper parts of the canopy and closer, in the horizontal plane, to the base of the plant. This resulted in much more restricted local seed shadows post-dispersal.
  6. Synthesis. The effect of competition on plant size is primarily a result of a reduction in initiation of branches. For species with limited dispersal ability, this results in a greatly modified seed shadow at short distances. In the case of agricultural weeds, the concentration of fruits at greater heights when competing with a crop might result in a greater proportion being dispersed long distances by harvesting machinery, but they would be fewer in number.

Introduction

The trajectory followed by a dispersing propagule (seed, fruit or vegetative unit) is influenced by a range of physical and biological processes. Schurr, Steinitz & Nathan (2008) refer to ‘source’ factors and ‘path’ factors. Most ecological studies, especially models, have focussed on path factors, in particular the over-riding influence of wind, water and animal vectors in causing movement; the characteristics of the recipient environment are also important, indirectly, by changing the behaviour of vectors and, directly, by impeding the propagule (Pounden et al. 2008) or by removing it from a carrier. Source factors include position on the parent plant (where is it released from), timing of propagule maturity (when is it ready to disperse: e.g. Nathan, Safriel & Noy-Meir 2001), threshold force required for release (what is required to initiate dispersal: e.g. Greene & Johnson 1992) and additional force applied by the plant at release (e.g. Garrison, Miller & Raspet 2000). Position on the parent plant has long been recognized as crucial to dispersal distance: propagules released from a greater height have further to fall and therefore a greater potential for sideways movement due to wind (e.g. Andersen 1991; Tackenberg 2003; Nathan et al. 2011a) and they may be more susceptible to updrafts (Nathan & Katul 2005); those produced within a dense canopy will be released into lower wind speeds (Finnigan & Brunet 1995). Release height also has implications for dispersal of propagules on the outsides of animals (Sorensen 1986; Hughes et al. 1994), but not so much for those forcibly propelled into the air (Cousens, Dytham & Law 2008).

Simulation models for dispersal trajectories assume a ‘point source’: if a propagule is released at point X1 in a specified set of conditions, at what point X2 does it reach the end of its path? Release height is usually assumed to be a species characteristic, taken from the literature or from data bases giving typical plant heights (Tackenberg 2003), or is assumed to be at a fixed percentage of that typical height (Greene & Johnson 1996; Nathan et al. 2011a). The potential importance of variation in release height within the species may be examined in models by allowing the height to vary stochastically according to an assumed distribution (supported by field observations – Nathan, Safriel & Noy-Meir 2001; Nathan et al. 2002, 2011b). However, a real plant is a ‘distributed’ source, that is, a population of point sources, and not a single point source. For many species, propagule release points on a plant vary considerably, both horizontally and vertically (Cousens, Dytham & Law 2008), and do not appear to be concentrated tightly around a characteristic height (Hard 1964; Trapp 1988). It has been proposed that both vertical and horizontal distributions of propagules will vary in predictable species-dependent ways and with growing conditions such as competition (Cousens & Rawlinson 2001). Although this variation has been predicted to be of little consequence for long-distance dispersal in a wind-dispersed tree (Nathan, Safriel & Noy-Meir 2001), it could be of considerable significance in determining the shape of the seed shadow close to the parent (Clark et al. 1999), especially in species with heavier propagules (Cousens & Rawlinson 2001). However, we have remarkably few data on the actual vertical distributions of propagule release sites within a plant and almost no data on their horizontal distributions (Cousens, Dytham & Law 2008); without these, it is difficult to determine their true consequences for dispersal.

The number and positions of propagules at the time that its seeds are ready to disperse are the outcome of the interactions of growth and developmental dynamic processes over the plant's lifetime. These include meristem activity [e.g. apical dominance and control (Cline 1997); internal responses to resource availability (de Kroon et al. 2009)], resource capture and resource allocation (which is in turn governed by genetic and environmentally driven behaviour, such as phenology and inflorescence structural ‘formula’). The ‘architecture’ of the plant, divided conceptually by researchers into geometry (the number of component structures – including reproductive units, their sizes, angles and so on) and topology (the way in which the structures are connected together; Room, Maillette & Hanan 1994; Godin, Costes & Sinoquet 1999), arises as a consequence. Architectural analysis has been used, amongst other things, to quantify (and then simulate) species morphology, to investigate phylogenetic relationships and evolutionary aspects of inflorescence structural development (Prusinkiewicz et al. 2007), to predict light interception and photosynthesis (Duursma et al. 2012) and, in one case, to simulate interspecific competition (Cici, Adkins & Hanan 2008). We expect the growing environment to modify plant architecture (Bennett & Leyser 2006). Shading, for example, will cause the suppression of lateral meristems through apical dominance (Cline 1991, 1997), thereby reducing branch number and – inevitably – leaf and reproductive output. Thus, interference between plants affects quantitative aspects of stem geometry (e.g. Geber 1989; Weiner, Berntson & Thomas 1990), and this can be correlated with scale and pattern of dispersal (Thiede & Augspurger 1996; Wender, Polisetti & Donohue 2005). Although individual fruit initiation and development have been the subject of intensive physiological study, translation of this knowledge to an understanding of the placements of seeds within an entire plant has rarely been considered. It would seem to us that an architectural analysis would be a logical way in which to begin to understand the processes leading from the growing environment to its consequences for dispersal – that is source effects.

The aims of this study were therefore the following: (i) to analyse the distribution of propagules within a non-wind-adapted annual plant (as a contrast with our greater familiarity with wind-dispersed trees), (ii) to examine how this distribution may vary under highly contrasting conditions for growth (with and without competition), (iii) to interpret these distributions with respect to plant architecture (both geometry and topology) and (iv) to determine the consequences for dispersal in this species.

Materials and methods

Studied Species

Originally from the Mediterranean, the annual plant Raphanus raphanistrum L. (wild radish) has spread as an agricultural and waste-ground weed to many countries. Thus, it has attracted the attention of agricultural researchers seeking to understand its life cycle, impacts on crops and responses to management options (Reeves, Code & Piggin 1981; Cheam 1986; Cousens et al. 2001). It has also been used as a model in ecological and evolutionary research (e.g. Conner, Franks & Stewart 2003; Hegde et al. 2006; Dudley & File 2007; Elam et al. 2007; Cousens, Young & Tadayyon 2010).

Raphanus raphanistrum plants have a vegetative rosette phase, where they produce no stems; the duration of this varies with time of year at which seedlings emerge (Reeves, Code & Piggin 1981). Developing buds can be seen in the centre of the rosette just before the main stem elongates (‘bolts’). Once bolting of the main stem has begun, additional stems can sometimes emerge from the rosette (particularly where resources are abundant), presumably from meristems in the axils of rosette leaves. Fruits are produced along racemes over a number of weeks. Each fruit may contain up to 15 seeds, although usually much fewer. Those fruits initiated towards the end of the plant's life tend to be smaller. Depending on the weather and pollinator activity, fruits may be aborted early in development. As fruits mature, they fall to the ground in the sequence of their initiation; unless something destructive happens, the denuded, dead stems are left as a rigid structure.

In a crop, the timing and height of harvesting will determine how many R. raphanistrum fruits are cut off and dispersed elsewhere within the field, or to other fields perhaps many kilometres away, and how many fall to the ground around the parent plant. Where mature fruits detach, the abscission layer leaves a distinctive cup-shaped scar; fruits aborted without producing seeds do not leave such a mark. After some weeks, fruits on the ground separate into single-seeded segments, whereas those entering a harvester will break into segments immediately.

Experimental Design

An experiment was established at the field station of the Burnley Campus of the University of Melbourne (145°02′ E, 38°14′ S). The site has a silty loam soil and received 627 mm of rain during in the calendar year of the experiment. Existing weeds were sprayed with 360 g L−1 glyphosate at a rate of 10 mL L−1 and the soil was cultivated before sowing. Plots were 2 × 2 m, with a space of 0.90 m between them: commercial weed-suppressive matting was laid between plots. Six R. raphanistrum seeds, from a population in Kent, Western Australia (118°22′E, 34°43′S), were sown at the centre of each plot on 4 July 2003. Plots were irrigated with 18 L of water once the seeds had been sown. Rainfall was the only source of water thereafter. Seedlings were thinned to one plant per plot when it was considered that the remaining one would survive to maturity. There were six replicate plots.

Additional plots were sown with wheat (Triticum aestivum L. cv. Frame) as well as R. raphanistrum to enable us to examine the consequent changes in architecture. Plot size and R. raphanistrum density were the same as before. Wheat seeds were sown by hand in 20 rows per plot at a depth of 1.5 cm. Intrarow spacing was adjusted to achieve wheat densities of 90, 180 and 360 plants per m2. Where seedlings failed to emerge, their positions were filled by transplants from a ‘reserve’ area, ensuring that target densities were achieved. Mortality thereafter was negligible. Unfortunately, a storm caused several crop plots to lodge; the remainder were therefore pooled as a single ‘with competition’ treatment.

Data Collection

A three-dimensional digitizer (Isotrak II®: Polhemus, Colchester, VT, USA) was used to capture the branching systems of the R. raphanistrum plants and the locations of their propagule (fruit) release sites. Data capture was facilitated using the software package Floradig (Hanan & Room 2000; Hanan & Wang 2004). At the end of the growing season, after most fruits had fallen to the ground (January–February 2004), each R. raphanistrum plant was cut at its base and taken to the laboratory. At that stage, the dead plant ‘skeleton’ was rigid and reasonably represented the mature plant at the time of fruit release. Height of the wheat at maturity was approximately 110 cm.

To better explain our procedures, we define three terms from theoretical work on ‘binary tree’ structures, graph objects combining nodes and joining edges. When using a mathematical abstraction of a plant, nodes of binary trees usually correspond to botanical nodes, the points where leaves and new branches are borne upon a parent branch. To make the digitizing of very large plant structures possible, however, we ignore those intermediate nodes that have made no contribution to the structure. We refer to the section of stem between two consecutive nodes as a stem segment, which therefore defines the adjacency between two nodes. In studies of the mathematics of branching structure and graph theory, analogous terms to stem segment might be edge or link. The concept of a stem segment thus differs slightly from that of an internode, which is usually strictly defined as the length of stem between two successive leaves (and any subsequent branching that occurs from the axils of those leaves): a stem segment may consist of more than one internode if some axillary buds failed to develop. Finally, in recognition that ‘parentage’ of stem segments may be important; a module is defined as the sequence of internodes produced by a single shoot apical meristem, which may also comprise of a number of stem segments.

Three-dimensional digitizing captures both topological and geometrical information about botanical branching (Godin, Costes & Sinoquet 1999). As each node is visited with a stylus, Floradig records both the x, y, z coordinates of the node (z dimension defined as the vertical axis, x and y as horizontal axes) and its topological information (i.e. its position relative to other stem segments and nodes). For each plant, digitizing began at the base of the plant where the main stem emerges from the soil surface. Nodes were digitized, in turn, along each module. Upon arriving at a new branching point, the child module was then mapped to its end, at which time digitizing of the parent module was resumed. The spatial coordinates of every fruit base (where fruits were still attached) and fruit abscission scar (where fruits had already fallen to the ground) were also recorded using Floradig.

Raw plant architecture data exported from Floradig were imported into a Microsoft Access® data base (Microsoft, Redmond WA, USA). The r statistical software (R Development Core Team 2011) was then used to extract data from this data base and to process the raw architecture data. Through simple algorithms, detailed statistical information was obtained at a whole plant or individual module level, along with information on the structural organization of parent and child modules.

Locations of fruits after dispersal were also mapped using the digitizer. In this case, however, only x and y coordinates were recorded. Their individual points of origin on the maternal plant, however, could not be determined.

Extraction of Information

Positions of fruit release sites within a canopy

There are various ways of analysing the spatial pattern of the ‘population’ of fruit release sites independently of the shoots connecting them, that is as a purely statistical exercise. Assuming an isometric structure, horizontal and vertical frequency distributions of the positions of the abscission layers of fruits (the starting points for dispersal trajectories) relative to the base of the main stem (the dispersal destination in the previous generation) were constructed for each plant. These horizontal and vertical distributions were characterized using a two-parameter Weibull distribution; the two parameters – shape and scale – were estimated using a maximum likelihood approach in r. Significance of the fit of the distribution was determined from the Kolmogorov–Smirnov test statistic. The Weibull distribution was chosen specifically because it can describe a wide range of shapes and can be skewed in either direction, thus allowing us to explore plasticity in canopy shape using a single mathematical function. If the shape parameter is < 2.6, the Weibull distribution is positively skewed; if > 3.7, the distribution is negatively skewed. It also fitted most of our data reasonably well, while other distributions such as the normal and lognormal often fitted poorly. Indeed, fits to the Weibull were compared with those of the lognormal (which, like other similar functions, is fixed in shape) using the Akaike Information Criterion and in 24 of 36 cases resulted in a better description of the data (Table S1, Supporting Information).

The spatial patterns of release sites within the canopy were quantified using three complementary indices originally proposed by Villéger, Mason & Mouillot (2008) for analysis of multidimensional functional diversity; we substituted the three spatial coordinates for the multiple trait dimensions and conducted the analyses in r. These indices (see original paper for full details) are

  1. Spatial occupancy (SO): the volume of the minimum convex hull (a polyhedron) around all positions, which represents the minimum amount of three-dimensional space filled by the fruit release points. Dimensions are length3.
  2. Spatial evenness (SEI): the regularity of fruits along the minimum spanning tree (MST: Rangel, Diniz-Filho & Bini 2010) linking all locations. This measures the regularity with which fruits are distributed within the spatial volume occupied. The index is dimensionless, taking values between 0 and 1 and decreases when distances between fruits are less even. [Note that the statistical MST shares no logical relationship to the topological tree of the actual plant.]
  3. Spatial divergence (SDI): the way that fruits are distributed from the centre to the border of the convex hull. Spatial divergence approaches zero when most fruits are very close to the centre of gravity, and it approaches unity when most fruits are very distant from the centre of gravity. The index is also dimensionless.

The distribution of fruit heights – relative to the height of the cutter bar – determines how many seeds could potentially enter a combine harvester, the primary long-distance dispersal vector in this species (i.e. assuming that all fruits are still on the plant at harvest). Cumulative frequency distributions of distance from the uppermost point in the canopy were therefore constructed.

Component architectural units (geometry)

To summarize plant geometry, we extracted frequency distributions of the following: module lengths; stem segment lengths; raceme lengths; and module angles. A raceme was defined as the section of a module between its apex and its lowermost fruit. The angle of a module relative to horizontal, which may change along its length, was calculated as the weighted mean of the angles of each of its stem segments, where weights were the length of each stem segment. In each case, kernel density estimates (nonparametric estimates of the probability density function) were used to depict the distribution, using r. The maximum plant height, total number of stem segments, number of modules and the summed length of modules were extracted as measures of plant size, while the total number of fruits, either still remaining on a plant, or past presence indicated by abscission scar, were obtained as a measure of reproductive output.

Branching structure (topology)

We used two topological indices: the mean stem segment order (MO), a measure of where in the branching structure most of the stem has developed, and the tree asymmetry index (TAI), which provides a measure of where a branching structure sits in the spectrum between perfect and incomplete binary trees (van Pelt, Verwer & Uylings 1989; van Pelt et al. 1992). TAI can be treated as a measure of apical dominance and has a range from 0 to 1, where values near 1 indicate a thin binary tree and values near 0 indicate a more compact, or branchy, binary tree. Welch's t-test (Ruxton 2006) was used to test the statistical significance of the effect of competition on TAI. As the TAIs are bounded [0, 1], a logit transform, (log(y/[1 − y]), was used to map the TAIs monotonically to the whole real line (−∞, ∞) to fulfil linear modelling assumptions (Warton & Hui 2011). We also produced kernel density estimates for the number of stem segments of each branch order (see Appendix S1 for a detailed explanation of branch orders and binary trees).

Seed shadow

Dispersal distance was defined as the final horizontal displacement of the fruit from the base of the parent plant primary stem. Displacement from the base of the parent is the appropriate measurement from a population dynamics perspective, since it relates propagule location in one generation to propagule locations in the next (although clearly it is not the appropriate measure when studying trajectories of individual fruits). We calculated mean and maximum dispersal distances and area over which fruits were dispersed (the two-dimensional convex hull for fruits on the ground, using the qhull 2003.1 software – Barber, Dobkin & Huhdanpaa 1996). Finally, we calculated the mean and standard deviations of distances of fruits along the MST constructed through them, using the sam program v4 (Rangel, Diniz-Filho & Bini 2010): this gives information on the evenness of spread of fruits on the ground. We applied Hoffman & Jain's (1983) method to normalize these measures (Dussert et al. 1989). Comparison with the same parameters calculated for the horizontal distribution of abscission scars on the plants (the expected values for dispersal if all fruits fell directly to the ground, that is dispersal due solely to plant growth) was used to indicate the influence of source factors on short-distance dispersal.

Results

The architecture of R. raphanistrum plants, and hence the pre-dispersal distribution of fruits in space, was modified considerably by growing in a wheat crop. Examples of the three-dimensional branching structures captured with Floradig are shown in Fig. 1.

Figure 1.

Example Raphanus raphanistrum branching structures, as captured by the Floradig software. Colours are not natural and have been selected merely for emphasis of structures. Oblique views of (a) Plant 3 (without competition), (b) Plant 8 (with competition), (c) and (d) show the respective views from vertically above. All axes are in millimetres.

Positions of Fruit Release Sites within a Canopy

In general, the Weibull distributions fitted the vertical and horizontal seed position data well (Fig. S1), although there was poor fit for small plants having very few fruits (Fig. 2b). Fit to the Weibull was usually much better than the lognormal for large plants and little different in small plants with few fruits (Table S2). Under competition, seed release sites were further away from the ground on average, with Weibull scale parameter double the value found in the absence of competition (Table 1). Competition also changed the shape of the height distribution of fruits, with production being concentrated relatively more towards the top of the crown (i.e. the tail was towards the ground – large Weibull shape parameter – compared with away from the ground in the absence of competition). Plants were geometrically thinner under competition, with fruit release points being concentrated closer to the main stem (Table 1 and Fig. 3a). It was also apparent that for plants grown without competition there was a ‘hole’ in the centre of plants with respect to fruit placement (lower left corner of Fig. 2a), due to the plant's more horizontal pattern of development. Cumulative frequency distributions of fruit release height also show that a greater proportion of fruits occurred low down on plants in the absence of competition (Fig. 3b).

Table 1. Mean Weibull parameters for frequency distributions of fruit release height, horizontal distance from plant base while still on the plant, and distance from plant base post-dispersal
Plant numberRelease height (mm)Horizontal distance pre-dispersal (mm)Horizontal distance post-dispersal (mm)
ScaleShapeScaleShapeScaleShape
  1. Standard errors are in brackets.

  2. a

    Two-sample t-test comparing with- and without-competition plants, assuming unequal variances. Significant results are shown in bold.

  3. b

    Data loge-transformed prior to analysis.

Without competition216 (28.1)1.89 (0.26)476 (54.6)3.78 (0.27)549 (58.8)2.86 (0.35)
With competition429 (41.4)9.04 (2.94)192 (44.0)2.82 (0.51)196 (30.6)2.25 (0.15)
Pa < 0.01 < 0.05 b < 0.01 0.08 < 0.001 0.15
Figure 2.

Scatterplot showing radial distances and heights of propagule release sites, relative to the base of the stem. Grey histograms show the vertical and horizontal frequency distributions of fruit release sites in the canopy relative. The lower histogram shows the frequency distribution of radial distances after dispersal. Curves are the fitted Weibull distributions (see Table 1 for parameter values). (a) Plant 3 (no competition), (b) Plant 8 (with competition).

Figure 3.

Cumulative distributions of (a) horizontal distances and (b) heights of fruits from the plant base, prior to dispersal. Solid lines show plants grown without competition.

The spatial volume containing fruit release sites decreased by two orders of magnitude under competition (Table 2, Table S1). Spatial evenness within the crown was unaffected, while spatial diversity decreased slightly.

Table 2. Mean indices for spatial positions of fruit release sites within the crown
Plant numberSpatial occupancy (m3)Spatial evennessSpatial diversity
  1. See text for definitions. SEs are given in brackets.

  2. a

    Two-sample t-test comparing with- and without-competition plants, assuming unequal variances. Significant results are shown in bold.

  3. b

    Spatial occupancy was log-transformed prior to analysis (means are therefore geometric means).

Without competition0.343 (0.127)0.806 (0.015)0.814 (0.010)
With competition0.00405 (0.071)0.785 (0.021)0.761 (0.019)
Pa < 0.05 b > 0.05 < 0.05

Component Architectural Units

The number of stem segments, total length of all modules and number of fruits were all reduced considerably by competition (Table 3). One plant growing without wheat had a total stem length of 240 m. With competition, there tended to be fewer short modules, more long stem segments (i.e. realized branching points were spaced further apart), a greater proportion of shorter racemes and more modules with angles close to vertical (Fig. 4). Plant height was unaffected by competition (Table 3). In three of the largest plants, growing without competition, the length of the primary stem was almost double the height of the plant, indicating that the stems were considerably bent; for other plants, the primary stem length was usually within 20% of the plant height. The number of fruits per raceme was not affected by competition (Table 3); the significantly greater number of fruits per plant in plants growing without competition was thus a result of the significantly larger number of modules produced (Table 3).

Table 3. Effect of competition on means of parameters related to plant size and reproductive output (SE in brackets)
 Plant height (m)Length of primary stem (m)aTotal branch length (m)Number of stem segmentsNumber of modulesNumber of fruitsNumber of fruits per raceme
  1. a

    In cases where the primary stem had been damaged (or otherwise failed to develop), this was taken as the length of the pathway from the dominant apical meristem to the plant base.

  2. b

    Paired two-sided t-tests, assuming unequal variances.

Without competition0.563 (0.102)0.877 (0.237)150.3 (29.91)1250 (542)625 (271)2218 (412)3.92 (1.38)
With competition0.605 (0.212)0.692 (0.201)11.2 (7.45)89 (137)45.2 (68.5)266 (194)4.37 (2.18)
Pb> 0.05> 0.05< 0.01< 0.01< 0.01< 0.01> 0.05
Figure 4.

Frequency distributions of (a) module length, (b) stem segment length, (c) raceme length and (d) branch angle relative to horizontal. All are derived using kernel density estimation. Solid lines indicate plants grown without competition.

Branching Structure

Branching asymmetry, or mean TAI, for plants grown with competition was very much greater (0.62, SD 0.21) than that for plants grown without competition (0.39, SD 0.04). The higher branching asymmetry in the plants grown under competitive conditions indicates more apical dominance, on average, and a lack of module development over the whole crown. This was also reflected by the mean and distribution of stem segment orders for plants grown with and without competition (Fig. S2). Although there was no significant difference in maximum height between plants with and without competition, the distribution of stem segment orders indicates lower altitudes and fewer branching events throughout the crowns of plants grown under competition.

Seed Shadow

Analysing the horizontal patterns of fruit positions, the adjusted standard deviation of distances within the MST indicated that fruits are more evenly spread (horizontally) on the plant than on the ground post-dispersal. The difference between post- and pre-dispersal increased with plant size (Fig. 5a), although this variable is confounded with the physical presence of wheat stems. The adjusted means of these MST distances suggest that fruits are also closer together on larger plants (Fig. 5b). Horizontal distributions of fruits pre- and post-abscission differed significantly for all large plants, with five of six plants having greater scale parameters after dispersal (Table S2). However, this significance was almost inevitable, given the very large number of observations (fruit coordinates). Regression through the origin for Weibull scale parameter post- vs. pre-abscission, using all 12 plants, gave a slope not significantly different from 1 [1.084, r2 = 0.94, P(slope = 1) > 0.05]. Regression of horizontal convex hull around fruits post- vs. pre-dispersal, however, showed that the area was 76% larger after dispersal [r2 = 0.87, P(slope = 1) < 0.001]. This was due to the influence of a small number of outlying fruits, travelling greater distances away from the edge of the crown.

Figure 5.

Correlation between minimum spanning tree (MST) parameters (in a horizontal plane) and fruit number per plant (as a surrogate for plant size). Solid line and filled symbols are for coordinates postrelease; dashed line and open symbols are for horizontal coordinates pre-dispersal. (a) Adjusted standard deviation of distances along the MST; (b) adjusted mean (see text for details). All regressions are significant (P < 0.05).

Discussion

The finding that competition reduces plant size and reproductive output is far from novel. Increased demand for resources decreases their per capita availability and thus reduces growth. Our results, however, help to elaborate how these changes are reflected in the architecture of a plant and the consequent implications for dispersal through alteration of the positions at which propagules are released. Although we did not examine leaf sizes or stem thicknesses, only lengths, numbers and positions of stems and fruits, it is clear from our study that the major component of the size reduction resulting from competition is through the number of modules. Similar conclusions can be reached from the few other studies that have recorded the effects of crowding on plant structural elements (Maillette 1985; Geber 1989; Weiner, Berntson & Thomas 1990; Donohue 1998; Zhang et al. 2008; Japhet, Zhou & Wang 2009). Under competition, fewer meristems initiate new shoots; the resulting simplified structure therefore bears fewer fruits. Although grasses produce tillers in excess, a proportion of which then die (e.g. Thorne & Wood 1987), and trees abort many stems formed in earlier years, in our annual dicotyledon, the response to competition was by reduction in module initiation rather than increased module mortality.

A small reduction in module formation early on will have multiplicative effects from which the plant is unlikely to recover, even if competition is removed. However, plants under intense competition still produced a few modules late in plant development. This may perhaps be because R. raphanistrum is able to escape some of the competition by wheat for light after it bolts (although it has few, small stem leaves in the upper canopy). Alternatively, this may be a programmed event in all plants: Weiner, Berntson & Thomas (1990) found the same phenomenon in monocultures of Impatiens pallida. The delay in module formation results in fewer long modules and a reduction in their mean length. The outcome is that branching structures under intense competition (and hence fruit distribution) tend to be ‘top-heavy’, whereas isolated plants have their centre of gravity at perhaps half to one-third the height of the plant.

The type of information that we have collected for R. raphanistrum could be used to develop structural formulae to be incorporated into architectural models, such as those based on L-systems (Prusinkiewicz et al. 1990) and the parameters could be varied according to the level of crowding and other environmental variables. Such models have been used most powerfully to illustrate the principle of the importance of metamer and module dynamics for plant ‘form’ (Room et al. 1994). They can also be used to estimate light penetration within canopies (Evers et al. 2007; Cieslak et al. 2008) and photosynthesis of whole plants. There is clearly the potential to simulate flower and fruit positions using structural models and hence to predict the statistics of propagule positions and dispersal patterns.

Competition had a major influence over the starting points for seed dispersal trajectories. In the absence of competition, R. raphanistrum fruit release positions were distributed across a broad range of heights with a mode at an average of 38% of the overall height of the plant. The distribution was skewed, rather than symmetrical. Under competition from a wheat crop, fruits were produced only towards the top of the canopy, with a mode on average at 76% of the maximum height. There are, perhaps surprisingly, very few data with which to compare these results. In one example, Trapp (1988) also found that fruits of the woodland understorey vine Amphicarpaea bracteata were distributed over a wide range of positions, with a mode at about one-third the height of the plants. A small number of seed height distributions have been recorded for trees growing in forests, with modes ranging from about 50% to 74% of tree height (Hard 1964; Nathan et al. 2002). A comparison of the growth forms of trees in forests and growing in the open would suggest that these release heights, as in the case of R. raphanistrum, should vary with intensity of competition (Cousens & Rawlinson 2001), as would the quantity of seeds produced. Models of seed dispersal by wind, however, generally assume a fixed seed release height (sometimes with limited variance) close to the top of a plant (Greene & Johnson 1996; Tackenberg 2003; Nathan et al. 2011b).

Changes in fruit position have consequences for both long-distance dispersal, that is, the movement of species through landscapes, and the structure of vegetation close to the parent plant. Both of these can be appreciated with respect to our results on R. raphanistrum. The literature on source effects to date, however, has focussed on the implications for long-distance dispersal, particularly release height in wind-dispersed species. Many arable weeds are not adapted for wind dispersal and few come into contact with animals, yet they have been highly successful invasive species. Those seeds produced at the tops of the plants, if remaining on the parent at maturity, can potentially enter a harvesting machine and be dispersed over tens of metres in the same field (Ballaré et al. 1987; Howard et al. 1991; Rew, Froud-Williams & Boatman 1996) or to fields many kilometres away. We showed that a greater proportion of seeds were initiated close to the top of the canopy in plants grown under competition with a wheat crop (e.g. if the cutter bar is at 30 cm, 80% of fruits are produced above that height under competition, compared with only 17% without a crop). However, we also found that a greater proportion of fruits in a wheat crop had already dispersed by the time the crop would have been harvested (97% vs. 45%: Taghizadeh 2007). This, together with the fact that plants without competition produce far more fruits, means that more long-distance dispersal could still occur from the shorter and broader plants found growing in gaps within the crop. To better understand the effects of competition on dispersal, we require a greater understanding of the phenology of seed dispersal (Taghizadeh, Nicolas & Cousens 2012). While plant identification books list flowering periods for all species, they rarely give timing of seed dispersal. While there are empirical data on dispersal phenology for some species, notably trees, experimental studies are uncommon.

The seed shadow immediately around the parent, which even in wind-dispersed species constitutes the majority of propagules (Cousens, Dytham & Law 2008), has important ecological consequences. The density and spatial pattern of seeds landing on the ground will determine the intensity of competition in habitats favourable to plant growth. As a result, it may affect local persistence, facilitating the coexistence of competing species in heterogeneous environments (Bolker & Pacala 1999; Snyder & Chesson 2003) and may thus increase regional biodiversity (Green 1994). It may reduce inclusive fitness of genetic lineages (see review in Cousens, Dytham & Law 2008), alter the probability of successful pollination (Kunin 1993; Mũnoz & Cavieres 2008) and the spatial distribution of predators (including the Janzen-Connell hypothesis; see also Nathan & Casagrandi 2004), and it may dictate the optimal management of weeds and endangered species (Moody & Mack 1988; Paice et al. 1998). Competition had clear impacts on the R. raphanistrum seed shadow close to the parent plant. Much of this effect resulted from the fact that most individual fruits fall a short distance down through the canopy, with the overall seed shadow being determined primarily by lateral growth and development of the maternal parent (source effects) rather than the trajectory of the propagule (path effects). Under competition, seeds were produced on shorter branches near the top of the canopy, restricting release points horizontally.

Clark et al. (1999) have also argued that a broad canopy in trees would result in a plateau in the seed density distribution beneath it. Cousens & Rawlinson (2001) built on that idea using simple geometric shapes to predict that, for heavy propagules and depending on the relationship between architecture and reproduction, both shape and scale of dispersal could be density dependent. We demonstrated here that scale of dispersal in R. raphanistrum is reduced by wheat competition, but found no significant effect on the shape of the distribution of dispersal distances. There is potential to use simulation models to explore the influence of canopy shape – and its modification by competition – on dispersal kernels. First, the three-dimensional ‘populations’ of trajectory sources on whole plants that we have captured could be combined with empirical kernels describing dispersal from a point source, to examine the resulting combined kernels for a whole plant (as Cousens & Rawlinson 2001 did with simple geometric canopy shapes). The capacity for dispersal could be varied by altering the point source kernel parameters, to see at what point parental architecture ceases to play a significant part in dispersal frequency distributions. Secondly, the release height frequency distributions that we have recorded could be used as stochastic input into mechanistic point source models for wind dispersal (or those that already build in frequency distributions of parameters: e.g. Nathan, Safriel & Noy-Meir 2001; Nathan et al. 2002; Soons, Nathan & Katul 2004). The sensitivity of their predictions could be explored over a much wider range of falling velocities than in previous stochastic simulations (Nathan, Safriel & Noy-Meir 2001). Thirdly, L-system models (Cici, Adkins & Hanan 2008) or, requiring much more development, functional–structural models (Barthélémy & Caraglio 2007; Vos et al. 2010) could be developed that generate the different plant architectures – and hence seed release sites. Again, these could be combined with point models for dispersal trajectories.

In conclusion, given the clear effects of competition on canopy structure and fruit positions, we should perhaps be cautious when modelling the spread of populations into habitat that has been denuded (or which contains only species of shorter stature) and in which the furthest-establishing individuals will be growing under low competition. Under such conditions, there will be many more seeds produced per plant, and at lower heights on average, leading to a different shape of dispersal kernel (Cousens, Dytham & Law 2008). Although many models of population spread (invasion rate) incorporate density-dependent fecundity, none to our knowledge have included density-dependent dispersal kernels.

Acknowledgements

We thank Alex Campbell for technical support during field work, Lisa Crowfoot for advice and her assistance in sowing, Marie-Josée Fortin for assistance with MST analyses and David Peel for his assistance in preparing three-dimensional graphics.

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