5
1,3
2
1
1
10
( 1 Key Laboratory of Arid and Grassland Agroecology at Lanzhou University, Ministry of
Education , Lanzhou 730000, China; 2 * College of Life Sciences, Zhejiang University , Hangzhou,
310027, China; 3 Institute of Modern Physics, the Chinese Academy of Sciences , Lanzhou 730000,
China)
15
Tel: +86-571-88206590 Fax: +86-571-88206590
Email: liuj219@163.com
, wanggx@zju.edu.cn
1

The effects of increased intraspecific competition on size hierarchies (size inequality) and reproductive allocation were investigated in populations of the annual plant spring wheat ( Triticum aestivum) . A series of densities (100, 300, 1000, 3000 and 10000 plants/m 2 ) along a gradient of competition intensity were designed in this experiment. The results showed that
5 average shoot biomass decreased with the increased density. And reproductive allocation was negatively correlated to Gini coefficient (R 2 = 0.927), which suggested that reproductive allocation is inclined to decrease as size inequality increases. These results suggested that both vegetative and reproductive structure were significantly affected by intensive competition. On the other hand, results also indicated that there were different relationships between plant size and
10 reproductive allocation pattern in different densities. In the lowest density population lacking competition (100 plants/m 2 ), individual reproductive allocation was size-independent but, in high density populations (300, 1000, 3000 and 10000 plants/m 2 ) those competition occurred, individual reproductive allocation were size-dependent: the small proportional larger individuals were winners in competition and got higher reproductive allocation (lower marginal reproductive
15 allocation, lower MRA), and the large proportional smaller individuals were suppressed by larger ones and got lower reproductive allocation (higher MRA). In conclusion, our results support the prediction that elevated intraspecific competition would result in higher levels of size inequality and decreased reproductive allocation (negative relationship between them). However, deeply analysis indicated that these frequency- and size-dependent reproductive strategies were not
20 evolutionarily stable strategies.
Keywords: competition; density; reproductive allocation.
Foundations : Supported by National Natural Science Foundation of China (90102015,
2

30170161) and Cooperation Project of International in China and Greece (2003DFB00034).
In plant populations, increase density can intense plant-plant competition directly (Pianka
1981). And competition among plants is an important factor in affecting size hierarchies (Bonan
1988; Weiner 1985; Pan et al. 2003a, b), growth rate (Ehleringer 1984; Weiner & Thomas 1992),
5 survivorship (White, 1981; Tanner, 1997; van Kleunen et al., 2001), and reproductive output
(Ehleringer 1984; Weiner & Thomas 1992; van Kleumen et al. 2001; Soto-Pinto et al., 2000).
Among these components, size hierarchies and reproductive output have been mostly investigated because they are of tremendous ecological and evolutionary significance.
It has long been recognized that size inequality always increased with increasing density
10 (Weiner 1985). The increase of size inequality may affect total reproductive output (Weiner 1985;
Sugiyama & Bazzaz 1997; Pan et al. 2003a, b). Weiner (1988) presented a simple linear model of size-dependent reproductive output to explain the decrease in reproductive allocation (RA) in plants grown at high densities. And it has also been reported that, in water deficits and mulching with clear plastic film conditions in spring wheat ( Triticum aestivum ) populations, there is a
15 negative correlation between RA and Gini coefficient (Pan et al. 2003a, b). It was suspected that this negative correlation would exist along an elevated intraspecific competition gradient.
Unfortunately, direct evidence along density gradient is still lacked to prove this prediction. So, in the present experiment, we designed a wide range of densities for further analysis.
The purpose of this study was to explore (1) the relationship between size inequality and RA
20 in a wide range of densities from no competition to intensive competition (which enduring self-thinning) and (2) size-dependent reproductive patterns in different densities.
3

Size inequality
Average shoot biomass per plant decreased with the increased density in 20th June (Figure 1), which means the increased strength of intraspecific competition suppressed plant growth.
5 RA was negatively correlated to G of the population (R 2 = 0.927, Figure 2). The negative correlation suggests that RA is inclined to decrease as size inequality increases. This result supports the theory that stand uniformity of field crops is an important aspect of high yield formation (Glenn & Daynard 1974).
Size-dependent reproductive allocation
10 To investigate the relationships between RA and plant size and between spike size and plant size, data in 20 th June was analyzed when spring wheat grown in grain filling stage and no individuals died because of ripening. For all five populations, spike size increased linearly with plant size (above-ground biomass) (Figure 3, Table 2). Meanwhile, RA increased inversely with plant size in the four competitive densities (300, 1000, 3000 and 10000/m 2 ) (Figure 4, Table 3).
15 Apparently, individual spike size and RA in competitive populations in spring wheat were size-dependent. However, in density 100/m 2 , RA kept constant in different plant sizes (Figure 4,
Table 3). So, when the population lacks competition, individual RA is size-independent.
20 Four competition levels were investigated in this study: (1) no competition (populations
4

sowing in 100/m 2 ); (2) slight competition (populations sowing in 300/m 2 ); (3) intermediate competition (population sowing in 1000/m 2 ); and (4) intensive competition (populations sowing in
3000/m 2 and 10000/m 2 which endured self-thinning in the growth period). The results indicated that the relationship between plant size and RA of these populations developed in different ways.
5 Reproductive allocation and size structure
Weiner (1988) presented a simple linear model ( W
R
 aW
P
 b ) between weight of plant reproductive structure (spike biomass, W ) and plant size (shoot biomass,
R
W ) to explain the
P decrease in RA in plants grown in high densities. He suggested that plants must reach a certain size before they can devote energy to reproductive biomass. Thus, the slope and the x-intercept of
10 the linear model should be positive. The linear relationship was confirmed in all of the five densities in the present study, except that the x-intercept in 100/m 2 was negative (Fig. 5, Table 3).
Pan et al. (2003a) developed Weiner’s theory and transformed the formula as below:
RA

W
R
W
P
 a
 b W
P
Where a is defined as innate RA, which represented the maximum RA (RA max
) of the
15 species. The slope of the inverse curve is the additional RA from each additional unit of the W p
, which is defined as marginal reproductive allocation (MRA, dRA / dWp
  b / x
2
). And MRA is an indicator of reproductive potentiality. The declined in MRA as plant size increases is called diminishing marginal reproductive allocation (Pan et al. 2003a). It is believed that there is a trade-off between plant size and MRA, and a population must consist of a large proportion of
20 small individuals with high MRA and a small proportion of large individuals with low MRA. So these frequency- and size- dependent reproductive strategies in plant populations are thought of a
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good case for evolutionarily stable strategy (ESS). However, there are several deficiencies in this contention.
In competitive populations, large individuals are strong competitors and they have chances to utilize all their potential reproductive ability. So the diminished MRA means that large individuals
5 have higher individual fitness, and can generate offspring more successfully. Small individuals are weak competitors with high MRA. If other individuals give up competition, they will improve their RA. However, in dense populations, small individuals risked density-dependent mortality more than large individuals (Weiner 1985). So compared with large ones, small individuals are easy to give up the competition. Moreover, spring wheat is an annual semelparous species, and
10 this determined that small individuals with high MRA have little chance to improve their RA. So, in this experiment, the diminished MRA is not bad for large individuals and high MRA is not good for small individuals. That is, trade-off between plant size and MRA is invalid.
A strategy or strategy mixture that cannot be invaded by novel strategies is called an evolutionarily stable strategy (ESS or ESS mixture. Falster and Westoby, 2003). So we can test a
15 population for ESS by whether it has the capacity to exclude alternate strategies from invading.
Potential invading strategies can be thought of as rare mutants within the existing population, or as initially rare species colonizing from elsewhere. It has been widely recognized that modern seed crops, which are seeking maximum population yield, are of evolutionarily unstable, and require ongoing artificial selection to maintain the evolutionarily unstable strategy (Zhang et al. 1999;
20 Falster and Westoby 2003). In this study, the frequency- and size- dependent reproductive strategies in dense spring wheat populations are of evolutionarily unstable too, because neither large plant size with high reproductive capacity nor small plant size with low reproductive
6

capacity is a successful strategy. Furthermore, in self-thinning populations, the later strategy will be eliminated from the serious competitive populations, and the previous strategy will fail when faces a more competitive strategy such as the mutant that developed large plant size and low RA.
So these strategies are not stable against invasion by rare mutant or deviant strategies. In fact,
5 without artificial management, most of crop populations will be replaced by other wild species, or will be replaced by more competitive mutants.
Size-dependent reproductive allocation patterns in different densities
In this study, different size-dependent reproductive patterns are shown along the different densities. In population without competition (density treatment in 100 plants/m 2 ), all members
10 (large ones and small ones) can develop their maximum potential reproductive ability. So MRA equal to zero constantly (Figure 4, Table 3) and their reproductive pattern are size-independent.
This implies that plant RA is decided by its intrinsic property when lacking competition. While in the higher density populations (density treatments in 300, 1000, 3000, and 10000 plants/m 2 ) with competition, just as found by Weiner (1988) and Pan et al. (2003a, b), there are significant
15 correlations between plant size and reproductive structure (Figure 3, Table 2) and between plant size and RA (Figure 4, Table 3). Along the higher density treatments, the increased size inequality suggested the proportion of small ones increased and the proportion of large ones decreased. So, it is the small ones that mainly contributed to the great growth redundancy, for the small ones had relative lower RA in the higher density treatments. Furthermore, the relative lower RA in large
20 proportional small ones (even some barren shoots existed self-thinning populations) incurred average RA decreased along the density. So it can be concluded that there were negative
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correlations between size inequality (as measured by Gini coefficient) and RA (Figure 2) within these competitive populations.
In conclusion, this study supported the prediction (Pan et al. 2003a) that elevated intraspecific competition would result in higher levels of size inequality and decreased RA. And there were
5 inverse correlations between plant size and RA in competitive populations.
These facts imply that reproductive strategies in competitive populations are frequency- and size- dependent. But we are not sure that they are evolutionarily stable so far, because there was no evidence to prove that they can exclude other competitive strategies, especially in artificial managed populations.
10 Field experiment was conducted in the year of 2003 at Yuzhong experimental station of
Lanzhou University(36 º03´ N, 103 º53´E and 1517m in altitude). The main climatic conditions are presented in Table 1. The soil is a loess-like loam, with a bulk density of 1.37g/cm 3 , and a field water holding capacity (FWHC, maximum capillary held water) of 25% (gravimetrically). High organic fertilizer inputs were imposed to the experimental plot before sowing.
15 Seeds of spring wheat ( Triticum aestivum L., cv. Longchun No.15) were sprinkled in some plots 50×50 cm 2 at five densities (in each density three replicates were used in this study): 100,
300, 1000, 3000 and 10000 seeds/m 2 , respectively. The total irrigation was 50×5 mm. Rainfall during the period from sowing to the last harvest was 229 mm (Table 1). Sowing occurred on
18-20 March 2003, and harvest was taken on 20 June. The plots were surrounded by supports of
20 wire-netting to prevent the plants from lodging (especially in high densities) and 25 cm guard rows to avoid marginal effect. Plants were sprayed with chlorpyriphos (Dow Agrosciences, USA)
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against pests attack and streptomycin solution against bacteria. High fertilizer inputs (irrigated with 500ml solution which content 1% urea and 0.2% potassium dihydrogen phosphate per plot every two weeks) were imposed during the growth stage.
Plants grown in the central plot were harvested at ground level. 100-150 lived individuals
5 were randomly collected from the plants, which come from three plots. The individuals were put in paper bags separately, dried (65 ℃ , 48h), and weighed. Data collected for each plot included:
(dry) shoot biomass per plant (total sample size is 100-150 in each treatment for calculating Gini coefficient, but in density 100 plants/m 2 , the total sample size is 40-70). And in the samples, shoot biomass and spike biomass (for calculating RA which is equal to spike biomass/shoot biomass) of
10 each plant were weighed separately.
15
Hierarchies were defined in terms of the degree of inequality in the frequency distribution as measured by the Gini coefficient (Weiner & Solbrig 1984). Gini coefficients range from 0
(absolute equality in the frequency distribution) to 1 (absolute inequality) (Bonan 1988). The Gini coefficient was calculated using the formula:
G
 i n n 

1 j

1 x i
 x j
 
Where x i
and x j
represent the masses of all possible pairs of individuals, and n is the sample size. Calculated G values were multiplied by n
 n

1

to give unbiased values G

. Confidence intervals for Gini coefficients were determined using a ‘bootstrapping’ technique (Dixon et al.
1987, Weiner 1985). In this study, G

was calculated for each of 200 artificial samples of the same
20 size as the original sample, which are taken from the original sample with replacement.
Confidence intervals for G

values are determined from the distribution of G

values for these
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bootstrapped samples using a bias-corrected percentile method.
Bonan GB (1988). The size structure of theoretical plant populations spatial patterns and
5 neighborhood effects. Ecology 69 , 1721-1730.
Dixon PM, Weiner J, Mitchell-Olds T, Woodley R (1987). Bootstsrapping the gini coefficient of inequality. Ecology 68 , 1548-1551.
Ehleringer JR (1984). intraspecific competition effects on water relations, growth and reproduction in Encelia farinosa . Oecologia 63 , 153-158.
10 Falster DS, Westody M (2003). Plant height and evolutionary games. Trends Ecol Evol 18 ,
337-343.
Glenn FB, Daynard TB (1974). Effects of genotype, planting pattern, and planting density on plant-to-plant variability and grain yield of corn. Can J Plant Sci 54 , 323-330.
Pan XY, Wang GX, Chen JK, Wei XP (2003a). Elevated growth redundancy and size inequality
15 in spring wheat populations mulched with clear plastic film. J Agr Sci 140 , 193-204.
Pan XY, Wang GX, Yang HM, Wei XP (2003b). Effect of water deficits on within-plot variability in growth and grain yield of spring wheat in northwest China. Field Crops Res 80 ,
195-205.
Pianka ER (1981). Competition and niche theory . In May RM eds. Theoretical ecology:
20 principles and applications. pp. 167-196. Second Edition. Blackwell Scientific Publication.
Soto-Pinto L, Perfecto I, Castillo-Hernandez J, Caballero-Nieto J (2000). shade effect on coffee production at the northern Tzeltal zone of the state of Chiapas, Mexico. Agr, Ecosyst &
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Environ 80 , 61-69.
Sugiyama S, Bazzaz FA (1997). Plasticity of seed output in response to soil nutrients and density in Abutilon theophrasti : implications for maintenance of genetic variation. Oecologia 112 ,
35-41.
5 Tanner JE (1997). Interspecific competition reduces fitness in scleractinian corals.
J Exp Marine
Bio and Ecol 214 , 19-34. van Kleumen M, Fischer M, Schmid B (2001). Effects of intraspecific competition on size variation and reproductive allocation in a clonal plant. Oikos 94 , 515-524.
10
Weiner J (1985). Size hierarchies in experimental populations of annual plants. Ecology 66 ,
743-752.
Weiner J (1988). The influence of competition on plant reproduction. In Lovett Doust J. Lovett
Doust L. eds. Plant reproductive ecology: patterns and strstegies . pp. 228-245. New York:
Oxford University Press.
15
Weiner J, Solbrig OT (1984). The meaning and measurement of size hierarchies in plant populations. Oecologia 61 , 334-336.
20
Weiner J, Thomas SC (1992). Competition and allometry in three species of annual plants.
Ecology 73 , 648-656.
White J (1981). The allometric interpretation of the self-thinning rule. J Theo Bio 89 : 475-500.
Zhang DY, Sun GJ, Jiang XH (1999). Donald’s ideotype and growth redundancy: a game theoretical analysis. Field Crops Res 61 , 179-187.
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5
10
Figure 1.
Mean plant biomass (above-ground) in different density treatments in 20 th June.
Figure 2.
Relationships between Gini coefficients of spring wheat populations and reproductive allocation (RA) (data in 20 th June). The regression line is y = -1.464x + 0.5221, R 2 = 0.927.
Figure 3.
Linear relationship between spike size and plant size (above-ground biomass) in different spring wheat populations in 20 th June.
 indicate the individuals with spikes which used in fitting the line;  indicate the barren individuals which was excluded in fitting the line. See Table 2 for regression coefficients.
Figure 4.
Inverse relationship between RA and plant size (above-ground biomass) in different spring wheat populations in 20 th June.
 indicate the individuals with spikes which used in fitting the line;  indicate the barren individuals which was excluded in fitting the line. See Table 3 for regression coefficients.
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10
Table 1.
The mean climatic conditions of the experimental site in China (Data come from
Lanzhou meteorological administration)
Year
Mean annual
2003
Annual mean temperature
( ℃ )
Annual mean precipitation
(mm)
9.1 328
Precipitation during growing season (mm)
158
Annual mean evaporation
(mm)
1365
Evaporation during growing season
(mm)
938
Relative humidity
(%)
59
10.8 376 229 1113 703 58
Table 2.
Parameters of linear regression* between spike size (y) and plant size (above-ground
5 biomass, x) for individuals of spring wheat in different densities in 20 th June.
Density in sowing
(plants/m 2 )
100
300
1000
3000
10000
Density in
20 th June
Slope (a
1
) y-intercept
(b
1
)
101±2
279±6
0.271±0.009 0.206±0.103
0.312±0.005 -0.021±0.033
952±24 0.321±0.004 -0.005±0.007
2288±164 0.308±0.005 -0.030±0.004
5424±620 0.290±0.005 -0.011±0.002
* The model is y
 a
1 x
 b
1 x-intercept
(-b
1
/a
1
)
-0.760
0.067
0.016
0.097
0.038
R 2 Sample size
0.958
0.973
46
100
0.977 148
0.960 151(2**)
0.970 150(39**)
** Number of barren individuals in the sample. To fit the model, the barren individuals were excluded.
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Table 3.
Parameters (±S.E.) of inverse regression* between RA (y) and plant size (above-ground biomass, x) for individuals of spring wheat in different densities in 20 th June.
Density in sowing
(plants/m 2 )
100
300
1000
3000
10000
Density in
20 th June
101±2
Slope b
2 y-intercept a
2
279±6
952±24
0.032±0.058 0.290±0.010
-0.044±0.010
-0.008±0.001
0.319±0.004
0.323±0.002
2288±164 -0.009±0.001 0.264±0.004
5424±620 -0.005±0.001 0.264±0.006
* The model is y
 b
2
1 x
 a
2
R 2
0.007
0.153
0.218
0.376
0.225
Sample size
46
100
148
151(2**)
150(39**)
** Number of barren individuals in the sample. To fit the model, the barren individuals were
5 excluded.
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5
10
15
12
10
8
6
4
2
0
100 300 1000 3000 10000 density
Figure 1.
Mean plant biomass (above-ground) in different density treatments in 20 th June.
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10000/m2
300/m2
3000/m2
100/m2
1000/m2
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0 0.1
0.2
Gini coefficient
0.3
Figure 2.
Relationships between Gini coefficients of spring wheat populations and reproductive allocation (RA) (data in 20 th June). The regression line is y = -1.464x + 0.5221, R 2 = 0.927.
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5
10
15
20
25
30
35
40
7
6
5
4
3
2
1
0
0
7
6
5
4
3
2
1
0
0
2
1000 plants per m 2
1.5
1
0.5
0
0
100 plants per m 2
10 20
P lant size (g)
300 plants per m 2
10
P lant size (g)
2 4
P lant size (g)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
3 000 plants per m 2
1 2
P lant size (g)
0.5
0.4
0.3
0.2
0.1
0
0
10000 plants per m 2
0.5
1
P lant size (g)
30
20
6
3
1.5
Figure 3.
Linear relationship between spike size and plant size (above-ground biomass) in different spring wheat populations in 20 th June.
 indicate the individuals with spikes which used in fitting the line;  indicate the barren individuals which was excluded in fitting the line. See Table 2 for regression coefficients.
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5
10
15
20
25
30
35
40
100 plants per m
2
0.4
0.3
0.2
0.1
0.3
0.2
0.3
0.2
0.4
0.3
0
0
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
300 plants per m
2
P
10
0.4
0.1
0
0
0.4
0.1
0
0
0.2
0.1
0
0
10 20
P lant size (g)
1000 plants per m 2
P
4
3000 plants per m
2
1 2
P lant size (g)
10000 plants per m
2
0.5
1
P lant size (g)
30
20
3
6
1.5
Figure 4.
Inverse relationship between RA and plant size (above-ground biomass) in different spring wheat populations in 20 th June.
 indicate the individuals with spikes which used in fitting the line;  indicate the barren
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individuals which was excluded in fitting the line. See Table 3 for regression coefficients.
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