Appendix S1: Size symmetry of competition among B. nigra genotypes and heterospecifics
The pattern of size symmetry among competitors can be an indicator of competitive
strategies. Size symmetric patterns, in which a plant’s size or biomass determines its competitive
effect on its neighbor, tend to occur when plants follow a scramble strategy for below ground
resources, since resource uptake can be determined by the size of the root system (von Wettberg
& Weiner 2003). Size asymmetric patterns, in which competitive effect is independent of size,
suggest plants are preempting resources (e.g. shading) or interfering with their competitor’s
ability to acquire resources (e.g. through allelopathy) (Schenk 2006).
We tested whether the competitive effect of each plant type (high sinigrin B. nigra, low
sinigrin B. nigra, and heterospecifics) on each other type was size symmetric or asymmetric
using competitive outcomes in the field setting from a previous experiment. Differences in size
symmetry among the various interactions would provide preliminary evidence that alternative
competitive strategies could underlie the intransitive network observed in this system. In a
related species, patterns of size symmetry were accurate predictors of the strength of allelopathic
inhibition (Lankau 2009b). However, this is not a direct test of competitive strategies, and so is
presented as circumstantial evidence and as an inspiration for the hypotheses of our experimental
study presented in the main paper.
To evaluate asymmetries in pair-wise competitive interactions, we used data from a
previously published field experiment, in which we created communities of each plant type (high
sinigrin B. nigra, low sinigrin B.nigra, or a mixture of three heterospecific species, see (Lankau
& Strauss 2007). Each community type was then invaded with each plant type. Each replicate
plot consisted of 24 neighbor plants surrounding one invader.
We counted the number of seeds produced by each species when acting as an invader in a
patch of another species or genotype as a measure of its fitness, and measured the stem diameter
of all neighbor plants near the end of the season. We then used species-specific allometric
relationships between stem diameter and total biomass (R2 > 0.80 for all species) to predict
biomass for all neighbor plants.
We used these data to explore how the fitness of each invader was related to the summed
biomass of the 24 neighbor plants with which they grew. We did this for all combinations of
invader and community types, with the following exceptions. In order to have a large enough
sample size to detect trends (N=21), we combined data from all three heterospecific species
(N=7 for each combination of invader species and community type). Since heterospecific species
produced different numbers of seeds, we divided the seed production of each individual by the
species mean, and then combined the relativized data across all heterospecific species.
Additionally, the fitness of B. nigra invaders did not differ between high and low sinigrin B.
nigra communities. Therefore, for B. nigra invaders only, we combined both high and low
sinigrin B. nigra communities, and tested whether competition between high or low sinigrin B.
nigra invaders and general B. nigra communities was size symmetric or not. Because
heterospecific fitness did differ when invading high vs. low sinigrin communities, we tested for
size symmetry separately for high vs. low sinigrin B. nigra communities with heterospecific
invaders.
For all treatments except one (heterospecifics invading low B nigra communities), many
plants did not survive to set seed. Therefore, we used zero inflated negative binomial (ZINB)
models to relate community biomass to invader fitness. ZINB models are mixture models which
simultaneously model two processes; one which only produces zero values, and one which
produces integer values according to a negative binomial distribution. In this case, these
submodels can be interpreted as survival and fecundity processes. One can then test whether one,
both, or neither of these processes depends on a variable of interest; in this case, the biomass of
the community. ZINB was the best supported model according to AIC weights among a set of
candidate error distributions (Gaussian, poisson, negative binomial, zero inflated poisson). We
used likelihood ratio tests to determine the significance of the community biomass effect
separately for each process. For heterospecifics invading low sinigrin B. nigra communities, all
invaders survived to set seed, so a generalized linear model with a negative binomial error
distribution provided the best fit.
Comparison of size symmetry of competition
Intraspecific competition between B. nigra invaders and B nigra communities (transitions
E and F in Fig. 1) was size symmetric, since B. nigra community biomass had a significant effect
on the fitness of low sinigrin B. nigra invaders and a marginally significant effect on high
sinigrin B. nigra invaders (Table A1). In contrast, high sinigrin B. nigra genotypes showed size
asymmetric competition with heterospecifics (transitions A and B in Fig. 1), as community
biomass had no significant effect on the fitness of high sinigrin B. nigra invaders in
heterospecific communities or vice versa (Table A1). The biomass of the low sinigrin B. nigra
community significantly affected the fitness of heterospecific invaders, indicating size-symmetry
(transition C in Fig. 1) (Table A1); however, the biomass of the heterospecific community did
not affect the fitness of low sinigrin B. nigra invaders, indicating size-asymmetry (transition D in
Fig. 1).
In general, community biomass only affected the fecundity component of the ZINB
mixture models. However, for high sinigrin B. nigra invaders in heterospecific communities,
increasing community biomass surprisingly and significantly increased invader survival. This
positive relationship is not indicative of size–symmetric competition (which requires a
significant negative relationship); but perhaps indicates facilitation, at least for early survival.
As the analysis of size symmetry relationships comes with serious caveats, one must be
cautious in their interpretation. First, this observational approach is not a direct test of
competitive strategies, which would require experimental manipulations. Secondly, tests of sizesymmetry patterns are complicated by differences in statistical power. Since a finding of size
asymmetry is in essence the lack of evidence for size symmetry, low statistical power could lead
to erroneous conclusions of asymmetric patterns when the interaction is symmetric but too weak
to detect with the given sample size. To reduce this potential bias, we combined plots of different
types when previous findings suggested they behaved similarly (e.g. combining the three
heterospecific invaders). While these results are necessarily preliminary, they do suggest that the
three plant types may utilize different competitive strategies. For instance, competition between
B. nigra genotypes was generally size symmetric, indicative of simple scramble competition for
resources. This was also true for heterospecifics invading low sinigrin B. nigra communities.
However, interactions between high sinigrin B. nigra genotypes and heterospecifics were size
asymmetric, which is more suggestive of interference competition, such as might occur if high
levels of sinigrin have allelopathic or anti-mycorrhizal effects. Somewhat surprisingly, low
sinigrin B. nigra genotypes showed size asymmetric patterns when invading heterospecific
communities. These differences in competitive strategies may play a role in driving the
intransitive network of interactions between these three plant types.
References
Lankau R.A. & Strauss S.Y. (2007). Mutual feedbacks maintain both genetic and species
diversity in a plant community. Science, 317, 1561-1563.
Schenk H.J. (2006). Root competition: beyond resource depletion. Journal of Ecology, 94, 725739.
von Wettberg E.J. & Weiner J. (2003). Larger Triticum aestivum plants do not preempt nutrientrich patches in a glasshouse experiment. Plant Ecology, 169, 85-92.
Table S1. Log-likelihood ratios for ZINB models of invader fitness with versus without
community biomass as an explanatory variable in the negative binomial sub-model, for each of
the transitions outlined in Fig. 1. Bold values indicate that models including community biomass
had a significantly higher likelihood (at P<0.05), indicating size-symmetric competition.
Italicized values indicate a marginally significant effect (P<0.10).
* Since high and low sinigrin B. nigra invaders did not differ in their response to the sinigrin
level of B. nigra communities, data from high and low sinigrin B. nigra communities were
combined for these transitions.
Tests of size-symmetry
Transition
A.
C.
D.
E.
B.
F.
Invader
Heterospecifc
Heterospecifc
Low Sinigrin
Low Sinigrin
High Sinigrin
High Sinigrin
Community
High Sinigrin
Low Sinigrin
Heterospecific
High Sinigrin*
Heterospecific
Low Sinigrin*
LR
1.00
9.37
0.36
4.5
0.84
2.9
P
0.32
0.002
0.55
0.03
0.36
0.09
Symmetric?
N
Y
N
Y
N
Y
Appendix S2: Analysis of abiotic soil factors among plant communities
High sinigrin
B. nigra
Low sinigrin
B. nigra
Mixed
heterospecific
cation
exchange
capacity
% organic
matter
NO3
2.48
0.09
10.60
1.07
15.40
0.56
463
18
1001
21
1030
27
6.58
0.04
16.23
0.29
2.42
0.07
10.50
2.59
15.00
0.58
440
23
993
11
1008
8
6.58
0.04
15.82
0.18
2.35
0.15
13.50
6.51
17.00
2.74
470
45
1023
14
1025
14
6.50
0.14
16.70
0.40
P
K
Mg
Ca
pH
Means and standard errors for eight abiotic soil factors. NO3, P, K, Mg and Ca are presented as parts per million. Cation exchange
capacity is in units of milliequivalients/100 grams. No measure differed significantly among the three types of plant communities.