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\begin{document}

\title{Trait Dissimilarity and Hierarchy Predict Spatial Co-occurrence Patterns
of Tree Species in a Subtropical Forest}



\author[1]{Yin deyi}%
\author[2]{Yu Liu}%
\author[3]{Qing Ye}%
\author[4]{Marc Cadotte}%
\author[5]{Fangliang He}%
\affil[1]{ South China Botanical Garden, Chinese Academy of Sciences}%
\affil[2]{East China Normal University}%
\affil[3]{South China Botanical Garden, Chinese Academy of Sciences}%
\affil[4]{University of Toronto}%
\affil[5]{University of Alberta}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
1. The dissimilarity and hierarchy of trait values that characterize
niche and fitness differences, respectively, have been increasingly
applied to infer mechanisms driving community assembly and to explain
species co-occurrence patterns. Here, we predict that limiting
similarity should result in the spatial segregation of functionally
similar species, while functionally similar species will be more likely
to co-occur together either due to environmental filtering or
competitive exclusion of inferior competitors (hereafter hierarchical
competition). 2. We used a fully mapped 50-ha subtropical forest plot in
southern China to explore how pairwise spatial associations were
influenced by trait dissimilarity and hierarchy between species in order
to gain insight into assembly mechanisms. We assessed pairwise spatial
associations using two summary statistics of spatial point patterns at
different spatial scales and compared the effects of trait dissimilarity
and trait hierarchy of different functional traits on the interspecific
spatial associations. These comparisons allow us to disentangle the
effects of limiting similarity, environmental filtering and hierarchical
competition on species co-occurrence. 3. We found that trait
dissimilarity was generally negatively correlated with interspecific
spatial associations, meaning that species with similar trait values
were more likely to co-occur together and thus supporting environmental
filtering or hierarchical competition. We further found that leaf area,
wood density and maximum height had stronger trait hierarchy effects on
the pairwise spatial associations relative to their corresponding trait
dissimilarity effects, which suggests that hierarchical competition
played a more (or at least equally) important role in structuring our
forest community compared to environmental filtering. 4. This study
employed a novel method to disentangle the relative importance of
multiple assembly mechanisms in structuring co-occurrence patterns,
especially the mechanisms of environmental filtering and hierarchical
competition, which lead to indistinguishable co-occurrence patterns.
This study also reinforced the importance of trait hierarchy rather than
trait dissimilarity in driving neighborhood competition.%
\end{abstract}%



\sloppy


\textbf{Introduction}

The ``entangled bank'' metaphor of Darwin has inspired generations of
community ecologists to explore the rules governing species coexistence
and co-occurrence (Chesson, 2000; Gause, 1934; MacArthur, 1958; Ricklefs
\& Schluter, 1993; Tilman, 1982). Studies on species co-occurrence in
species-rich communities over the past decades have reinforced the
importance of the relationship between trait-mediated species
differences and spatial distribution patterns among species in
understanding the processes underlying coexistence and patterns of
biodiversity (Chesson, 2000, 2013; He \& Biswas, 2019; HilleRisLambers,
Adler, Harpole, Levine, \& Mayfield, 2012; Kraft, Godoy, \& Levine,
2015; Laughlin, 2014; Li et al., 2018).

Species differences quantified by trait dissimilarity are frequently
used as a proxy for the niche differences among species that are
believed to drive species co-occurrence by influencing species' response
to environmental conditions and neighborhood interaction (Burns \&
Strauss, 2011; Cadotte, Carboni, Si, \& Tatsumi, 2019; Cavender-Bares,
Kozak, Fine, \& Kembel, 2009; Kraft \& Ackerly, 2010). With such
approaches, the environment is often assumed to act as a filter that
selects for species possessing similar traits, leading to aggregated
interspecific spatial associations between species with similar traits,
while the pairwise spatial repulsion between species with similar traits
are thought to result from limiting similarity via competition
(Cavender-Bares \& Wilczek, 2003; He \& Biswas, 2019). However, the
assumed link between species differences and co-occurrence only holds
when the measured traits dissimilarity actually reflect niche
differences and influence neighborhood competition (Cadotte, Davies, \&
Peres-Neto, 2017). When these assumptions do not hold, for example,
neighborhood competition is not driven by trait dissimilarity but by
competitive advantage associated with particular trait values (i.e.
trait hierarchy) (Kunstler et al., 2016, 2012), the pattern that species
with similar functional traits co-occur together could also be the
result of competitive exclusion of inferior competitors (hereafter
hierarchical competition) in the absence of niche segregation when trait
similar species have similarly high fitness -e.g. trees with resource
conservative traits (Chesson, 2000; Lasky, Uriarte, Boukili, \& Chazdon,
2014; Mayfield \& Levine, 2010). Therefore, the relationship between
interspecific spatial associations and species differences characterized
by trait dissimilarity and trait hierarchy is key for disentangling the
relative importance of multiple assembly mechanisms, especially those
leading to identical co-occurrence patterns, e.g. environmental
filtering and hierarchical competition .

Trait dissimilarity and trait hierarchy can be characterized
respectively as absolute and hierarchical (i.e. directional)
interspecific trait differences to represent species niche and fitness
differences (Kunstler et al., 2012). Bivariate spatial point pattern
analysis is a primary tool for estimating the degree of pairwise species
co-occurrence patterns departing from independence (Fig. 1a and Fig.
1b), and understanding the underlying processes that cause the departure
from independence (He \& Duncan, 2000; Wiegand et al., 2007; Wiegand \&
Moloney, 2014). Associations with trait dissimilarity and trait
hierarchy provide the bivariate analysis with a basis for detecting the
relative importance of multiple assembly processes (Carmona, de Bello,
Azc\selectlanguage{ngerman}árate, Mason, \& Peco, 2019; Kunstler et al., 2016, 2012; Lasky et
al., 2014; Shen, Wiegand, Mi, \& He, 2013; Wiegand et al., 2007, 2017).
It is notable that the relative importance of different assembly
mechanisms and their signatures on spatial associations is highly
scale-dependent (Gianuca et al., 2016; Smith, Sandel, Kraft, \& Carey,
2013).

In this study, we predict that limiting similarity should result in
functionally similar species occupying segregated areas (i.e.
functionally similar-spatial repulsive pattern), leading to a positive
relationship between the absolute functional trait distance (trait
dissimilarity) and pairwise spatial associations (Fig. 1c). While, at
the same time, functionally similar species would co-occur together more
likely (i.e. forming functionally similar-spatial aggregated pattern)
resulting from either environmental filtering or hierarchical
competition (HilleRisLambers et al., 2012; Mayfield \& Levine, 2010),
leading to a negative relationship between the absolute functional trait
distance and spatial associations Fig. 1d). To disentangle which of
these two processes in the case of Fig. 1d , environmental filtering and
hierarchical competition, is responsible for the functionally
similar-spatial aggregated pattern, it is necessary to simultaneously
test and compare the relative strengths of trait dissimilarity and trait
hierarchy on pairwise spatial associations. If environmental filtering
prevails, we would expect that the strength of trait dissimilarity
should be greater than that of trait hierarchy (Fig. 1e), and if
hierarchical competition drives the community assemblage, the effects of
trait hierarchy are expected to be stronger than that of trait
dissimilarity (Fig. 1f).

To link forest assembly mechanisms to trait difference- spatial
association relationships and test the three hypotheses above (Fig. 1c,
d, e and f), we addressed the following questions about spatial
associations: (1) How are pairwise spatial associations correlated with
trait dissimilarity and trait hierarchy? (2) Do the spatial
pattern-trait difference relationships remain consistent across
different spatial scales? Moreover, little attention has been paid to
variation in abundances among the focal tree species and relative
importance of different assembly mechanisms. In this study, we explored
how the magnitude that the hierarchical competition effects outcompete
the environmental filtering effects was related to the abundance of each
focal species when trait hierarchy effects were detected.

To address these questions, we analyzed the bivariate spatial
associations of 80 common species in a fully mapped 50 ha (1000× 500 m)
plot in Heishiding nature reserve in southern China using spatial point
pattern analysis. To reveal how trait dissimilarity and hierarchy
determine species co-occurrence patterns in the study forest, we
evaluated the support for the three hypotheses by assessing the spatial
pattern-trait difference relationships across different spatial scales.
We then related the relative strengths of trait hierarchy and trait
dissimilarity on spatial associations to the abundance of each focal
species to better understand the underlying mechanisms.

\textbf{Materials and methods}

\textbf{Dataset}

The study area is located in the Heishiding Nature Reserve (HSD; 111°52
E, 23°27 N), Guangdong Province, China. Stems with diameters at breath
height (DBH) \textgreater{} 1 cm were measured, identified and mapped in
a 50 ha plot established in 2013, providing us with the distribution and
abundance of 213 tree/shrub species with 213,969 individuals in total
(Yin \& He, 2014). The HSD plot is one of the sites of the CTFS-Forest
Global Earth Observatory, which is a worldwide network dedicated to
advancing long-term study of the world's forests
(\emph{http://www.ctfs.si.edu;}Anderson-Teixeira et al., 2015).

We chose adult trees for analysis in this study because the spatial
distributions of adults would better reflect the effect of ecological
processes (e.g. dispersal limitation, environmental filtering and biotic
interactions) on their growth and survival over time. To obtain a
sufficiently large sample size for point pattern analyses, in this study
we included 80 common tree species (each with at least 50 individuals
with DBH \textgreater{} 10 cm) including a total of 27,453 individuals
in 52 genera and 33 families.

\textbf{Spatial point pattern analysis of pairwise species association}

We test the null hypothesis that species pairs are spatially
independent, as opposed to showing patterns of attraction or repulsion.
If two species show attraction in their spatial distributions, we will
find more points of species \emph{j} within the neighborhood of
species\emph{i} than expected under independence of the two species.
Conversely, if the two species show segregation, we will find fewer
points of species \emph{j} within the neighborhood of species
\emph{i}than expected. To assess pairwise spatial associations, we used
seminal techniques of bivariate point pattern analysis based on the
distributions of distances of all pairs of points between the two
species (Lotwick \& Silverman, 1982; Wiegand \& Moloney, 2014; Wiegand
et al., 2017). Two summary statistics, bivariate pair-correlation
function (pcf) \emph{g\textsubscript{ij}} (\emph{r} ) and bivariate
distribution function \emph{D\textsubscript{ij}} (\emph{r} ) of nearest
neighbor distances, were used in this analysis. The bivariate
pair-correlation function \emph{g\textsubscript{ij}} (\emph{r} ) can be
estimated using the quantity\selectlanguage{greek}\emph{λ\textsubscript{j}g\textsubscript{ij}}\selectlanguage{english}
(\emph{r} ), where \selectlanguage{greek}\emph{λ\textsubscript{j}}\selectlanguage{english} is intensity (i.e. density)
of species\emph{j} in the whole study area, measuring the mean density
of trees of species \emph{j} at distance\emph{r} away from a tree of the
focal species \emph{i} (Ripley, 1981; Stoyan \& Stoyan, 1994).
\emph{D\textsubscript{ij}} (\emph{r} ) could be defined as the
probability that trees of the focal species \emph{i} have their nearest
species \emph{j} neighbor(s) within distance \emph{r}(Diggle, 1983).
\emph{D\textsubscript{ij}} (\emph{r} ) can provide additional
information of the spatial patterns that is not provided by the
bivariate pair-correlation function\emph{g\textsubscript{ij}} (\emph{r}
), especially in the extremely heterogeneous cases for focal species,
e.g., many individuals of focal species \emph{i} have no species
\emph{j} neighbor but few have many species \emph{j} neighbors (Wang et
al., 2010; Wiegand et al., 2007).

The independence of bivariate spatial point patterns is examined through
the comparison of the summary statistics of the observed bivariate
patterns with those of the null model, i.e., the observed patterns are
compared against the simulated null model to test whether the hypothesis
holds. In this study, we implemented the null model by keeping the
locations of the focal species \emph{i} unchanged while randomizing the
distribution of species \emph{j} by the method of Toroidal shift, which
maintains most of structure of species \emph{j} (Lotwick \& Silverman,
1982). The null model of Toroidal shift removes the effects of
environmental heterogeneity and the interspecific interactions, while
retains the spatial structures of individual species. If a summary
statistic of the observed bivariate spatial pattern significantly
differs from the expectation of the null model, it is reasonable to
conclude that the departure results from species interactions or
environmental heterogeneity.

To assess the magnitude of departures from the null model, for each
species pair and for each observed summary
statistic\emph{S\textsubscript{0}} (\emph{r} )
(i.e.,\emph{g\textsubscript{ij}} (\emph{r} )
or\emph{D\textsubscript{ij}} (\emph{r} )), we computed their
standardized effect size \emph{z} (\emph{r} ) as:

\(z(r)=\frac{S_{0}(r)-\mu_{\text{null}}(r)}{\sigma_{\text{null}}(r)}\), (1)

where \emph{S\textsubscript{0}(r)} is the observed summary function
(either \emph{g\textsubscript{ij}} (\emph{r} )
or\emph{D\textsubscript{ij}} (\emph{r} )), and
\selectlanguage{greek}µ\selectlanguage{english}\textsubscript{null}(\emph{r} ) and \selectlanguage{greek}σ\selectlanguage{english}\textsubscript{null}(\emph{r} )
are respectively the average and the standard deviation of the summary
functions for 999 bivariate patterns simulated according to the null
models (Chanthorn, Wiegand, Getzin, Brockelman, \& Nathalang, 2018; Wang
et al., 2018; Wiegand, Grabarnik, \& Stoyan, 2016). For a given
distance\emph{r} , the hypothesis of independence for a species pair can
then be accepted if -\emph{z} \selectlanguage{greek}\textsubscript{α}\selectlanguage{english}(\emph{r} )
\textless{}\emph{z} (\emph{r} ) \textless{} \emph{z}
\selectlanguage{greek}\textsubscript{α}\selectlanguage{english}(\emph{r} ) at a given pointwise significance level of
\selectlanguage{greek}α. \selectlanguage{english}For \(\alpha\)= 0.05,\emph{z} \selectlanguage{greek}\textsubscript{α}\selectlanguage{english}= 1.96, which
is equivalent to testing whether the observed summary statistic is
located within the 2.5\textsuperscript{th} and 97.5\textsuperscript{th}
percentiles of the corresponding null model distribution. When\emph{z}
(\emph{r} ) \textgreater{} 1.96, the observed summary statistic is
larger than the expectation of the null model with error rate \selectlanguage{greek}α\selectlanguage{english}= 0.025,
and the species pairs are spatially attracted at distance\emph{r} .
While \emph{z} (\emph{r} ) \textless{} -1.96 suggests repulsion at
distance \emph{r} . The distance \emph{r} in this study was chosen to be
5, 30 and 50 m to test the effect of scale on spatial patterns. Because
the association between two species might be asymmetric, we analyzed the
spatial patterns between two species twice with each species serving as
the focal species, i.e. species \emph{i} versus species \emph{j} and
species\emph{j} versus species \emph{i} . Specifically, we examined the
interspecific spatial associations of 80 \selectlanguage{ngerman}× 79 = 6320 species pairs in
this study for two different summary statistics of bivariate spatial
point pattern analysis: \emph{g\textsubscript{ij}} (\emph{r} )
and\emph{D\textsubscript{ij}} (\emph{r} ). All the spatial association
analyses were conducted in R (R Core Team, 2018) and using the package
of ``spatstat'' (Version 1.62-2, Baddeley, Rubak, \& Turner, 2015).

\textbf{Species Trait Dissimilarity and Hierarchy}

We focused on six key functional traits here: leaf area (LA;
cm\textsuperscript{2}), specific leaf area (SLA; cm\textsuperscript{2}
g\textsuperscript{-1}, calculated as leaf area/dry mass), leaf dry
matter content (LDMC; g g\textsuperscript{-1}, calculated as leaf dry
mass/fresh mass), wood density (WD; g cm\textsuperscript{-3}, calculated
as trunk wood dry mass/fresh volume), wood dry matter content (WDMC; g
g\textsuperscript{-1}, calculated as dry wood mass/fresh wood mass) and
tree maximum height (H\textsubscript{max}; m) for each of the 80 species
in this study. These traits represent leading axes of ecological
variation among tree species that have been previously implicated in
interspecific variation in resource use efficiency, species
interactions, and life history strategies and are frequently used in
analyses of the functional structure of forest communities (Kraft \&
Ackerly, 2010; Kunstler et al., 2016; Li et al., 2018). Specifically, LA
is important for energy balance and hydraulic architecture (Ackerly \&
Cornwell, 2007). SLA and WDMC are key elements of the leaf and wood
economic spectrum and correlate with procurement of resources (Chave et
al., 2009; Wright et al., 2004). LDMC is indicative of a plant species'
resource use strategy that links to the trade-off between a rapid
assimilation and growth (Díaz et al., 2004). WD is significant in
relation to growth, stress-tolerance and survival rates (Chave et al.,
2006). H\textsubscript{max} is a key determinant of light competition
(Westoby, Falster, Moles, Vesk, \& Wright, 2002). Data on these traits
on species-level were collected and measured from the HSD plot (He,
Chen, Zhao, Cornelissen, \& Chu, 2018), in which H\textsubscript{max}was
estimated by averaging the top 1\% tallest trees for each species in the
plot.

We calculated two kinds of species differences based on each single
trait: absolute trait distance and hierarchical trait distance, to
evaluate the effects of trait dissimilarity and trait hierarchy on
interspecific spatial associations, respectively (Kunstler et al.,
2012). Absolute trait distance between species \emph{i} and \emph{j} was
calculated as \textbar{}\emph{t\textsubscript{i}}
-\emph{t\textsubscript{j}} \textbar{} where \emph{t\textsubscript{i}}
and \emph{t\textsubscript{j}} are the functional trait values of the
respective species, whilst hierarchical trait distance was calculated
as\emph{t\textsubscript{i}} -\emph{t\textsubscript{j}} . In both trait
distance measures, species \emph{i} is the focal species in
correspondence to that in the spatial point pattern analysis. As
species' niche dissimilarity might be better measured by a multi-trait
than by a single trait approach (Kraft et al., 2015), we also computed
species absolute distance in a multidimensional space defined by the 6
(centered and standardized) functional traits .

\textbf{Relationships between pairwise spatial associations and trait
dissimilarity and hierarchy}

The pairwise spatial associations (estimated as SES
of\emph{g\textsubscript{ij}(r} ) and \emph{D\textsubscript{ij}}
(\emph{r} ), represented as \emph{z\textsubscript{ij}} below) was
modeled as a function of trait dissimilarity and trait hierarchy between
species\emph{i} and \emph{j} , in a linear mixed model using the `lmer'
in the R package `lme4' (Bates, Mächler, Bolker, \& Walker, 2015), in
which the focal species were treated as random intercept allowing
intercepts to vary among each focal species and we used each explanatory
predictor as random slopes to evaluate the effects of each predictor on
spatial associations for different focal species. The model takes the
general form:

\(z_{\text{ij}}=a+a_{i}+\sum_{m=1}^{n}{\left(b_{m}\ +b_{\text{im}}\right)x_{\text{mij}}+\varepsilon_{\text{ij}}}\)\emph{,} (2)

where \emph{z\textsubscript{ij}} represents the spatial associations
between species \emph{i} and species \emph{j} with the focal
species\emph{i} , \emph{x\textsubscript{mij}} represents
the\emph{m\textsuperscript{th}} explanatory predictors of trait distance
(with n predictors in total), which could either be absolute or
hierarchical trait distances, \emph{a} is the fixed intercept
and\emph{b\textsubscript{m}} is fixed slope of
the\emph{m\textsuperscript{th}} explanatory predictor for the overall
regression, while \emph{a\textsubscript{i}} is the random intercept for
the focal species \emph{i} and \emph{b\textsubscript{im}} is the random
slope for the \emph{m\textsuperscript{th}} explanatory predictor for the
focal species \emph{i} .

We first exclusively applied the absolute trait distances of six
individual traits: LA, SLA, LDMC, WD, WDMC and H\textsubscript{max} in
equation (2) to evaluate the effects of absolute trait distances on the
pairwise spatial associations to distinguish the assembly mechanisms of
limiting similarity (Fig. 1c) and environmental filtering or
hierarchical completion (Fig. 1d). If absolute trait distances have
positive effects on pairwise spatial associations, it suggests
functionally similar species tend to be spatially repulsive and
indicates the operation of competition via limiting similarity in the
forest (Fig. 1c). If absolute trait distance have negative effects on
pairwise spatial associations, it indicates functionally similar species
tend to co-occur together, presumably caused by either environmental
filtering or hierarchical competition (Fig. 1d) that needs to be further
tested. In addition, we also applied absolute trait distances estimated
by multiple traits separately to equation (2) to test the effects of
trait dissimilarity on pairwise spatial association because of the
collinearity between absolute trait distances of individual and multiple
traits.

To further test the mechanisms of environmental filtering and
hierarchical competition when absolute trait distances have negative
effects on pairwise spatial associations (Fig. 1d), we simultaneously
included variables of both absolute and hierarchical trait distances and
tested the relative importance of absolute and hierarchical trait
distances in explaining the pairwise spatial associations by comparing
the absolute values of the coefficients of the absolute trait distances
and their corresponding hierarchical trait distances for each focal
species. To do this, we compared the differences in the 95\% confidence
intervals of the coefficients (absolute values) of each absolute trait
distance and its corresponding hierarchical trait distance for each
focal species and we then grouped species into three categories, which
are (1) hierarchical trait distances had stronger effects, (2) absolute
trait distances had stronger effects and (3) hierarchical trait
distances had comparable effects to absolute trait distances.

\textbf{Relating the magnitude that trait hierarchy effects outcompete
trait dissimilarity effects to the abundance of focal species}

We measured the magnitude that trait hierarchy effects outcompete trait
dissimilarity effects (MHD) by the differences in the absolute values of
coefficients of hierarchical trait distances and absolute trait
distances in the full model in equation (2) for different functional
traits and for each focal species. If trait hierarchy had stronger
effects than trait dissimilarity, MHD is supposed to be significantly
larger than 0; If trait dissimilarity had stronger effects than trait
hierarchy, MHD is expected to be smaller than 0. We then assessed the
relationship between MHD and the abundance of each focal species to
explore how the effects of different mechanisms vary among species with
different abundance.

\textbf{Results}

\textbf{Pairwise spatial associations}

The pairwise spatial associations assessed by\emph{g\textsubscript{ij}}
(\emph{r} ) indicate that interspecific spatial independence (-1.96 \selectlanguage{english}[?]
\emph{z} (\emph{r} ) \selectlanguage{english}[?] 1.96) was the dominant pattern across the three
different spatial scales (accounting for 82.09\%, 83.05\% and 85.30\%,
respectively) (Table 1). There were 315, 375 and 346 repulsion cases
(\emph{z} (\emph{r} ) \textless{} -1.96) out of the 6320 pairs
(accounting for 4.98\%, 5.93\% and 5.47\%) at the spatial scales of 5,
30 and 50 m, respectively. Attraction was more commonly observed with
817, 696 and 583 cases (\emph{z} (\emph{r} ) \textgreater{} 1.96)
(accounting for 12.93\% 11.01\% and 9.22\%) than repulsion cases at the
three scales. The same trends were also found in the spatial association
evaluated by the summary statistic of\emph{D\textsubscript{ij}}
(\emph{r} ), in which, spatial independence was also the dominating
pattern between species (Table 1).

\textbf{Relationships between spatial pattern and absolute trait
distances}

By fitting the linear mixed regression model (2) using absolute trait
distances of individual traits exclusively, we found statistical support
for negative effects of the absolute trait distances measured by
individual traits on pairwise spatial associations assessed by the two
summary statistics (\emph{g\textsubscript{ij}} (\emph{r} ) and
\emph{D\textsubscript{ij}} (\emph{r} )) across different spatial scales
(Fig. 2). The coefficients of absolute trait distances of individual
traits of LA, WD and H\textsubscript{max} were consistently negative for
both summary statistics across spatial scales. SLA (at\emph{r} =5 m) and
WDMC showed slightly negative effects on pairwise spatial associations,
while LDMC did not show significant effects. As for absolute trait
distances based on multiple traits, negative effects on spatial
associations were also observed consistently across summary statistics
and spatial scales (Fig. S1).

For the 80 focal species, we found that the effects of absolute trait
distances were non-significant for most of the focal species on their
pairwise spatial associations as the 95\% confidence intervals of
coefficients intercepted 0 (Fig. 2). While for the remaining focal
species, in general, more focal species' spatial associations were
negatively correlated to absolute trait distances than those were
positively correlated (Fig. 2).

\textbf{Comparison between the strengths of trait dissimilarity and
hierarchy on spatial patterns}

As the absolute trait distances of individual traits used in this study
generally had negative effects on pairwise spatial associations, which
supports environmental filtering or hierarchical competition (Fig. 1d),
we compared the strengths between trait hierarchy and trait
dissimilarity on pairwise spatial associations by simultaneously
including explanatory predictors of both absolute and hierarchical trait
distances in equation (2) to distinguish these two mechanisms. For the
80 focal species in this study, we found that LA, WD, and
H\textsubscript{max} consistently showed stronger trait hierarchy
effects on pairwise spatial associations than trait dissimilarity
effects for more focal species across different summary statistics and
spatial scales (Fig. 3 and Fig. S2-S6). For SLA and WDMC under
situations where we observed negative relationships between trait
dissimilarity and spatial associations, the strengths of trait hierarchy
did not vary significantly from the strengths of trait dissimilarity
effects (Fig. 3 and Fig. S3, Fig. S4 and Fig. S6).

\textbf{The relationship betweenthe magnitude that trait hierarchy
effect outcompetes trait dissimilarity effect and the abundance of focal
species}

Overall, LA, WD and H\textsubscript{max} showed stronger trait hierarchy
effects than trait dissimilarity effects on their pairwise spatial
associations for the 80 focal species. For LA and WD, we observed a
positive relationship between the magnitude that trait hierarchy effects
outcompete trait dissimilarity effects (MHD) and the abundance of each
focal species, while for the trait of H\textsubscript{max}, the MHD
decreased with the abundance of focal species (Fig. 4).

\textbf{Discussion}

Trait dissimilarity effects were widely considered to explain species
co-occurrence and coexistence over the past decade (Burns \& Strauss,
2011; He \& Biswas, 2019; Kraft \& Ackerly, 2010). Consistent to the
findings in He \& Biswas (2019), we observed negative relationships
between trait dissimilarity and pairwise spatial associations in this
study across different summary statistics and spatial scales for
individual and multiple functional traits (Fig. 2), except LDMC that
showed non-significant effects on pairwise spatial associations.
However, while necessary, this evidence is not sufficient to support
that environmental filtering is the dominant mechanism. Instead of
simply interpreting this negative relationship as a result of
environmental filtering and absence of competition (He and Biswas 2019),
we pointed out that hierarchical competition that selects species with
traits conferring competitive advantages (i.e. hierarchical competition)
could also be able to produce a negative relationship between trait
dissimilarity and pairwise spatial associations, which is identical to
the result of environmental filtering (Fig. 1d).

By comparing the relative strengths of trait dissimilarity and hierarchy
on pairwise spatial associations, we demonstrated that competitive
hierarchies captured by the traits of LA, WD and
H\textsubscript{max}better explained species co-occurrence than trait
dissimilarity (Fig. 3 and Fig. S2-6), which supports the hypothesis that
hierarchical competition contributes to the co-occurrence patterns. As
for the trait of SLA and WDMC, we observed that the effects of trait
dissimilarity and hierarchy were comparable on the pairwise spatial
associations.

Taking together the effects of both trait dissimilarity and trait
hierarchy on pairwise spatial associations, we infer that except LDMC,
other traits showed either stronger (e.g. LA, WD and
H\textsubscript{max}) or comparable (SLA and WDMC) trait hierarchy
effects relative to trait dissimilarity effects on interspecific spatial
associations, indicating that the effects of hierarchical competition on
the co-occurrence patterns in our forest plot were greater than or
comparable to the effects of environmental filtering. Other traits may
show stronger effects of environmental filtering or limiting similarity
in structuring the forest community, but we currently lack the trait
data to capture such effects.

This study provides a novel method to disentangle the relative
importance of multiple assembly mechanisms in structuring co-occurrence
patterns by assessing the effects of trait hierarchy and trait
dissimilarity on pairwise spatial associations. By linking the pairwise
spatial associations, which reflect signatures left by different
assembly mechanisms to the effects of trait dissimilarity and trait
hierarchy, our study provides alternative perspectives and better
understanding in the underlying mechanisms that govern the co-occurrence
pattern (He \& Duncan, 2000; Wiegand et al., 2007; Wiegand \& Moloney,
2014).

The negative relationship between trait dissimilarity and pairwise
spatial associations was typically interpreted as evidence for no signal
of competition and inferred as a result of environmental filtering (He
\& Biswas 2019). However, this interpretation could be misleading
because the negative relationship between trait dissimilarity and
pairwise spatial associations could also be caused by neighborhood
competition that selects species with particular trait values
independent of environmental filtering (Carmona et al., 2019;
HilleRisLambers et al., 2012; Mayfield \& Levine, 2010). In this study,
we found support for the hypothesis that hierarchical competition leads
to the negative relationship between trait dissimilarity and pairwise
spatial associations as well.

This study also strongly suggests that trait dissimilarity has little
effects on neighborhood competition and that neighborhood competition is
more likely to be driven by trait hierarchy, which is consistent to the
findings in Kunstler et al. (2012; 2016) and Carmona et al. (2019). If
trait dissimilarity was positively correlated to pairwise spatial
associations, we would infer that trait dissimilarity affects the
neighborhood competition and leads species with similar trait occupying
segregated areas. However, which is not the case in this study. Now that
the positive relationship between trait dissimilarity and spatial
associations was absent and effects of hierarchical competition that
exclude inferior competitors were found, we therefore speculate that
neighborhood competition in our forest plot was more likely to be driven
by trait hierarchy but not by trait dissimilarity as presumed (Carmona
et al., 2019; Kunstler et al., 2012).

The two metrics summarizing spatial point patterns
(\emph{g\textsubscript{ij}} (\emph{r} ) and\emph{D\textsubscript{ij}}
(\emph{r} )) that we used in this study showed no significant
differences in the effects of trait dissimilarity and trait hierarchy on
spatial associations for each trait (Fig. 2 and Fig. 3). We therefore
speculate that extreme heterogeneity of species distributions were not
prevalent in our forest plot (Wiegand et al., 2007). Since these two
summary statistics respectively characterize the mean number of
individuals and the nearest neighbors of the second species around the
focal species, the findings that these two summary statistics of spatial
point patterns reveal similar trait effects suggest that the
neighborhood interspecific competitive effects on the focal trees come
from both the average neighbor density and the nearest neighbors of the
other species at least within the scale of 50 m.

By linking the magnitude that trait hierarchy effects outcompete trait
dissimilarity effects (MHD) on pairwise spatial associations to the
abundance of focal species, we found inconsistency among the three
traits LA, WD and H\textsubscript{max} that all showed trait hierarchy
effects on population fitness (Fig. 4). This inconsistency suggests that
different fitness components, e.g., growth, survival and reproduction of
each species, might be unequally influenced by traits and a trait might
positively affect one component but negatively affects another, e.g.,
growth-survival trade-off and reproduction-survival trade-off (Laughlin,
Gremer, Adler, Mitchell, \& Moore, 2020). These unequal effects on
different components of fitness and trade-offs might therefore influence
the abundance of the focal species and lead to variations in the
relationships between MHD and focal species abundance for different
traits.

In conclusion, we disentangled the assembly mechanisms of limiting
similarity, environmental filtering and hierarchical completion in
structuring our forest community by assessing and comparing the effects
of trait dissimilarity and trait hierarchy on pairwise spatial
associations in this study. More specifically, we found that limiting
similarity was weak or absent and hierarchical competition played a more
(or at least equally) important role than environmental filtering in
structuring the co-occurrence patterns in our forest community. This
study also reinforced the importance of trait hierarchy, rather than
trait dissimilarity, in driving interspecific competition.

\textbf{Acknowledgements}

Data for this study were collected by the former SYSU-Alberta Joint Lab
for Biodiversity Conservation. This work was supported by the National
Natural Science Foundation of China (Grant NO. 31901107) and Natural
Science Foundation of Guangdong Province (Grant NO. 2018A030310384). DY
gratefully acknowledges financial support from China Scholarship Council
and Mitacs Globalink Early Career Fellowship-China. MWC and FH were both
supported by the Natural Sciences and Engineering Research Council of
Canada.

\par\null

\textbf{Author contributions:} DY, MWC and FH designed the study. DY led
the analyses. DY, MWC and FH wrote the manuscript with contribution from
all authors.

\textbf{Conflict of Interest:} The authors declare no conflict of
interest.

\textbf{Data Availability Statement}

The data of species distribution of HSD plot and functional traits used
in this article will be deposited in Dryad (doi:10.5061/dryad.9kd51c5ft)
once this paper is published in the journal.

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Table 1. The number and percentages of different types of pairwise
spatial point patterns assessed by the standardized effect size (SES) of
two different summary statistics, bivariate pair-correlation function
(\emph{g\textsubscript{ij}} (\emph{r} )) and bivariate distribution
function of nearest neighbor (\emph{D\textsubscript{ij}} (\emph{r} )),
at three spatial scales.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Summary statistics (SES)\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Spatial scale (m)\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Distribution\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Distribution\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Distribution\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Repulsion\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Independence\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Attraction\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\emph{g\textsubscript{ij}} (\emph{r})\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
315 (4.98\%)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
5188 (82.09\%)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
817 (12.93\%)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
375 (5.93\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5249 (83.05\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
696 (11.01\%)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
50\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
346 (5.47\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5391 (85.30\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
583 (9.22\%)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{D\textsubscript{ij}}(\emph{r})\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
250 (3.96\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5393 (85.33 \%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
677 (10.71\%)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
608 (9.62\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5039 (79.73\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
673 (10.65\%)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
50\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
617 (9.76\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5326 (84.27\%)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
377 (5.97\%)\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Figure Legends

\textbf{Figure 1} . Conceptual framework to illustrate hypotheses of
this study. (a) and (b) respectively show spatial associations of
repulsion and attraction between two species at coarse spatial scale.
(c) and (d) show the predicted relationships between pairwise spatial
associations and absolute trait distance under different processes of
community assembly: (c) limiting similarity, if absolute trait distance
has positive effects on pairwise spatial associations; and (d)
environmental filtering or hierarchical competition, if absolute trait
distance has negative effects on pairwise spatial associations. In the
case of (d), if absolute trait distance has stronger effects on pairwise
spatial association than hierarchical trait distance, we infer that
environmental filtering mainly drives the co-occurrence pattern (e); if
the hierarchical trait distance has stronger effects on pairwise spatial
associations than absolute trait distance, the effect of hierarchical
competition is thought to drive the co-occurrence pattern (f).
Abbreviation: SA= pairwise spatial associations.

\textbf{Figure 2} . Effects of absolute trait distances on the pairwise
spatial associations in equation 2 that only includes the absolute trait
distances as explanatory predictors. The left panels show coefficients
of each variable of absolute trait distances with variance. The right
panels present percentages of the 80 focal species whose spatial
associations are positively (brown circles), negatively (blue circles)
and non-significantly (gray circles) correlated with each variable of
absolute trait distances. The panels from Row 1-6 represent the results
for spatial associations assessed by bivariate pair-correlation function
(\emph{g\textsubscript{ij}} (\emph{r} ), pcf) across different spatial
scales at \emph{r} = 5 m, 30 m and 50 m and bivariate distribution
function of nearest neighbor (\emph{D\textsubscript{ij}} (\emph{r} ))
at\emph{r} = 5 m, 30 m and 50 m, respectively. Abbreviation: LA=leaf
area, SLA=specific leaf area, LDMC=leaf dry matter content, WD=wood
density and H\textsubscript{max}=maximum height, abdist means absolute
trait distance.

\textbf{Figure 3.} Comparison between the strengths of hierarchical and
absolute trait distances on spatial associations for the 80 foal
species. The strengths of hierarchical and absolute trait distances were
respectively given by the absolute values of the coefficients of the
variables of hierarchical and absolute trait distances of different
functional traits in the full model of equation 2. Each circle
represents one focal species. Brown, blue and gray circles respectively
represent that hierarchical trait distances had stronger, weaker and
non-significantly different effects on the pairwise spatial associations
relative to their corresponding absolute trait distances. The results
presented here are for spatial associations assessed by bivariate
pair-correlation function (\emph{g\textsubscript{ij}} (\emph{r} ), pcf)
at\emph{r} =50 m.

\textbf{Figure 4.} The relationships between the abundance of focal
species and the magnitude that the effects of trait hierarchy outcompete
trait dissimilarity (MHD). MHD was given by the differences in the
coefficients (absolute values) of hierarchical trait distances of each
trait and their corresponding coefficients (absolute values) of absolute
trait distances in the full model of equation 2. Each circle represents
one focal species. Brown, blue and gray circles respectively represent
that hierarchical trait distances of had stronger, weaker and
non-significantly different effects on the spatial associations relative
to their corresponding absolute trait distances. The results presented
here are for spatial associations assessed by bivariate pair-correlation
function (\emph{g\textsubscript{ij}} (\emph{r} ), pcf) at \emph{r} =50
m.

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