Modelling species interactions in macroevolution and macroecology
Xu, Liang
DOI:
10.33612/diss.125954510
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Publication date: 2020
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Xu, L. (2020). Modelling species interactions in macroevolution and macroecology. University of Groningen. https://doi.org/10.33612/diss.125954510
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4
The spatially explicit
phylogenetic Janzen-Connell
effect predicts realistic
macroecological and
macroevolutionary patterns
Liang Xu, Hanno Hildenbrandt & Rampal S.
Etienne
This chapter is under review.
4
Abstract
The Janzen-Connell (J-C) hypothesis states that species-specific natural ene-mies (pathogens, predators) induce local-density dependence which explains high diversity observed in tropical tree communities. However, these natural enemies often attack phylogenetically related species as well. Here, we use a spatially explicit model to study the predictions of a phylogenetic J-C effect for common diversity patterns. The species-area relationship is triphasic, while the species-abundance distribution has a rare species mode (neutral sce-nario), a two modes (large dispersal distance) or a single interior mode (small dispersal distance). Small dispersal distance forms clusters of species with large phylogenetic distance to the community while large dispersal distance makes species distribute uniformly. Phylogenetic trees show diversification slowdowns and imbalance, consistent with empirical patterns. However, the phylogenetic relatedness effect reduces diversity. We conclude that the spa-tially explicit phylogenetic J-C effect explains commonly observed diversity patterns, but hyperdiversity only results when the natural enemies are ex-tremely species-specific.
Key words: competition; simulations; phylogeny; species-abundance
dis-tribution; spatial explicit model; Janzen-Connell; phylogenetic relatedness effect; biodiversity; species-area relationship.
4
Introduction
The high diversity in many ecological communities, such as the Amazon rain
forest hosting over 1 , tree species Ter Steege et al. 2 2 , never ceases to
amaze. How such diversity is maintained has puzzled biologists for decades. One of the leading explanations of high biodiversity is the Janzen-Connell J-C effect,
originally proposed by Janzen Janzen and Connell Connell 4 . The J-C effect
posits a reduction of species recruitment in areas of high conspecific density, be-cause host-specific natural enemies such as seed predators, parasites, herbivores and pathogens are attracted disproportionally by locally abundant species. As a result, rare species are at a recruitment advantage, leading to high diversity. The J-C effect thus involves density-dependence in a spatial context; the attenuation of the effect with distance has been referred to as distance-dependence.
Since the J-C hypothesis was first proposed, it has received much attention.
The number of articles on the J-C hypothesis is substantial Comita et al. and
review papers that summarize studies testing the J-C hypothesis have been
pe-riodically published Clark and Clark 2 , Hammond and Brown , Takeuchi and
Nakashizuka2 . In a meta-analysis of empirical studies, Comitaet al. Comita
et al. reported strong support for both distance- and density-dependent
predic-tions. However, although the J-C effect is generally accepted as a plausible driver of high diversity, uantitative predictions are still largely lacking, leading some to doubt the ability of the J-C effect to explain uantitatively the high observed biodiversity
Armstrong , Becker et al.12, Hubbell . Only recently, a first uantitative model
was presented by Leviet al. Levi et al.1 who incorporated distance-responsive
natural enemies into the classic neutral theory Hubbell to account for the J-C
effect. ith simulations of their model they showed that the J-C mechanism can
lead to hyperdiversity.
hile Leviet al.’s model Levi et al.1 presents important pioneering work, it
has several unrealistic features that may affect the uantitative predictions. Firstly, the model assumes an exclusion zone around a tree that dies in which conspecifics of the dead tree are prohibited to replace it. However, the J-C effect changes more smoothly with distance than an abrupt change at the border of the exclusion zone.
For example, Hubbell et al. Hubbell et al. found that the negative effects of
conspecific density are locally strong but decay with distance from the focal plant. Second, the model assumes the classical dichotomy between conspecifics and het-erospecifics, where all heterospecifics of an abundant species regardless of their evolutionary relatedness to the abundant species are at an e ual advantage. How-ever, natural enemies are often able to attack multiple species and the likelihood of attack by a particular enemy decreases with phylogenetic distance between the
attacked species Gilbert et al. , Gilbert and ebb 4, Liu et al.11 , Ness et al.
14 . Specifically, the rate of spread of plant pathogens increases with the density
of multiple susceptible species that are phylogenetically closely related Gilbert and
ebb 4 . Novotny et al. Novotny et al. 142 analyzed data of over
her-bivorous species feeding on 1 plant species in New Guinea, and found that most herbivores feed on phylogenetically closely related plant species. If the J-C effect
4
attenuates with phylogenetic distance, its ability to explain high diversity may be
compromised. Third, the model by Levi et al. 2 1 does not consider another
important spatial factor: dispersal limitation. Dispersal limitation is known to affect diversity patterns such as the species abundance distributions SAD Etienne et al.
, Rosindell and Cornell 1 ,1 , Rosindell et al.1 1 and community
phyloge-netic structure Germain et al. 2, Pigot and Etienne1 , Ram rez et al.1 , eigelt
et al. 21 . Evidently, while rare species have a relative advantage in competing
for empty sites compared to abundant species in the context of the J-C effect, they cannot successfully invade if they are too far away.
Here, we overcome these three shortcomings by developing an individual-based dynamic model with a spatially explicit phylogenetic J-C effect. Our model is a non-neutral extension of the standard neutral model of biodiversity in which the constantly changing phylogeny and abundance affect recruitment in a spatial grid. The model has four key parameters, i.e. the strength of the Janzen-Connell effect i.e. how disproportionately natural enemies are attracted by abundant species , the strength of phylogenetic relatedness i.e. how uickly the J-C affect attenuates with phylogenetic distance , the interaction distance of the J-C effect i.e. how uickly the J-C effect attenuates with spatial distance and the dispersal distance of
individuals. e explore the predictions of our spatial phylogenetic Janzen-Connell
SPJC model for species richness, the SAD, the species-area relationship SAR , the phylogenetic distribution in space, and phylogenetic properties such as tree balance
and lineages-through-time LTT plots. e find that the spatially explicit
phyloge-netic J-C effect can generate a variety of ecological and phylogephyloge-netic community patterns which are consistent with empirical observations. However, hyperdiversity only results when pathogens or predators are species-specific.
Model description and analysis
A general colonization model with spatially explicit phylogenetic
Janzen-Connell effect
e consider species dynamics in a spatial grid of𝑁 cells. e assume that at
each time step one individual dies, chosen at random, as in the standard, spatially
implicit, neutral model Etienne4 , Hubbell as well as spatially explicit versions
Rosindell and Cornell 1 , Rosindell et al. 1 2 . The empty cell is colonized by
offspring of an individual anywhere in the grid, depending on its proximity. However, in contrast to the neutral model, the probabilities of colonizing the empty cell are not e ual for all individuals at the same spatial distance, but depend on the phylogenetic distance to the individuals surrounding the empty cell and hence this also accounts
for their spatial distance and - at the species level - the abundance . e assume
that the relative probability of species𝑖 colonizing the cell is
𝑝,explicit= 1 − 𝜓
∑ (exp (−𝜙 ⋅ 𝐷 ( )) ⋅ exp (−𝑑 , /(2𝜎 )))
∑ exp (−𝑑 , /(2𝜎 ))
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where𝐷 ( )is the phylogenetic distance between species𝑖 and species 𝑗 in cell 𝑘,
𝑑 , is the distance between cell𝑘 and the empty cell 𝑜, 𝜓 determines the strength
of the J-C effect, 𝜎 determines the spatial extent of the J-C effect, and 𝜙
mea-sures the size of the phylogenetic effect. The Gaussian kernel exp (−𝜙 ⋅ 𝐷 ( ))
describes the differential contribution to the colonization probability from very small
for a phylogenetically remotely related species large𝐷 ( ) to very large for a
con-specific 𝐷 ( ) . hen the J-C effect is absent, i.e. 𝜓 = 0, the model reduces
to a spatially explicit neutral model. hen𝜙 approaches infinity, the J-C effect is
restricted to closely related species as in the classic J-C hypothesis only the term
𝐷 contributes to the sum , but when𝜙 is small, even a species 𝑖 that is
phy-logenetically distant from the individuals surrounding the empty cell experiences a
reduced colonization probability; when𝜙 = 0, we arrive again at the neutral model,
because all species are affected e ually they all have the same relative
probabil-ity . hen𝜎 is small, only individuals immediately surrounding the empty cell
determine the colonization probability i.e. those individuals attract enemies that attack their conspecifics and phylognetically related species and thus reduce these species’ colonization probability .
The phylogenetic distance between all species pairs can be summarized in a matrix D, defined by D = ( 0 𝐷 ⋯ 𝐷 𝐷 0 ⋯ 𝐷 ⋮ ⋮ ⋱ ⋮ 𝐷 𝐷 ⋯ 0 ) 4.2
where the entry𝐷 denotes the interspecific phylogenetic distance between species
𝑖 and 𝑗. e thus do not model the dynamics of the host-pathogen interaction
explicitly, but use the phylogenetic distance as a proxy for the likely host range of natural enemies.
E . 4.1describes the relative colonization probabilities if all species are e ually
able to disperse to the empty cell, regardless of their distance to it. These
coloniza-tion probabilities must therefore be weighted by the probability of dispersal𝑝 | ,
of the individual in cell 𝑘 belonging to species 𝑖 to the vacant site 𝑜. e assume
that this probability follows a normal distribution determined by the geographic
dis-tance from the individual’s site to the vacant site,𝑑 , , and the dispersal distance
of individuals𝜎 Rosindell and Cornell1 , which is assumed to be the same
across all species:
𝑝 | , ∼ 1
√2𝜋𝜎
exp (− 𝑑 ,
2𝜎 ) . 4.
hen𝜎 is infinite, all individuals can move anywhere in the community with
e ual probability.
4
belonging to species𝑖 becomes
𝑝 | ,explicit=
𝑝 | , 𝑝,explicit
∑ 𝑝| ( ), 𝑝 ( ),explicit
. 4.4
The model reduces to a spatially implicit model when setting the dispersal ability of
individuals𝜎 and the spatial interaction distance of the phylogenetic J-C effect
𝜎 to infinity. Then we obtain the spatially implicit colonization probability of an
individual of species𝑖
𝑝 | ,implicit=
𝑝,implicit
∑ 𝑝( ),implicit
4.
where the spatially implicit relative colonization probability of species𝑖 is given by
𝑝,implicit= 1 − 𝜓
∑ (exp (−𝜙 ⋅ 𝐷 ( )))
𝑁 . 4.
e illustrate this formula with a simple tree of 4 species and their abundances in a spatially implicit context by comparing the relative colonization probabilities E .
4. for different𝜙 Fig.4.1.
The simulation process
e assume that the community has a fixed size𝑁 and we start with two species,
one common species with abundance𝑛 = 𝑁 − 1 and one rare species with
abun-dance 𝑛 = 1. The initial phylogeny tree has two e uivalent branches. The initial
phylogenetic distance matrix D can be written as ( 01 10 ). At each time step Fig.
4.2 , one individual in the community is randomly chosen to be removed. The
abun-dance of the corresponding species decreases by one. If the species is a singleton,
the death event results in extinction. e then remove that species from the
com-munity and the phylogeny. The corresponding column and row in the phylogenetic distance matrix D are removed as well. After random death the cell is colonized
immediately. The colonizer is a new species if speciation occurs with probability𝑣
or offspring of an existing species with probability1 − 𝑣. If birth occurs, one
individ-ual is sampled according to the aforementioned colonization probability E . 4.4 .
After the birth event, the abundance of the corresponding species increases by 1. If speciation occurs, we sample one individual again using the colonization probability
E . 4.4 and let the corresponding species speciate. To update the abundance
and phylogenetic relatedness, we extend the abundance vector by adding the new
species with 1 individual the point mutation assumption Hubbell and we
ex-tend the phylogenetic relatedness matrix by adding one column and one row. The phylogenetic relatedness of the new species to the others are the same as that to the sampled parent species plus 1 while to the parent species this distance e uals 1. Finally, at every time step we update the phylogenetic relatedness matrix E .
4
Figure 4.1: The relative colonization probabilities for 4 species of a simple tree when . . Panel A shows the tree with tips labeled by their abundances. The phylogenetic relatedness matrix is therefore given by D ( ) . Panel B shows the colonization probabilities against the variable . hen is small, the rare species Species suffers the negative effect from phylo-genetically related species, thus, possesses a low colonization probability as Species 4. ith increasing , natural enemies become more host-specific and the rarity advantage increases due to the J-C ef-fect. Thus, Species is less affected by its conspecific density and finally reaches a highest colonization probability.
4
4.2 by adding 1 to every entry except the diagonal entries. These steps are
re-peated until a prescribed time is reached. e call this se uence of events the tree
replacement.
Parameter settings
Our aim is to examine to what extent the phylogenetic J-C effect results in differ-ent patterns compared to neutral theory and how differdiffer-ent J-C interaction distances and dispersal distances affect these patterns. To assess the effect of different
spa-tial scales, we set the regional grid size to𝑁 = 333 and study the diversity of two
additional local scales within this grid 𝑁 = 55 , 111 by sampling all possible
non-overlapping areas of that scale in the grid and measure the species richness. e
explore different numerical combinations of the four parameters𝜓, 𝜙, 𝜎 , 𝜎 . e
vary the strength of the phylogenetic J-C effect𝜓 in the range (0, 0.25, 0.5, 0.75, 1),
which describes scenarios ranging from neutrality to a very strong J-C effect. The
parameter𝜙 uantifies the width of the phylogenetic relatedness effect which we
vary in the range of (1, 10 , 10 , 10 , 10 , 0) corresponding to a phylogenetic
distance range of (√ ,√ × 10 ,√ × 10 ,√ × 10 ,√ × 10 , +∞). The
specia-tion rate is set at 𝜈 = 0.0001,which means that there are 10 tree replacements
on average between speciation events. The total number of tree replacements in the simulation which determines the maximum phylognetic distance is set to
10 for computational tractability. e chose three values each for𝜎 and 𝜎 :
(0.1, 1, 10) referring to low distance, intermediate distance and high distance, which
results in distance scenarios. e ran 1 replicate simulations for each of the
2 parameter combinations leading to a total of 2 simulations, each of which
took up to days.
Model analysis
e studied patterns of species richness, species abundance distributions and the species-area relationship. Furthermore, we developed a new metric to study how the phylogenetic J-C effect affects the spatial distribution of the species. The new metric is based on the mean of inverse pairwise phylogenetic distance MPID,
Ness et al.14 . In contrast to other widely used metrics such as the phylogenetic
distance to the phylogenetically nearest neighbor NND, ebb et al.212 and mean
phylogenetic distance to all other species MPD, Hill and otanen , amosi et al.
2 , MIPD increases with increasing relatedness of the focal species to others in
the community nonlinearly, thus measuring species-level phylogenetic similarity in a community. Here we introduce a metric of phylogenetic similarity by weighting the phylogenetic distances with abundances, the abundance-weighted MPID, or
A MIPD. For species𝑖, A MIPD is defined as:
𝐴𝑊𝑀𝐼𝑃𝐷 = ∑ 𝑛 𝑛 (𝐷, )
∑ ∑ 𝑛 𝑛 (𝐷 , )
4
Figure 4.2: Schematic representation of one tree replacement of the model for a grid size of . Each cell can host one tree which is labeled with a number. After one individual’s death, the individual colonization probability is computed for all individuals based on their phylogenetic relatedness given by the phylogenetic tree and density denoted by the number of circles with the same number and color and further weighted by the interaction distance of the phylogenetic J-C effect denoted by the red zone around the vacant site in the center and the dispersal distance of individuals the green zone around individuals; dispersal zones of only two individuals are shown . The chosen individual gives birth to a new individual, but this individual may undergo speciation with probability . species 1 arises from speciation in species 4 and inherits the phylogenetic distance to other species from its parent.
4
where 𝑛 is the abundance of species 𝑖. A species can attain a high A MIPD if it
is closely related to the other species small𝐷, , or if it has a high abundance or
both, i.e. large𝑛 or 𝑛 . e plotted the A MIPD values for all individuals across
space.
To analyze the phylogenetic tree balance, we computed the Colless index𝐼
Bortolussi et al.1 , Colless 1, Mooers12 and the𝛽-statistic Aldous ,4, Blum
and Fran ois14, Bortolussi et al.1 . The Colless index sums the absolute
differ-ences in tip number between the daughter clades at a node for all nodes in a tree and divides this by the maximum possible Colless value of that tree size. Assess-ing the Colless index of different parameters allows us to compare the imbalance of generating trees. However, although the Colless index is widely used, it has
been reported to depend on tree size Mooers12 . As an alternative measure of
tree balance we used the𝛽-statistic that maximizes the likelihood in the 𝛽-splitting
model of clade growth Aldous ,4, Blum and Fran ois14 , which has also been
applied widely Blum and Fran ois 14, Gascuel et al. , Pigot et al.1 . hen
𝛽 = 0, it represents the same balance as a pure-birth process the Yule model Yule
G. 221 . A positive 𝛽 value indicates a more balanced tree than the Yule process
while a negative value implies a more unbalanced tree.
e measured the rate of lineage accumulation with the𝛾-statistic Pybus and
Harvey1 and theΔ𝑟-statistic Etienne and Rosindell , Pigot et al.1 . The
𝛾-statistic is one of the most commonly used indices of species accumulation but it
has been shown to depend on the size of the tree Etienne and Rosindell , McPeek
12 . TheΔ𝑟-statistic is an alternative statistic which is computed as Magall n and
Sanderson11 , Pigot et al.1
Δ𝑟 = ln ( ) ( )− ln ( ) ( ) ln ( ) ( )+ ln ( ) ( ) 4.
where𝐿(𝑡) denotes the number of lineages at time 𝑡 that survive up to the present
and𝑇 is the crown age.
To compare the metrics to empirical observations, we used two data sets. e
downloaded a data set of empirical phylogenetic trees from TreeBASE www.treebas
e.org and a data set used byMcPeek McPeek 12 . After filtering out the trees
that lacked information on branch lengths, or had less than extant species Davies
et al.4 , we finally arrived at and 14 phylogenetic trees, respectively for
com-paring the metrics to our simulated data. e report only results for the first data
set in the main text. Both data sets and the results for the second data set can
be found in the Supplementary Material. e note that these empirical phylogenies
cover a wide range of taxa, including taxa that may not be associated with a J-C
effect but see Discussion . e used them anyway to get an idea of the range of
4
Results
Species richness
The J-C effect promotes biodiversity but less so when the J-C effect extends
to phylogenetically more remote species small 𝜙 . hen 𝜓 = 0 or 𝜙 0, the
model reduces to the spatially explicit neutral model. e will therefore call the
combinations with𝜙 = 0 or 𝜓 = 0 the neutral parameter combinations, and refer
to other parameter sets as the non-neutral parameter combinations. For nonzero𝜓
species richness increases with increasing𝜙 see Fig. 4. . At the largest values of
𝜙, the system resembles the classic J-C scenario which has highest diversity. The interaction distance of the phylogenetic J-C effect and the dispersal distance have further impact on the species richness. Small dispersal distance produces more species than large dispersal distance for all parameter combinations at the regional
scale 𝑁 = 333 . In contrast, larger interaction distance of the phylogenetic J-C
effect results in more species than a smaller interaction distance, but the increase is not as substantial as that produced by changing the dispersal distance. Thus, the highest species richness is observed when the dispersal distance is smallest
𝜎 = 0.1 and the interaction distance of the phylogenetic J-C effect is largest
𝜎 = 10 together with the largest values of 𝜙 and 𝜓 𝜙 = 1, 𝜓 = 1 . This species
richness is almost 1 times larger than the richness that is generated by the standard
neutral theory in the same grid. For small spatial scales 𝑁 = 55 , 111 , Fig. 4. ,
we found that increasing dispersal distance increases species richness, implying that changing the scale from large to small shows a change in the dispersal-diversity relationship from negative to positive.
Species-area relationships
The phylogenetic J-C effect generates a clear triphasic species-area relationship
in line with data and neutral model predictions Hubbell , Rosindell and Cornell
1 , for all parameter settings, except, remarkably, the neutral scenario Fig. 4.4
and Figs. S -S44 . However, this is due to the fact that the neutral simulations
have not reached e uilibrium. Indeed, running the simulations longer results in a triphasic SAR for the neutral scenario as well Fig. S4 . Hence, the phylogenetic J-C effect creates the triphasic shape much faster than the neutral model can.
Species abundance distribution
The SAD is affected by all four factors, i.e. 𝜓, 𝜙, 𝜎 , 𝜎 Fig. 4.4 and Fig.
S1 -S1 . hen the individual dispersal distance is small 𝜎 = 0.1 , there are
many intermediately abundant species for the non-neutral parameter combinations
see Fig. 4.4 , generating a lognormal-like SAD. ith such dispersal limitation,
decreasing𝜓 or 𝜙 converts the species-abundance distribution from a distribution
with a single interior mode Rosindell and Cornell 1 to a distribution with a
single rare species mode of the neutral type Rosindell et al. 1 1 . A large
phy-logenetic J-C interaction distance 𝜎 = 10 tends to sharpen the interior mode,
un-4
Figur e 4 .: Species richness for incr easing spatial scale A -C. In each panel, the blocks of bars repr esent the combinations of thr ee di ffer ent inter action distances of the ph ylogenetic J-C ef fect and thr ee di ffer ent dispersal distances. Each block of bars repr esents combinations of and . The top surf ace of each bar is the mean div ersi ty acr oss 1 replicates, and the err or line in each bar repr esents the first and thir d uanti les.4
der a broadly applied phylogenetic J-C effect with highly limited dispersal. Notethat under high dispersal limitation, there is always a very abundant species in the
community. In contrast, a large dispersal distance 𝜎 = 10 produces a
two-mode species-abundance distribution Rosindell and Cornell 1 for non-neutral
parameter combinations Fig. S1 -S12 . Changing the phylogenetic J-C interaction
distance𝜎 has little influence on the shape of the species-abundance distribution.
No dominant species is found in this scenario.
Spatial distribution
High mobility of individuals tends to randomly distribute species of different phylogenetic relatedness in the community while limited mobility results in patchy
clustering Fig. 4.4and Fig. S1-S . For the neutral parameter combinations,
indi-viduals with high A MIPD dominate the community red dots in Fig. 4.4. hen the
dispersal distance is large, there are a few individuals with low A MIPD distributed
widely over the community blue dots in Fig. 4.4. Increasing 𝜓 greatly reduces
the number of phylogenetically dominant species large A MIPD . For the highest
values of𝜓 and 𝜙, the community is filled with individuals of distinct A MIPD,
in-dicating species of different classes of phylogenetic distance to the community are
distributed uniformly over the community. hen the dispersal distance is small,
there is a clear pattern of clustering of individuals with a large phylogenetic
dis-tance to the community for all parameter combinations. ith increasing 𝜓, more
low-A MIPD individuals appear and more clusters emerge. Larger interaction dis-tance of the phylogenetic J-C effect seems to lead to larger low-A MIPD clusters.
Lineage accumulation
The phylogenetic J-C effect tends to slow down lineage accumulation while the neutral theory yields an accelerating accumulation pattern see the
linege-through-time plots in Figs. 4.4and S1 -S2 and the distribution of slowdown metrics in Fig.
4. and Fig. S2 -S2 . The Δ𝑟s for the non-neutral parameter combinations are
smaller than−0.5 for all distances, suggesting a substantial slowdown in
diversifi-cation. In contrast,Δ𝑟s are slightly higher than 0 for the neutral model with large
dispersal distance Fig. 4. . The𝛾-statistic shows a similar pattern, but the further
slowdown measured by the𝛾-statistic with increasing 𝜓 for non-neutral parameter
combinations decreases when dispersal increases. This may be due to the known
negative relationship between the𝛾-statistic and tree size McPeek12 , Phillimore
and Price1 4 . TheΔ𝑟 estimates of our simulations all fall in the range of
empir-ical estimates, while the scenarios for small𝜙 10 and large dispersal distance
𝜎 = 10 and for small 𝜓 0.25 and small dispersal distance 𝜎 = 0.1 also
produce realistic𝛾 estimates Fig. S2 . Interestingly, the estimates of the neutral
model are found to be compatible with the empirical estimates for both statistics
Fig. 4. , S2 -S2 and Fig. S 2-S . This deviates from Davieset al.’s conclusion
that the neutral model generates unrealistically positive 𝛾 Davies et al.4 . This
results from a discrepancy between the empirical estimates we found and the ones
4
Neutr al high dispersal SPJC high dispersal & inter action distance SPJC inter mediate dispersal& high inter
action distance
SPJC lo
w dispersal
& high inter
action distance 1 10 100 1 10 100 Area No. of species 0 20 1 3 5 7 9 11 13 15 17 Ab undance (log2) Frequency 2 10 50 400 10 8 6 4 2 0 Time No. of species 1 10 100 1 10 100 Area No. of species 0 20 1 3 5 7 9 11 13 15 17 Ab undance (log2) Frequency 2 10 50 400 10 8 6 4 2 0 Time No. of species 1 10 100 1 10 100 Area No. of species 0 20 1 3 5 7 9 11 13 15 17 Ab undance (log2) Frequency 2 10 50 400 10 8 6 4 2 0 Time No. of species 1 10 100 1 10 100 Area No. of species 0 20 40 1 3 5 7 9 11 13 15 17 Ab undance (log2) Frequency 2 10 50 400 10 8 6 4 2 0 Time No. of species T ree SAR SAD SPD LTT Figur e 4 .4: Distinct ecological and ph ylogenetic pat terns pr oduced b y di ffer ent par ameter combinations. The gener ating par ameters fr om left to right ar e , , ; ., , , ; ., , , and ., , ., , respectiv ely . The ph ylogenetic tr ees each repr esent one sample out of 1 replicates gener ated b y the af or ementioed par ameters. The gr a y shading of S AR and LT T plots repr esents inter uantiles minimum, 2th per centile, th per centile, maximum whi le two uanti les 2.th per centile, .th per centiles ar e added for LT T plots. In the S AD plots, the red bars repr esent the a v er age number of species wi th abundances on log scale while the blue err or lines repr esent the standar d deviation of the 1 replicates. In the spatial distribution SPD plots, each dot in the grid repr esents one individual. The color of the dot denotes the abundance-weighted mean of in v erse ph ylogenetic distance to the communi ty A MIPD. The mor e red the dot is, the mor e ph ylogenetical ly related to the communi ty the species of that individual is. Con v ersely , the blue dots repr esent individuals that ar e ph ylogenetical ly remote fr om the communi ty . The whi te dots denote individuals of species wi th intermediate A MIPD .
4
check their results against ours because their data was not made available.Phylogenetic tree balance
Negative𝛽 values are generated by all parameter settings, indicating more
un-balanced trees than those produced by the Yule model Fig. S . Phylogenetic
tree balance generally increases with stronger J-C effect larger 𝜓 , and further
increases with weaker phylogenetic effect smaller 𝜙 but the size of the effect
depends on the dispersal distance and the interaction distance. A large dispersal distance tends to yield more balanced trees than a small dispersal distance. The interaction distance of the phylogenetic J-C effect seems to have little influence on the balance when the dispersal distance is large, but tends to make trees more
balanced when the dispersal distance is small. The Colless index𝐼 seems to tell
the same story Fig. S 1 . Most trees from the two empirical data sets show
neg-ative 𝛽-statistics and positive Colless indices, implying unbalanced trees but less
imbalance than for trees generated by the neutral model Figs. S -S 1 and Figs.
S 4-S .
Discussion
e have presented a spatially explicit model based on experimental evidence
that J-C effect extends to phylogenetically related species Liu et al. 11 . In the
model the J-C effect depends on the phylogenetic distance between a potential col-onizer and the individuals surrounding an empty site, and on the spatial distance between these neighboring individuals and the empty site. Through simulations, we confirm the efficacy of the J-C effect to maintain high biodiversity but this is reduced by the phylogenetic relatedness effect. In general, we find a palette of community patterns for different values of the strength, and the interaction distance of the phy-logenetic J-C effect and the dispersal distance, ranging from low diversity in neutral
scenarios to hyperdiversity of the original J-C theory Levi et al.1 , from a single
mode the rare species mode or the intermediately abundant species mode to a dual mode the rare species mode and the interior mode species-abundance
distri-bution Rosindell and Cornell1 , from pull-of-the-present lineage accumulation to
slowdowns in lineage accumulation, and from unbalanced to balanced phylogenies. The SARs show a triphasic shape that is in line with previous theoretical
predic-tions and empirical patterns Chave and Leigh 2 , Durrett and Levin 4 , Hubbell
, Rosindell and Cornell1 . However, it is attained much faster under a
phylo-genetic J-C effect than in the neutral scenario. This supports the criticism that the dynamics of the standard neutral model are too slow to lead to empirically observed
patterns within a realistic time period Missa et al.124, Nee1 , Ricklefs1 .
The J-C effect has been shown to be pervasive and to play an important role in the maintenance of high species diversity in many communities Marhaver et al.
12 , Petermann et al.1 , particularly in forests Liu et al. 11 and grasslands
Petermann et al.1 . Our results agree with this conclusion and demonstrate that
J-C effects embedded in the neutral model substantially increase species richness. However, we also show that extending the J-C effect to phylogenetically related
4
species tends to reduce the diversity increase solely due to the original J-C effect, which only distinguished between conspecifics and heterospecifics. This implies that neglecting this phylogenetic relatedness mechanism exaggerates the power of the J-C effect to explain hyperdiversity. In practice, if closely related species share natural enemies, newly born individuals suffer negative density dependence not only from conspecifics but also from their close relatives and have a greater probability to go extinct than under a standard J-C effect with purely species-specific enemies. As a conse uence, hyperdiversity cannot be maintained at the same level as by the standard J-C effect.
Furthermore, we have shown that diversity decreases with increasing dispersal, in line with the literature that argues that dispersal tends to homogenize the region
and thus reduces diversity at a regional scale Cottenie and De Meester , Loreau
112, Mou uet and Loreau1 . This homogenization means that dominant
com-petitors are able to distribute themselves widely and thus structure the region in
a monotonous fashion Cadotte et al.2 , Cadotte and Fukami24 , which directly
leads to a less diverse community. In contrast, on the local community scale diver-sity is generally thought to be enhanced by dispersal via introducing new species
Loreau and Mou uet 11 , Tilman 2 4 . Our study also agrees with this
conclu-sion: at small spatial scales larger dispersal distance leads to higher local diversity. Species are observed to distribute more uniformly as mobility increases, and thus have a higher chance to explore the unfilled niches in local communities, leading to higher local diversity. In sum, the influence of dispersal on diversity may differ on
local and regional scales Cadotte22 , also under a phylogenetic J-C effect.
The SARs produced by the phylogenetic J-C effect show the same general tripha-sic pattern, but the exact shape varies for different parameters of the model, so
this may explain the large variance empirically observed slopes illiamson 21 .
Species with large dispersal distance tend to spread over the community, being easily sampled even when the survey area is small. This results in a fast and stable increase in the first phase, but it takes large area for the richness increase to decel-erate. In contrast, a small dispersal distance reduces the sampling probability for rare species. Increasing the size of survey areas captures more rare species, which leads to a short second phase and uick arrival at the third phase. Indeed, the local, regional and continental scales of the three phases must be defined relative
to the dispersal distance Hubbell , Rosindell and Cornell1 .
Our exploration of how the phylogenetic J-C effect influences the SAD for differ-ent distances demonstrates that the J-C effect is universally disadvantageous to the most abundant species as expected but has different impact on rare or moderate species abundances depending on dispersal distance. A rare species mode arises because rare species benefit due to negative density dependence. The interior mode shown in the SAD for the non-neutral parameter combinations with little dis-persal limitation implies that the intermediately abundant species are not sufficiently abundant to be substantially constrained by the J-C effect but they are sufficiently abundant to be at an advantage for sampling due to high dispersal. Increasing
strength of the phylogenetic J-C effect 𝜓 decreases the number of the most
4
the dispersal distance decreases, the intermediately abundant species benefit evenmore, resulting in the sharpened interior mode. This is consistent with the empirical observation of the tropical moist forest trees on Barro Colorado Island Rosindell
and Cornell1 .
Our model predicts a broad range of species accumulation and phylogenetic balance patterns which is also observed in the empirical data Blum and Fran ois
14, J nsson et al. 4, McPeek12 , Mooers12 , Mooers and Heard12 , Nee et al.
1 , Phillimore and Price 1 4, Rabosky and Lovette 1 2 . A strong phylogenetic
J-C effect tends to slow down species accumulation. Because the phylogenetic J-C effect favors rare, phylogenetically remote, species, species born in the deep past can survive, leaving a signature of an early burst of diversity. A slowdown in lineage accumulation then follows. Our model thus provides a more mechanistic
explana-tion for the hypothesis of diversity-dependent speciaexplana-tion Etienne et al. 1 . In
contrast, with a weak J-C effect and/or a broad phylogenetic host range where the model tends to the neutral scenario, our model is able to account for accelerating
species accumulation as follows. hen reducing J-C effects, rare species are lost
more uickly, leading to a high extinction rate. Conse uently, the lineage accumu-lation rate increases, a phenomenon known as the pull-of-the-present Nee et al.
1 , Phillimore and Price 1 4, Rabosky and Lovette 1 2 . The phylogenetic J-C
effect generates less imbalance than the neutral model, although abundant species are still at a sampling advantage colonizing empty sites. This is consistent with
the empirical patterns. e note that the lower imbalance could result because the
system may not have reached e uilibrium yet. So to what extent the phylogenetic J-C effect also produces less unbalanced trees than the neutral model in e uilibrium
remains to be resolved. e also note that the two most extreme strengths of the
phylogenetic relatedness effect that we used 𝜙 = 0, 1 are probably not realistic.
A too high value of𝜙 excludes the replacement of the dead individual by an
indi-vidual of the same species as its neighbors. An extremely small value of𝜙 allows
universal attack of natural enemies to any species. A realistic value of𝜙 might be
estimated by comparing predicted phylogenetic tree shape and species abundance distributions with empirical data.
In this paper, the two empirical data sets cover a wide range of taxa including plants and animals. J-C effects may not apply to many taxa, especially animal taxa. Indeed, a classic J-C effect may not be realistic for many animal taxa because predators or pathogens are often not host-specific. However, by extending the classic J-C model to include phylogenetic relatedness, applicability of our model increases. It has been reported that phylogenetic signal plays a role in predator
prey body-size relationships Brose et al. 1 , Naisbit et al. 1 1 . Our study with
phylogenetic relatedness extension applies to this scenario. Moreover, our model also allows very weak or even absent J-C effects.
e emphasize that the interaction distance of the phylogenetic J-C effect and individual dispersal ability are important factors in determining species richness, spatial distribution, the SAD and phylogenetic patterns in the community. In fact,
many species are strongly dispersal-limited Clark and Clark2 , Seidler and Plotkin
Dis-4
Neutr al SPJC high dispersal & inter action distance SPJC inter mediate dispersal & inter action distance SPJC lo w dispersal & inter action distance ●●●● ● ● ● ● ● ● −1 0 1 ● ● ●● ● −15 −10 −5 0 5 ● ●● ●●●●●● ●●● ●●●●●●●●● ● ●●●●●● 0 0.5 1 ●●● ●●●●●●●●●●●●●●●●●●●●●●●●● −2 −1 0 High Inter mediate Lo w Dispersal ● ● −1 0 1 ● ● −15 −10 −5 0 5 ● ● ● ● 0 0.5 1 ● ●● −2 −1 0 0.25 0.75 1 ψ ●● ● ● ● ● −1 0 1 −15 −10 −5 0 5 ● ● 0 0.5 1 ● ● −2 −1 0 0.25 0.75 1 ψ ● −1 0 1 −15 −10 −5 0 5 ●●●●● ● ●● ● ● 0 0.5 1 ●●●●● ● ●● ●● −2 −1 0 0.25 0.75 1 ψ T ree ∆ r γ I m β Figur e 4 .: Distinct distributions of species ac cumulation and imbalance statistics pr oduced by di ffer ent par ameter combinations. The gener ating par ameters fr om left to right ar e 1 for the neutr al scenarios wi th , : ; ; . , 2 for the lar ge spatial distance scenarios ) : ., ; ., ; , , for the intermediate spatial distance scenarios : ., ; ., ; , , 4 for the smal l spatial distance scenarios . : ., ; ., ; , respectiv ely . The ph ylogenetic tr ees each repr esent one sample out of 1 replicates gener ated b y the af or ementioned par ameters. In the bo x plots, sol id lines, bo xes and whisk ers denote the th, 2th/th and th/th per centiles, respectiv ely . The sol id horiz ontal line and dashed horiz ontal lines repr esent the median and inter uartile range -of empirical estimates of the corr esponding statistic for ph ylogenetic tr ees in T reeBA SE, respectiv ely .4
persal limitation determines patterns of diversity and can be used to explain speciescoexistence Etienne and Alonso4 , Macdougall and Turkington11 . A large
dis-persal distance together with the phylogenetic J-C effect leads to a community where species of different phylogenetic distances distribute uniformly. Thus, natu-ral enemies adapted to different phylogenetic host ranges may also spread widely. In contrast, when the dispersal distance is small, a patchy community where indi-viduals with large phylogenetic distance to the community cluster is formed. This does not necessarily mean that the species within patches are phylogenetically re-lated to each other. They can be species of low abundance and phylogenetically unrelated. These species therefore are less affected by the negative density effect and likely stay away from natural enemies by forming such diverse subcommunities. A large interaction distance of the phylogenetic J-C effect regulates species density at a large spatial scale and conse uently results in large patches, further promoting diversity. Due to computational limitations, it remains unclear whether the patchy pattern vanishes in the long run.
Our simulations are limited computationally. But still, our study provides insight into patterns in a pre-e uilibrium system or a transient period at the onset of com-munity assembly. Further research analyzing the spatially explicit phylogenetic J-C effect at e uilibrium and the relationship between the transient state and the e ui-librium state will help in understanding the underlying mechanisms of community assembly.
Although we have shown the phylogenetic relatedness effect counteracts the promotion of diversity due to a classic J-C effect, the extent of this effect is yet unknown. Empirical evidence in tropical tree communities suggests that the effect
may be different for common and rare species Comita et al. 2, lironomos .
Specifically, rare species may suffer more from the conspecific negative density
effect than common species do Comita et al. 2. The power of J-C effects to
maintain hyperdiversity may then be further reduced because rare species are even less at an advantage. Therefore, more studies on heterogeneity among species are
imperative. e have provided predictions for a variety of patterns under a null
model of no differences between species to which the results of these studies can be compared.
4
Supporting Information
Figures S1-S9. The spatial distribution of species with A MIPD values under
different dispersal and interaction distances.
Figures S10-S18. The SAD plots under different dispersal and interaction
dis-tances.
Figures S19-S27. The lineage-through-time LTT plots under different dispersal
and interaction distances.
Figures S28-S31. The distribution of the estimates of𝛾, Δ𝑟, 𝛽 and Colless index
from simulations compared with the estimates from empirical trees extracting
from TreeBASE.
Figures S32-S35. The distribution of the estimates of 𝛾, Δ𝑟, 𝛽 and Colless in-dex from simulations compared with the estimates from 14 empirical trees from
McPeek’s 2 data.
Figures S36-S44. The species-area relationship under different dispersal and
interaction distances.
Figure S45. The species-area relationship from simulations under different
dis-persal distances 1, 1 , 1 , 1 and two numbers of time steps 10 , 10 for
