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\begin{document}
\title{Niche-based process and neutral dynamics emerge the per capita
ecological difference and equivalence among species at different
spatio-temporal-environmental scales}
\author[1]{takayuki yunoki}%
\affil[1]{Universidad Autónoma del Beni José Ballivián}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
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\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Reconciling niche-based process and neutral dynamics in a portion of an
infinite system, the regional species pool may be already not free
parameter, and the divergent ecological-evolutionary mechanisms may
operate consistently. The individual-based model was implemented in the
two-dimensional grid with periodic boundary condition. The model was
explored using a fixed speciation rate, and a range of system sizes,
dispersal rates, environmental structures and initial conditions of
regional species pool. The model communities in the center of system had
a fixed population size, and approximated from an area encompassing
independent biogeographic units to an area packed in a biogeographic
unit with open boundary conditions, and presented the three
environmental structures; four humps, linear and random. Across
scenarios, the number of guilds in system achieved first to a stationary
state; then, the species richness converged eventually to a dynamical
equilibrium through speciation-extinction balance. In simulations, the
per capita ecological difference among species only contributed to the
probabilities of immigration success, so the weighted lottery process
was more efficient and immediate at higher dispersal rates. The increase
of functional redundancy in model communities suggested that the
relative role of neutral dynamics increased in an area encompassing
independent biogeographic units. The variation partitioning based on
canonical analysis inferred that not only the neutral dynamics among the
species of single guild, but also the competition-colonization trade-off
among the species of more than two guilds with similar environmental
optimum and different levels of specialization operated in the spatial
structures found within and among patchy habitats. Ecologist to
disentangle the influence of alternative processes must shift focus from
the contribution of local competitions and regional dispersals to
detecting the spatio-temporal-environmental scales on which the per
capita ecological difference and equivalence among species are emerged
through divergent ecological-evolutionary mechanisms.%
\end{abstract}%
\sloppy
\textbf{Introduction}
Ecologist traditionally relied on the deterministic process, such as
environmental niche, and the coexistence of species was explained by a
stationary state of ecologically different species (Gause, 1934;
Hutchinson, 1957). Recently ecologist recognized also the role of
stochastic process. The neutral dynamics were derived from the primary
assumption of per capita equivalence among individuals and community
saturation, such as ecological drift, random speciation and migration,
and the coexistence of species was explained by a dynamical equilibrium
of ecologically equivalent species in a set of local communities
(Durrett \& Levin, 1996; Hubbell, 2001; Rosindell, Hubbell, \& Etienne
2011). In contemporary ecology, the reconciling of these divergent
ecological-evolutionary mechanisms is a promising perspective to explain
the origin and maintenance of biodiversity (Hubbell, 2001; Leibold \&
Mcpeek, 2006; Munoz \& Huneman, 2016; Rosindell et al., 2011).
Neutral dynamics were based on individual-based model. The models were
implemented mostly in the spatially-implicit and hierarchical
conjecture, in that the extinction was balanced by the speciation under
panmixis; while, the local extinction was balanced by the immigrats from
a metacommunity. The regional dynamics were predicted by population size
and speciation rate of metacommunity, and the local dynamics were
predicted by further two parameters of population size and dispersal
rate of local community (Hubbell, 2001; Etienne, 2005; Etienne, 2007;
Etienne \& Oiff, 2004; Hankin, 2007; Munoz, Couteron, Ramesh, \& Etienne
2007). However, the spatially-implicit conjecture seems inconsistent in
that the neutral dynamics assume panmixis in a metacommunity; whereas,
dispersal-limitation to each local community embedded in it (Etienne,
2007). The spatially-explicit conjecture was one step approach allowing
the speciation and dispersal-limitation across spatio-temporal scales. A
metacommunity was usually a portion of an infinite system, and the
models were implemented in a grid of local communities specifying
neighbourhood or more general dispersal kernel (Durrett \& Levin, 1996;
Hubbell, 2001; Chave \& Leigh, 2002; Chave, Muller-Landau, \& Levin
2002; Pigolotti \& Cencini, 2009).
Reconciling niche-based process and neutral dynamics in
spatially-implicit conjecture, ecologist tried to explain the community
assembly in successional patchy habitats, in that the vacant local
community created by perturbation was initially colonized by the
immigrants from a metacommunity under the ecological equivalence among
species; then, the competitive exclutions were followed in each local
community (Mouquet, Munguia, Kneitel, \& Miller 2003). In stable
environment, the immigrants from a metacommunity was filtered along
environmental gradients, and the coexistence of species in each local
community was achieved under the per capita equivalence among
individuals in homogeneous environment (Jabot, Etienne, \& Chave 2007;
Janzen, Haegeman, \& Etienne 2015; Munoz, Ramesh, \& Couteron 2014;
Munoz et al., 2018). In spatially-implicit conjecture; however, the
regional dynamics were not predicted but usually specified by a fixed
metacommunity. Strikingly, if the per capita ecological difference among
species contributed to the competitions in each local community or the
dispersals from a metacommunity; in general, the spatio-temporal scales
on which the per capita ecological difference and equivalence among
species contributed to metacommunity dynamics were credible assumpsions.
Reconciling niche-based process and neutral dynamics in
spatially-explicit conjecture, a metacommunity may be a portion of an
infinite system. The regional species pool may be already not free
parameter, and the divergent ecological-evolutionary mechanisms may
operate consistently at different spatio-temporal-environmental scales.
For instance, exploring the neutral model with nearest neighboring
communities, an approximate scale on which individuals were expected to
diffuse before speciation was predicted by a pair of speciation and
dispersal rates (Cencini, Pigolotti, \& Mu\selectlanguage{ngerman}ñoz 2012). In other words, the
area of model communities must exceed an approximate scale predicted by
these parameters to encompass at least one independent biogeographic
unit. In the synthetic model with periodic boundary condition, where the
environmental gradient repeats continuously across opposite sides of
system, the relative role of neutral dynamics may increase in an area
encompassing independent biogeographic units because the species
richness but the number of functional groups (i.e. guilds) may increase
through speciation.
In the present study, the individual-based model was implemented in the
two-dimensional grid with periodic boundary condition. In simulations,
the model parameters and the species properties in simulation outcomes
were known by researcher, and the focus was to detecting the
spatio-temporal-environmental scales on which the per capita ecological
difference and equivalence among species were emerged through divergent
ecological-evolutionary mechanisms. Exploring the model across a range
of parameters, I proved specifically three hypotheses. First, the
competitive exclusion may be advanced by the per capita ecological
difference among species so the number of guilds may achieve first to a
stationary state; while, the competitive exclusion may be retarded by
the per capita ecological equivalence among species so the species
richness may converge eventually to a dynamical equilibrium through
extinction-speciation balance (Leibold \& Mcpeek, 2006). Second, the
relative role of neutral dynamics may increase in an area encompassing
independent biogeographic units. Third, the neutral dynamics may operate
among the species of each guild in patchy habitats (Leibold \& Mcpeek,
2006; Economo \& Keitt, 2008). The trajectory and contrast between
alternative processes establish the false premises that the niche-based
process is only important in each local community; while, the neutral
dynamics are only important in a set of local communities. I discuss
finally the implication of false premises and consistent patterns
observed in the present study for the performance of heuristic methods,
the manner of their applications, and the interpretation of their
results in field observations.
\textbf{Materials and Methods}
\emph{Simulation description}
The model was implemented in the rectangular two-dimensional grid with
periodic boundary condition (Fig. 1). In simulations, the per capita
ecological difference among species only contributed to the
probabilities of immigration success; while, the per capita speciation,
birth and death rates among individuals in local community were
equivalent regardless of their identities.
The scenario was specified first by the standard parameters of neutral
model; number of sites, speciation rate \selectlanguage{greek}\emph{ν} \selectlanguage{english}with point mutation
mode of speciation and niche conservatism, number of individuals in
regional species pool \emph{JM} , dispersal rate \emph{m} , and number
of individuals in local community \emph{J} . Then, a grid of local
communities with coordinate (\emph{x} , \emph{y} ) and environmental
gradient \emph{E} was specified in matrix \textbf{landscape} , and an
initial condition of regional species pool; individuals code, species
code, guilds code, their environmental optimum and tolerance was
specified in matrix \textbf{pool.t0} (Fig. 2a).
Based on a number of sites, a weights matrix for nearest neighboring
communities with spatial weights 1/8 was generated in a grid onto torus
(matrix \textbf{nb.mat} ). The individuals of regional species pool were
assigned to initial locations at random (matrix \textbf{LC.t0} ). At
each time step, all individuals were removed and replaced with
probability\selectlanguage{greek}\emph{ν} \selectlanguage{english}by new species (matrix \textbf{new.sp} ). The matrix
of remained individuals (matrix \textbf{LC.t0.without.new.sp} ) was
standardized for each site by row sum (matrix \textbf{LC.t0.RA} ), and
multiplied by matrix \textbf{nb.mat} to generate a set of probabilities
of immigration success of individuals to each local community under
neutral dynamics (matrix \textbf{I.RA} ). The matrix \textbf{I.RA} was
multiplied element wise by a matrix of habitat associations of
individuals to sites (matrix\textbf{HA.siteBYind} ), in that assigned
weights depended on the value of probability density function for normal
distribution given the mean as environmental optimum of individuals and
the standard deviation as tolerance of individuals for the local
environment of sites, and standardized for each site by row maximum. The
element wise multiplication was standardized for each site by row sum to
generate a set of probabilities of immigration success of individuals to
each local community under environmental filtering (matrix \textbf{EF}
). The parents of each local community were chosen with replacement by a
weighted lottery using a corresponding probability vector in \emph{m} x
matrix \textbf{EF} + (1-\emph{m} ) x matrix \textbf{LC.t0.RA} as the sum
of immigrant (left term) and local birth (right term) parents
(matrix\textbf{LC.t1.without.new.sp} ). Finally, the
matrix\textbf{LC.t1.without.new.sp} was combined with the
matrix\textbf{new.sp} ; then, the extinct lineages of individuals were
removed (matrix \textbf{LC.t1} ). Also the matrix \textbf{pool.t0} was
adjusted for regional species pool (matrix \textbf{pool.t1} ). The
ancestors of new species were identified by the ancestor individuals
codes and number of time steps in matrix \textbf{LC.t1} , and identified
by these codes in matrix \textbf{pool.t1} for individuals and species
levels; while, the decendants from a common ancestor individual were
identified by same code, and each lineage was grouped in a single column
in matrix\textbf{LC.t1} and row in matrix \textbf{pool.t1} . The
matrix\textbf{pool.t1} and matrix \textbf{LC.t1} were the input data for
next time step (Fig. 2b).
I used a speciation rate \selectlanguage{greek}\emph{ν} \selectlanguage{english}= 0.001 and a number of individuals in
local community \emph{J} = 16 individuals. The small system was
simulated in a grid of 20\selectlanguage{ngerman}×20 local communities using a \emph{JM} = 6400
individuals for two lower dispersal rates \emph{m} = (0.01, 0.09). The
large system was simulated in a grid of 40×40 local communities
using\emph{JM} = 25600 individuals for the highest dispersal rate
\emph{m} = 0.81. In small system, the environmental gradient \emph{E}
presented three structures; random, one wave and 16 humps. In large
system, the environmental gradient was quadrupled and presented three
structure; random, two waves and 64 humps. In all cases, the
environmental gradient was bounded between 0 and 1, and repeated
continuously across opposite sides of system (Fig 1). The initial
condition of regional species pool was varied by the number of
functional groups \emph{g} , habitat associations and population sizes
of guilds. In small system, the environmental optimum of guilds was
assigned following a uniform distribution between 0 and 1, and the
tolerance of guilds between 0 and 10. The population sizes of guilds
were generated splitting \emph{JM} at\emph{g} -1 points. These points
were \emph{g} -1 integers sampled from a uniform distribution between 1
and \emph{JM} -1 and sorted by their values. The simulations in each
combination of dispersal rate and environmental structure were started
from the same set of five levels of\emph{g} = (1, 8, 40, 160, 500), five
habitat associations and five population sizes of guilds except for the
case of \emph{g} = 1 (i.e. the simulations were started from 25 habitat
associations for which only one population size of a guild was
possible). In large system, the initial condition of regional species
pool was quadrupled. The simulations in each environmental structure
were started from the same set of five levels of \emph{g} and five
habitat associations of guilds; however, only one case of population
sizes of guilds was explored because the computation in large system was
intensive and time-consuming. So that 825 scenarios, 750 = 2x3x4x5x5 +
2x3x1x25 were simulated in the small system with two lower dispersal
rates and 75 = 1x3x5x5 in the large system with the highest dispersal
rate.
In the neutral model with nearest neighboring communities and \selectlanguage{greek}\emph{ν} \selectlanguage{english}=
0.001, the approximate scales on which individuals were expected to
diffuse before speciation were three for \emph{m} = 0.01, nine
for\emph{m} = 0.09, and 28 for \emph{m} = 0.81 (Cencini et al., 2012).
The model was explored using a fixed speciation rate, and a range of
system sizes, dispersal rates, environmental structures and initial
conditions of regional species pool. The model communities were a grid
of 10\selectlanguage{ngerman}×10 local communities in the center of system, and approximated
from an area encompassing independent biogeographic units to an area
packed in a biogeographic unit with open boundary conditions (i.e. the
individuals diffused across borders of system were expected to originate
new species at the opposite sides of model communities), and presented
the three environmental structures; four humps, linear and random (Fig.
1). Arguing from the approximate scales, the model communities in large
system with \emph{m} = 0.81 was packed nine times more compactly within
a biogeographic unit than small system with \emph{m} = 0.01 in each
environmental structure. The real ecosystem may be huge, and the
extinction may be balanced by minimum speciation rate (Bell, 2003), and
ecologist may study often an area packed much more compactly within a
biogeographic unit. At present; however, the computation in larger
system with lower speciation rate is not possible. The data analyses
were performed on R version 3.6.3 (R Core Team, 2019) using the packages
spdep (Bivand et al., 2019), vegan (Oksanen et al., 2019), PCNM
(Legendre, Borcard, Blanchet, \& Dray 2012), randomizr (Coppock, Cooper,
\& Fultz 2019), reshape2 (Wickham, 2017), dplyr (Wickham, François,
Henry, Müller, \& RStudio 2019), entropart (Marcon \& Hérault, 2019),
packfor (Dray, Legendre, \& Blanchet 2016), pgirmess (Giraudoux,
Antonietti, Beale, Pleydell, \& Treglia 2018), and ape (Paradis et al.,
2019). R sources are available in
https://github.com/takayukiyunoki/spatialIBM.git.
\emph{Check convergence to a dynamical equilibrium}
In initial simulations, I noticed that the number of guilds in system
achieved first to a stationary state; then, the species richness
achieved eventually to a dynamical equilibrium through
speciation-extinction balance. Furthermore, setting the same seeds in
random number generator, the simulation outcomes from alternative
diversities; monodominance (i.e. all individuals of each guild were
single species) and infinite (i.e. all individuals of each guild were
different species) converged when the species of each guild in regional
species pool were originated from the different common ancestor
individuals in the simulation outcome from monodominance guilds
(hereafter convergence time). The simulations reported here were started
from monodominance guilds.
\emph{Relative role of neutral dynamics increase in an area encompassing
independent biogeographic units}
The species-neutral and functional diversities were calculated using
the\emph{q} order two for the model communities at convergence time. The
functional diversity was based on the similarity matrix between pairs of
species calculated as the overlapping percentage of Gaussian functions
(Marcon \& Hérault, 2015). Then, the functional uniqueness and
redundancy proposed by Ricotta et al. (2016) were used to represent
approximately the relative roles of alternative processes. In the model
communities resulted with only one guild and more than two guilds, these
measures were compared across ecological-evolutionary scales in each
environmental structure.
\emph{Neutral dynamics operate among the species of each guild in patchy
habitats}
The variation partitioning based on canonical analysis (i.e. redundancy
analysis; Borcard, Legendre, \& Gillet 2011; Peres-Neto \& Legendre,
2010) and the autocorrelation method (Diniz-Filho et al., 2012) were
also used to infer the relative roles of alternative processes. In
general, the applications followed Yunoki \& Torres (2016); Yunoki,
Torres, Pouilly, \& Hablützel (2017); Yunoki, Torres, \& Cholima (2018);
Yunoki, Torres, \& Cholima (2019).
The variation partitioning was applied for the model communities at
convergence time. In model communities, the species response curves
might be often unimodal, so that the species abundances data was
Hellinger transformed prior to analysis and the first and second-order
orthogonal environmental variables were used (Borcard et al., 2011;
Gilbert \& Bennett, 2010). The standard forward selection procedure was
used because the habitat associations among the species of each guild
were equivalent and these species might have similarities regarding
their environmental and spatial associations (Borcard et al., 2011;
Peres-Neto \& Legendre, 2010). If more than two guilds were coexisted in
model communities and if the pure environmental component was
significant, the hierarchical guild structure was identified by
the\emph{k} -means partitioning of linear combination scores (scaling 1)
and simple structure index criterion. If the hierarchical guild
structure was significant, the principal coordinates of neighbour
matrices (PCNM) were constructed to model the spatial structures within
and among patchy habitats in the residual variation of species
composition between sites. The portion explained by each component was
obtained by the adjusted coefficient of determination in overall and
hierarchical models, and its significance was estimated by a
randomization test applying an alpha of 0.05.
The functional uniqueness and redundancy of model communities were
compared to the relative portions explained by environmental and pure
spatial components in the total explaind variation of overall model;
then, the total explained variation and these relative portions were
compared between overall and hierarchical models. Furthermore, the
number of guilds coexisted in model communities was compared to the
number of habitat types identified by hierarchical guild structure.
In the model communities resulted with only one guild, the
autocorrelation method was applied for the species abundances predicted
by true spatial and false environmental components. In the model
communities resulted with more than two guilds, this method was applied
for the true environmental component of overall model, and the spatial
structures found by hierarchical model in each environmental context.
The correlograms were calculated using the number of distance classes
computed by Sturges method in overall model; while, three or two
distance classes in each environmental context. In all cases, the Mantel
correlation between matrices of correlation coefficients and correlogram
distances among species was tested against the null hypothesis of less
than zero applying an alpha of 0.05. Appendix A presents the summary
statics of scenarios.
\textbf{Results}
In small sytem, six scenarios started from one guild and the eleventh
habitat association were collapsed, because the environmental tolerance
of guild was nearly zero (\textless{} 0.0052). The results presented
here were based on 819 simulation outcomes.
Across scenarios, the number of guilds in system achieved first to a
stationary state; then, the species richness converged eventually to a
dynamical equilibrium through speciation-extinction balance. The number
of guilds achieved to a stationary state faster in higher dispersal
rates (Fig. 3).
In the model communities resulted with only one guild, the functional
uniqueness was zero; however, the relative portion explained by
environmental component in total explained variation was positively
biased in linear environmental gradient (Fig. 4a). The type I error of
pure environmental component was inflated in these scenarios. The
spatial and pure spatial components were always significant (Fig. 4b).
In the model communities resulted with more than two guilds, the
functional uniqueness and redundancy presented the opposite pattern
across ecological-evolutionary scales. The functional uniqueness
increased in an area packed within a biogeographic unit, that was
referred well by the relative portion explained by environmental
component in the total explained variation of overall model (Fig. 5a).
The power of pure environmental component increased in these scenarios.
The spatial and pure spatial components were always significant (Fig.
5b).
If the pure environmental component of overall model was significant,
the hierarchical guild structure and the spatial structures found within
and among patchy habitats were usually significant (Fig. 5b).
Furthermore, the total explained variation and the relative portions
explained by environmental and pure spatial components in total explaind
variation were similar between overall and hierarchical models; however,
the number of guilds coexisted in model communities was often larger
than the number of habitat types identified by the \emph{k} -means
partitioning of linear combination scores (scaling 1) and simple
structure index criterion (Fig. 5a).
In the model communities resulted with only one guild, the Mantel
correlations of true spatial component approached to zero in an area
packed within a biogeographic unit (Fig. 6a). They were always
significant in an area encompassing independent biogeographic units, and
vanished only in some scenarios for an area packed within a
biogeographic unit (Fig. 6b). The Mantel correlations of false
environmental component also approached to zero in an area packed within
a biogeographic unit (Fig. 6a); however, they were often significant,
and did not control correctly the false detection in linear
environmental gradient (Fig. 6b).
In the model communities resulted with more than two guilds, the Mantel
correlations of true environmental component negatively departed in an
area packed within a biogeographic unit (Fig. 7a), and tended to emerge
the pattern of spatial autocorrelations (Fig. 7b). The Mantel
correlations of the spatial structures found by hierarchical model in
each environmental context were often significant (Fig. 7b).
\textbf{Discussion}
Reconcilling niche-based process and neutral dynamics in a portion of an
infinite system, the regional species pool was already not free
parameter. In general, the divergent ecological-evolutionary mechanisms
operated consistently, and emerged the per capita ecological difference
and equivalence among species at different spatio-temporal-environmental
scales as expectations.
First, the number of guilds in system achieved first to a stationary
state; then, the species richness converged eventually to a dynamical
equilibrium through speciation-extinction balance. The convergence to a
dynamical equilibrium from any initial diversities was perspected in
neutral spatially-explicit conjecture (Hubbell, 2001). I argued from the
duality of neutral model (Cencini et al. 2012) that the simulations
started from monodominance guilds might achieve to a dynamical
equilibrium at convergence time because all walkers of each guild were
coalesced or annihilated.
In simulations, the per capita ecological difference among species only
contributed to the probabilities of immigration success, so the weighted
lottery process in system was more efficient and immediate, and the
functional uniqueness so the relative role of niche-based process in
model communities increased at higher dispersal rates. However, if the
ecological difference contributes to only competitions, or both
competitions and dispersals, these patterns relative to dispersal rates
may be altered.
Second, in the model communities resulted with more than two guilds, the
increase of functional redundancy suggested that the relative role of
neutral dynamics increased in an area encompassing independent
biogeographic units. The pattern of system convergence suggested that
the relative role of neutral dynamics might increase at broader temporal
scale through speciation as well.
The third hypothesis was not completely true. In the model communities
resulted with more than two guilds, the functional uniqueness and
redundancy were refered well by the relative portions explained by
environmental and pure spatial components in the total explained
variation of overall model. Furthermore, the total explained variation
and these relative portions were similar between overall and
hierarchical models; however, the number of guilds coexisted in model
communities was often larger than the number of habitat types identified
by hierarchical guild structure. It was intuitively true that not only
the neutral dynamics among the species of single guild, but also the
competition-colonization trade-off among the species of more than two
guilds with similar environmental optimum and different levels of
specialization operated in the spatial structures found within and among
patchy habitats.
The trajectory and contrast between alternative processes establish the
false premises that the niche-based process is only important in each
local community; while, the neutral dynamics are only important in a set
of local communities (Leibold \& Mcpeek, 2006). The critic of variation
partitioning based on canonical analysis was primary based on the false
premises and the complexity to refer the overall parameters of selection
strength and dispersal rate of simulations (Gilbert \& Bennett, 2010;
Smith \& Lundholm, 2010); however, the neutral assumption can be broken
by the difference of dispersal abilities, and the efficiency of weighted
lottery process is dependent of dispersal rates as noted above. To
compare the performance of existing approaches to disentangle the
influence of niche-based process and neutral dynamics (e.g. generalised
additive model and tree-based machine learning used in macroecology;
Viana, Keil, \& Jeliazkov 2019), ecologist must shift focus from the
contribution of local competitions and regional dispersals to detecting
the spatio-temporal-environmental scales on which per capita ecological
difference and equivalence among species are emerged. In this focus, the
autocorrelation method (Diniz-Filho et al., 2012) and the analysis of
functional ecology (e.g. Pillar \& Duarte, 2010) can be combined
straightforward to infer divergent ecological-evolutionary mechanisms.
In the present study, the first and second-order orthogonal
environmental variables were used to model unimodal relationship. In the
model communities resulted with only one guild, the functional
uniqueness was zero; however, the relative portion explained by
environmental component in total explained variation was positively
biased in linear environmental gradient, and the type I error of pure
environmental component was inflated in these scenarios. The species
composition might be contrasted between opposite sides of model
communities because of the approximate scales of three for \emph{m} =
0.01, nine for \emph{m} = 0.09 and 28 for \emph{m} = 0.81, and the
phylogenetically closely related species might be clumped there. In the
model communities resulted with more than two guilds, the functional
uniqueness and redundancy were refered well by the relative portions
explained by environmental and pure spatial components. The
insufficiency of raw environmental variable to model unimodal
relationship (Gilbert \& Bennett, 2010), and its dependence on
environmental structures (Smith \& Lundholm, 2010) seemed to be solved
mostly by the use of orthogonal environmental variables; furthermore,
the neutral dynamics and competition-colonization trade-off were refered
well in the spatial structures found within and among patchy habitats.
Although the orthogonal environmental variables might increase the
spurious correlation between species distribution and environmental
structure across scenarios, this problem would be eventually corrected
by the method proposed recently using a constrained randomization of
environmental variables (Wagner \& Dray, 2015; Clappe, Dray, \&
Peres-Neto 2018).
The performance of autocorrelation method (Diniz-Filho et al., 2012) was
unexpected but interesting, and the spatial autocorrelation pattern of
alternative processes reversed across ecological-evolutionary scales.
The neutral dynamics always emerged the pattern of spatial
autocorrelations in an area encompassing independent biogeographic
units; while, the relative role of niche-based process increased and
tended to emerge the pattern of spatial autocorrelations in an area
packed within a biogeographic unit. It was intuitively true that the
phylogenetically closely related species were clumped, and the neutral
dynamics might vanish the pattern of spatial autocorrelations if the
model communities were packed much more compactly within a biogeographic
unit. Furthermore, the neutral dynamics through speciation as well as
competition-colonization trade-off might emerge the pattern of spatial
autocorrelations in patchy habitats.
In the fish communities of Bolivian Amazon lowlands, we observed the
hierarchical guild structure across a range of spatio-temporal scales
(Yunoki \& Torres, 2016; Yunoki et al., 2017; Yunoki et al., 2018;
Yunoki et al., 2019). We presumed that only the neutral dynamics emerged
the spatial structures among patchy habitats if all environmental
factores were included in analysis, that the neutral dynamics did not
emerge the pattern of spatial autocorrelations, and that the neutral
dynamics should not be associated with functional species traits. The
last argument is because of neutral assumption. The temporal structures
found in the successional patchy habitats on a fine spatio-temporal
scale usually presented autocorrelation patterns, and were accompanied
by the seasonal and inter-annual change of functional species traits. We
interpreted these patterns as environmental filtering. The spatial
structures found among patchy habitats on a very broad spatial scale
presented the autocorrelation pattern in turbid rivers but in varzea
lakes, and the spatial structures found in turbid rivers and transparent
black-clear water bodies but in varzea lakes were accompanied by the
divergence of functional species traits (i.e. traits divergence pattern
associated to hierarchical guild structure; see Pillar \& Duarte, 2010).
Furthermore, the group of sedentary species was dominant in turbid
rivers and transparent black-clear water bodies, and presented
autocorrelation patterns there; while, the group of migratory species
was dominant in varzea lakes, and did not present autocorrelation
pattern there. We interpreted these patterns like the natural selection
of sedentary species in the stable environment of turbid rivers and
transparent black-clear water bodies as the species might have been
adapted to a minor environmental factor missing from analysis, and the
neutral dynamics of migratory species in the seasonal environment of
varzea lakes (Yunoki et al., 2019); however, the natural selection of
sedentary species in turbid rivers and transparent black-clear water was
doubtful. Just as the patterns of nucleotide and amino acid substitution
in population genetics (Holsinger, 2015), the natural selection may
operate in the initial stage of diversification when the population
sizes of each species may be huge; then, conserved for their
descendants, and this expectation seems to be approximated by the mode
of speciation and a range of initial conditions of regional species pool
implemented here. The massive extinction of archaic faunas triggered by
climate change during the Paleogene, and the roles of niche conservatism
and environmental heterogeneity originated by principal geomorphological
features (e.g. water types) for the origin of modern biodiversity during
the Neogene were also perspected in the recent synthesis of biogeography
of Neotropical freshwater fishes (Albert \& Reis, 2011). The simulations
reported here were simple and unrealistic in many aspects; however,
established the similar patterns with our field observations and seemed
to allow their interpretations. The spatial structures and
autocorrelation pattern found among patchy habitats of turbid rivers and
transparent black-clear water bodies on a very broad spatial scale
between north and south of Bolivian Amazon lowlands associated with the
functional species traits of fish communities; furthermore, the
autocorrelation patterns found there for the group of sedentary species
but migratory species could be explained by the competition-colonication
trade-off, and the speciations of sedentary species with
niche-conservatism.
The niche-based process is deterministic and results first in a
stationary state of guilds; while, the neutral dynamics are stochastic
and result eventually in a dynamical equilibrium of species through
speciation-extinction balance. The relative role of neutral dynamics
increases at broader spatio-temporal scales because the species richness
but the number of guilds increases through speciation. The neutral
dynamics among the species of single guild and the
competition-colonization trade-off among the species of more than two
guilds with similar environmental optimum and different levels of
specialization operate in patchy habitats. The neutral assumption can be
broken by the difference of dispersal abilities, and the efficiency of
weighted lottery process is dependent of dispersal rates. The
implication of present study is that the methodological advance and
field studies to disentangle the influence of alternative processes must
shift focus from the contribution of local competitions and regional
dispersals to detecting the spatio-temporal-environmental scales on
which the per capita ecological difference and equivalence among species
are emerged through divergent ecological-evolutionary mechanisms.
Data accessibility
R sources are available in
https://github.com/takayukiyunoki/spatialIBM.git. Appendix A presents
the summary statics of scenarios. Bolivian Amazon lowland fish
metacommunity data. Freshwater Metadata Journal 7: 1-6.
http://dx.doi.org/10.15504/fmj.2015.7
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Figure legends
Figure 1. The environmental structures of model communities in a grid of
10 x 10 local communities in the center of small system. The
environmental structure was quadrupled for large system.
Figure 2. A work flow script illustrating individual-based model. (a)
parameters (b) first time step.
Figure 3. System convergence; one-dimensional scatter plots showing the
time ratio to stationary guild number in the convergence time of species
richness. The number of scenarios started from multiple guilds was
provided following the text of axis-x in parentheses.
Figure 4. Summary statics of the model communities resulted with only
one guild were compared across ecological-evolutionary scales in three
environmental structures. (a) Functional uniqueness and redundancy were
compared to the relative portions explained by environmental and pure
spatial components in total explained variation. (b) Type I error rate
of environmental and pure environmental components and power rate of
other components. The number of model communities was provided following
the text of axis-x in parentheses.
Figure 5. Summary statics of the model communities resulted with more
than two guilds were compared across ecological-evolutionary scales in
three environmental structures. (a) Functional uniqueness and redundancy
were compared to the relative portions explained by environmental and
pure spatial components in the total explained variation of overall
model; then, the total explained variation and these relative portions
were compared between overall and hierarchical models. The portions
explained in hierarchical model was calculated for the scenarios in that
the hierarchical guild structure was significant. vs.guild-habitat, the
number of guilds coexisted in model communities was compared to the
number of habitat types identified by hierarchical guild structure. (b)
Power rate of all components in overall and hierarchical models. The
number of model communities was provided following the text of axis-x in
parentheses.
Figure 6. Performance of autocorrelation method in the model communities
resulted with only one guild. (a) Mantel correlation of false
environmental and true spatial components. (b) Mantel test against the
null hypothesis of less than zero. The numbers of false environmental
and true spatial components were provided following the text of axis-x
in parentheses.
Figure 7. Performance of autocorrelation method in the model communities
resulted with more than two guilds. (a) Mantel correlation of true
environmental component in overall model and pure spatial components in
each environmental context. (b) Mantel test against the null hypothesis
of less than zero. The number of true environmental components in
overall model and the number of environmental contexts in hierarchical
model were provided following the text of axis-x in parentheses.
Competing Interests
I have no conflicts of interest to disclose.
Author Contributions
T.Y. developed the theoretical formalism, performed the numerical
simulations and analytic calculations, and wrote the original draft and
review.
Acknowledgements
I would like to thank editor in chief Prof. Jennifer Firn for the
opportunity to revise my manuscript, also associate editor and two
anonymous reviewers for the careful review and constructive suggestions.\selectlanguage{english}
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