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\begin{document}

\title{Temporal beta-diversity patterns are highly dependent on fundamental
parameters of neutral dynamics}



\author[1]{Ryosuke Nakadai}%
\affil[1]{National Institute for Environmental Studies}%


\vspace{-1em}



  
  \date{May 29, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Temporal changes in community composition are a facet of biodiversity
change and are referred to as temporal beta diversity. Macroecological
patterns of temporal beta diversity have gained attention because of the
recent biodiversity crisis. However, no one has seriously studied how
temporal beta diversity differs from spatial beta diversity, and the
most basic neutral dynamics and temporal beta-diversity patterns remain
unknown. Therefore, the present study aimed to reveal the basic
properties of temporal beta-diversity patterns under neutral dynamics
and identify their differences from those of spatial beta-diversity
patterns. A simulation of neutral dynamics was conducted to test the
parameter dependency of temporal beta-diversity patterns. Specifically,
four fundamental parameters of the neutral model---the fundamental
biodiversity number, local community size, mortality rate, and
immigration rate---were studied. To describe the form of the simulated
temporal distance-decay patterns based on both the Bray--Curtis and
S\selectlanguage{ngerman}ørensen dissimilarity indices, a three-parameter negative exponential
function was fitted for each simulated dissimilarity matrix. The
negative exponential function was successfully fitted to all the
simulated results and three estimated parameters and the intercepts of
the function were plotted along the change in the four parameters of the
neutral model. The simulated results demonstrated that upper limits
exist in the temporal distance-decay patterns; thus, the temporal
distance-decay curves saturate before reaching a completely dissimilar
state. Additionally, the form of the curve strongly depends on the four
parameters of the neutral model. These results suggest that the
relationship between local communities and virtual species pools differs
in temporal and spatial beta diversity. Specifically, they suggest that
the species pool is spatially variable but temporally constant.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{Introduction}

Temporal changes in community composition are a facet of biodiversity
change and are referred to as temporal beta diversity (Hatosy et al.,
2013; Baselga, Bonthoux, \& Balent, 2015; Legendre, 2019). Recently, the
focus of temporal beta-diversity studies has expanded to multiple sites
and a large spatial scale, that is, to macroecological contexts (Brice,
Cazelles, Legendre, \& Fortin, 2019; Gotelli et al., 2022).
Macroecological patterns of temporal beta diversity have gained
increasing attention during the ongoing biodiversity crisis resulting
from various anthropogenic disturbances and climate change impacts
(Dornelas et al., 2014; Brice et al., 2019; Magurran, Dornelas, Moyes,
\& Henderson, 2019). Although the use of beta-diversity indices in
temporal beta-diversity studies is generally identical to that in
spatial beta-diversity studies, no one has seriously studied how
temporal beta diversity differs from spatial beta diversity. Therefore,
so far, temporal beta-diversity studies have been conducted based on
various uncertain assumptions dependent on spatial knowledge. This lack
of basic knowledge about temporal beta diversity could lead to
inaccurate assessments of biodiversity changes. Thus, revealing the
basic properties of temporal beta-diversity patterns is an urgent issue.

The unified neutral theory proposed by Hubbell (2001) demonstrated that
various types of common biodiversity patterns (e.g. species abundance
distribution) are reproduced under both ecological neutrality and
zero-sum assumptions (Rosindell, Hubbell, \& Etienne, 2011; Shinohara,
Nakadai, Suzuki, \& Terui, 2023). The neutral model would provide
valuable base knowledge under the simplest conditions as a starting
point (Rosindell et al. 2011; Rosindell, Hubbell, He, Harmon, \&
Etienne, 2012; Takeuchi, Ohtsuki, \& Innan, 2022). The dynamics under a
neutral model (i.e. neutral dynamics) would provide basic knowledge
regarding temporal beta-diversity studies just as they have provided so
far for other biodiversity patterns. Rosindell et al. (2011) argued that
studying dynamics under a neutral model is a future challenge. Several
previous studies (Dornelas et al., 2014; Sgardeli, Zografou, \& Halley,
2016) related to temporal beta diversity have used predictions under
neutral dynamics as a baseline to quantify targeted factors (i.e.
climate change impacts). However, the effect of each parameter on the
general temporal beta-diversity pattern under neutral dynamics remains
unexplored. The present study aimed to reveal the basic properties of
temporal beta-diversity patterns under neutral dynamics and identify
their differences from those of spatial beta-diversity patterns.
Specifically, the parameter dependency of four variables, viz.,
fundamental biodiversity number, local community size, mortality rate,
and immigration rate, were examined.

\textbf{Materials and methods}

\emph{Simulation}

To reveal the parameter dependency of temporal beta-diversity patterns
under neutral dynamics, simulations were performed using the R package
``ecolottery'' (Munoz et al., 2018). This study focused on four
fundamental parameters of the neutral model (Hubbell, 2001): fundamental
biodiversity number (\selectlanguage{greek}θ\selectlanguage{english}), local community size (\emph{J} ), mortality
rate (\emph{d} ), and immigration rate (\emph{m} ) (Fig. 1a and b).
Fundamental biodiversity number (\selectlanguage{greek}θ\selectlanguage{english}) is a value associated with the
properties of species pool diversity (Fig. 1a); specifically, species
diversity in the species pool and their evenness increase as the
fundamental biodiversity number increases, when the number of
individuals included is the same (for the detailed derivation of
fundamental biodiversity number, see Hubbell, 2001). In two extreme
cases, the species pool includes only one species when the fundamental
biodiversity number is zero (\selectlanguage{greek}θ \selectlanguage{english}= 0), and all species in the species pool
have one individual when the fundamental biodiversity number is infinite
(\selectlanguage{greek}θ \selectlanguage{english}= [?]). The local community size indicates the total number of
individuals in a targeted local community. Under the zero-sum
assumption, the number (\emph{J} ) is the same throughout the community
dynamics for each simulation. Mortality rate (\emph{d} ) indicates the
proportion of mortal individuals in the local community at each time
step; thus, \emph{J} \selectlanguage{ngerman}× \emph{d} is the actual number of mortal
individuals (\emph{D} ) (Fig. 1b). The mortality rate (\emph{d} ) is
identical to the turnover rate under the zero-sum assumption because the
number of mortal individuals is identical to that of recruited (or
birthed) individuals. The immigration rate (\emph{m} ) is the proportion
of immigrated individuals in the number of recruited (or birthed)
individuals at each time step; thus, \emph{J} × \emph{d} ×\emph{m} is
the number of immigrated individuals (\emph{M} ) and \emph{J}× \emph{d}
× (1 -- \emph{m} ) is the number of locally recruited (or birthed)
individuals (\emph{D} -- \emph{M} ) (Fig. 1b). The details of these
parameters are summarised in Table 1.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1} Schematic image of neutral dynamics simulation and
temporal beta diversity patterns. The definitions of each parameter in
the figure is summarized in Table 1.

Table 1 List of terms used in the main text\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
Term & Definition\tabularnewline
\midrule
\endhead
\selectlanguage{greek}θ & Fundamental biodiversity number\tabularnewline
\emph{J} & Total number of individuals in the local
community\tabularnewline
\emph{d} & Mortality rate\tabularnewline
\emph{D} & Total number of mortal individuals {[}\emph{J} \selectlanguage{ngerman}×
\emph{d}{]}\tabularnewline
\emph{m} & Immigration rate\tabularnewline
\emph{M} & Total number of immigrated individuals {[}\emph{J} \selectlanguage{ngerman}× \emph{d}
× \emph{m}{]}\tabularnewline
\emph{J}\textsubscript{M} & Total number of individuals in the species
pool (i.e. metacommunity)\tabularnewline
\selectlanguage{greek}δ & a parameter of the negative exponential function that is related to
the relative position of the intercept against the upper
limit\tabularnewline
\selectlanguage{greek}ε & a parameter of the negative exponential function that is related to
the curvature of the curve\tabularnewline
\selectlanguage{greek}ζ & a parameter of the negative exponential function that is related to
the upper limit\tabularnewline
\bottomrule
\end{longtable}

The base parameter values were set as follows: species pool (i.e.
metacommunity) size (\emph{J} \textsubscript{M}) = 1,000,000
individuals; fundamental biodiversity number (\selectlanguage{greek}θ\selectlanguage{english}) = 100; local community
size (\emph{J} ) = 1,000; mortality rate (\emph{d} ) = 0.1; immigration
rate (\emph{m} ) = 0.1. Based on the base parameter values of this
model, the parameter-dependency patterns were studied by changing the
four targeted parameters (\selectlanguage{greek}θ, \selectlanguage{english}\emph{J} , \emph{d} , and \emph{m} ). For
the fundamental biodiversity number (\selectlanguage{greek}θ\selectlanguage{english}), 100 numbers were randomly
selected between 1 and 1,000, without allowing duplicates. For the local
community size (\emph{J} ), 25 numbers were randomly selected for each
order of magnitude (10\textsuperscript{2}--10\textsuperscript{5}); thus,
100 numbers were selected in total. For both mortality rate (\emph{d} )
and immigration rate (\emph{m} ), 100 numbers were determined between
0.01--1.00, in 0.01 increments.

At the beginning of each simulation, local community members were chosen
depending on the set number of local community size, and 1,100 time
steps, including the initial state, were conducted for each simulation
(Fig. 1b). After the simulation, the information of local community
dynamics between time step 1 (T1) and time step 99 (T99) were excluded
from the following analysis for testing parameter dependency because the
randomness of the initial sampling could affect the community dynamics
at the beginning phase. The dynamics from T100 to T1100 were targeted
for the main analysis, and thus, a 1001 time-series dataset was used for
each simulation (Fig. 1b). The Bray--Curtis dissimilarity index (Odum,
1950) and S\selectlanguage{ngerman}ørensen dissimilarity index (Sørensen, 1948) were calculated
for each simulation.

The preliminary analysis revealed that the temporal distance-decay curve
rarely reached one (i.e. completely dissimilar); thus, upper limits
exist at less than one in temporal beta diversity under neutral
dynamics. Therefore, to describe the form of the simulated temporal
distance-decay patterns of both the Bray--Curtis and Sørensen
dissimilarity indices, a negative exponential curve was fitted for each
dataset (Fig. 1c). The equation for the negative exponential function is
as follows:

\(TBD=-\delta\times e^{-\varepsilon\ \times\ td}+\zeta\),

where TBD is the temporal beta diversity value, \emph{e} is Napier's
constant, td is the temporal distance between a pair of communities, and
\selectlanguage{greek}δ, ε, \selectlanguage{english}and \selectlanguage{greek}ζ \selectlanguage{english}are the parameters of the negative exponential function
(Table 1). The changes in the curve shape with parameter changes are
summarised in Fig. 2. The parameter \selectlanguage{greek}ζ \selectlanguage{english}determines the position of the
upper limit of the curve; thus, a larger \selectlanguage{greek}ζ \selectlanguage{english}indicates higher upper limits
in the temporal distance-decay of temporal beta diversity (Fig. 2c).
Parameter \selectlanguage{greek}δ \selectlanguage{english}determines the relative position of the intercept against
parameter \selectlanguage{greek}ζ \selectlanguage{english}(i.e. the upper limit). The \selectlanguage{greek}ζ -- δ \selectlanguage{english}value indicates the
intercept of the curve; thus, a larger \selectlanguage{greek}δ \selectlanguage{english}indicates a lower position of
the intercept (Fig. 2a). Parameter \selectlanguage{greek}ε \selectlanguage{english}determines the curvature of the
curve; thus, a larger \selectlanguage{greek}ε \selectlanguage{english}indicates a higher curvature of the curve (Fig.
2b). All estimated parameter values without errors were used in the
analysis to check parameter dependency in the present study. Although
Mart\selectlanguage{ngerman}ín-Devasa, Martínez\selectlanguage{english}-Santalla, Gomez\selectlanguage{english}-Rodriguez, Crujeiras, \&
Baselga, (2022) recently developed a method to compare the fit of three
different functions on distance-decay curves, judging the best-fitted
function for a distance-decay curve was the main use of the method and
ecologically interpreting the changes in parameter values was difficult
based on their methods. Therefore, the three-parameter negative
exponential function was used in this study owing to the differences in
purpose.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2} Representative examples showing parameter properties
in the three-parameter negative exponential function.

\textbf{Results}

We successfully fitted the negative exponential function to all the
simulated results and plotted the three estimated parameters (\selectlanguage{greek}δ, ε, \selectlanguage{english}and
\selectlanguage{greek}ζ\selectlanguage{english}) and intercepts (\selectlanguage{greek}ζ -- δ\selectlanguage{english}) along with the change in the parameter values
of the neutral model (\selectlanguage{greek}θ, \selectlanguage{english}\emph{J} , \emph{d} , and \emph{m} ). The blue
and orange circles indicate the results of the Bray--Curtis and S\selectlanguage{ngerman}ørensen
dissimilarity indices, respectively. First, as the fundamental
biodiversity number (\selectlanguage{greek}θ\selectlanguage{english}) increased, the parameters \selectlanguage{greek}δ \selectlanguage{english}and \selectlanguage{greek}ζ \selectlanguage{english}and the
intercepts (\selectlanguage{greek}ζ -- δ\selectlanguage{english}) increased (Fig. 3a, i, m), but the parameter \selectlanguage{greek}ε
\selectlanguage{english}remained constant (Fig. 3e). Second, as the local community size
(\emph{J} ) increased, the parameters \selectlanguage{greek}δ \selectlanguage{english}and \selectlanguage{greek}ζ \selectlanguage{english}and the intercepts (\selectlanguage{greek}ζ --
δ\selectlanguage{english}) decreased (Fig. 3b, j, n); however, the parameter \selectlanguage{greek}ε \selectlanguage{english}increased and
then remained constant when \emph{J} was larger than approximately
10,000 (Fig. 3f). Third, as mortality rate (\emph{d} ) increased, the
parameters \selectlanguage{greek}δ \selectlanguage{english}and \selectlanguage{greek}ζ \selectlanguage{english}and the intercepts (\selectlanguage{greek}ζ -- δ\selectlanguage{english}) decreased (Fig. 1c, k,
o), but the parameter \selectlanguage{greek}ε \selectlanguage{english}increased (Fig. 3g). Finally, as immigration
rate (\emph{m} ) increased, the parameters \selectlanguage{greek}δ \selectlanguage{english}and \selectlanguage{greek}ζ \selectlanguage{english}and the intercepts (\selectlanguage{greek}ζ
-- δ\selectlanguage{english}) decreased (Fig. 3d, l, p), but the parameter \selectlanguage{greek}ε \selectlanguage{english}increases (Fig.
3h).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3} Relationships between parameters of the negative
exponential function and those of the neutral model. The blue and the
orange circles indicate the results of the Bray--Curtis and S\selectlanguage{ngerman}ørensen
dissimilarity indices, respectively.

\textbf{Discussion}

The simulated results under ecologically neutral dynamics demonstrated
that the upper limits exist in temporal distance-decay patterns; thus,
the temporal distance-decay curves saturate before reaching a completely
dissimilar state. In addition, the form of the curve strongly depends on
four parameters of the neutral model: fundamental biodiversity number,
local community size, mortality rate, and immigration rate. These
results emphasise the importance of considering the basic information of
the species pool and local communities as four parameters in the present
study when temporal beta-diversity studies are expanded to
macroecological contexts. No studies have seriously considered the
differences between space and time; therefore, this study is the first
to explore biodiversity changes from both basic and applied
perspectives.

\emph{Macroecological interpretation of the targeted parameters in the
neutral model}

Previous studies have discussed four targeted parameters (\selectlanguage{greek}θ, \selectlanguage{english}\emph{J}
,\emph{d} , and \emph{m} ) of the neutral model in relation to
geographical and climatic contexts (Turner, 2004). Here, for each
parameter, the results of parameter dependency were interpreted from a
macroecological perspective.

First, the fundamental biodiversity number (\selectlanguage{greek}θ\selectlanguage{english}) was calculated as the
product of species pool size (\emph{J} \textsubscript{M}) and speciation
rate per individual in the species pool (\emph{v} ); however, the
detailed equations differ among studies depending on the precision
(Hubbell, 2001; He \& Hu, 2005; Etienne \& Alonso, 2007). Changes in
speciation rates along geographical and climatic gradients are well
reported (Mannion, Upchurch, Benson, \& Goswami, 2014; Rabosky et al.,
2018); thus, the fundamental biodiversity number should vary along
geographical and climatic gradients. Fukaya, Kusumoto, Shiono, Fujinuma,
\& Kubota. (2020) recently estimated the fundamental biodiversity number
of woody plant species at regional scales and found large variations
among the four regions in Japan. In addition, speciation rates differ
among taxonomic groups (Schluter \& Pennell, 2017). In the simulated
results, the upper limits (\selectlanguage{greek}ζ\selectlanguage{english}) varied largely along the values of the
fundamental biodiversity number (Fig. 3i). Therefore, even if the
temporal beta-diversity values are identical, the meanings of the
changes are different; for example, 0.4 is approximately the maximum
value when the fundamental biodiversity number is 100, but that is half
of the upper limit when the number is 600 (Fig. 3i). Therefore, when
estimating the fundamental biodiversity number is difficult, considering
the differences in species pool properties due to geography, climate,
and taxonomy can be essential for future macroecological studies of
temporal beta diversity.

Second, local community size is strongly associated with the relative
influence of stochastic drift (Chave, 2004). The simulated results
showed that both the upper limit of temporal beta diversity and the
intercept increased as the size became smaller (Fig. 3j, n). These
results suggest that the probability differences in individual turnover
among the same species (i.e., apparent compositional equilibrium;
Nakadai, 2020) affect the temporal beta-diversity patterns.
Specifically, large local communities have more opportunities to obtain
individuals that are of the same species as the dead individuals in the
previous time step and cause less apparent compositional changes. In
natural situations, local community sizes are directly related to
habitat sizes, so small islands and conservation areas are likely to
have more large compositional fluctuations over time.

Third, the mortality rates are identical to the turnover rates under the
zero-sum assumption. If the contribution of individual turnover to
compositional shift is constant, a larger amount of individual turnover
causes more apparent compositional changes, and thus, larger temporal
beta diversity (Nakadai, 2022). Simulation results support this fact,
because the parameter \selectlanguage{greek}ε, \selectlanguage{english}which is related to the curvature of the curve,
linearly increases as mortality rates increase; thus, the curve becomes
steeper (Fig. 3g). In contrast, the upper limits (\selectlanguage{greek}ζ\selectlanguage{english}) decreased as the
mortality rates increased (Fig. 3k). This result may be attributed to
the fact that the increased mortality and turnover rates result in more
individuals being randomly selected from the species pool, keeping the
species composition of the local community close to that of the species
pool. In nature, higher temperatures facilitate faster growth and
shorter life span (Keil \& de Magalhaes, 2015); therefore, mortality
rates would be higher toward the tropics, resulting in less stable
compositional dynamics.

Finally, immigration rates are the degree of habitat isolation from
species sources, which is an influential factor in island ecosystems and
both the protection and maintenance of conservation areas (MacArthur \&
Wilson, 1967; Prugh, Hodges, Sinclair, \& Brashares, 2008; Fahrig,
2013). The parameter dependency of temporal beta-diversity patterns
against immigration rates was similar to that against mortality rates
(Fig. 3d, h, l, p). Specifically, the parameter \selectlanguage{greek}ε \selectlanguage{english}increased linearly,
and the upper limits (\selectlanguage{greek}ζ\selectlanguage{english}) decreased as immigration rates increased (Fig.
3i, h). The interpretation of these results is the same as that of the
mortality rate as discussed in the above paragraph; thus, larger
immigration rates facilitate a similar community composition as that of
the species pool. This process can reduce the temporal variability of
species composition in the local community. Therefore, in nature,
isolated island ecosystems and isolated conservation areas would be more
temporally unstable.

\emph{Differences between space and time in biodiversity}

The largest difference between spatial and temporal beta diversity was
the property of the species pool. In the spatial context, if an observer
moves sufficiently far from one location to a different region, the
composition of the species pool will differ, and eventually, there will
be no common species between the first and the second place; thus, the
value of spatial beta diversity reaches 1. In contrast, in a temporal
context, if it is not assumed that the composition of the species pool
changes over time, it is rare to have a situation where common species
are completely absent from the species composition at the outset.
Surely, in evolutionary time scale, the species pool would gradually
change, but at the ecological time scale (e.g. less than a hundred
years), dramatic changes in the species pool should not be hypothesised
as a normal condition. However, the influence of recent climate change
and other anthropogenic disturbances will change the composition of the
species pool through species distributional shifts (Dornelas et al.,
2014; Koide, Yoshikawa, Ishihama, \& Kadoya, 2022). Therefore, these
influences would increase the upper limits of temporal beta diversity.
The present study focused only on neutral dynamics to understand the
fundamental properties of temporal beta diversity. However, in the
future, more complex models should be studied to understand the
influence of climate change and other anthropogenic disturbances.

\textbf{Conclusions}

The present study demonstrated the strong parameter dependency of
temporal beta-diversity patterns on the four fundamental parameters of
the neutral model. The results of the present study caution that
macroecological studies of temporal beta diversity are challenging
without considering these four parameters in any case. Neutral dynamics
is a starting point for discussing the real drivers of temporal
beta-diversity patterns. In simulation studies, relaxing the zero-sum
and neutrality assumptions would provide more realistic patterns
comparable to empirical patterns (Jabot, 2010; Jabot \& Chave, 2011;
Munoz \& Huneman, 2016; Takeuchi et al., 2022). Moving forward, two
future study directions of temporal beta diversity, more generally
biodiversity changes, are recommeded. One is toward the linking of
biodiversity changes with the modern co-existence theory and other
studies focusing on species co-existence, which would pave the way for a
new field of study. For example, under variable climate conditions,
different types of storage effects, which is a kind of mechanism
facilitating species co-existence (Chesson \& Warner, 1981; Chesson,
2000), would affect the apparent compositional changes; the persistence
of long-lived individuals could contribute to decreasing the change in
the short term, but the existence of buried seeds could contribute to
less variability in community composition in the long term. The other is
toward an explicit consideration of the spatial connections among the
temporal beta-diversity patterns. Macroecological studies of temporal
beta diversity often consider different sites as independent, but in
reality, close distance sites are often connected. For example, animals
move across sites and plants provide seeds to neighbouring sites (Howe
\& Smallwood, 1982; Bowler \& Benton, 2005). For a deeper mechanistic
understanding of temporal beta diversity, it is important to identify
the direct effects through connections from simple synchronic responses
to similar climate changes due to site closeness. Many future tasks
remain to be accomplished in the study of temporal beta diversity, which
is important in both basic and applied research.

\textbf{References}

Baselga, A., Bonthoux, S., \& Balent, G. (2015). Temporal beta diversity
of bird assemblages in agricultural landscapes: land cover change vs.
stochastic processes. \emph{PLoS One} , \emph{10} (5), e0127913.

Bowler, D. E., \& Benton, T. G. (2005). Causes and consequences of
animal dispersal strategies: relating individual behaviour to spatial
dynamics. \emph{Biological Reviews} , \emph{80} (2), 205--225.

Brice, M. H., Cazelles, K., Legendre, P., \& Fortin, M. J. (2019).
Disturbances amplify tree community responses to climate change in the
temperate-boreal ecotone. \emph{Global Ecology and Biogeography, 28}
(11), 1668--1681.

Chave, J. (2004). Neutral theory and community ecology. \emph{Ecology
Letters} , 7(3), 241--253.

Chesson, P. (2000). Mechanisms of maintenance of species
diversity.\emph{Annual Review of Ecology and Systematics, 31} , 343--366

Chesson, P. L., \& Warner, R. R. (1981). Environmental variability
promotes coexistence in lottery competitive systems. \emph{The American
Naturalist,} \emph{117} (6), 923--943

Dornelas, M., Gotelli, N. J., McGill, B., Shimadzu, H., Moyes, F.,
Sievers, C., \& Magurran, A. E. (2014). Assemblage time series reveal
biodiversity change but not systematic loss. \emph{Science} ,\emph{344}
(6181), 296--299.

Etienne, R. S., \& Alonso, D. (2007). Neutral community theory: how
stochasticity and dispersal-limitation can explain species
coexistence.\emph{Journal of Statistical Physics} , \emph{128} (1),
485--510.

Fahrig, L. (2013). Rethinking patch size and isolation effects: the
habitat amount hypothesis. \emph{Journal of Biogeography} , \emph{40}
(9), 1649--1663.

Fukaya, K., Kusumoto, B., Shiono, T., Fujinuma, J., \& Kubota, Y.
(2020). Integrating multiple sources of ecological data to unveil
macroscale species abundance. Nature communications, 11(1), 1-14.

Gotelli, N. J., Moyes, F., Ant\selectlanguage{ngerman}ão, L. H., Blowes, S. A., Dornelas, M.,
McGill, B. J., \& Magurran, A. E. (2022). Long\selectlanguage{english}-term changes in temperate
marine fish assemblages are driven by a small subset of
species.\emph{Global Change Biology, 28(1),} 46--53.

Hatosy, S. M., Martiny, J. B. H., Sachdeva, R., Steele, J., Fuhrman, J.
A., \& Martiny, A. C. (2013). Beta diversity of marine bacteria depends
on temporal scale. \emph{Ecology} , \emph{94} , 1898--1904.

He, F., \& Hu, X. S. (2005). Hubbell's fundamental biodiversity
parameter and the Simpson diversity index. \emph{Ecology Letters}
,\emph{8} (4), 386--390.

Howe, H. F., \& Smallwood, J. (1982). Ecology of seed
dispersal.\emph{Annual Review of Ecology and Systematics} , \emph{13} ,
201--228.

Hubbell, S. P. (2001). \emph{The unified neutral theory of biodiversity
and biogeography (MPB-32).} Princeton: Princeton University Press.

Jabot, F. (2010). A stochastic dispersal-limited trait-based model of
community dynamics. \emph{Journal of Theoretical Biology} ,\emph{262}
(4), 650--661.

Jabot, F., \& Chave, J. (2011). Analyzing tropical forest tree species
abundance distributions using a nonneutral model and through approximate
Bayesian inference. \emph{The American Naturalist} , \emph{178} (2),
E37--E47.

Keil, G., Cummings, E., \& de Magalhaes, J. P. (2015). Being cool: how
body temperature influences ageing and longevity. \emph{Biogerontology}
,\emph{16} (4), 383--397.

Koide, D., Yoshikawa, T., Ishihama, F., \& Kadoya, T. (2022). Complex
range shifts among forest functional types under the contemporary
warming. \emph{Global Change Biology} , \emph{28} (4), 1477--1492.

Legendre, P. (2019). A temporal beta-diversity index to identify sites
that have changed in exceptional ways in space--time
surveys.\emph{Ecology and Evolution, 9} , 3500--3514.

MacArthur, R. H., \& Wilson, E. O. (1967). \emph{The theory of island
biogeography.} Princeton: Princeton University Press.

Magurran, A. E., Dornelas, M., Moyes, F., \& Henderson, P. A. (2019).
Temporal \selectlanguage{greek}β \selectlanguage{english}diversity: A macroecological perspective. \emph{Global
Ecology and Biogeography, 28} , 1949--1960.

Mannion, P. D., Upchurch, P., Benson, R. B., \& Goswami, A. (2014). The
latitudinal biodiversity gradient through deep time. \emph{Trends in
Ecology \& Evolution} , \emph{29} (1), 42--50.

Mart\selectlanguage{ngerman}ín\selectlanguage{english}-Devasa, R., Martinez\selectlanguage{english}-Santalla, S., Gomez\selectlanguage{english}-Rodriguez, C.,
Crujeiras, R. M., \& Baselga, A. (2022). Species range size shapes
distance\selectlanguage{english}-decay in community similarity. \emph{Diversity and
Distributions} . 28~(7), 1348--1357.

Munoz, F., Grenie, M., Denelle, P., Taudiere, A., Laroche, F., Tucker,
C., \& Violle, C. (2018). Ecolottery: simulating and assessing community
assembly with environmental filtering and neutral dynamics in
R.\emph{Methods in Ecology and Evolution} , \emph{9} (3), 693--703.

Munoz, F., \& Huneman, P. (2016). From the neutral theory to a
comprehensive and multiscale theory of ecological equivalence. \emph{The
Quarterly Review of Biology} , \emph{91} (3), 321--342.

Nakadai, R. (2020). Degrees of compositional shift in tree communities
vary along a gradient of temperature change rates over one decade:
Application of an individual-based temporal beta-diversity
concept.\emph{Ecology and Evolution, 10} (24), 13613--13623.

Nakadai, R. (2022). Development of novel temporal beta-diversity indices
for assessing community compositional shifts accounting for changes in
the properties of individuals. \emph{Ecological Indicators, 143,}109427.

Odum, E. P. (1950). Bird populations of the highlands (North Carolina)
plateau in relation to plant succession and avian
invasion.\emph{Ecology, 31,} 587--605

Prugh, L. R., Hodges, K. E., Sinclair, A. R., \& Brashares, J. S.
(2008). Effect of habitat area and isolation on fragmented animal
populations. \emph{Proceedings of the National Academy of Sciences}
,\emph{105} (52), 20770--20775.

Rabosky, D. L., Chang, J., Cowman, P. F., Sallan, L., Friedman, M.,
Kaschner, K., \ldots{} Alfaro, M. E. (2018). An inverse latitudinal
gradient in speciation rate for marine fishes. \emph{Nature} ,
\emph{559} (7714), 392--395.

Rosindell, J., Hubbell, S. P., \& Etienne, R. S. (2011). The unified
neutral theory of biodiversity and biogeography at age ten. \emph{Trends
in Ecology \& Evolution} , \emph{26} (7), 340--348.

Rosindell, J., Hubbell, S. P., He, F., Harmon, L. J., \& Etienne, R. S.
(2012). The case for ecological neutral theory. \emph{Trends in Ecology
\& Evolution} , 27(4), 203--208.

Schluter, D., \& Pennell, M. W. (2017). Speciation gradients and the
distribution of biodiversity. \emph{Nature} , \emph{546} (7656), 48--55.

Sgardeli, V., Zografou, K., \& Halley, J. M. (2016). Climate change
versus ecological drift: Assessing 13 years of turnover in a butterfly
community. \emph{Basic and Applied Ecology} , \emph{17} (4), 283--290.

Shinohara, N., Nakadai, R., Suzuki, Y., \& Terui, A. (2023).
Spatiotemporal dimensions of community assembly. \emph{Population
Ecology} , 1--12.

Sorensen, T. A. (1948). A method of establishing groups of equal ampli-
tude in plant sociology based on similarity of species content and its
application to analyses of the vegetation on Danish commons. Biologiske
Skrifter, 5, 1--34.

Takeuchi, Y., Ohtsuki, H., \& Innan, H. (2022). Non\selectlanguage{english}-zero\selectlanguage{english}-sum neutrality
test for the tropical rain forest community using long\selectlanguage{english}-term
between\selectlanguage{english}-census data. \emph{Ecology and Evolution} , \emph{12} (1),
e8462.

Turner, J. R. (2004). Explaining the global biodiversity gradient:
energy, area, history and natural selection. Basic and Applied Ecology,
5(5), 435-448.

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