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\begin{document}

\title{Partition among niche and neutral explanations for metacommunity
patterns of fish from Cerrado streams}



\author[1]{Thiago Bernardi Vieira}%
\author[1]{Liriann Chrisley Da Silva}%
\author[1]{Jessica Silva}%
\author[2]{Lilian Casatti}%
\author[3]{Renato de  Romero}%
\author[4]{Francisco Leonardo  Garro}%
\author[5]{Pedro Aquino}%
\author[6]{Paulo Santos Pompeu}%
\author[7]{Paulo De Marco}%
\affil[1]{Universidade Federal do Pará - Campus Altamira}%
\affil[2]{Universidade Estadual Paulista Julio de Mesquita Filho - Campus de Sao Jose do Rio Preto}%
\affil[3]{Instituto Federal de Alagoas, Campus Marechal Deodoro}%
\affil[4]{Pontifícia Universidade Católica de Goiás}%
\affil[5]{Universidade de Brasília}%
\affil[6]{Universidade Federal de Lavras}%
\affil[7]{Universidade Federal de Goiás}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
The Species-Sorting concept, one of the models developed to explain
patterns in metacommunity structure, suggests that relationships between
biological communities and environmental conditions is the basic means
of the species selection processes. A second concept is Neutral Theory,
and the idea of neutral dynamics underpinning metacommunity structure,
cannot be overlooked. The third mechanism is the Mass-Effect concept,
that focuses on the interaction between environmental condition and
neutral effects. In the present study, we partitioned fish communities
in streams between niche and neutral theory concepts, identifying the
best representation of metacommunity structure, and assessed if linear
and hydrographic distance were equivalent in the representation of
neutral processes. The result points to the importance of species
sorting mechanisms in structuring fish communities with neutral
processes best represented by the linear distances. These results are
important for the fish fauna conservation leading to three
considerations: (i) the variation of the landscape and habitat is
important for the stream fish, (ii) the natural barriers are an
important landscape component to be considered, and (iii) the artificial
barriers (dams and impoundments) need to be planned taking in account
the catchment basin as the landscape unit.%
\end{abstract}%



\sloppy


\textbf{Partition among niche and neutral explanations for metacommunity
patterns of fish from Cerrado streams}

Thiago Bernardi Vieira\selectlanguage{ngerman}¹, Liriann Chrisley Da
Silva¹\textsuperscript{,}*\textsuperscript{,+}, Jessica Conceição da
Silva¹, Lilian Casatti\textsuperscript{2,+}, Renato de Mei
Romero\textsuperscript{3,+}, Francisco Leonardo
Tejerina-Garro\textsuperscript{4,+}, Pedro De Podestà Uchôa de
Aquino\textsuperscript{5,+}, Paulo dos Santos
Pompeu\textsuperscript{6,+}\textsubscript{,} and Paulo De Marco
Jr.\textsuperscript{7}

¹ Programa de Pós Graduação em Biodiversidade e Conservação,
Universidade Federal do Pará. Faculdade de Ciências Biológicas, Campus
Altamira. Rua Coronel José Porfírio 2515, São Sebastião, 68372-040,
Altamira, PA, Brazil.

\textsuperscript{2} Instituto de Biociências Letras e Ciências Exatas de
São José do Rio Preto, Universidade Estadual Paulista, Rua Cristóvão
Colombo, 2265, 15054-470, São José do Rio Preto, SP, Brazil.

\textsuperscript{3} Instituto Federal de Alagoas, Campus Marechal
Deodoro, Programa de Pós-Graduação em Tecnologias Ambientais -- PPGTEC.
Rua Lourival Alfredo, 176, 57160-000, Marechal Deodoro, AL, Brazil.

\textsuperscript{4} Centro de Biologia Aquática, Escola de Ciências
Agrárias e Biológicas, Pontifícia Universidade Católica de Goiás,
Goiânia, Brasil; Laboratório de Biodiversidade, Programa de
Pós-Graduação em Sociedade, Tecnologia e Meio Ambiente Centro
Universitário de Anápolis, Anápolis, GO,
Brazil.\textsuperscript{5}Departamento de Zoologia, Universidade de
Brasília, Campus Universitário Darcy Ribeiro, 70910-900, Brasília, DF,
Brazil.

\textsuperscript{6} Programa de Pós-graduação em Ecologia Aplicada,
Departamento de Biologia, Universidade Federal de Lavras - UFLA,
37200-000, Lavras, MG, Brazil.

\textsuperscript{7} Theory, Metapopulation and Landscape Lab,
Departamento de Ecologia, Instituto de Ciências Biológicas, Universidade
Federal de Goiás Campus II, 131, 74001-970, Goiânia, GO, Brazil.

* lirianncns@gmail.com

\textsuperscript{+} these authors contributed equally to this work

\section*{Abstract}

{\label{abstract}}

The Species-Sorting concept, one of the models developed to explain
patterns in metacommunity structure, suggests that relationships between
biological communities and environmental conditions is the basic means
of the species selection processes. A second concept is Neutral Theory,
and the idea of neutral dynamics underpinning metacommunity structure,
cannot be overlooked. The third mechanism is the Mass-Effect concept,
that focuses on the interaction between environmental condition and
neutral effects. In the present study, we partitioned fish communities
in streams between niche and neutral theory concepts, identifying the
best representation of metacommunity structure, and assessed if linear
and hydrographic distance were equivalent in the representation of
neutral processes. The result points to the importance of species
sorting mechanisms in structuring fish communities with neutral
processes best represented by the linear distances. These results are
important for the fish fauna conservation leading to three
considerations: (i) the variation of the landscape and habitat is
important for the stream fish, (ii) the natural barriers are an
important landscape component to be considered, and (iii) the artificial
barriers (dams and impoundments) need to be planned taking in account
the catchment basin as the landscape unit.

\textbf{Keywords} : Ichthyofauna, Connectivity, Stream network,
Mass-Effect, Species-Sorting, Environmental gradient.

\emph{} \textbf{INTRODUCTION}

Fish stream communities favors the explicitly evaluation of current
metacommunity theories. On one side, a classical interpretation of the
relationships between environmental conditions and the composition of
fish communities is closely linked to Niche Theory, predicting that the
resources and conditions of a given environment dictate the distribution
of species over space and time (Hutchinson 1957). Studies of
relationships between species composition, environmental conditions
(e.g. water temperature, dissolved oxygen content, substrate type) and
resources (e.g. places of refuge, food) have had an important impact on
our understanding of how those systems work (Hutchinson 1957).
Considering the four general models currently used to explain
metacommunity patterns (Leibold et al. 2004), SpeciesSorting assumes
that the environment gradient is the only factor structuring the
communities (Cottenie 2005; Landeiro et al. 2011). On the other hand,
the explicitly spatial structure of riverine systems (Presley et al.
2010) and the existence of some complex models of linkage among aquatic
habitats within basin (e.g. river pulse and marginal lakes), favors the
view that dispersal within the metacommunity may account for a
signification portion of the explanation of species composition patterns
(Landeiro et al. 2011). This later explanation is usually referred as a
neutral framework (Leibold 2004). Even though both factors may interact,
we are still looking for a set of more general predictions from which it
is expected that each of the models can be better applied.

The effect of environmental conditions such as water velocity, dissolved
oxygen and water temperature successfully explain common patterns
observed on fish communities of tropical streams (Penczak et al. 1994;
Zeni and Casatti 2013). Nevertheless, the choice of environmental
descriptors and the quality of its statistical description is subject to
doubts. Often these conditions are measured as a single value (Aquino et
al. 2009; Esguícero 2011). In contrast, the use of repeated measurements
(Ferreira and Casatti 2006; Araújo and Tejerina-garro 2007; Takahashi et
al. 2013) may favor a better description of the natural stochasticity of
environmental conditions in streams. Better designs for environmental
conditions measurement may account for environmental heterogeneity (the
variation on the habitat conditions along the environmental gradient) of
the stream system, which is recognized a long time (Angermeier and
Schlosser 1989; Das et al. 2012), but frequently neglected.
Environmental heterogeneity can have important effects on biological
diversity (Vandermeer 1972; Whitaker Jr 1972), suggesting that variation
of in-stream conditions is a more important predictor of fish species
diversity (Angermeier and Schlosser 1989; Beisner et al. 2006; Das et
al. 2012), and other aquatic communities than average values (Fukaya et
al. 2014; Vieira et al. 2013). For example, the relationship between
aquatic macroinvertebrate diversity and the heterogeneity of substrates
in streams (Bond and Downes 2000; Landeiro et al. 2012) .

Dispersal-related process may also exert some challenges related to data
acquisition and interpretation. The Neutral Theory (Hubbell 2001)
proposes that all individuals of the same trophic guild, have the same
ability to compete (regardless of resources and present conditions at
the place), thus having constant growth in any environment. In such
scenario the author proposes that dispersal is the main source of
increase local community diversity at an ecological time framework.
Thus, it is expected that the spatial component (distance between
sampling sites) or geographical barriers (physical obstacles to
migration between locations) are the only mechanisms responsible for
structuring the community. In the studies of stream ecology, we observe
the frequent use of linear distance as a measurement of connectivity.
However, this distance may be not informative, since strict aquatic
organisms (such as fish) can move only through the hydrographic network.
Connectivity measures based on the stream network is beginning to be
used in the interpretation of patterns on estuarine fish communities
(Fullerton et al. 2010) and other aquatic organisms (Landeiro et al.
2012; Obolewski et al. 2009; Jacobson and Faust 2014). The main problem
in using linear distances is the comparison of streams present in
different hydrographic units. Usually, streams in the same basin (or
sub-basins) are more similar than streams in different basins even if
streams in different basins are geographically closer (linear distance)
than streams within the same basin (hydrographic distance; Landeiro et
al. 2012).

There is no simple dichotomy between communities structured by niche
processes and neutral processes in nature (Cottenie 2005), as many
natural communities are structured both by local conditions and
resources (niche-related processes), and species' dispersion abilities
(Cottenie 2005; Thompson and Townsend 2006). The combined effects of
different processes on communities are united under the theory of
Mass-Effect (Leibold et al. 2004), which describes meta-community
processes as the product of both environmental gradients and the
dispersal ability of the species. The quantification of the relative
importance of niche and neutral processes can be evaluated using
variance partitioning techniques (Cottenie 2005; Beisner et al. 2006;
Peres-Neto and Legendre). These techniques allow to quantifying the
percentage explanation related only to environmental conditions and
resources, only to space, and to the interaction between the two sets
(Legendre and Legendre 2003). Obviously, the choice of descriptive
variables for both sets -- environment and space -- may have a
determinant effect on the results and on the interpretation of how both
explanations interact.

The evaluation of how space and environmental variables are related to
community composition allow to a more explicit analysis of the now
classic mechanisms for metacommunity patters developed by Leibold et al.
(2004). Communities that relate solely to the environmental gradient
would be structured by the Species Sorting mechanism, whereas
communities that relate only to space are structured by Neutral or Patch
Dynamics, and the interaction between space and the environmental
gradient is taken as communities where Mass-Effect processes are
predominant (Leibold et al. 2004; Cottenie 2005). Previous study have
suggested that the metacommunity considering all species pool, or
considering only detritivores, insectivores, or omnivores was structured
by a nested co-occurrence pattern with hyperdispersed species loss and a
mass-effect mechanism. However, core species (species pool without the
rare species) displayed a Clementsian pattern and were structured by a
Species Sorting mechanism (Vieira et al. 2020). So, our goals were: (i)
identify the best representation of local conditions (average values or
variance of conditions); (ii) evaluate the importance of linear and
hydrographic distance in neutral processes; and (iii) evaluate the
relative explanatory power of environmental and space variables to
determine which of the four models proposed by Leibold et al. (2004)
account for observed patterns in Brazilian Cerrado fish communities.

\textbf{MATERIALS AND METHODS}

\textbf{Data collection}

To test the hypotheses, we used a database composed of 76 streams of
three distinct hydrographic regions of Brazil: (i) Araguaia-Tocantins;
(ii) Paraná; and (iii) São Francisco, with all streams located within
the Cerrado biome (Fig 1) and can be accessed in Vieira et al. (2020).
All sampled streams are first- to third-order, georeferenced; the
ichthyofauna was sampled by trawl or electric fishing at least along 50
m of the channel. The local environmental conditions measured were
turbidity, conductivity, pH, dissolved oxygen, water velocity, width and
depth channel (three measurements in each stream).

\textbf{Fig 1.} Location of the 76 sampled streams (points) in the three
hydrographic regions considered of the Brazilian Cerrado biome.

\textbf{Data analysis}

As the points sampled are geographically aggregated, the autocorrelation
of the data was tested through the Moran's Index. Spatial maps of
suitable vectors are considered the best way to control autocorrelation
and are good representatives of the spatial structure present in the
data (Mauricio Bini et al. 2009). The eigenvectors of the first
eigenvalues \selectlanguage{english}\selectlanguage{english}are related to the local structuring of communities,
species with small dispersion skills. In order to perform spatial
eigenvectors maps is necessary to know the relationship between all
pairs of points present in the analysis, known as the Weight (W) matrix
(Grffith et al. 2006). In this way we define four W: (i) Global W
(Appendix 1 - S1 - GW), defined by the linear distance between all
streams (Appendix 2); (ii) Local W (Appendix 1 - S1 - LW), defined by
the linear distance between streams present in the same hydrographic
unit. Streams in different units had no interaction and connectivity
values equal to zero (Appendix 2); (iii) Water W (Appendix 1 - S1 - WW),
defined by the hydrographic distance. The same way as in Local W,
streams in different units had no interaction and connectivity values
equal to zero (Appendix 2); and (iv) W Hydalt (Appendix 1 - S1 - HW),
defined by the hydrographic distance between the points weighted by the
slope (Appendix 2).

We measured ecological diversity using two distinct metrics: (i) species
richness and (ii) beta diversity. Species richness was defined as the
number of species present at the site of interest. The beta diversity
was calculated according to the procedure described by Baselga (2010),
which defines beta diversity as the Sorensen dissimilarity index.
Diversity indices were calculated for both the total fish community and
for different feeding guilds (detritivores, insectivores and omnivores).
The classification of the fish species by trophic guild were performed
considering the literature. We used generalized linear models (GLM) to
identify the best way to represent environmental conditions for streams
fish communities. We compared models of community diversity indices and
the average of the environmental conditions with a second model
including the average together with the standard deviations of
environmental conditions as predictor variables. This procedure was
adopted to identify the best way to describe environment conditions, the
average or variance. The GLM models was performed using all W matrices
(Table 1) to identify the best means to represent neutral processes
(linear or hydrographic distances). To avoid multicollinearity, a
Principal Component Analysis (PCA) was performed with the average
values, and a second PCA with the average values \selectlanguage{english}\selectlanguage{english}together with the
standard deviation values \selectlanguage{english}\selectlanguage{english}of the descriptors, the first two axes of
explanation of the PCA being used as predictor variables on the models.
After identifying the best way to represent environmental conditions
(mean or mean with standard deviation), GLMs were performed for each
trophic guild and all W matrices. This procedure was used to identify if
results found for the whole community were equivalent to those found for
individual feeding guilds.

\textbf{Table 1.} Models used to determine the best set of descriptors
of environmental conditions and spatial structure considering the
richness and beta diversity of ichthyofauna.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Diversity metric & W Matrix & Environmental condition\tabularnewline
\midrule
\endhead
Richness & Global W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
& Local W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
& Water W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
& Hydalt W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
Beta diversity & Global W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
& Local W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
& Water W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
& Hydalt W & Average\tabularnewline
& & Average plus Standard Deviation\tabularnewline
\bottomrule
\end{longtable}

All analyses were performed in the Spatial Analysis for Macroecology --
SAM software (Rangel 2010). For all models, we compute the Moran's I and
the Akaike Information Criterion (AIC) and the Variation of the AIC
([?]AIC). To test the relative effects of different metacommunity
processes, the variance was partitioned into: (i) environmental
conditions; (ii) spatial processes; (iii) shared variance between the
environmental and space; and (iv) not explained.

\textbf{RESULTS}

The richness and beta diversity of ichthyofauna had a significant
spatial structure with values of Moran's I higher than 0.1 (Table 2).
Richness of omnivores showed the greatest degree of spatial structure
(Moran's I=0.316, p\textless{}0.001), and the richness of detritivores
the lowest (Moran's I=0.120, p=0.010). The beta diversity of the
detritivores, insectivores and omnivores presented non-significant
effects of spatial autocorrelation.

\textbf{Table 2.} Autocorrelation index of Moran (Moran's I) performed
by richness and beta diversity for all community and trophic guild.
Moran's I - Autocorrelation index of Moran; p - Type one error
probability; I (max) - The highest value of Moran's I to the variable;
I/I(max) - The Moran's I corrected by maximum value.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Diversity metric & Ichthyofauna & Moran's I & p & I (max) &
I/I(max)\tabularnewline
\midrule
\endhead
Richness & All & 0.234 & \textless{}0.001 & 0.737 & 0.318\tabularnewline
& Detritivorous & 0.120 & \textless{}0.010 & 0.610 &
0.198\tabularnewline
& Insectivorous & 0.180 & \textless{}0.001 & 0.628 &
0.287\tabularnewline
& Omnivorous & 0.316 & \textless{}0.001 & 0.807 & 0.392\tabularnewline
Beta diversity & All & 0.208 & \textless{}0.001 & 0.758 &
0.274\tabularnewline
& Detritivorous & 0.052 & \textless{}0.211 & 0.680 &
0.076\tabularnewline
& Insectivorous & 0.020 & \textless{}0.517 & 0.551 &
0.037\tabularnewline
& Omnivorous & -0.039 & \textless{}0.618 & 0.748 & -0.052\tabularnewline
\bottomrule
\end{longtable}

The PCA performed with average values of the environmental conditions
explained 33.26\% of variation in fish diversity in the first axis,
18.79\% in the second axis, and a total of 52.05\% across both axes
(Appendix 3). The pattern found by the ranking was: (i) conductivity,
pH, dissolved oxygen and channel width positively related to the first
axis; (ii) turbidity and water velocity positively to the second axis;
and (iii) channel depth negatively to the second axis (Appendix 3). The
PCA performed with both average values and standard deviation of
environmental conditions explained 21.02\% of the variance in the first
axis and 16.66\% in the second one (Appendix 3). The pattern found by
the ranking was: (i) standard deviation of the channel width, standard
deviation and average turbidity and average water velocity positively
related to the first axis; (ii) standard deviation and average depth of
the channel and the standard deviation of pH, conductivity and dissolved
oxygen negatively to the first axis; and (iii) average channel width,
pH, dissolved oxygen and conductivity and the standard deviation of
water temperature positively to the second axis (Appendix 3).

Best models of richness and beta diversity of fish species included
average and standard deviation of the local conditions and the spatial
eigenvalues maps performed from Local W (Appendix 3). The richness model
had a high r-squared value (r\selectlanguage{ngerman}² = 0.623), with 56.30\% of variance
explained by environmental conditions, 6\% by spatial maps and 0.3\% by
interactions between niche and neutral effects (Table 3). Beta diversity
had an even higher r-square value (r² = 0.758), with 64.40\% of variance
explained by environmental conditions, 6.70\% by spatial maps, and
4.80\% by interactions between environmental and spatial processes
(Table 3).

\textbf{Table 3.} Models of linear regression between the axis of PCA
performed with the averages and standard deviation of the environmental
conditions and the beta diversity and richness of the Cerrado stream
fish community. r2 - Correlation coefficient; F -Fisher`s F; p - Type
one error probability; AIC - Information criteria of Akaike; \selectlanguage{greek}Δ \selectlanguage{english}AIC -
Akaike variation; CN - Condition Number; Moran's I - Autocorrelation
index of Moran for variable; Res Moran's I - Autocorrelation index of
Moran for residual; A.B - Environmental component; A:B - Shared
Component; B.A - Spatial Component;1-(A+B) - Residual.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllllllll@{}}
\toprule
& W Matrix & Environmental Condition & r\selectlanguage{ngerman}² & F & p & AIC & \selectlanguage{greek}Δ \selectlanguage{english}AIC & CN &
Moran's I & Res Moran's I & Variation partition & Variation partition &
Variation partition & Variation partition\tabularnewline
\midrule
\endhead
& & & & & & & & & & & A.B & A:B & B.A & 1-(A+B)\tabularnewline
Richness & Global W & Average & 0.346 & 4.433 & \textless{}0.001 &
481.831 & 10.977 & 1.802 & 0.759 & -0.007 & 0.217 & 0.098 & 0.031 &
0.654\tabularnewline
& & Average and Standard Deviation & 0.553 & 4.566 & \textless{}0.001 &
477.503 & 6.649 & 3.692 & 0.447 & -0.059 & 0.425 & 0.103 & 0.026 &
0.447\tabularnewline
& \textbf{Local W} & Average & 0.335 & 4.226 & \textless{}0.001 &
483.071 & 12.217 & 1.887 & 0.586 & 0.001 & 0.308 & 0.008 & 0.020 &
0.665\tabularnewline
& & \textbf{Average and Standard Deviation} & \textbf{0.623} &
\textbf{5.320} & \textbf{\textless{}0.001} & \textbf{470.854} &
\textbf{0.000} & \textbf{3.381} & \textbf{0.468} & \textbf{-0.077} &
\textbf{0.563} & \textbf{0.003} & \textbf{0.060} &
\textbf{0.377}\tabularnewline
& Water W & Average & 0.349 & 4.493 & \textless{}0.001 & 481.476 &
10.622 & 1.539 & 0.480 & 0.005 & 0.230 & 0.085 & 0.034 &
0.651\tabularnewline
& & Average and Standard Deviation & 0.535 & 4.239 & \textless{}0.001 &
480.570 & 9.716 & 1.841 & 0.684 & -0.046 & 0.416 & 0.112 & 0.007 &
0.465\tabularnewline
& Hydalt W & Average & 0.380 & 3.983 & \textless{}0.001 & 483.364 &
12.510 & 2.539 & 0.442 & -0.003 & 0.158 & 0.157 & 0.064 &
0.620\tabularnewline
& & Average and Standard Deviation & 0.578 & 4.334 & \textless{}0.001 &
480.467 & 9.613 & 2.880 & 0.563 & -0.045 & 0.356 & 0.171 & 0.050 &
0.422\tabularnewline
Beta Diversit & Global W & Average & 0.740 & 18.504 & \textless{}0.001 &
204.389 & 37.178 & 3.054 & 0.315 & -0.150 & 0.248 & 0.389 & 0.093 &
0.260\tabularnewline
& & Average and Standard Deviation & 0.773 & 10.759 & \textless{}0.001 &
188.237 & 21.026 & 4.236 & 0.307 & -0.146 & 0.281 & 0.411 & 0.081 &
0.227\tabularnewline
& \textbf{Local W} & Average & 0.680 & 9.262 & \textless{}0.001 &
176.345 & 9.134 & 3.170 & 0.340 & -0.084 & 0.566 & 0.081 & 0.034 &
0.320\tabularnewline
& & \textbf{Average and Standard Deviation} & \textbf{0.758} &
\textbf{7.540} & \textbf{\textless{}0.001} & \textbf{167.211} &
\textbf{0.000} & \textbf{4.811} & \textbf{0.294} & \textbf{-0.112} &
\textbf{0.644} & \textbf{0.048} & \textbf{0.067} &
\textbf{0.242}\tabularnewline
& Water W & Average & 0.665 & 14.566 & \textless{}0.001 & 187.973 &
20.762 & 2.318 & 0.296 & -0.085 & 0.604 & 0.043 & 0.019 &
0.335\tabularnewline
& & Average and Standard Deviation & 0.723 & 8.925 & \textless{}0.001 &
177.066 & 9.855 & 2.751 & 0.262 & -0.110 & 0.662 & 0.029 & 0.032 &
0.277\tabularnewline
& Hydalt W & Average & 0.726 & 12.633 & \textless{}0.001 & 191.297 &
24.086 & 2.891 & 0.220 & 0.045 & 0.595 & 0.052 & 0.079 &
0.274\tabularnewline
& & Average and Standard Deviation & 0.786 & 9.437 & \textless{}0.001 &
180.815 & 13.604 & 3.306 & 0.238 & 0.088 & 0.655 & 0.037 & 0.094 &
0.214\tabularnewline
\bottomrule
\end{longtable}

When the community was partitioned into trophic guilds, richness and
beta diversity of insectivorous and omnivorous species presented the
spatial eigenvalues maps, performed from the Local W matrix, as the best
representation of spatial processes (Table 4). However, for detritivores
the W Hydalt model was the best representation of spatial processes
(Appendix 3).

\textbf{Table 4.} Linear regression models between trophic guilds of
Cerrado stream ichthyofauna and PCA axes performed with averages and
standard deviation of environmental conditions. r2 - Correlation
coefficient; F -Fisher`s F; p - Type one error probability; AIC -
Information criteria of Akaike; \selectlanguage{greek}Δ \selectlanguage{english}AIC - Akaike variation; CN - Condition
Number; Moran's I - Autocorrelation index of Moran for variable; Res
Moran's I - Autocorrelation index of Moran for residual; A.B -
Environmental component; A:B - Shared Component; B.A - Spatial
Component;1-(A+B) -- Residual\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllllllll@{}}
\toprule
Trophic guild & Trophic guild & W Matrix & r\selectlanguage{ngerman}²: & F & p & AIC & \selectlanguage{greek}Δ \selectlanguage{english}AIC &
CN & Moran's I & Res Moran's I & Variation Partition & Variation
Partition & Variation Partition & Variation Partition\tabularnewline
\midrule
\endhead
& & & & & & & & & & & A.B & A:B & B.A & 1-(A+B)\tabularnewline
Richness & Detritivorous & \textbf{Hydalt W} & \textbf{0.612} &
\textbf{5.820} & \textbf{\textless{}0.001} & \textbf{305.729} &
\textbf{0.000} & \textbf{2.758} & \textbf{0.255} & \textbf{-0.073} &
\textbf{0.438} & \textbf{0.072} & \textbf{0.102} &
\textbf{0.388}\tabularnewline
& & Local W & 0.606 & 4.865 & \textless{}0.001 & 314.247 & 8.518 & 4.139
& 0.232 & -0.058 & 0.408 & 0.101 & 0.096 & 0.394\tabularnewline
& & Water W & 0.542 & 4.371 & \textless{}0.001 & 318.292 & 12.563 &
1.841 & 0.396 & -0.056 & 0.407 & 0.103 & 0.033 & 0.458\tabularnewline
& & Global W & 0.517 & 3.942 & \textless{}0.001 & 322.446 & 16.717 &
3.692 & 0.316 & -0.042 & 0.475 & 0.035 & 0.007 & 0.483\tabularnewline
& Insectivorous & \textbf{Local W} & \textbf{0.508} & \textbf{3.517} &
\textbf{\textless{}0.001} & \textbf{369.312} & \textbf{0.000} &
\textbf{2.745} & \textbf{0.408} & \textbf{-0.040} & \textbf{0.284} &
\textbf{0.146} & \textbf{0.077} & \textbf{0.492}\tabularnewline
& & Hydalt W & 0.481 & 3.422 & \textless{}0.001 & 369.698 & 0.386 &
2.758 & 0.517 & -0.025 & 0.308 & 0.123 & 0.050 & 0.519\tabularnewline
& & Global W & 0.502 & 3.438 & \textless{}0.001 & 370.181 & 0.869 &
3.876 & 0.282 & -0.028 & 0.391 & 0.040 & 0.071 & 0.498\tabularnewline
& & Water W & 0.438 & 2.879 & 0.002 & 375.737 & 6.425 & 1.841 & 0.622 &
-0.005 & 0.325 & 0.106 & 0.007 & 0.562\tabularnewline
& Omnivorous & \textbf{Local W} & \textbf{0.569} & \textbf{4.496} &
\textbf{\textless{}0.001} & \textbf{311.615} & \textbf{0.000} &
\textbf{3.502} & \textbf{0.656} & \textbf{-0.106} & \textbf{0.395} &
\textbf{0.115} & \textbf{0.059} & \textbf{0.431}\tabularnewline
& & Water W & 0.564 & 4.416 & \textless{}0.001 & 312.389 & 0.774 & 2.751
& 0.701 & -0.103 & 0.436 & 0.073 & 0.055 & 0.436\tabularnewline
& & Global W & 0.511 & 3.856 & \textless{}0.001 & 317.529 & 5.914 &
3.692 & 0.680 & -0.078 & 0.326 & 0.183 & 0.002 & 0.489\tabularnewline
& & Hydalt W & 0.534 & 3.376 & \textless{}0.001 & 325.031 & 13.416 &
2.949 & 0.781 & -0.085 & 0.403 & 0.107 & 0.025 & 0.466\tabularnewline
Beta Diversity & Detritivorous & \textbf{Hydalt W} & \textbf{0.307} &
\textbf{3.256} & \textbf{0.002} & \textbf{46.594} & \textbf{0.000} &
\textbf{1.577} & \textbf{0.088} & \textbf{\textless{}0.001} &
\textbf{0.188} & \textbf{0.020} & \textbf{0.100} &
\textbf{0.693}\tabularnewline
& & Global W & 0.261 & 2.962 & 0.007 & 48.748 & 2.154 & 1.859 & 0.534 &
-0.030 & 0.169 & 0.039 & 0.054 & 0.739\tabularnewline
& & Local W & 0.249 & 2.428 & 0.019 & 52.767 & 6.173 & 1.922 & 0.162 &
-0.035 & 0.185 & 0.022 & 0.041 & 0.751\tabularnewline
& & Hydalt W & 0.216 & 2.308 & 0.030 & 53.267 & 6.673 & 1.680 & 0.235 &
-0.024 & 0.196 & 0.012 & 0.008 & 0.784\tabularnewline
& Insectivorous & \textbf{Global W} & \textbf{0.332} & \textbf{2.170} &
\textbf{0.020} & \textbf{23.221} & \textbf{0.000} & \textbf{2.806} &
\textbf{0.067} & \textbf{-0.049} & \textbf{0.064} & \textbf{0.016} &
\textbf{0.252} & \textbf{0.668}\tabularnewline
& & Local W & 0.101 & 0.938 & 0.491 & 28.034 & 4.813 & 1.887 & 0.150 &
-0.053 & 0.071 & 0.009 & 0.021 & 0.899\tabularnewline
& & Water W & 0.096 & 0.892 & 0.528 & 28.411 & 5.190 & 1.680 & 0.103 &
-0.055 & 0.081 & 0.001 & 0.016 & 0.904\tabularnewline
& & Hydalt W & 0.084 & 0.765 & 0.634 & 29.456 & 6.235 & 2.413 & 0.125 &
-0.043 & 0.083 & -0.003 & 0.004 & 0.916\tabularnewline
& Omnivorous & \textbf{Global W} & \textbf{0.231} & \textbf{2.200} &
\textbf{0.033} & \textbf{4.718} & \textbf{0.000} & \textbf{2.334} &
\textbf{0.101} & \textbf{-0.084} & \textbf{0.027} & \textbf{-0.029} &
\textbf{0.133} & \textbf{0.769}\tabularnewline
& & Local W & 0.185 & 1.084 & 0.389 & 11.528 & 6.810 & 3.158 & 0.185 &
-0.088 & 0.135 & -0.038 & 0.087 & 0.815\tabularnewline
& & Water W & 0.180 & 0.808 & 0.671 & 22.033 & 17.315 & 3.450 & 0.120 &
-0.074 & 0.118 & -0.020 & 0.082 & 0.820\tabularnewline
& & Hydalt W & 0.253 & 1.475 & 0.148 & 8.172 & 3.454 & 2.881 & 0.017 &
-0.071 & 0.134 & -0.036 & 0.155 & 0.747\tabularnewline
\bottomrule
\end{longtable}

\textbf{DISCUSSION}

In the analyses of richness and beta diversity, we found that
environmental conditions captured most of the variation in fish species
diversity, suggesting that environmental conditions were satisfactorily
represented using average values and standard deviations, whereas the
spatial component contributed little to structuring fish communities.
Interpretation of spatial processes and its association with dispersion,
made using spatial eigenvalue maps, has to be done carefully because
they bring not only information on spatial structuring but also on
environmental conditions (Diniz-Filho et al. 2003; Hawkins et al. 2007).

The beta diversity of different guilds, especially insectivores and
omnivores species, displayed little correlation with environment
conditions and a greater one with spatial processes. This result may be
explained by the spatial component representing collinear unmeasured
environmental conditions rather than effects of space itself, or that
insectivorous and omnivorous fish have greater dispersion abilities. A
higher dispersal capacity can hide effects of environmental gradients,
as species can rapidly colonize sites that have unfavorable conditions,
and suppress effects of local extinction (Gr\selectlanguage{ngerman}önroos et al. 2013). If this
was the case for insectivorous and omnivorous species, Mass Effect may
be the predominant mechanism structuring their communities. In contrast,
detritivores fish and the total community were structured by Species
Sorting effects, or an interaction between Mass Effect and Species
Sorting (Cottenie 2005), as these communities showed a strong
relationship with environmental conditions and a weak one with space.

Although the Local W model was the best representation of space for the
entire ichthyofauna community, we observed a weak relationship between
fish communities (richness and total beta diversity) and spatial
components. This weak association may have occurred due to two factors:
(i) the ability of fish to actively select habitats would be more
important than dispersion, indicating the SpeciesSorting mechanism of
metacommunity structure (Leibold 2004), which is considered the main
mechanism responsible for structuring natural meta communities (Cottenie
2005; Van der Gucht et al. 2007; Vanschoenwinkel et al. 2007; Landeiro
2011), (ii) the ''path'' along which fish species have dispersed is
environmentally unsuitable, restricting their dispersion (Grönroos et
al. 2013). Although the characteristics of streams were controlled in
order to be representative of natural conditions, the connection between
these points was not controlled. Thus, it may be that sites, although
preserved, are connected by non-suitable drainage that act as a barrier
and limit the dispersion of ichthyofauna (Grönroos et al. 2013).

Linear distances without considering hydrographic units fail to
represent spatial process in stream fishes communities. The use of the
linear distance is a simplistic and insufficient way to measure spatial
processes in aquatic systems (Landeiro 2011). When including the
geographic barriers into the linear distance procedure (called Local W
here), the linear distance was able to provide a good representation of
the geographic patterns of the fish community. The performance of Local
W is better than the dendritic distance (W Water), shown previously as
the best means to represent spatial processes in aquatic systems. Using
Local W, we were able to identify a simple and robust way of
representing spatial processes considering the physical barriers
separating communities. This result was consistent across all components
of the community (\emph{i.e.} overall community or discrete feeding
guilds) and ecological descriptors (\emph{i.e.} species richness or beta
diversity).

A second feature of our results is related to the dispersion of
detritivores fish, which cannot be represented using simple Euclidian
distances between points, considering or not geographic barriers or
hydrological distances. The best way to represent space process for this
guild was applying the Hydalt W model. It considers the dendritic
distance between points (and barriers), and the direction of the flow.
The application of connectivity models associated with flow direction is
advocated by some authors as being the most suitable for aquatic
organisms (Pearson et al. 2007; Peterson and Ver Hoef 2010). However,
with the analysis of our data, we observed that this approach is more
complex than the Euclidian distance (considering barriers - Local W),
and was only necessary for detritivores fish.

The low dispersion of stream fish is evidenced by the negative
relationship between fish communities and spatial filters. Considering
that small eigenvalues \selectlanguage{english}\selectlanguage{english}are related to local structuring and higher
eigenvalues \selectlanguage{english}\selectlanguage{english}to larger scale structuring (Grffith et al. 2006; Blanchet
et al. 2008), we interpret that fishes from stream are dispersing across
small spatial scales, as richness and beta diversity were negatively
related to the filters. This result supports the idea of \selectlanguage{english}\selectlanguage{english}preserved
spots connected by altered ''paths''. Thus, fish species with low
dispersal ability tend to express spatial structure more clearly than
ones with higher dispersal ability (Thompson and Townsend 2006; Astorga
et al. 2011).

Species Sorting predicts a correlation of metacommunity structure only
with environmental gradients (Leibold et al. 2004). The interaction of
space (dispersion) and environment in the structuring of metacommunities
is attributed solely to the Mass Effect model\textsuperscript{2}.
However, is it not possible to separate these two mechanisms, and
metacommunities that are related to space and environment are understood
as interaction between Species Sorting and Mass Effect (Cottenie 2005;
Vieira and Tejerina-Garro 2020; Brasil et al. 2019). This interaction
was found in 29\% (46) of the communities analyzed by Cottenie (2005)
and also found for fish (Landeiro et al. 2011; Vieira and Tejerina-Garro
2020; Vieira et al. 2020) and other groups (Brasil et al. 2019).
However, the ichthyofauna show a greater correlation with environmental
conditions than spatial processes, suggesting that Species Sorting is
the key mechanism in structuring fish communities (37\% of the
metacommunity analyzed by Cottenie (2005) show this result). This result
does not rule out the occurrence of dispersion (Cottenie 2005; Landeiro
et al. 2011; Vieira and Tejerina-Garro 2020; Brasil 2019), but
reinforces the idea that dispersion occurs locally and weakly (negative
relation with the spatial eigenvectors maps).

Species Sorting is related to many freshwater organisms, such as
macroinvertebrates (Gronroos et al. 2013; Heino et al. 2013), snails
(Hoverman et al. 2011) and bacteria (Van der Gucht et al. 2007). The
influence of the Species Sorting mechanism in communities at large
scales (three basins) was found indicating that there was no variation
in the metacommunities among basins, but a continuous variation
according to an environmental gradient (Heino et al. 2014). Dispersion
has little influence on metacommunity patterns at large scales (Gronroos
et al. 2013; Heino et al. 2013). In fact, dispersion decrease at large
scales as the same way that environmental gradient increase the
correlation with metacommunity structure (Gronroos et al. 2013; Astorga
et al. 2011). In addition, fish can only migrate using drainage and some
species tend not to migrate or are prevented from migrating due to
physical barriers such waterfalls or dams. Furthermore, species that
actively disperse tend to select the environment in which they will
settle, further reducing effects of spatial structure (Gronroos et al.
2013).

The variation partitioning of fish communities between environmental
conditions and geographic space tend to associate environmental
conditions with niche (i.e. environmental conditions) or neutral (i.e.
geographic distances) theory (Smith and Lundholm 2010). When communities
are more correlated with environmental conditions than geographic
distance, the communities are structured by niche theory. On the other
hand, when the geographic distance are more correlated than environment,
the discussion is focused on neutral theory. This dichotomous view is
overly simplistic and does not reflect the complexities of the multiple
mechanisms that concurrently structure natural communities. Communities
are not the effect of only one of these two theories, but the
interaction between them (Juen and De Marco 2012). More recent analyses
(Cottenie 2005; Van der Gucht et al. 2007; Gronroos et al. 2013; Astorga
et al. 2011; Vieira and Tejerina-Garro 2020; Vieira et al. 2020; Brasil
et al. 2019; Heino 2011) demonstrate the association of the community
with the mechanisms proposed by Leibold et al. (2004). In this case, the
relationship between communities and environmental conditions are
related to the Species Sorting mechanism, the relationship between
community and space to the neutral or Patch Dynamic mechanisms, and the
interaction between space and conditions related to the Mass Effect
mechanism (Cottenie 2005). However, the dissociation of Mass Effect and
Species Sorting is not trivial, since the dispersion limitation in
communities within Species Sorting can produce a pattern with
relationship between space and environmental conditions, a Mass Effect
dynamic (Cottenie 2005).

Therefore, we conclude that the ichthyofauna of Cerrado streams are
structured by an interaction between Mass Effect and Species Sorting
mechanisms. Among the trophic guilds considered, only the beta diversity
of insectivores and omnivores is influenced by the geographical space,
suggesting an effect of Neutral or Patch Dynamic models. Finally, we
found that the linear distance measures that take into account the
physical barriers (Local W in this study) are the best representations
of spatial patterns for the fish communities, except for the
detritivores that are influenced by the flow direction variable in the
connectivity models (Hydalt W). Regarding the environmental conditions,
it is necessary that these were represented by the average and some
metric (e.g. heterogeneity of substrates, beta diversity and metrics
variance) that measures their variation to best evaluate the degree of
environmental heterogeneity.

\textbf{Acknowledgements}

We would like to thank the lab staff at the Aquatic Ecology Laboratory
of the UFC. TBV would like to thank Coordenacao de Aperfeicoamento de
Pessoal de Nivel Superior (CAPES) for the grant provided during his
doctoral degree. Part of these study was funded by CNPq/PPBIO (agreement
\# 457463/2012-0) and CNPq/ICMBio (agreement \# 552009/2011-3), CNPq
grant (Process 471283/2006-1), The International Fund for Ecological
Research, grant no. 00543 and Aperfeicoamento de Pessoal de Nivel
Superior - Brasil (CAPES) Finance Code 001. LC is financially supported
by CNPq (301877/2017-3).

\textbf{Author contributions statement}

T.B.V. Formal Analysis-Lead, writing-original and draft-lead, L.C.D.S.,
J.C.S., L.C., R.M.R., F.L.T.G., P.D.P.U.A., P.S.P. writing-review and
editing and P.D.M.J. supervision-lead. All authors reviewed the
manuscript.

\textbf{Competing interests}

The authors declare no competing interests.

\textbf{Supporting information captions}

Appendix 01 -- Figure 1

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