Null models for study Rotifers and Crustaceans Zooplankton species richness in Chilean Patagonian lakes Modelos nulos para o estudo de riqueza de espécies de Rotíferos e Crustáceos Zooplanctônicos na Patagônia Chilena

Aims: The Patagonian lakes are characterized by their oligotrophy that is the cause of low species number in their zooplankton assemblage. The aim of the present study is to analyze the crustacean and rotifers species number pattern in Patagonian lakes among a latitudinal gradient (40-51 °S). Results: The results revealed that there are direct significant correlations between total species with rotifer species, and chlorophyll concentration with crustacean species number, and an inverse association between latitude with total species. Conclusion: The results of co-occurrence species null model revealed presence of regulator factors in one of three simulations, that would be due to the presence of many species repeated in studied sites. Similar patterns were observed in Argentinean Patagonian lakes.

Ríos-Escalante, 2010), but there are not detailed descriptive studies for rotifers assemblages, there are only basic descriptions about presence/absence rotifers species (Campos et al., 1989(Campos et al., , 1992(Campos et al., , 1988(Campos et al., , 1990(Campos et al., , 1994a, b;, b;Villalobos, 1999).The aim of the present study is to analyze the crustacean and Rotifera zooplankton assemblages in Chilean Patagonian lakes with the aim of determine if the assemblages are random or structured.
Data was analyzed in three steps: a first step is determine if the rotifer, crustacean and total zooplankton species was associated with the mentioned parameters, for this purpose, it was previously verified the normality using a Shapiro test, and as this condition was not found, it was applied a Spearman non parametric correlation test using software "R" (R Development Core Team, 2009).
In the following steps a species absence/ presence matrix was constructed, with the species in rows and the sites in columns (Table 2).As second step consisted, it was applied a UPGMA cluster analysis using Neighbour-joining method for determine potential similarities between sites on the basis of species associations using the R package Phangorn (Schliep, 2011).Thirdly we calculated

Introduction
The use of models for understand ecological patterns can involve the random presence in some determined cases for populations and community scales (Hilborn & Mangel 1997), that can be applied for statistical applications (Zar 1999;Gotelli & Ellison, 2013).At community ecology scale is proposed the null models that involve the absence of regulator factors in community structures (Harvey et al., 1983;Gotelli & Graves, 1996;Gotelli, 2000Gotelli, , 2001)).The aim of the null models view point is based in randomization or absence of process and regulator factors on community ecology, and the null hypothesis is based that community is random or without defined structure (Harvey et al., 1983;Gotelli & Graves, 1996).On these null models one of the most applied in community ecology is the co-occurrence species that involves a presence-absence species matrix for a defined sites list with the aim of determine if the species associations are random or structured (Gotelli & Graves, 1996;Gotelli, 2000).These models are based mainly in terrestrial environments (Tondoh, 2006;Tiho & Josens, 2007) and in freshwater environments (De los Ríos, 2008;De los Ríos-Escalante et al., 2011).This kind of model has been applied mainly in field crustacean zooplankton studies on Chilean Patagonian lakes for understand the random or structuration in zooplankton species associations, unfortunately there are not other similar studies for other lakes (De los Ríos, 2008;De los Ríos-Escalante et al., 2011).
The Patagonian lakes are characterized by their oligotrophy and low species number in their zooplankton assemblages (Soto & Zúñiga, 1991;De los Ríos-Escalante, 2010).Similar pattern has been observed for Argentinean Patagonian lakes (Modenutti et al., 1998).The literature has been focused mainly in Crustacean species number (Soto & Zúñiga, 1991;Modenutti et al., 1998;De los Table 1.Geographical location, maximum depth (Zmax in m), surface (km 2 ), chlorophyll "a" concentration (μg/L), and rotifer and crustacean species number for sites considered in the present study.a Checkerboard score ("C-score"), which is a quantitative index of occurrence that measures the extent to which species co-occur less frequently than expected by chance (Gotelli, 2000).A community is structured by competition when the C-score is significantly larger than expected by chance (Gotelli, 2000;Tondoh, 2006;Gotelli & Entsminger, 2007;Tiho & Josens, 2007;Ehouman et al., 2009).
Thirdly we compared co-occurrence patterns with null expectations via simulation.Gotelli & Ellison (2013) suggested the as statistical null models Fixed-Fixed: in this model the row and column sums of the matrix are preserved.Thus, each random community contains the same number of species as the original community (fixed column), and each species occurs with the same frequency as in the original community (fixed row).The null model analyses were performed using the package EcosimR version 7.0 (Gotelli & Ellison, 2013;Carvajal-Quintero et al., 2015).Finally, it was applied a correspondence analysis with the presence-absence data with the aim of determine the potential groups of lakes and their respective zooplankton components.This analysis was perfomormed using the R-package CA (Nenadic & Greenacre, 2007).

Results
The correlation results revealed the absence of significant associations between studied parameters (Table 3).The results of cluster analysis revealed for total species and Rotifera the presence of three main groups, the first joined by Sarmiento and Del Toro lakes, the second joined by Los Palos, Escondida and Riesco lakes, and the third joined by Llanquihue, Todos los Santos, Rupanco and Puyehue lakes (Figure 2), whereas for crustacean the groups observed were first joined by Sarmiento, Del Toro, Llanquihue and Todos los Santos lakes, the second joined by Los Palos, Escondida and Riesco lakes, and the third group joined by Rupanco and Puyehue lakes (Figure 2).
The results of co-occurrence null model species revealed the presence of regulator factors for total, crustaceans and rotifer species (Table 4), that is confirmed by respective simulation graphs (Figure 3).
The results CA analysis agree with UPGMA about the presence of three main groups joined the first with Sarmiento and Del Toro lakes, the second joined by Riesco, Los Palos and Escondida lakes, and the third joined by Todos Los Santos, Rupanco, Puyehue and Llanquihue lakes (Table 5, Figure 4).

Discussion
The results revealed that the zooplankton species associations are not random, this mean the existence of regulator factors, this is supported first by marked significantly of co-occurrence species null models, that would avoid the presence of type I and type II errors (Gotelli, 2000;Veech, 2012).Although the correlation analysis does not denote significant associations, the literature mentioned an inverse relation between species richness latitude, and a direct association between species richness and chlorophyll a (De los Ríos-Escalante, 2010, 2013).This is because, there is an inverse association between chlorophyll and latitude in large and deep  lakes due mixing depth increasing, that generate an strong physical stressor for phytoplankton activity (Soto, 2002;De los Ríos-Escalante, 2010).
The role of rotifers and crustacean zooplankton is important because they are main grazers in Patagonian lakes (Woelfl, 2007;Woelfl et al., 2010; Figure 3. Graphs with simulated and observed species associations based on null model co-occurrence analysis for total species (up), rotifer species (center) and crustacean species (down).Acta Limnologica Brasiliensia, 2016, vol.28, e11 Montecino et al., 2011;Modenutti, 2014).In this scenario, the literature described a direct relation between chlorophyll concentration and crustacean species richness for Patagonian lakes (De los Ríos-Escalante, 2010, 2013), but the chlorophyll concentration is inversely related with latitude for these lakes (Soto, 2002, De los Ríos-Escalante, 2010).It was not found significant associations between crustacean zooplankton species richness with surface and depth (Soto & Zúñiga, 1991;De los Ríos-Escalante, 2010, 2013).These results would agree partially with observations for northern hemisphere lakes where it was found the direct association between crustaceans species number with chlorophyll concentration, nevertheless in northern hemisphere lakes it was found a direct association between crustacean species number with surface (Dodson, 1992;Karatayev et al., 2008;Dodson et al., 2009;Van Egeren et al., 2011).
In the present study, the lacks of coincidences between correlation test with null models would support the literature descriptions about null models because these are statistically robust (Tondoh, 2006;Tiho & Josens, 2007;Gotelli & Ulrich, 2012).The present study would suggest compare null model analysis with traditional statistical null hypothesis for improve the data analysis.

Table 2 .
Rotifera and crustacean species reported for sites considered in the present study.

Table 3 .
Results of correlation between studied parameters with Rotifera, crustacean and total species number.
"P" values lower than 0.05 denotes significant association.

Table 4 .
Results of null model co-occurrence species for total species number, rotifer and crustacean species for studied sites.
* "P" values lower than 0.05 denotes the presence of regulator factors.

Table 5 .
Results of correspondence analysis for presence-absence species matrix.