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Received Date : 16-Aug-2014 Revised Date : 05-Jan-2015 Accepted Date : 12-Jan-2015 Article type
: Resource Article
Correlation between genetic diversity and environmental suitability: taking uncertainty from ecological niche models into account
JOSÉ ALEXANDRE F. DINIZ-FILHO1*; HAUANNY RODRIGUES2; MARIANA PIRES DE CAMPOS TELLES3; GUILHERME DE OLIVEIRA4; LEVI CARINA TERRIBILE5; THANNYA NASCIMENTO SOARES4 ; and JOÃO CARLOS NABOUT3 1. Departamento de Ecologia, Universidade Federal de Goiás (UFG), Goiânia, Goiás, Brasil; 2. Programa de Pós-Graduação em Genética & Biologia Molecular, Instituto de Ciências Biológicas, UFG; 3. Instituto de Ciências Biológicas, Departamento de Genética, UFG, Goiânia, Goiás, Brasil; 4. Centro de Ciências Agrárias, Ambientais e Biológicas, Setor de Biologia, Universidade Federal do Recôncavo da Bahia (UFRB), Cruz das Almas, BA, Brasil; 5. Laboratório de Macroecologia, Regional Jataí, UFG, Goiás, Brasil; 6. Universidade Estadual de Goiás (UEG), Unidade de Ciências Exatas e Tecnológicas, Anápolis, Goiás, Brasil.
*Correspondence to: José Alexandre Felizola Diniz-Filho, Universidade Federal de Goiás (UFG), Instituto de Ciências Biológicas, Departamento de Ecologia, Cx.P. 131, 74001-970 Goiânia, GO. Telephone: +55 62 3521-1752; E-mail: [email protected]
Author contributions: JAFD-F designed the study and wrote the first draft; HR performed correlation and uncertainty analyses; JCN, GO and LCT obtained occurrence and This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1111/1755-0998.12374 This article is protected by copyright. All rights reserved.
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environmental data and performed the niche models; MPCT and TNS performed field work and molecular analyses. All authors significantly contributed to the final version of the manuscript.
Keywords: heterozygosity, niche modelling, uncertainty, suitability, tropical tree, Cerrado.
ABSTRACT The hindcast of shifts in the geographical ranges of species as estimated by Ecological Niche Modeling (ENM) has been coupled with phylogeographical patterns, allowing the inference of past processes that drove population differentiation and genetic variability. However, more recently, some studies have suggested that maps of environmental suitability estimated by ENM may be correlated to species’ abundance, raising the possibility of using environmental suitability to infer processes related to population demographic dynamics and genetic variability. In both cases, one of the main problems is that there is a wide variation in ENM development methods and climatic models. In this study, we analyze the relationship between heterozygosity (He) and environmental suitability from multiple ENMs for 25 population estimates for Dipteryx alata, a widely distributed, endemic tree species of the Cerrado region of Central Brazil. We propose a new approach for generating a statistical distribution of correlations under randomly generated ENM. The confidence intervals from these distributions indicate how model selection with different properties affects the ability to detect a correlation of interest (e.g., the correlation between He and suitability). Additionally, our approach allows us to explore which particular ensemble of ENMs produces the better result for finding an association between environmental suitability and He. Caution is necessary when choosing a method or a climatic dataset for modeling geographic distributions, but the new approach proposed here provides a conservative way to evaluate the ability of ensembles to detect patterns of interest.
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INTRODUCTION Ecological Niche Modeling (ENM; see Jimenez-Valverde et al. 2008; Araújo & Peterson 2012) has been widely used to describe the potential geographic distribution of a species, under the assumption that the environmental variables that comprise ecological niches can be used to describe the suitability of regions within the species’ range, particularly at broad scales (Soberon 2007; Colwell & Rangel 2011). ENMs can be built using several methods or algorithms that attempt to correlate the occurrence of a species and environmental data. Once a model is fitted, the results can be projected into environmental data obtained for other regions or time frames (past or future). Thus, the ENM models provide an adequate and relatively simple approach to infer changes in the geographical distribution of a species under biological invasions or climate changes (Franklin 2009; Peterson et al. 2011).
Some studies have shown that besides the inference of broad scale geographical ranges, the ENM map of environmental suitability within a species range, which indicates the probability of occurrence or “distance” to optimum environmental conditions, may be correlated to the species’ abundance (e.g., Nabout et al. 2011; Torres et al. 2012; MartínezMeyer et al. 2012). This opens the possibility of using these environmental suitability estimates to infer demographic data, which, in turn, can be related to the genetic variability of a population across geographical space (Hedrick 2008). This relationship, for example, would be the basis of several geographic patterns of genetic diversity, such the loss of genetic diversity along environmental gradients or central-peripheral patterns (e.g., Vucetich and Waite 2003; Eckert et al. 2008; Diniz-Filho et al. 2009a; Lira-Noriega & Manthey 2014).
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The hindcast of environmental suitability and shifts in geographical range limits has also been coupled with phylogeographical patterns, allowing for the inference of past processes that have driven population differentiation and genetic variability (e.g., Richards et al. 2007; see Alvarado-Serrano & Knowles 2014 for a recent review). Despite the enormous gain in knowledge obtained by coupling ENMs with genetic and phylogeographic data, there are some potential pitfalls in this association, and a careful evaluation of models and scenarios is necessary (see Alvarado-Serrano & Knowles 2014).
Alvarado-Serrano and Knowles (2014) stressed the applications, advances and precautions of using ENMs in phylogeographical studies. However, one of the most important sources of uncertainty in ENMs, which is not discussed in detail by those authors, is the variation among the predictions from the different methods used in the modeling process and the variation among climatic data, which causes significant uncertainty in environmental suitability estimates (Araújo & New 2007; Elith & Graham 2009; Diniz-Filho et al 2009b; Buisson et al. 2010; Rangel & Loyola 2012; Fitzpatrick et al. 2013). Our goal in this study was to evaluate the relationship between ENM-predicted environmental suitability and the genetic diversity of Dipteryx alata (Fabaceae) populations (a socio-economically important tree species that is widely distributed throughout the Cerrado region of Central Brazil), considering the uncertainty associated with ENM methods and climatic data used in the modeling process.
Previous genetic analyses of D. alata across its geographic range showed a significant amount of population structure both among and within populations (Soares et al. 2008; Collevatti et al. 2010, 2013a; Diniz-Filho et al. 2012). Recently, Soares et al. (2014) used an ensemble forecast approach and showed that genetic diversity within a population, as
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(ENFA), Euclidian Distance (ED), Gower Distance (GD), Mahalanobis Distance (MD); 2) Statistical methods: Generalized Linear Models (GLM), Generalized Additive Models (GAM); and 3) Machine Learning methods: Genetic Algorithm for Rule Set Production (GARP), Maximum Entropy (Maxent), Flexible Discriminant Analysis (FDA), Multivariate Adaptive Regression Splines (MARS), Generalized Boosted Models (GBM), Neural Networks (ANN) and Random Forest (RNDFOR).
The methods above were used to correlate the occurrences of D. alata with five environmental variables (mean annual temperature and temperature range, precipitation during the wettest month, precipitation during the driest month, and precipitation during warmest quarter) that were derived from four coupled Atmosphere-Ocean Global Circulation Climatic Models (AOGCMs, which are CCSM, GISS, MIROC and MRI) along with subsoil pH. (climate data can be downloaded from http://ecoclimate.org; see “Data Accessibility” section for subsoil pH data). Thus, a total of 2800 geographic distribution models for D. alata (14 ENMs X 4 AOGCMs X 50 cross-validation replications) were generated (see Terribile et al 2012 for details on data and modeling). Overlaying all of these maps allowed us to calculate the frequency of models that indicate the presence of the species in a given cell grid, which was used as an overall surrogate of environmental suitability (the ‘ensemble’ forecasting approach – see Araújo & New 2007; Diniz-Filho et al. 2009).
Each map of environmental suitability for each of the 14 ENMs and four AOCGM combinations was overlaid with the geographical coordinates of the 25 D. alata populations for which genetic data were available to define their “local” suitability. The suitability was then correlated to the He values using Pearson’s correlations (significance tests were based on geographically effective degrees of freedom using Dutilleul’s 1993 correction). We then
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used a model II two-way Analysis of Variance (ANOVA) without replication to evaluate how sources of uncertainty (methods or AOGCMs, used as factors in ANOVA) contribute to variation in the correlation between suitability and He (Diniz-Filho et al. 2009; Buisson et al. 2010; de Oliveira et al. 2014).
We also used a new approach to evaluate how different combinations of models (ensembles) provide correlations between environmental suitability and He among the 25 populations. Although it is simple to combine all models into a “full” ensemble (as originally proposed by Araújo & New 2007), this approach assumes that all models are equally adequate and provide random variation around the “true” environmental envelope or geographic distribution. Because this may not necessarily be accurate, a simple alternative is to analyze correlations for each method or obtain correlations with ensembles for different “classes” of models (Rangel & Loyola 2012). In this study, we statistically expand this last reasoning by generating 10,000 random model combinations (both ENMs and AOGCMs) and varying the number of models selected in each combination. We then calculated the mean suitability for each particular ensemble-producing combination and correlated this to He. Thus, we generated a statistical distribution of correlations under randomly generated ensembles, and the confidence interval of the distributions indicates how the selection of the various models affects our ability to detect the correlation of interest. With the approach, we propose that it is possible to determine whether the model selected by a researcher when generating an ensemble will qualitatively affect their ability to detect the pattern of interest (i.e., the correlation between He and suitability). At the same time, this approach allows us to explore whether the predictions from particular ensembles of ENM methods and climate models are better suited for finding an association between environmental suitability and He.
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An R-script for performing these analyses is provided on Dryad (see “Data Accessibility” section).
RESULTS There is no significant correlation between mean suitability (full ensemble) and He values among the 25 populations of D. alata (r = 0.237; P = 0.224 with 19 degrees of freedom according to Dutilleul correction) (Fig. 2A). However, this correlation varies based on different combinations of ENM and AOGCM, with the highest value of 0.59 found for the combination of GARP based on CCSM environmental data and the lowest value of -0.341 found for FDA, based on MRI environmental data. The mean of the correlations across all ENMs and AOGCMs was equal to 0.122 (this is smaller than the correlation with ensemble models) (Table 1). Ensembles of different method classes (envelope, statistical and machine learning) also produce different correlations with He, with the highest values obtained for machine learning methods (r = 0.292).
The correlations derived from the 10,000 random combinations of ENMs and AOGCM (Fig. 3) was, on average, equal to 0.215 ± 0.109, ranging from -0.346 to 0.685. The 95% confidence interval does not encompass zero (0.00028 – 0.429), with only 4% of the correlations smaller than zero (Fig. 3), suggesting that regardless of the model combinations used to generate the ensemble, there is a tendency for finding a positive correlation between He and suitability.
In the randomly generated ensembles, the highest correlation of 0.685 was generated by the combination of GARP and GAM, both based on CCSM data. The second highest correlation of 0.667 was generated by the combination of GARP and MAXENT, also based
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on CCSM data. In fact, the GARP-CCSM model appears in all of the top 1% of the correlations of suitability and He, followed by MAXENT-CCSM and GAM-CCSM. The frequency of ENMs and AOGCMs in the top 10% of model combinations that generated the highest correlations with He (Table 1) is GARP, MAXENT and GAM (all modeled using CCSM), in that order.
An ANOVA showed that most of the variation among correlations was due to the effect of ENM, explaining 36% of the variance (compared to 16% for the effect of AOGCM). The highest mean correlation of ENMs (across the AOGCMs) was obtained for MAXENT (Fig. 2B), followed by GARP (Fig. 2C) and Neural Networks. The correlation between the He and MAXENT predictions is leveraged by the three populations despite being relatively high and significant (r = 0.438; P = 0.037). For the AOGCMs, only CCSM (across all ENMs) provided relatively high correlations.
DISCUSSION Our main finding in this study is that inferences based on ENMs, as performed here for the correlation between environmental suitability and heterozygosity, can vary drastically due to uncertainty from the methods and climatic data. Explicitly accounting for this uncertainty can allow for a better evaluation of how conclusions are qualitatively affected (Diniz-Filho et al. 2009). The approach of generating random ensembles to generate an statistical distribution that allows the evaluation of uncertainty would qualitatively affect the interpretation of the pattern of interest and, in our analyses, supports a positive correlation between He and ENM suitability. Of course, the proposed approach, although used here for testing the correlation between ENMs and He, can be generalized to any approach coupling ENM and phylogeography or population genetics.
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A significant and positive correlation between He and ENM suitability, as observed here for some models and based on randomly generated ensembles, can be interpreted as an effect of neutral dynamics with variable population densities, under the assumption that higher environmental suitability leads to higher population densities (Diniz-Filho et al. 2009a; Nabout et al. 2011; Van Der Wal et al. 2009; Tôrres et al. 2012; Lira-Noriega & Manthey 2014). The correlation between He and environmental suitability would then reflect the effects of variable population size in geographical space that, under distinct environmental conditions, leads to a well-known pattern in which larger populations are able to maintain more genetic diversity. Thus, we assume that the environmental models used here are mechanistically related to species niche and this is justified by using the term Ecological Niche Modeling (ENM) to define the models used here (according to the terminology proposed by Araujo & Peterson 2012).
From a methodological point of view, our analyses show a high uncertainty associated with ENMs and AOGCMs for D. alata in the Brazilian Cerrado. However, if all models are equivalent and capture different aspects of ecological niches and environmental suitability, then the distribution of correlations of randomly generated ensembles does suggest a positive correlation, with a confidence interval that does not include zero. Our method validates that ensembles may be a powerful approach to eliminate idiosyncrasies of various models (see Tessarolo et al. 2014 for a theoretical analysis based on simulated data). More importantly, our method also allows for the establishment of the variance of the statistics of interest under randomly generated ensembles and can thus determine whether any analyses are providing statistically significant results.
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The advantage of the randomly generated model ensembles that Araújo and New (2007) propose is that it may be difficult to adequacy define models using currently available performance statistics (such as AUC or TSS), particularly because of their different properties (used to broadly define the “classes” by Rangel & Loyola 2012). Thus, it is not straightforward to state that models with a better fit would necessarily provide higher correlations with He. Conversely, it is difficult to interpret the meaning of ensembles because different models possess different fit and ecological or biological interpretations (see Peterson et al. 2012). The approach that we propose in this study overcomes this problem.
An additional, important issue is that, as noted in a previous study (Torres et al. 2012), not all methods provide high correlations between suitability and abundance; further, this correlation is also not necessarily related to model fit statistics. Thus, it is possible that some of the models provide more informative results for the correlation of suitability with He, regardless of their fit (although machine learning methods, which possess a higher fit in TSS, on average, tend to provide a higher correlation with He - see Table 1). Thus, although we do not have data on abundance for the 25 populations of D. alata that we analyzed, it may be useful to evaluate which models or model combinations provide higher correlations between environmental suitability and He.
On average, higher correlations were found when modeling suitability using GARP and MAXENT and not for simple envelope models, such as BIOCLIM (although BIOCLIM with CCSM provide a correlation that is much higher than the mean or full ensemble, equal to 0.503). The MAXENT is one of the most popular methods available today (Elith et al. 2011), though criticisms related to over-fitting are common (Franklin 2009; Peterson et al. 2012). Torres et al. (2012) found a higher correlation between abundance and ENM
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predictors for simple envelope models, although MAXENT also provided significant results. However, Martínez-Meyer et al. (2012) recently found significant correlations between abundance and ENM predictions using GARP, similar to our results. Torres et al. (2012) indeed noted that the simplest methods would better capture abundance because they would better reflect overall niche properties driving abundance, but this will only hold under strong equilibrium between occurrences and models and on much broader geographical scales. Indeed, previous analyses of D. alata showed strong potential non-equilibrium between species and climate and range expansion in the Cerrado since the Last Glacial Maximum (Terribile et al. 2012; unpublished data). Additionally, in our analyses, the correlation between He and abundance (presumably estimated by ENM suitability) occurred on a much smaller scale than that analyzed by Torres et al. (2012). It would therefore be expected that more sophisticated methods, which capture more complexity in the relationship between the environment and occurrence or abundance, work better than simple bioclimatic envelope models.
There is also a clear pattern with the AOGCMs, and it is interesting to highlight that the highest correlation based on CCSM suggests that some models may be more appropriate for modeling suitability across tropical regions. Indeed, this model was shown to perform better in predicting precipitation patterns in such regions (Schaller et al. 2011). Differences between AOGCM predictions are expected due to differences in initial conditions, parameters, and structural uncertainties in the experimental design of each climate model (Knutti et al. 2010), which has motivated the wide application of ensemble approaches in most studies of niche and species distribution modeling (Buisson et al. 2010, Collevatti et al. 2013b, 2014). However, our study indicates that some models might perform better in certain areas, thus supporting the idea of selecting models after a careful prediction assessment
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according to the aims of the study can better results. Our simulations also provide a new approach for investigating how ensembles can be used to determine which combination of ENMs and AOGCMs provide more informative results and about the variance of the ensemble strategy.
In conclusion, our analyses clearly show that coupling wide-ranging genetic data with ENM predictions would provide interesting results and that using our approach may be useful for showing how uncertainty will affect ecological or biological conclusions. Our new approach using ensembles generated by random combination of models suggests a positive correlation between He and environmental suitability. Additionally, analyses of individual ENMs also suggest that using full ensembles (which provide, in principle, non-significant results) may give misleading results. Much higher correlations were observed here for some combinations of ENMs and AOGCMs based on machine-learning methods. Regardless, as noted by Diniz-Filho et al. (2009b), it is usually of more interest to understand how ENMs and AOGCMs vary. Our results bring to phylogeography and populations genetics a methodological discussion about variation among ENMs that has plagued the ecological literature for the last 10 years. Caution is necessary when choosing a method or a climatic dataset for modeling species, but the approach that we propose is able to evaluate the ability of ensembles to detect patterns of interest (such as the correlation between suitability and He). Our advice, based on the current analyses and our previous experience with ENMs, is to optimize ensemble approaches to forecast and/or hindcast environmental suitability and geographical ranges to evaluate how uncertainty will qualitatively change ecological and evolutionary interpretations.
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Acknowledgements We thank three anonymous reviewers for many suggestions that improved previous versions of this paper. Our research program integrating macroecology and molecular ecology of plants has been continuously supported by several grants and fellowships to the research network GENPAC (“Geographical Genetics and Regional Planning for natural resources in Brazilian Cerrado”) from CNPq/MCT/CAPES/FAPs and CNPq “Universal” 474141/2012-8, and by the “Núcleo de Excelência em Genética e Conservação de Espécies do Cerrado” GECER (PRONEX/FAPEG/CNPq CP07-2009). We thank Thiago F. Rangel for providing access to computational platform BIOENSEMBLES. JAFDF, JCN, LCT, MPCT and TNS are also supported by productivity grants from CNPq.
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Collevatti RG, Terribile LC, Oliveira G, Lima-Ribeiro MS, Nabout JC, Rangel TF, Diniz-Filho JAF (2013b) Drawbacks in paleodistribution modelling: the case of South American seasonally dry forests. J. Biogeogr, 40, 345-358. Colwell RK, Rangel TF (2009) Hutchinson's duality: The once and future niche. Proceedings of the National Academy of Sciences USA, 106, 19644-19650. Diniz-Filho JAF, Nabout JC, Bini LM, Soares TN, Telles MPC, de Marco Jr P, Collevatti RG (2009a) Niche modelling and landscape genetics of Caryocar brasiliense (“Pequi” tree: Caryocaraceae) in Brazilian Cerrado: an integrative approach for evaluating central–peripheral population patterns. Tree Gen Geno, 5, 617-627. Diniz-Filho JAF, Bini LM, Rangel TF, Loyola RD, Hof C, Nogues-Bravo D, Araújo MB (2009b) Partitioning and mapping uncertainties in ensembles of forecasts of species turnover under climate change. Ecography, 32, 897-906. Diniz-Filho JAF, Melo DB, Oliveira G, Collevatti RG, Soares TN, Nabout JC, Lima JS, Dobrowolski R, Chaves LJ, Naves RV, Telles MPC (2012) Planning for optimal conservation of geographical genetic variability within species. Conser. Genetics 13:1085-1093. Dutilleul, P (1993) Modifying the t test for assessing the correlation between two spatial processes. Biometrics, 49, 305-314. Eckert CG, Samis KE, Lougheed SC (2008) Genetic variation across species' geographical ranges: the central-marginal hypothesis and beyond. Mol Ecol 17:1170-1188. Elith J, Graham C (2009) Do they? How do they? why do they differ? — on finding reasons for differing performances of species distribution models. Ecography, 32, 66-77. Elith J, Phillips SJ, Hastie T, Dudík M, Chee, YE, Yates CJ (2011) A statistical explanation of MaxEnt for ecologists. Divers Distrib, 17, 43-57. Franklin J (2009) Mapping species distribution: spatial inference and prediction. Cambridge Univ. Press, Cambridge. Fitzpatrick MC, Gotelli NJ, Ellison AM (2013) MaxEnt versus MaxLike: empirical comparisons with ant species distributions. Ecosphere, 4, art55. Goudet J (2005) Hierfstat, a package for R to compute and test variance components and F-statistics. Mol Ecol Notes, 5, 184-186.
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Jimenez-Valverde A, Lobo JM, Hortal (2008) Not as good as they seem: the importance of concepts in species distribution modelling. Diversity and Distributions, 14, 885-890. Lima NE, Lima-Ribeiro MS, Tinoco CF, Terribile LC, Collevatti RG (2014) Phylogeography and ecological niche modelling, coupled with the fossil pollen record, unravel the demographic history of a Neotropical swamp palm through the Quaternary. J Biogeogr, 41, 673–686. Lira-Noriega A, Manthey JD (2014) Relationship of genetic diversity and niche centrality: a survey and analysis. Evolution, 68, 1082–1093. Martínez-Meyer E, Diáz-Porras D, Peterson AT, Yánez-Arenas (2012) Ecological niche structure and rangewide abundance patterns of species. Biol Lett, 9, 1-5. Nabout JC, Oliveira G, Magalhães MR, Terribile LC, Severo FA (2011) Global climate change and the production of Pequi fruits (Caryocar brasiliense) in the Brazilian Cerrado. Nat Conser, 9, 5560. Oliveira, G, Rangel TF, Lima-Ribeiro MS, Terribile LC, Diniz-Filho JAF (2014) Evaluating, partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records. Ecography, 37, 637-647. Peterson AT, Soberón J, Pearson RG, Anderson RP, Martínez-Meyer E, Nakamura M, Araújo MB (2011) Ecological niches and geographical distributions. Princeton Univ. Press, Princeton. Rangel TF, Loyola RD (2012) Labeling ecological niche models. Nat Conser, 10, 119-126. Richards CL, Carstens BC, Knowles LL (2007) Distribution modeling and statistical phylogeography: an integrative framework for testing biogeographic hypotheses. J. Biogeogr, 34, 1833-1845. Soares TN, Chaves LJ, Telles MPC, Diniz-Filho JAF, Resende LV (2008) Landscape conservation genetics of Dipteryx alata (“baru” tree: Fabaceae) from Cerrado region of central Brazil.Genetica. Genetica 132:9-19. Soares TN, Melo DB, Resende LV, Vianello RP, Chaves LJ, Collevatti RG, Telles MPC (2012) Development of microsatellite markers for the neotropical tree species Dipteryx alata (Fabaceae). Am J Bot, 99, E72-E73. Soares TN, Diniz-Filho JAF, Nabout JC, Telles MPC, Terribile LC, Chaves LJ (2014). Patterns of genetic variability in central and peripheral populations of Dipteryx alata (Fabaceae) in the Brazilian Cerrado. Plant Systematics and Evolution (online early).
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DATA ACCESSIBILITY The following data and achieves are available from DRYAD http://dx.doi.org/10.5061/dryad.3cp3t:
- Sampling localities, codes, latitudes and longitudes, Heterozygosity for 25 populations of D. alata in Brazilian Cerrado (Baru25pops.xlsx)
- Genotypes for 8 microsatellite loci for 642 individuals of D. alata from 25 populations (baru_FSTAT_8loci.dat)
- R-script for the analyses shown in this paper, including generating heterozygosity by
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resampling and the random selection of ENMs for ensemble correlations (ENM_selection.R)
- Vector of heterozygosity used in the analyses (he.txt)
- Environmental suitabilities of ENMs in the 25 populations of D. alata (ENM.txt)
- Occurrence records for D. alata in Brazilian Cerrado (D_alata_occurrence_records.txt)
- Occurrence records in a Neotropical grid with resolution of 0.5o (D_alata_neotropic_grid.txt), used in BIOENSEMBLES;
- One of the environmental data (CCSM climatic model for current time) in the Neotropical grid
used
in
the
modeling
(be_biovar_CCSM_0k_neotropic.txt
-
other
process similar
www.ecoclimate.org)
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with data
sets
BIOENSEMBLES are
available
at
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Table 1. Mean correlation between expected heterozygosity He and environmental suitability (r) for different methods for Ecological Niche Modeling (ENM) and climatic models (AOGCM), and for different classes of methods (see Rangel & Loyola 2012). F is the frequency of ENMs/AOGCMs appearing in the 10,000 random combinations of models providing highest correlations between He and suitability. Source ENM
Model BIOCLIM ED ENFA FDA GAM GBM GD GLM GARP MARS MD MAXENT ANN RNDFOR
r F 0.089 -0.028 0.070 0.078 0.283 0.136 -0.073 -0.093 0.262 0.170 -0.104 0.353 0.345 0.105
0.14 0.02 0.13 0.12 0.19 0.08 0.15 0.08 0.28 0.14 0.08 0.20 0.16 0.05
AOGCM
CCSM GISS MIROC MRI
0.197 -0.048 -0.009 -0.043
0.17 0.09 0.13 0.11
CLASS
Envelope Statistical ML
0.167 -0.097 0.291
-
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Figure legends Figure 1. Modeled geographic distribution of Dipteryx alata in Brazilian Cerrado, shown as the average frequency of 14 ENMs and 4 AOGCMs. Red regions indicate more overlap of models and higher environmental suitability. Circles indicate values of He per 25 populations estimated using microsatellite data.
Figure 2. Relationship between expected He and suitability, for ensemble of all ENMs and AOGCMs (A), for MAXENT (B), and GARP (C). Correlations were, respectively, 0.237, 0.437 and 0.377.
Figure 3. Frequency distribution of correlations between He and suitability, using 10,000 random combinations of ENMs and AOGCMs creating ensembles. Highest correlation of 0.685 was produced by averaging GARP and GAM modeled using CCSM.
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Received Date : 16-Aug-2014 Revised Date : 05-Jan-2015 Accepted Date : 12-Jan-2015 Article type
: Resource Article
Correlation between genetic diversity and environmental suitability: taking uncertainty from ecological niche models into account
JOSÉ ALEXANDRE F. DINIZ-FILHO1*; HAUANNY RODRIGUES2; MARIANA PIRES DE CAMPOS TELLES3; GUILHERME DE OLIVEIRA4; LEVI CARINA TERRIBILE5; THANNYA NASCIMENTO SOARES4 ; and JOÃO CARLOS NABOUT3 1. Departamento de Ecologia, Universidade Federal de Goiás (UFG), Goiânia, Goiás, Brasil; 2. Programa de Pós-Graduação em Genética & Biologia Molecular, Instituto de Ciências Biológicas, UFG; 3. Instituto de Ciências Biológicas, Departamento de Genética, UFG, Goiânia, Goiás, Brasil; 4. Centro de Ciências Agrárias, Ambientais e Biológicas, Setor de Biologia, Universidade Federal do Recôncavo da Bahia (UFRB), Cruz das Almas, BA, Brasil; 5. Laboratório de Macroecologia, Regional Jataí, UFG, Goiás, Brasil; 6. Universidade Estadual de Goiás (UEG), Unidade de Ciências Exatas e Tecnológicas, Anápolis, Goiás, Brasil.
*Correspondence to: José Alexandre Felizola Diniz-Filho, Universidade Federal de Goiás (UFG), Instituto de Ciências Biológicas, Departamento de Ecologia, Cx.P. 131, 74001-970 Goiânia, GO. Telephone: +55 62 3521-1752; E-mail: [email protected]
Author contributions: JAFD-F designed the study and wrote the first draft; HR performed correlation and uncertainty analyses; JCN, GO and LCT obtained occurrence and This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1111/1755-0998.12374 This article is protected by copyright. All rights reserved.
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environmental data and performed the niche models; MPCT and TNS performed field work and molecular analyses. All authors significantly contributed to the final version of the manuscript.
Keywords: heterozygosity, niche modelling, uncertainty, suitability, tropical tree, Cerrado.
ABSTRACT The hindcast of shifts in the geographical ranges of species as estimated by Ecological Niche Modeling (ENM) has been coupled with phylogeographical patterns, allowing the inference of past processes that drove population differentiation and genetic variability. However, more recently, some studies have suggested that maps of environmental suitability estimated by ENM may be correlated to species’ abundance, raising the possibility of using environmental suitability to infer processes related to population demographic dynamics and genetic variability. In both cases, one of the main problems is that there is a wide variation in ENM development methods and climatic models. In this study, we analyze the relationship between heterozygosity (He) and environmental suitability from multiple ENMs for 25 population estimates for Dipteryx alata, a widely distributed, endemic tree species of the Cerrado region of Central Brazil. We propose a new approach for generating a statistical distribution of correlations under randomly generated ENM. The confidence intervals from these distributions indicate how model selection with different properties affects the ability to detect a correlation of interest (e.g., the correlation between He and suitability). Additionally, our approach allows us to explore which particular ensemble of ENMs produces the better result for finding an association between environmental suitability and He. Caution is necessary when choosing a method or a climatic dataset for modeling geographic distributions, but the new approach proposed here provides a conservative way to evaluate the ability of ensembles to detect patterns of interest.
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INTRODUCTION Ecological Niche Modeling (ENM; see Jimenez-Valverde et al. 2008; Araújo & Peterson 2012) has been widely used to describe the potential geographic distribution of a species, under the assumption that the environmental variables that comprise ecological niches can be used to describe the suitability of regions within the species’ range, particularly at broad scales (Soberon 2007; Colwell & Rangel 2011). ENMs can be built using several methods or algorithms that attempt to correlate the occurrence of a species and environmental data. Once a model is fitted, the results can be projected into environmental data obtained for other regions or time frames (past or future). Thus, the ENM models provide an adequate and relatively simple approach to infer changes in the geographical distribution of a species under biological invasions or climate changes (Franklin 2009; Peterson et al. 2011).
Some studies have shown that besides the inference of broad scale geographical ranges, the ENM map of environmental suitability within a species range, which indicates the probability of occurrence or “distance” to optimum environmental conditions, may be correlated to the species’ abundance (e.g., Nabout et al. 2011; Torres et al. 2012; MartínezMeyer et al. 2012). This opens the possibility of using these environmental suitability estimates to infer demographic data, which, in turn, can be related to the genetic variability of a population across geographical space (Hedrick 2008). This relationship, for example, would be the basis of several geographic patterns of genetic diversity, such the loss of genetic diversity along environmental gradients or central-peripheral patterns (e.g., Vucetich and Waite 2003; Eckert et al. 2008; Diniz-Filho et al. 2009a; Lira-Noriega & Manthey 2014).
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The hindcast of environmental suitability and shifts in geographical range limits has also been coupled with phylogeographical patterns, allowing for the inference of past processes that have driven population differentiation and genetic variability (e.g., Richards et al. 2007; see Alvarado-Serrano & Knowles 2014 for a recent review). Despite the enormous gain in knowledge obtained by coupling ENMs with genetic and phylogeographic data, there are some potential pitfalls in this association, and a careful evaluation of models and scenarios is necessary (see Alvarado-Serrano & Knowles 2014).
Alvarado-Serrano and Knowles (2014) stressed the applications, advances and precautions of using ENMs in phylogeographical studies. However, one of the most important sources of uncertainty in ENMs, which is not discussed in detail by those authors, is the variation among the predictions from the different methods used in the modeling process and the variation among climatic data, which causes significant uncertainty in environmental suitability estimates (Araújo & New 2007; Elith & Graham 2009; Diniz-Filho et al 2009b; Buisson et al. 2010; Rangel & Loyola 2012; Fitzpatrick et al. 2013). Our goal in this study was to evaluate the relationship between ENM-predicted environmental suitability and the genetic diversity of Dipteryx alata (Fabaceae) populations (a socio-economically important tree species that is widely distributed throughout the Cerrado region of Central Brazil), considering the uncertainty associated with ENM methods and climatic data used in the modeling process.
Previous genetic analyses of D. alata across its geographic range showed a significant amount of population structure both among and within populations (Soares et al. 2008; Collevatti et al. 2010, 2013a; Diniz-Filho et al. 2012). Recently, Soares et al. (2014) used an ensemble forecast approach and showed that genetic diversity within a population, as
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(ENFA), Euclidian Distance (ED), Gower Distance (GD), Mahalanobis Distance (MD); 2) Statistical methods: Generalized Linear Models (GLM), Generalized Additive Models (GAM); and 3) Machine Learning methods: Genetic Algorithm for Rule Set Production (GARP), Maximum Entropy (Maxent), Flexible Discriminant Analysis (FDA), Multivariate Adaptive Regression Splines (MARS), Generalized Boosted Models (GBM), Neural Networks (ANN) and Random Forest (RNDFOR).
The methods above were used to correlate the occurrences of D. alata with five environmental variables (mean annual temperature and temperature range, precipitation during the wettest month, precipitation during the driest month, and precipitation during warmest quarter) that were derived from four coupled Atmosphere-Ocean Global Circulation Climatic Models (AOGCMs, which are CCSM, GISS, MIROC and MRI) along with subsoil pH. (climate data can be downloaded from http://ecoclimate.org; see “Data Accessibility” section for subsoil pH data). Thus, a total of 2800 geographic distribution models for D. alata (14 ENMs X 4 AOGCMs X 50 cross-validation replications) were generated (see Terribile et al 2012 for details on data and modeling). Overlaying all of these maps allowed us to calculate the frequency of models that indicate the presence of the species in a given cell grid, which was used as an overall surrogate of environmental suitability (the ‘ensemble’ forecasting approach – see Araújo & New 2007; Diniz-Filho et al. 2009).
Each map of environmental suitability for each of the 14 ENMs and four AOCGM combinations was overlaid with the geographical coordinates of the 25 D. alata populations for which genetic data were available to define their “local” suitability. The suitability was then correlated to the He values using Pearson’s correlations (significance tests were based on geographically effective degrees of freedom using Dutilleul’s 1993 correction). We then
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used a model II two-way Analysis of Variance (ANOVA) without replication to evaluate how sources of uncertainty (methods or AOGCMs, used as factors in ANOVA) contribute to variation in the correlation between suitability and He (Diniz-Filho et al. 2009; Buisson et al. 2010; de Oliveira et al. 2014).
We also used a new approach to evaluate how different combinations of models (ensembles) provide correlations between environmental suitability and He among the 25 populations. Although it is simple to combine all models into a “full” ensemble (as originally proposed by Araújo & New 2007), this approach assumes that all models are equally adequate and provide random variation around the “true” environmental envelope or geographic distribution. Because this may not necessarily be accurate, a simple alternative is to analyze correlations for each method or obtain correlations with ensembles for different “classes” of models (Rangel & Loyola 2012). In this study, we statistically expand this last reasoning by generating 10,000 random model combinations (both ENMs and AOGCMs) and varying the number of models selected in each combination. We then calculated the mean suitability for each particular ensemble-producing combination and correlated this to He. Thus, we generated a statistical distribution of correlations under randomly generated ensembles, and the confidence interval of the distributions indicates how the selection of the various models affects our ability to detect the correlation of interest. With the approach, we propose that it is possible to determine whether the model selected by a researcher when generating an ensemble will qualitatively affect their ability to detect the pattern of interest (i.e., the correlation between He and suitability). At the same time, this approach allows us to explore whether the predictions from particular ensembles of ENM methods and climate models are better suited for finding an association between environmental suitability and He.
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An R-script for performing these analyses is provided on Dryad (see “Data Accessibility” section).
RESULTS There is no significant correlation between mean suitability (full ensemble) and He values among the 25 populations of D. alata (r = 0.237; P = 0.224 with 19 degrees of freedom according to Dutilleul correction) (Fig. 2A). However, this correlation varies based on different combinations of ENM and AOGCM, with the highest value of 0.59 found for the combination of GARP based on CCSM environmental data and the lowest value of -0.341 found for FDA, based on MRI environmental data. The mean of the correlations across all ENMs and AOGCMs was equal to 0.122 (this is smaller than the correlation with ensemble models) (Table 1). Ensembles of different method classes (envelope, statistical and machine learning) also produce different correlations with He, with the highest values obtained for machine learning methods (r = 0.292).
The correlations derived from the 10,000 random combinations of ENMs and AOGCM (Fig. 3) was, on average, equal to 0.215 ± 0.109, ranging from -0.346 to 0.685. The 95% confidence interval does not encompass zero (0.00028 – 0.429), with only 4% of the correlations smaller than zero (Fig. 3), suggesting that regardless of the model combinations used to generate the ensemble, there is a tendency for finding a positive correlation between He and suitability.
In the randomly generated ensembles, the highest correlation of 0.685 was generated by the combination of GARP and GAM, both based on CCSM data. The second highest correlation of 0.667 was generated by the combination of GARP and MAXENT, also based
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on CCSM data. In fact, the GARP-CCSM model appears in all of the top 1% of the correlations of suitability and He, followed by MAXENT-CCSM and GAM-CCSM. The frequency of ENMs and AOGCMs in the top 10% of model combinations that generated the highest correlations with He (Table 1) is GARP, MAXENT and GAM (all modeled using CCSM), in that order.
An ANOVA showed that most of the variation among correlations was due to the effect of ENM, explaining 36% of the variance (compared to 16% for the effect of AOGCM). The highest mean correlation of ENMs (across the AOGCMs) was obtained for MAXENT (Fig. 2B), followed by GARP (Fig. 2C) and Neural Networks. The correlation between the He and MAXENT predictions is leveraged by the three populations despite being relatively high and significant (r = 0.438; P = 0.037). For the AOGCMs, only CCSM (across all ENMs) provided relatively high correlations.
DISCUSSION Our main finding in this study is that inferences based on ENMs, as performed here for the correlation between environmental suitability and heterozygosity, can vary drastically due to uncertainty from the methods and climatic data. Explicitly accounting for this uncertainty can allow for a better evaluation of how conclusions are qualitatively affected (Diniz-Filho et al. 2009). The approach of generating random ensembles to generate an statistical distribution that allows the evaluation of uncertainty would qualitatively affect the interpretation of the pattern of interest and, in our analyses, supports a positive correlation between He and ENM suitability. Of course, the proposed approach, although used here for testing the correlation between ENMs and He, can be generalized to any approach coupling ENM and phylogeography or population genetics.
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A significant and positive correlation between He and ENM suitability, as observed here for some models and based on randomly generated ensembles, can be interpreted as an effect of neutral dynamics with variable population densities, under the assumption that higher environmental suitability leads to higher population densities (Diniz-Filho et al. 2009a; Nabout et al. 2011; Van Der Wal et al. 2009; Tôrres et al. 2012; Lira-Noriega & Manthey 2014). The correlation between He and environmental suitability would then reflect the effects of variable population size in geographical space that, under distinct environmental conditions, leads to a well-known pattern in which larger populations are able to maintain more genetic diversity. Thus, we assume that the environmental models used here are mechanistically related to species niche and this is justified by using the term Ecological Niche Modeling (ENM) to define the models used here (according to the terminology proposed by Araujo & Peterson 2012).
From a methodological point of view, our analyses show a high uncertainty associated with ENMs and AOGCMs for D. alata in the Brazilian Cerrado. However, if all models are equivalent and capture different aspects of ecological niches and environmental suitability, then the distribution of correlations of randomly generated ensembles does suggest a positive correlation, with a confidence interval that does not include zero. Our method validates that ensembles may be a powerful approach to eliminate idiosyncrasies of various models (see Tessarolo et al. 2014 for a theoretical analysis based on simulated data). More importantly, our method also allows for the establishment of the variance of the statistics of interest under randomly generated ensembles and can thus determine whether any analyses are providing statistically significant results.
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The advantage of the randomly generated model ensembles that Araújo and New (2007) propose is that it may be difficult to adequacy define models using currently available performance statistics (such as AUC or TSS), particularly because of their different properties (used to broadly define the “classes” by Rangel & Loyola 2012). Thus, it is not straightforward to state that models with a better fit would necessarily provide higher correlations with He. Conversely, it is difficult to interpret the meaning of ensembles because different models possess different fit and ecological or biological interpretations (see Peterson et al. 2012). The approach that we propose in this study overcomes this problem.
An additional, important issue is that, as noted in a previous study (Torres et al. 2012), not all methods provide high correlations between suitability and abundance; further, this correlation is also not necessarily related to model fit statistics. Thus, it is possible that some of the models provide more informative results for the correlation of suitability with He, regardless of their fit (although machine learning methods, which possess a higher fit in TSS, on average, tend to provide a higher correlation with He - see Table 1). Thus, although we do not have data on abundance for the 25 populations of D. alata that we analyzed, it may be useful to evaluate which models or model combinations provide higher correlations between environmental suitability and He.
On average, higher correlations were found when modeling suitability using GARP and MAXENT and not for simple envelope models, such as BIOCLIM (although BIOCLIM with CCSM provide a correlation that is much higher than the mean or full ensemble, equal to 0.503). The MAXENT is one of the most popular methods available today (Elith et al. 2011), though criticisms related to over-fitting are common (Franklin 2009; Peterson et al. 2012). Torres et al. (2012) found a higher correlation between abundance and ENM
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predictors for simple envelope models, although MAXENT also provided significant results. However, Martínez-Meyer et al. (2012) recently found significant correlations between abundance and ENM predictions using GARP, similar to our results. Torres et al. (2012) indeed noted that the simplest methods would better capture abundance because they would better reflect overall niche properties driving abundance, but this will only hold under strong equilibrium between occurrences and models and on much broader geographical scales. Indeed, previous analyses of D. alata showed strong potential non-equilibrium between species and climate and range expansion in the Cerrado since the Last Glacial Maximum (Terribile et al. 2012; unpublished data). Additionally, in our analyses, the correlation between He and abundance (presumably estimated by ENM suitability) occurred on a much smaller scale than that analyzed by Torres et al. (2012). It would therefore be expected that more sophisticated methods, which capture more complexity in the relationship between the environment and occurrence or abundance, work better than simple bioclimatic envelope models.
There is also a clear pattern with the AOGCMs, and it is interesting to highlight that the highest correlation based on CCSM suggests that some models may be more appropriate for modeling suitability across tropical regions. Indeed, this model was shown to perform better in predicting precipitation patterns in such regions (Schaller et al. 2011). Differences between AOGCM predictions are expected due to differences in initial conditions, parameters, and structural uncertainties in the experimental design of each climate model (Knutti et al. 2010), which has motivated the wide application of ensemble approaches in most studies of niche and species distribution modeling (Buisson et al. 2010, Collevatti et al. 2013b, 2014). However, our study indicates that some models might perform better in certain areas, thus supporting the idea of selecting models after a careful prediction assessment
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according to the aims of the study can better results. Our simulations also provide a new approach for investigating how ensembles can be used to determine which combination of ENMs and AOGCMs provide more informative results and about the variance of the ensemble strategy.
In conclusion, our analyses clearly show that coupling wide-ranging genetic data with ENM predictions would provide interesting results and that using our approach may be useful for showing how uncertainty will affect ecological or biological conclusions. Our new approach using ensembles generated by random combination of models suggests a positive correlation between He and environmental suitability. Additionally, analyses of individual ENMs also suggest that using full ensembles (which provide, in principle, non-significant results) may give misleading results. Much higher correlations were observed here for some combinations of ENMs and AOGCMs based on machine-learning methods. Regardless, as noted by Diniz-Filho et al. (2009b), it is usually of more interest to understand how ENMs and AOGCMs vary. Our results bring to phylogeography and populations genetics a methodological discussion about variation among ENMs that has plagued the ecological literature for the last 10 years. Caution is necessary when choosing a method or a climatic dataset for modeling species, but the approach that we propose is able to evaluate the ability of ensembles to detect patterns of interest (such as the correlation between suitability and He). Our advice, based on the current analyses and our previous experience with ENMs, is to optimize ensemble approaches to forecast and/or hindcast environmental suitability and geographical ranges to evaluate how uncertainty will qualitatively change ecological and evolutionary interpretations.
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Acknowledgements We thank three anonymous reviewers for many suggestions that improved previous versions of this paper. Our research program integrating macroecology and molecular ecology of plants has been continuously supported by several grants and fellowships to the research network GENPAC (“Geographical Genetics and Regional Planning for natural resources in Brazilian Cerrado”) from CNPq/MCT/CAPES/FAPs and CNPq “Universal” 474141/2012-8, and by the “Núcleo de Excelência em Genética e Conservação de Espécies do Cerrado” GECER (PRONEX/FAPEG/CNPq CP07-2009). We thank Thiago F. Rangel for providing access to computational platform BIOENSEMBLES. JAFDF, JCN, LCT, MPCT and TNS are also supported by productivity grants from CNPq.
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Collevatti RG, Terribile LC, Oliveira G, Lima-Ribeiro MS, Nabout JC, Rangel TF, Diniz-Filho JAF (2013b) Drawbacks in paleodistribution modelling: the case of South American seasonally dry forests. J. Biogeogr, 40, 345-358. Colwell RK, Rangel TF (2009) Hutchinson's duality: The once and future niche. Proceedings of the National Academy of Sciences USA, 106, 19644-19650. Diniz-Filho JAF, Nabout JC, Bini LM, Soares TN, Telles MPC, de Marco Jr P, Collevatti RG (2009a) Niche modelling and landscape genetics of Caryocar brasiliense (“Pequi” tree: Caryocaraceae) in Brazilian Cerrado: an integrative approach for evaluating central–peripheral population patterns. Tree Gen Geno, 5, 617-627. Diniz-Filho JAF, Bini LM, Rangel TF, Loyola RD, Hof C, Nogues-Bravo D, Araújo MB (2009b) Partitioning and mapping uncertainties in ensembles of forecasts of species turnover under climate change. Ecography, 32, 897-906. Diniz-Filho JAF, Melo DB, Oliveira G, Collevatti RG, Soares TN, Nabout JC, Lima JS, Dobrowolski R, Chaves LJ, Naves RV, Telles MPC (2012) Planning for optimal conservation of geographical genetic variability within species. Conser. Genetics 13:1085-1093. Dutilleul, P (1993) Modifying the t test for assessing the correlation between two spatial processes. Biometrics, 49, 305-314. Eckert CG, Samis KE, Lougheed SC (2008) Genetic variation across species' geographical ranges: the central-marginal hypothesis and beyond. Mol Ecol 17:1170-1188. Elith J, Graham C (2009) Do they? How do they? why do they differ? — on finding reasons for differing performances of species distribution models. Ecography, 32, 66-77. Elith J, Phillips SJ, Hastie T, Dudík M, Chee, YE, Yates CJ (2011) A statistical explanation of MaxEnt for ecologists. Divers Distrib, 17, 43-57. Franklin J (2009) Mapping species distribution: spatial inference and prediction. Cambridge Univ. Press, Cambridge. Fitzpatrick MC, Gotelli NJ, Ellison AM (2013) MaxEnt versus MaxLike: empirical comparisons with ant species distributions. Ecosphere, 4, art55. Goudet J (2005) Hierfstat, a package for R to compute and test variance components and F-statistics. Mol Ecol Notes, 5, 184-186.
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DATA ACCESSIBILITY The following data and achieves are available from DRYAD http://dx.doi.org/10.5061/dryad.3cp3t:
- Sampling localities, codes, latitudes and longitudes, Heterozygosity for 25 populations of D. alata in Brazilian Cerrado (Baru25pops.xlsx)
- Genotypes for 8 microsatellite loci for 642 individuals of D. alata from 25 populations (baru_FSTAT_8loci.dat)
- R-script for the analyses shown in this paper, including generating heterozygosity by
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resampling and the random selection of ENMs for ensemble correlations (ENM_selection.R)
- Vector of heterozygosity used in the analyses (he.txt)
- Environmental suitabilities of ENMs in the 25 populations of D. alata (ENM.txt)
- Occurrence records for D. alata in Brazilian Cerrado (D_alata_occurrence_records.txt)
- Occurrence records in a Neotropical grid with resolution of 0.5o (D_alata_neotropic_grid.txt), used in BIOENSEMBLES;
- One of the environmental data (CCSM climatic model for current time) in the Neotropical grid
used
in
the
modeling
(be_biovar_CCSM_0k_neotropic.txt
-
other
process similar
www.ecoclimate.org)
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with data
sets
BIOENSEMBLES are
available
at
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Table 1. Mean correlation between expected heterozygosity He and environmental suitability (r) for different methods for Ecological Niche Modeling (ENM) and climatic models (AOGCM), and for different classes of methods (see Rangel & Loyola 2012). F is the frequency of ENMs/AOGCMs appearing in the 10,000 random combinations of models providing highest correlations between He and suitability. Source ENM
Model BIOCLIM ED ENFA FDA GAM GBM GD GLM GARP MARS MD MAXENT ANN RNDFOR
r F 0.089 -0.028 0.070 0.078 0.283 0.136 -0.073 -0.093 0.262 0.170 -0.104 0.353 0.345 0.105
0.14 0.02 0.13 0.12 0.19 0.08 0.15 0.08 0.28 0.14 0.08 0.20 0.16 0.05
AOGCM
CCSM GISS MIROC MRI
0.197 -0.048 -0.009 -0.043
0.17 0.09 0.13 0.11
CLASS
Envelope Statistical ML
0.167 -0.097 0.291
-
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Figure legends Figure 1. Modeled geographic distribution of Dipteryx alata in Brazilian Cerrado, shown as the average frequency of 14 ENMs and 4 AOGCMs. Red regions indicate more overlap of models and higher environmental suitability. Circles indicate values of He per 25 populations estimated using microsatellite data.
Figure 2. Relationship between expected He and suitability, for ensemble of all ENMs and AOGCMs (A), for MAXENT (B), and GARP (C). Correlations were, respectively, 0.237, 0.437 and 0.377.
Figure 3. Frequency distribution of correlations between He and suitability, using 10,000 random combinations of ENMs and AOGCMs creating ensembles. Highest correlation of 0.685 was produced by averaging GARP and GAM modeled using CCSM.
This article is protected by copyright. All rights reserved.
Accepted Article This article is protected by copyright. All rights reserved.
Accepted Article This article is protected by copyright. All rights reserved.
Accepted Article This article is protected by copyright. All rights reserved.
Accepted Article This article is protected by copyright. All rights reserved.
Accepted Article This article is protected by copyright. All rights reserved.
