Identification of areas of endemism from species distribution models: threshold selection and Nearctic mammals

Identificación de áreas de endemismo a partir de modelos de distribución de especies: selección de umbrales y mamíferos neárticos

Tania Escalante¹*, Gerardo Rodríguez-Tapia², Miguel Linaje³, Patricia Illoldi-Rangel⁴ and Rafael González-López¹

¹ Museo de Zoología "Alfonso L. Herrera", Depto. de Biología Evolutiva, Facultad de Ciencias, Universidad Nacional Autónoma de México. Apdo. Postal 70-399, C.P. 04510, México, D.F. Correo: *tee@ibunam2.ibiologia.unam.mx, jrglezlpz@gmail.com

³ Lab. de Sistemas de Información Geográfica, Depto. de Zoología, Instituto de Biología, Universidad Nacional Autónoma de México. Correo: miglinaje@gmail.com

⁴ Biodiversity and Biocultural Conservation Laboratory, Section of Integrative Biology, University of Texas at Austin. Correo: patz30@gmail.com

Artículo recibido el 18 de junio de 2012.
Aceptado el 05 de febrero de 2013.

Abstract

We evaluated the relevance of threshold selection in species distribution models on the delimitation of areas of endemism, using as case study the North American mammals. We modeled 40 species of endemic mammals of the Nearctic region with Maxent, and transformed these models to binary maps using four different thresholds: minimum training presence, tenth percentile training presence, equal training sensitivity and specificity, and 0.5 logistic probability. We analyzed the binary maps with the optimality method in order to identify areas of endemism and compare our results regarding previous analyses. The majority of the species tend to have very low values for the minimum training presence, whereas most of the species have a value of the tenth percentile training presence around 0.5, and the equal training sensitivity and specificity was around 0.3. Only with the tenth percentile threshold we recovered three out of the four patterns of endemism identified in North America, and detected more endemic species. The best identification of areas of endemism was obtained using the tenth percentile training presence threshold, which seems to recover better the distributional area of the mammals analyzed.

Key Words: Analysis of endemicity, Mammalia, Maxent, Nearctic region, optimality.

Resumen

Evaluamos la relevancia de la selección del umbral en los modelos de distribución de especies en la delimitación de las áreas de endemismo, usando como un caso de estudio a los mamíferos de América del Norte. Modelamos 40 especies de mamíferos endémicos de la región Neártica con Maxent, y transformamos esos modelos a mapas binarios usando cuatro umbrales diferentes: presencia mínima de entrenamiento, percentil diez de la presencia de entrenamiento, igual sensibilidad y especificidad de entrenamiento, y probabilidad logística de 0.5. Los mapas binarios los analizamos con el método de optimación con el objeto de identificar áreas de endemismo y comparar nuestros resultados con estudios previos. La mayoría de las especies mostró tendencias hacia valores muy bajos de la presencia mínima de entrenamiento, mientras que la mayoría tuvo un valor del percentil diez de la presencia de entrenamiento alrededor de 0.5, y de igual sensibilidad y especificidad de entrenamiento alrededor de 0.3. Únicamente con el percentil diez de la presencia de entrenamiento se recuperaron tres de los cuatro patrones de endemismo identificados para América del Norte y se detectaron más especies endémicas. La identificación de áreas de endemismo más eficiente se obtuvo usando el umbral del percentil diez de la presencia de entrenamiento, el cual parece recuperar mejor las áreas de distribución de los mamíferos analizados.

Palabras Clave: Análisis de endemismo, Mammalia, Maxent, región Neártica, optimación.

Introduction

Species distribution models (also named ecological niche models) are commonly used in biogeography. In particular, although they are more suited for the identification of ecological biogeographical patterns, they also have important applications in the identification of historical biogeographical patterns, namely, generalized tracks¹ and areas of endemism^2-6 where models have been used to improve their delimitation.

There are many modeling techniques (GLM, GAM, GARP, ENFA, Maxent, etc.), which can be used depending on the available records (data) for each species, environmental data and the required accuracy of the models. Some comparisons of the different modeling techniques have been performed^7-9 and although there are no general conclusions, Maxent^10-12 seems to perform better than others. Maxent generates probability maps of species presence in three output formats: raw, cumulative and logistic (see Maxent tutorial, http://www.cs.princeton.edu/~schapire/maxent/), being the last two the most used (in scales of 0-100 and 0-1, respectively).

As in conservation and environmental management practices¹³, in biogeography sometimes it is necessary to transform probabilistic data to presence/absence data (binary maps, i.e. 1 - 0). For this to be feasible, a probability threshold has to be established to the minimun level at which the distributions should be left out. As there are many possible uses for distribution models, some methods have been proposed in order to select the best threshold in Maxent to obtain a binary map for species (see Table I). They include the minimum (or lowest) training presence, threshold of a particular percentage (10, 50, 80%), sensitivity at 95%, some percentile training presence (10, 20), equal training sensitivity and specificity, etc. (Pawar et al.¹⁴ for further details). However, there has been some comparisons and evaluations that might allow to select the best threshold for other modeling algorithms generally related with prevalence, sensitivity and specificity^13,15-17, and specifically for Maxent^18-20 (see Table I). So, there is not a consensus about which is the way to select the best threshold.

Areas of endemism are basic biogeographic units, their identification is the first step of an evolutionary biogeographic analysis and they are a pre-requisite of any cladistic biogeographic analysis²¹. An area of endemism is an area of non-random distributional congruence of two or more taxa²², and the basis of biogeographic regionalizations²³. The identification of areas of endemism depends totally on maps of distribution of species and their generalization to spatial units. The most used units of study are grid-cells, although it is possible to use other regular polygons or even polygons with irregular forms. The most popular methods (Parsimony Analysis of Endemicity²¹ and Endemicity analysis^24,25) employ data matrices of presence/absence of species in quadrats. Thus, the identification of areas of endemism can be affected by the generalization of individual areas of distribution to the grid-cells. Some authors^6,26 pointed that the use of species distribution models (or ecological niche models) can modify the identification of areas of endemism due to the overprediction involved in them; however, this has not been proved.

We evaluate herein the relevance of the selection of the threshold in Maxent using four different options (minimum training presence, tenth percentile training presence, equal training sensitivity and specificity and 0.5 logistic probability), and its impact on the delimitation of areas of endemism, using as study case the mammals of the Nearctic region.

Material and methods

We compiled a database of 40 species of endemic mammals of North America (following Escalante et al.²⁷) corresponding to five orders (Table II). Those species gave score to some area of endemism in that publication, and shown sympatric patterns. Records were obtained from a database of mammals of Mexico (Mammex; Escalante etal., unpublished data), and four on-line databases: GBIF (http://www.gbif.org/), MaNIS (http://manisnet.org/), CONABIO (Remib; http://www.conabio.gob.mx/), and UNIBIO (Instituto de Biología, UNAM; http://unibio.ibiologia.unam.mx/). A record is considered as a unique combination of the name of the species and georreferenced site (latitude-longitude) (Table II). Localities of each species were geographically validated in a Geographic Information System (GIS; ArcGis 9.3)²⁹, using specialized bibliography^30,31 and two websites: North American Mammals (http://www.mnh.si.edu/mna/) and Infonatura (http://www.natureserve.org/infonatura/).

To construct the models in Maxent, 23 environmental data layers were used at a resolution of ~2 km (which is suitable for our study area): four topographic layers were obtained from Hydro1k (http://edc.usgs.gov/products/elevation/gtopo30/hydro/namerica.html) while19 climatic data layers were derived from the WorldClim database (http://www.worldclim.org/³²: altitude, aspect, compound topographic index, slope, annual mean temperature, mean diurnal range, isothermality, temperature seasonality, maximum temperature of warmest month, minimum temperature of coldest month, temperature annual range, mean temperature of wettest quarter, mean temperature of driest quarter, mean temperature of warmest quarter, mean temperature of coldest quarter, annual precipitation, precipitation of wettest month, precipitation of driest month, precipitation seasonality, precipitation of wettest quarter, precipitation of driest quarter, precipitation of warmest quarter and precipitation of coldest quarter.

For each species, 25% of the records were used to validate the model internally. The algorithm of Maxent uses a series of rules to calculate probabilities. For the present analysis, all rules were used, so the program selects the adequate one depending on the number of available data. The used rules are: (a) linear, which uses the variable by itself; (b) quadratic, which uses the square of the variable; (c) product, which uses the product of two variables; (d) threshold, which uses a binary transformation (0, 1) of a continuous variable using a threshold; and (e) hinge, which is like the lineal rule, but remains constant under the threshold. The algorithm determines which rule to use like follows: lineal if there are < 10 points; lineal + cuadratic if there are 10-14 points; lineal + cuadratic + hinge if there are 15-79 points; and all if there are > 80 points (http://www.cs.princeton.edu/~schapire/maxent/tutorial/tutorial.doc). The logistic value output was selected because is the easiest to conceptualize since it gives an estimate between 0 and 1 of probability of presence (see http://www.cs.princeton.edu/~schapire/maxent/tutorial/tutorial.doc for further details).

Model success was judged using two criteria: AUC > 0.7, and p < 0.05 for at least one binomial test¹⁴, and both obtained from the program. AUC, or area under the curve, is an index used to evaluate models because it provides a single measure of overall accuracy that is not dependent upon a particular threshold⁴³. The value of the AUC ranges between 0 and 1.0. Values of 0.5 implies that the scores for two groups (random and model) do not differ, while a score of1.0 indicates no overlap in the distributions, and the model is reliable. A value of 0.8 for the AUC means that for 80% of the time a random selection from the positive group will have a score greater than a random selection from the negative class. It is important to note that AUC values tend to be higher for species with narrow ranges, relative to the study area described by the environmental data. This does not necessarily mean that the models are better; instead this behavior is an artifact of the AUC statistic⁴³.

Models were generated in ascii format, and exported directly to the GIS.We selected four of the most common used thresholds for Maxent models in logistic format: the minimum training presence, the tenth percentile training presence, the equal training sensitivity and specificity (obtained from the output table of Maxent), and a logistic probability of 0.5. All pixels with a value under those thresholds were assigned a value of zero (0), which would represent absence of the species.

To analyze the influence of the four thresholds on the delimitation of areas of endemism, the 40 endemic species were analyzed, in order to prove if we identify the patterns previously discovered²⁷. We overlapped and intersected the binary maps obtained for each species, using each one of the four thresholds (minimum training presence, tenth percentile training presence, equal training sensitivity and specificity and logistic probability of 0.5) to a 4° latitude-longitude grid. Then, we built four matrices of presence/absence (one for each threshold), where the predicted presence of a species was coded as "1" and its absence was coded as "0". We performed four analysis of endemicity with the optimality method^24,25, one for each threshold. The optimality method calculates a score of endemicity for a taxon to a given area (grid), so, the endemicity for an area will be the sum of the scores of two or more taxa inhabitting it. From among different possible areas, those with the highest scores of endemicity are preferred.

 /img/revistas/tip/v16n1/a4i1.jpg

Results

We obtained 40 models from Maxent (one for each species). The average value for the AUC for training was 0.98 and 0.96 for testing (see Table II). The values for the minimum training presence, the tenth percentile training presence and the equal training sensitivity and specificity thresholds for each species are shown in Table II. The range for the minimum training presence was 0.002 - 0.312, for the tenth percentile presence was 0.209 - 0.664, and for the equal training sensitivity and specificity was 0.085-0.486, with averages of 0.065, 0.412 , and 0.303, respectively. Most of the species tend to have very low values for the minimum training presence, whereas most of species have a value of the tenth percentile training presence around of 0.5 , and the equal training sensitivity and specificity less than 0.5. An example of the differences between the binary maps resulting form the application of four thresholds is shown in Figures 1 and 2.

The results of the analyses of endemicity are shown in Tables III and IV. In the analysis using the minimum training presence threshold, we could recover only one pattern of endemism (Fig. 3): the Western pattern of Escalante et al.²⁷ With the tenth percentile threshold we recovered three patterns (Fig. 4): Nearctic, Western and Eastern; with the 0.5 value of probability as a threshold, we recovered two patterns (Fig. 5): Western and Eastern; and the same with the equal training sensitivity and specificity, two patterns were identified: Western and Eastern (Fig. 6). Moreover, the threshold where we obtained more endemic species was the tenth percentile, followed by the 0.5, the equal training sensitivity and specificity and the minimum training presence (Table IV). Only one pattern (the Northern pattern) of Escalante et al.²⁷ could not be recovered with any of the thresholds.

Discussion

It is known that the species distribution models have limitations when there are few numbers of occurrences (less than 5)^18,20,33.The performance of our models, in terms of AUC, however, did not show any differences with few and many records. None of the species had a value lower than 0.7 of AUC for training and testing. This can be due to the fact that Maxent performs well with small samples of records¹⁸; although it can be due also to some intrinsic feature of AUC, because the increment to geographical extents outside presence environmental domain generates higher scores of AUC⁴⁵.

Most species had values lower than 0.1 for the minimum training presence; whilst most mammals had values around 0.5 for the tenth percentile presence and 0.3 for the equal training sensitivity and specificity. Because our data came from museum collections in databases and bibliography, and despite our geographic validation, it is possible that some of them have outliers represented by inconsistences in georeference or identification of species, even after our verification. Then, those outliers can affect the minimum training presence lower value, because it forces the threshold to include them. However, it is possible that the minimum training presence threshold can be used when the input data had undergone a strict identification of outliers previous to the modelling, or when the data are from very systematic fieldwork, as in Giovanelli et al.⁴¹

We found that the more consistent identification of areas of endemism was obtained using the tenth percentile training presence threshold, followed by the 0.5 presence probability, at the same level to the equal training sensitivity and specificity, and the worst for the minimum training presence. The latter resulted the worst threshold, because it tends to enlarge too much the areas of distribution of the taxa, specially in cases where data come from several sources and dissimilar sample effort. Moreover some points can be out of the range of distribution of the modeled species (outliers), because recent taxonomic or nomenclatural changes. Again, it can be relevant to perform an analysis of identification of outliers before the modelling. According to our results, the best option is to use the tenth percentile training presence, which considers the probability at which 10% of the training presence records are omitted, specially the outliers. Other authors have used succesfully the 20th percentile in order to avoid bias by outlying records⁴⁰.

Pearson et al.¹⁸ selected two thresholds: the lowest presence threshold, being conservative and identifying the minimum predicted area possible whilst maintaining zero omission error in the training data; and a more liberal fixed thresholds that rejected only the lowest 10% of possible predicted values. Papes & Gaubert³³, following Pearson et al.¹⁸, mentioned that the acceptable threshold value will depend of the question: if the interest are general patterns, the liberal threshold is suitable, but for conservation where the over-prediction is not desirable, the conservative threshold is more adequate. For the identification of areas of endemism, we consider that it is necessary to use a conservative threshold, because a liberal threshold tends to mask some patterns. For example, the Nearctic pattern cannot be recovered, although there are five species that share their distributions²⁷. It is surprising that the Northern pattern was not recovered with any threshold. It was originally discovered with three endemic species²⁷, althought the overlapping of their distributional areas is evident, but the models show a discontinuity (at central Canada) that may affect the identification of the area of endemism.

Pearson et al.¹⁸ also found that it is possible to use a threshold lower than the lowest presence threshold (threshold 10, equivalent to our 0.1) when small numbers of presence data are available. In our case, it was not necessary, because even the tenth percentile training presence was better than the minimum training presence, and a lower threshold will prevent the correct identification of areas of endemism.

Conclusions

The identification of areas of endemism represents one of the main goals in biogeography. Its accurate identification depends on the appropiate inference of the individual areas of distribution. Although the field of selection of thresholds in modelling potential distributions is yet controversial, it is possible to obtain better results in analysis of endemism using the best approximation to real distributional areas. The testing of several thresholds before analyzing areas of endemism could be relevant in the identification of distributional patterns of the taxa, however, a threshold similar to the tenth percentile training presence can offer good results.

Acknowledgements

Niza Gámez, Rode A. Luna, Ana Lilia González, Estela Rivera and Lucero Cetina helped us with the integration of the database and the generation of the models. We thank the support of CONACyT project 80370. We thank the commentaries from Sergio Roig-Juñent, Patricio Pliscoff and Juan J. Morrone.

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Información sobre los autores

Tania Escalante

Tania Escalante es egresada de la carrera de Biología de la Facultad de Estudios Superiores Zaragoza, UNAM. Es Doctora en Ciencias por la Facultad de Ciencias, UNAM, y realizó dos posdoctorados en el Instituto de Biología de la UNAM (2004-2006 y 2006-2007). Ha impartido cerca de 30 cursos en la licenciatura y posgrado en la Facultad de Ciencias (UNAM), así como en licenciatura y posgrado en otras instituciones del país y del extranjero. Ha impartido, por invitación, 17 conferencias en México, Chile, Guatemala y España; y participado en 27 reuniones académicas, congresos y simposios en México, Argentina, Brasil y Chile. Ha dirigido ocho tesis de licenciatura y cinco tesis de posgrado. Ha publicado 26 trabajos científicos en las áreas de su especialidad (biogeografía, mastozoología y conservación). Posee alrededor de ciento cincuenta citas a sus trabajos, con un artículo que supera las treinta citas. Asimismo, ha publicado 25 capítulos de libros y es coautora de un libro. Algunas de las publicaciones más destacadas de la Dra. Escalante se han publicado en revistas indizadas internacionales como Journal of Biogeography, Biological Journal of the Linnean Society, Systematic Biology y Journal of Mammalogy. Actualmente, encabeza el grupo de trabajo de Biogeografía de la Conservación de la Facultad de Ciencias. Es responsable de un proyecto de CONABIO y también de un proyecto PAPIME, DGAPA-UNAM. Es miembro del SNI en el nivel I y en 2011 fue galardonada con el Reconocimiento Distinción Universidad Nacional Para Jóvenes Académicos.

Gerardo Rodríguez-Tapia

Gerardo Rodríguez-Tapia es Biólogo egresado de la Facultad de Estudios Superiores Zaragoza, UNAM, y actualmente estudia el doctorado en ciencias en el Instituto de Ecología de la UNAM. Es responsable de la Unidad de Geomática del mismo Instituto. Ha participado en 30 congresos y reuniones científicas nacionales e internacionales, e impartido 15 cursos de licenciatura sobre biogeografía y Sistemas de Información Geográfica aplicado a temas de biodiversidad. Cuenta con nueve artículos en revistas indizadas, nueve capítulos de libros y agradecimientos en casi 50 artículos de investigación y tesis de licenciatura y posgrado. Su línea de investigación está relacionada con los efectos del cambio climático en la distribución de las especies de mamíferos e insectos terrestres. A la fecha ha participado en 19 proyectos de investigación relacionados principalmente con temas de cambio climático, Sistemas de Información Geográfica y modelos de distribución potencial de especies.

Miguel Linaje

Miguel Linaje es Biólogo de la Facultad de Ciencias de la UNAM. Actualmente, imparte cursos de licenciatura en la UNAM y en otro periodo de tiempo lo hizo en el posgrado, realizando la misma actividad en otras instituciones del país, incluidos cursos cortos. Cuenta con más de 20 trabajos científicos publicados en las áreas de su especialidad (biogeografía, mastozoología y conservación), además de cinco capítulos de libros. Ha tenido a su cargo cinco proyectos de investigación.

Patricia Illoldi-Rangel

Rafael González-López

Rafael González-López es Biólogo de la Facultad de Ciencias, UNAM (2006-2010). Actualmente es estudiante de la Maestría en Geografía en el Centro de Investigaciones en Geografía Ambiental (CIGA, 2011-2013), campus Morelia de la UNAM. Su tesis de licenciatura se tituló "Caracterización biogeográfica de la provincia del Altiplano Mexicano con base en su mastofauna". Su tesis actual de maestría se titula "Modelación espacial del potencial de captura de carbono en los bosques de Quercus de la Cuenca del Lago de Cuitzeo, Michoacán". Durante la maestría realizó una estancia de investigación en la universidad de Yale y trabajó en Honduras.