Abstract
Usually in Ecology, the availability and quality of the data is not as good as we would like. For some species, the typical environmental study focuses on presence/absence data, and particularly with small animals as amphibians and reptiles, the number of presences can be rather small. The aim of this study is to develop a spatial model for studying animal data with a low level of presences; we specify a Gaussian Markov Random Field for modelling the spatial component and evaluate the inclusion of environmental covariates. To assess the model suitability, we use Watanabe-Akaike information criteria (WAIC) and the conditional predictive ordinate (CPO). We apply this framework to model each species of amphibian and reptiles present in the Las Tablas de Daimiel National Park (Spain).
Similar content being viewed by others
References
Acreman M, Almagro J, Alvarez J, Bouraoui F, Bradford R, Bromley J, Croke B, Crooks S, Cruces J, Dolz J, Dunbar M, Estrela T, Fernandez-Carrasco P, Fornes J, Gustard G, Haverkamp R, De La Hera A, Hernández-Mora N, Llamas R, Martinez CL, Papamasorakis J, Ragab R, Sánchez M, Vardavas I, Webb T (2000) Groundwater and river resources programme on a European scale (GRAPES). Technical report to the European Union ENV4–CT95-0186. Institute of Hydrology, Wallingford
Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: B. N. Petrov and F. Csaki (eds) Proceedings of the Second International Symposium on Information Theory. Akademiai Kiado, Budapest, pp 267–281. Reprinted in Breakthroughs in Statistics, ed. S. Kotz, 610–624. New York: Springer (1992)
Banerjee S, Carlin B, Gelfand A (2004) Hierarchical modeling and analysis for spatial data. CRC, London
Bishop CA, Gendron AD (1998) Reptiles and amphibians: shy and sensitive vertebrates of the Great Lakes basin and St. Lawrence river. Environ Monit Assess 53:225–244
Blangiardo M, Cameletti M (2015) Spatial and Spatio-temporal Bayesian models with R-INLA. Wiley
Blangiardo M, Cameletti M, Baio G, Rue H (2013) Spatial and spatio-temporal models with R-INLA. Spat Spatiotemporal Epidemiol 7:39–55
Brost BM, Hooten MB, Hanks EM, Small RJ (2015) Animal movement constraints improve resource selection inference in the presence of telemetry error. Ecology 96:2590–2597
Burger J, Snodgrass J (1998) Heavy metals in bullfrog (Rana catesbeiana) tadpoles: effects of depuration before analysis. Environ Toxicol Chem 17:2203–2209
Busby JR (1991) BIOCLIM: a bioclimatic analysis and predictive system. In: Margules C, Austin M (eds) Nature conservation: cost effective biological surveys and data analysis. CSIRO, Canberra, pp 64–68
Chakraborty A, Gelfand AE, Wilson AM, Latimer AM, Silander JA (2010) Modeling large scale species abundance with latent spatial processes. Ann Appl Stat 4(3):1403–1429
Clark JS (2005) Why environmental scientists are becoming Bayesians. Ecol Lett 8(1):2–14
Corn SP (2005) Climate change and amphibians. Anim Biodivers Conserv 28:59–67
Coronado R, Del Portillo F, Sáez-Royuela R (1974) Tablas de Daimiel National Park Guide. ICONA, Madrid
Cosandey-Godin A, Teixeira Krainski E, Worm B, Mills Flemming J (2015) Applying Bayesian spatiotemporal models to fisheries bycatch in the Canadian Arctic. Can J Fish Aquat Sci 72:1–12
Cots F, David Tàbara J, Werners S, McEvoy D (2007) Climate change and water adaptive management through transboundary cooperation. The case of the Guadiana river basin. Paper presented to the first International Conference on Adaptive and Integrative Water Management (CAIWA), Basel, Switzerland, November 2007
Crase B, Liedloff AC, Wintle BA (2012) A new method for dealing with residual spatial autocorrelation in species distribution models. Ecography 35(10):879–888
Cressie N, Calder CA, Clark JS, Hoef JMV, Wikle CK (2009) Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling. Ecol Appl 19:553–5701
Cummins CP (2003) UV-B radiation, climate change and frogs—the importance of phenology. Ann Zool Fenn 40:61–67
de Rivera ÓRD, López-Quílez A (2017) Development and comparison of species distribution models for forest inventories. ISPRS International Journal of Geo-Information 6(6):176
Diggle P, Ribeiro PJ (2007) Model-based Geostatistics. Springer-Verlag, New York
Dorazio RM (2014) Accounting for imperfect detection and survey bias in statistical analysis of presence-only data. Glob Ecol Biogeogr 23(12):1472–1484
Dorit, R L, Walker W F, Barnes R D (1991) Zoology. Saunders College Publishing. ISBN 978-0-03-030504-7
Elith J, Burgman MA (2002) Predictions and their validation: rare plants in the Central Highlands, Victoria, Australia. In: Scott JM, Heglund PJ, Morrison ML, Raphael MG, Wall WA, Samson FB (eds) Predicting Species Occurrences: Issues of Accuracy and Scale. Island Press, Covelo, pp 303–314
Elith J, Leathwick JR (2009) Species distribution models: ecological explanation and prediction across space and time. Annu Rev Ecol Evol Syst 40:677–697
Fellers GM, Mcconnell LL, Pratt D, Datta S (2004) Pesticides in mountain yellow legged frogs (Rana muscosa) from the Sierra Nevada Mountains of California, USA. Environ Toxicol Chem 23:2170–2177
Fithian W, Elith J, Hastie T, Keith DA (2015) Bias correction in species distribution models: pooling survey and collection data for multiple species. Methods Ecol Evol 6(4):424–438
Geisser S, Eddy W (1979) A predictive approach to model selection. J Am Stat Assoc 74:153–160
Gelfand AE, Silander JA, Wu SJ, Latimer AM, Rebelo PLAG, Holder M (2006) Explaining species distribution patterns through hierarchical modeling. Bayesian Anal 1(1):41–92
Gelfand AE, Diggle P, Fuentes M, Guttorp P (eds) (2010) Handbook of spatial statistics. Chapman & Hall, Boca-Raton
Gelman A, Shalizi C (2013) Philosophy and the practice of Bayesian statistics (with discussion). Br J Math Stat Psychol 66:8–80
Gendron AD, Marcogliese DJ, Barbeau S, Christin MS, Brousseau P, Ruby S, Cyr D, Fournier M (2006) Exposure of leopard frogs to a pesticide mixture affects life history characteristics of the lungworm Rhabdias ranae. Oecologia 135:469–476
Gibbons JW, Stangel PW (eds) (1999) Conserving amphibians and reptiles in the new millenium. Proceedings of the Partners in Amphibian and Reptile Conservation (PARC). Conference; 2–4 June 1999; Atlanta (GA).Aiken (SC): Savannah River Ecology Laboratory. Herp Outreach Publication #2
Gibbons JW, Scott DE, Ryan TJ, Buhlmann KA, Tuberville TD, Metts BS, Greene JL, Mills T, Leiden Y, Poppy S, Winne CT (2000) The global decline of reptiles, Déjà vu amphibians. BioScience 50(8):653–666
Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102(477):359–378
Golding N, Purse BV (2016) Fast and flexible Bayesian species distribution modelling using Gaussian processes. Methods Ecol Evol 7(5):598–608
Guisan A, Thuiller W (2005) Predicting species distribution: offering more than simple habitat models. Ecol Lett 8:993–1009
Guisan A, Edwards TC, Hastie T (2002) Generalized linear and generalized additive models in studies of species distributions: setting the scene. Ecol Model 157:89–100
Haining R, Law J, Maheswaran R, Pearson T, Brindley P (2007) Bayesian modelling of environmental risk: a small area ecological study of coronary heart disease mortality in relation to modelled outdoor nitrogen oxide levels. Stoch Env Res Risk A 21(5):501–509
Hatch AC, Blaustein AR (2003) Combined effects of UV-B radiation and nitrate fertilizer on larval amphibians. Ecol Appl 13:1083–1093
Hefley TJ, Hooten MB (2016) Hierarchical species distribution models. Current Landscape Ecology Reports 1(2):87–97
Henry PFP (2000) Aspects of amphibian anatomy and physiology: Society of Environmental Toxicology and Chemistry, 71–110
Hijman R, Graham C (2006) The ability of climate envelope models to predict the effect of climate change on species distributions. Glob Chang Biol 12(12):2272–2281
Hijmans RJ, Elith J (2015) Species distribution modelling with R. http://cran.r-project.org/web/packages/dismo/vignettes/sdm.pdf, The R foundation for statistical computing
Hooten MB, Wikle CK (2008) A hierarchical Bayesian non-linear spatio-temporal model for the spread of invasive species with application to the Eurasian collared-dove. Environ Ecol Stat 15(1):59–70
Hooten MB, Wikle CK, Dorazio RM, Royle JA (2007) Hierarchical spatiotemporal matrix models for characterizing invasions. Biometrics 63(2):558–567
Huang J, Ling CX (2005) Using AUC and accuracy in evaluating learning algorithms. IEEE Trans Knowl Data Eng 17(3):299–310
Hui FK (2016) Boral–Bayesian ordination and regression analysis of multivariate abundance data in R. Methods Ecol Evol 7(5):744–750
Hurlbert SH (1984) Pseudoreplication and the design of ecological field experiments. Ecol Monogr 54:187–211
IGME (Instituto Geológico y Minero de España) (2017) http://www.igme.es/zonas_humedas/daimiel/medio_fisico/clima.htm. Date visited: 01/03/2017
Illian JB, Martino S, Sørbye SH, Gallego-Fernández JB, Zunzunegui M, Esquivias MP, Travis JMJ (2013) Fitting complex ecological point process models with integrated nested Laplace approximation. Methods Ecol Evol 4:305–315. https://doi.org/10.1111/2041-210x.12017
Johnson DS, Hooten MB, Kuhn CE (2013) Estimating animal resource selection from telemetry data using point process models. J Anim Ecol 82(6):1155–1164
Kery M, Schaub M (2011) Bayesian population analysis using WinBUGS: a hierarchical perspective. Academic Press, Burlington
Latimer AM, Wu SS, Gelfand AE, Silander JA (2006) Building statistical models to analyze species distributions. Ecol Appl 16(1):33–50
Leathwick JR, Rowe D, Richardson J, Elith J, Hastie T (2005) Using multivariate adaptive regression splines to predict the distributions of New Zealand’s freshwater diadromous fish. Freshw Biol 50:2034–2052
Lecours V (2017) On the use of maps and models in conservation and resource management (warning: results may vary). Front Mar Sci 4:288
Li L, Qiu S, Zhang B, Feng CX (2015) Approximating cross-validatory predictive evaluation in Bayesian latent variable model with integrated IS and WAIC. Stat Comput 26:881–897. https://doi.org/10.1007/s11222-015-9577-2
Lindgren F, Rue H (2013) Bayesian spatial and spatio-temporal modelling with R-INLA. J Stat Softw
Lindgren F, Rue H, Lindström J (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach [with discussion]. J R Stat Soc B 73(4):423–498
Loarie SR, Carter BE, Hayhoe K, McMahon S, Moe R, Knight CA, Ackerly DD (2008) Climate change and the future of Californias endemic flora. PLoS One 3(6):e2502
MacKenzie DI, Nichols JD, Lachman GB, Droege S, Royle JA, Langtimm CA (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:2248–2255
MacKenzie DI, Nichols JD, Royle JA, Pollock KH, Bailey LL, Hines JE (2006) Occupancy estimation and modeling inferring patterns and dynamics of species occurrence. Academic Press
Meehan TD, Michel NL, Rue H (2017) Estimating animal abundance with N-mixture models using the R-INLA package for R arXiv preprint arXiv:1705.01581
Midgley GF, Thuiller W (2007) Potential vulnerability of Namaqualand plant diversity to anthropogenic climate change. J Arid Environ 70:615–628
Muñoz F, Pennino MG, Conesa D, López-Quílez A, Bellido JM (2013) Estimation and prediction of the spatial occurrence of fish species using Bayesian latent Gaussian models. Stoch Environ Res Risk Assess 27:1171–1180
Navarro V, García B, Sánchez D, Asensio L (2011) An evaluation of the application of treated sewage effluents in Las Tablas de Daimiel National Park, Central Spain. J Hydrol 401:53–64
Osborne PE, Foody GM, Suárez-Seoane S (2007) Non-stationarity and local approaches to modelling the distributions of wildlife. Divers Distrib 13(3):313–323
Ovaskainen O, Soininen J (2011) Making more out of sparse data: hierarchical modeling of species communities. Ecology 92(2):289–295
Pettit LI (1990) The conditional predictive ordinate for the normal distribution. J R Stat Soc Ser B 52(1):175–184
Piha H, Luoto M, Merilä J (2007) Amphibian occurrence is influenced by current and historic landscape characteristics. Ecol Appl 17(8):2298–2309
Pressey RL, Cabeza M, Watts EM, Cowling RM, Wilson KA (2007) Conservation planning in a changing world. Trends Ecol Evol 22:583–592
Qiao H, Soberón J, Peterson AT (2015) No silver bullets in correlative ecological niche modelling: insights from testing among many potential algorithms for niche estimation. Methods Ecol Evol 6(10):1126–1136. https://doi.org/10.1111/2041-210X.12397
R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
Roos M, Held L (2011) Sensitivity analysis in Bayesian generalized linear mixed models for binary data. Bayesian Anal 6(2):259–278
Royle JA (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60:108–115
Royle JA, Dorazio RM (2008) Hierarchical modeling and inference in ecology: the analysis of data from populations, metapopulations and communities. Academic Press
Royle JA, Kery M, Gautier R, Schmidt H (2007) Hierarchical spatial models of abundance and occurrence from imperfect survey data. Ecol Monogr 77:465–481
Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). J R Stat Soc Ser B 71:319–392
Russell JC, Hanks EM, Haran M (2016) Dynamic models of animal movement with spatial point process interactions. J Agric Biol Environ Stat 21(1):22–40
Sánchez-Ramos D, Sánchez-Emeterio G, Florín Beltrán M (2015) Changes in water quality of treated sewage effluents by their receiving environments in Tablas de Daimiel National Park, Spain. Environ Sci Pollut Res 23:6082–6090. https://doi.org/10.1007/s11356-015-4660-y
Simpson D, Lindgren F, Rue H (2011) Fast approximate inference with INLA: the past, the present and the future. Technical report at arxiv.org
Sower SA, Reed KL, Babbitt KJ (2000) Limb malformations and abnormal sex hormone concentrations in frogs. Environ Health Perspect 108:1085–1090
Sparling DW, Linder G, Bishop CA (eds) (2000) Ecotoxicology of amphibians and reptiles. Society of Environmental Toxicology and Chemistry (SETAC), Pensacola, pp 71–111
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc Ser B 64(4):583–616
Stuart S, Chanson JS, Cox NA, Young BE, Rodrigues ASL, Fishman DL, Waller RW (2004) Status and trends of amphibian declines and extinctions worldwide. Science 306:1783–1786
Underwood AJ (1981) Techniques of analysis of variance in marine biology and ecology. Oceanogr Mar Biol Annu Rev 19:513–605
van der Linde A (2005) DIC in variable selection. Statistica Neerlandica 59(1):45–56
Vehtari A, Lampinen J (2002) Bayesian model assessment and comparison using cross validation predictive densities. Neural Comput 14:2439–2468
Wade PR (2000) Bayesian methods in conservation biology. Conserv Biol 14(5):1308–1316. https://doi.org/10.1046/j.1523-1739.2000.99415.x
Warton DI, Blanchet FG, O’Hara RB, Ovaskainen O, Taskinen S, Walker SC, Hui FK (2015) So many variables: joint modeling in community ecology. Trends Ecol Evol 30(12):766–779
Watanabe S (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 11:3571–3594
Wikle CK (2003) Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology 84(6):1382–1394
Wintle BA, McCarthy MA, Volinsky CT, Kavanagh RP (2003) The use of Bayesian model averaging to better represent uncertainty in ecological models. Conserv Biol 17(6):1579–1590. https://doi.org/10.1111/j.1523-1739.2003.00614.x
Wisz MS, Hijmans RJ, Li J, Peterson AT, Graham CH, Guisan A (2008) Effects of sample size on the performance of species distribution models. Divers Distrib 14:763–773
Yustres A, Navarro V, Asensio L, Candel M, García B (2013) Groundwater resources in the Upper Guadiana Basin (Spain): a regional modelling analysis. Hydrogeol J 21(5):1129–1146
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Rivera, O.R., Blangiardo, M., López-Quílez, A. et al. Species distribution modelling through Bayesian hierarchical approach. Theor Ecol 12, 49–59 (2019). https://doi.org/10.1007/s12080-018-0387-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12080-018-0387-y