×

Markov random field models for vector-based representations of landscapes. (English) Zbl 1498.62297

Summary: In agricultural landscapes the spatial distribution of cultivated and seminatural elements strongly impacts habitat connectivity and species dynamics. To allow for landscape structural analysis and scenario generation, we here develop statistical tools for real landscapes composed of geometric elements, including 2D patches but also 1D linear elements (e.g., hedges). Utilizing the framework of discrete Markov random fields, we design generative stochastic models that combine a multiplex network representation, based on spatial adjacency, with Gibbs energy terms to capture the distribution of landscape descriptors for land-use categories. We implement simulation of agricultural scenarios with parameter-controlled spatial and temporal patterns (e.g., geometry, connectivity, crop rotation), and we demonstrate through simulation that pseudo-likelihood estimation of parameters works well. To study statistical relevance of model components in real landscapes, we discuss model selection and validation, including cross-validated prediction scores. Model validation with a view toward ecologically relevant landscape summaries is achieved by comparing observed and simulated summaries (network metrics but also metrics and appropriately defined variograms using a raster discretization). Models fitted to subregions of the Lower Durance Valley (France) indicate strong deviation from random allocation and realistically capture landscape patterns. In summary, our approach improves the understanding of agroecosystems and enables simulation-based theoretical analysis of how landscape patterns shape biological and ecological processes.

MSC:

62P12 Applications of statistics to environmental and related topics
62M40 Random fields; image analysis
60G60 Random fields
60K35 Interacting random processes; statistical mechanics type models; percolation theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adamczyk-Chauvat, K., Kassa, M., Kiêu, K., Papaïx, J. and Stoica, R. S. (2020). Gibbsian t-tessellation model for agricultural landscape characterization. Preprint. Available at arXiv:2007.16094.
[2] Baddeley, A. and MØller, J. (1989). Nearest-neighbour Markov point processes and random sets. International Statistical Review/Revue Internationale de Statistique 89-121. · Zbl 0721.60010
[3] Belgrano, A., Woodward, G. and Jacob, U. (2015). Aquatic Functional Biodiversity: An Ecological and Evolutionary Perspective. Academic Press, San Diego, CA.
[4] Besag, J. E. (1972). Nearest-neighbour systems and the auto-logistic model for binary data. J. Roy. Statist. Soc. Ser. B 34 75-83. · Zbl 0268.60088
[5] Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J. Roy. Statist. Soc. Ser. B 36 192-236. · Zbl 0327.60067
[6] Boccaletti, S., Bianconi, G., Criado, R., del Genio, C. I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z. and Zanin, M. (2014). The structure and dynamics of multilayer networks. Phys. Rep. 544 1-122.
[7] Bonhomme, V., Castets, M., Ibanez, T., Géraux, H., Hély, C. and Gaucherel, C. (2017). Configurational changes of patchy landscapes dynamics. Ecol. Model. 363 1-7.
[8] Boots, B., Okabe, A. and Sugihara, K. (1999). Spatial tessellations. Geographical Information Systems 1 503-526.
[9] Brier, G. W. (1950). Verification of forecasts expressed in terms of probability. Mon. Weather Rev. 78 1-3.
[10] Brown, L. D. (1986). Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory. Institute of Mathematical Statistics Lecture Notes—Monograph Series 9. IMS, Hayward, CA. · Zbl 0685.62002
[11] Büttner, G. and Maucha, G. (2006). The Thematic Accuracy of CORINE Land Cover 2000. Assessment Using LUCAS (Land Use/Cover Area Frame Statistical Survey). European Environment Agency, Copenhagen.
[12] Calabrese, J. M. and Fagan, W. F. (2004). A comparison-shopper’s guide to connectivity metrics. Front. Ecol. Environ. 2 529-536.
[13] Cressie, N. A. C. (1991). Statistics for Spatial Data. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Wiley, New York. · Zbl 0799.62002
[14] Cressie, N. A. C. (2015). Statistics for Spatial Data, Revised ed. Wiley Classics Library. Wiley, New York. · Zbl 1347.62005
[15] Cushman, S. A., McGarigal, K. and Neel, M. C. (2008). Parsimony in landscape metrics: Strength, universality, and consistency. Ecol. Indicators 8 691-703.
[16] Cushman, S. A., Gutzweiler, K., Evans, J. S. and McGarigal, K. (2010). The gradient paradigm: A conceptual and analytical framework for landscape ecology. In Spatial Complexity, Informatics, and Wildlife Conservation 83-108. Springer, New York.
[17] Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Series in Statistical and Probabilistic Mathematics 1. Cambridge Univ. Press, Cambridge. · Zbl 0886.62001
[18] Estrada, E. and Bodin, Ö. (2008). Using network centrality measures to manage landscape connectivity. Ecol. Appl. 18 1810-1825.
[19] Fienberg, S. E. (2010). Introduction to papers on the modeling and analysis of network data. Ann. Appl. Stat. 4 1-4.
[20] Foresight, U.(2011). The Future of Food and Farming. Final Project Report. The Government Office for Science, London.
[21] Frazier, A. E. and Kedron, P. (2017). Landscape metrics: Past progress and future directions. Current Landscape Ecology Reports 2 63-72.
[22] Gaetan, C. and Guyon, X. (2010). Spatial Statistics and Modeling. Springer Series in Statistics. Springer, New York. · Zbl 1271.62214
[23] Gallavotti, G. (1999). Statistical Mechanics: A Short Treatise. Texts and Monographs in Physics. Springer, Berlin. · Zbl 0932.82002
[24] Gardner, R. H. (1999). RULE: Map generation and a spatial analysis program. In Landscape Ecological Analysis 280-303. Springer, New York.
[25] Gardner, R. H. and Urban, D. L. (2007). Neutral models for testing landscape hypotheses. Landsc. Ecol. 22 15-29.
[26] Gardner, R. H., Milne, B. T., Turnei, M. G. and O’Neill, R. V. (1987). Neutral models for the analysis of broad-scale landscape pattern. Landsc. Ecol. 1 19-28.
[27] Garrigues, S., Allard, D., Baret, F. and Weiss, M. (2006). Quantifying spatial heterogeneity at the landscape scale using variogram models. Remote Sens. Environ. 103 81-96.
[28] Garrigues, S., Allard, D., Baret, F. and Morisette, J. (2008). Multivariate quantification of landscape spatial heterogeneity using variogram models. Remote Sens. Environ. 112 216-230.
[29] Gaucherel, C., Fleury, D., Auclair, D. and Dreyfus, P. (2006a). Neutral models for patchy landscapes. Ecol. Model. 197 159-170.
[30] Gaucherel, C., Giboire, N., Viaud, V., Houet, T., Baudry, J. and Burel, F. (2006b). A domain-specific language for patchy landscape modelling: The Brittany agricultural mosaic as a case study. Ecol. Model. 194 233-243.
[31] Gaucherel, C., Boudon, F., Houet, T., Castets, M. and Godin, C. (2012). Understanding patchy landscape dynamics: Towards a landscape language. PLoS ONE 7 e46064.
[32] Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102 359-378. · Zbl 1284.62093
[33] Green, P. J., Hjort, N. L. and Richardson, S. (2003). Highly Structured Stochastic Systems, Volume 27. Oxford Univ. Press, Oxford. · Zbl 1044.62110
[34] Grelaud, A., Robert, C. P., Marin, J.-M., Rodolphe, F. and Taly, J.-F. (2009). ABC likelihood-free methods for model choice in Gibbs random fields. Bayesian Anal. 4 317-335. · Zbl 1330.62126
[35] Hammersley, J. M. and Clifford, P. (1971). Markov fields on finite graphs and lattices. 46. Unpublished manuscript.
[36] Hesselbarth, M. H., Sciaini, M., With, K. A., Wiegand, K. and Nowosad, J. (2019). Landscapemetrics: An open-source R tool to calculate landscape metrics. Ecography 42 1648-1657.
[37] Hijmans, R. J., van Etten, J., Cheng, J., Mattiuzzi, M., Sumner, M., Greenberg, J. A., Lamigueiro, O. P., Bevan, A., Racine, E. B. et al. (2015). Package ‘raster’. R package.
[38] Hopcroft, J. and Tarjan, R. (1973). Algorithm 447: Efficient algorithms for graph manipulation. Commun. ACM 16 372-378.
[39] Inkoom, J. N., Frank, S., Greve, K. and Fürst, C. (2017). Designing neutral landscapes for data scarce regions in West Africa. Ecol. Inform. 42 1-13.
[40] Jensen, J. L. and MØller, J. (1991). Pseudolikelihood for exponential family models of spatial point processes. Ann. Appl. Probab. 1 445-461. · Zbl 0736.60045
[41] Kiêu, K., Adamczyk-Chauvat, K., Monod, H. and Stoica, R. S. (2013). A completely random T-tessellation model and Gibbsian extensions. Spat. Stat. 6 118-138.
[42] Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y. and Porter, M. A. (2014). Multilayer networks. J. Complex Netw. 2 203-271.
[43] Kupfer, J. A. (2012). Landscape ecology and biogeography: Rethinking landscape metrics in a post-FRAGSTATS landscape. Progress in Physical Geography 36 400-420.
[44] Lahiri, S. N. (2003). Resampling Methods for Dependent Data. Springer Series in Statistics. Springer, New York. · Zbl 1028.62002
[45] Langhammer, M., Thober, J., Lange, M., Frank, K. and Grimm, V. (2019). Agricultural landscape generators for simulation models: A review of existing solutions and an outline of future directions. Ecol. Model. 393 135-151.
[46] Latora, V. and Marchiori, M. (2001). Efficient behavior of small-world networks. Phys. Rev. Lett. 87 198701. · Zbl 1060.91520
[47] Le Ber, F., Lavigne, C., Adamczyk, K., Angevin, F., Colbach, N., Mari, J.-F. and Monod, H. (2009). Neutral modelling of agricultural landscapes by tessellation methods—application for gene flow simulation. Ecol. Model. 220 3536-3545.
[48] Lefebvre, M., Franck, P., Toubon, J.-F., Bouvier, J.-C. and Lavigne, C. (2016). The impact of landscape composition on the occurrence of a canopy dwelling spider depends on orchard management. Agriculture, Ecosystems & Environment 215 20-29.
[49] Lin, Y., Deng, X., Li, X. and Ma, E. (2014). Comparison of multinomial logistic regression and logistic regression: Which is more efficient in allocating land use? Front. Earth Sci. 8 512-523.
[50] Lü, L., Chen, D., Ren, X.-L., Zhang, Q.-M., Zhang, Y.-C. and Zhou, T. (2016). Vital nodes identification in complex networks. Phys. Rep. 650 1-63.
[51] Maalouly, M., Franck, P., Bouvier, J.-C., Toubon, J.-F. and Lavigne, C. (2013). Codling moth parasitism is affected by semi-natural habitats and agricultural practices at orchard and landscape levels. Agriculture, Ecosystems & Environment 169 33-42.
[52] Martin, E. A., Dainese, M., Clough, Y., Báldi, A., Bommarco, R., Gagic, V., Garratt, M. P. D., Holzschuh, A., Kleijn, D. et al. (2019). The interplay of landscape composition and configuration: New pathways to manage functional biodiversity and agroecosystem services across Europe. Ecol. Lett. 22 1083-1094.
[53] McGarigal, K. and Marks, B. J. (1995). FRAGSTATS: Spatial pattern analysis program for quantifying landscape structure. Gen. Tech. Rep. PNW-GTR-351. Portland, OR: US Department of Agriculture, Forest Service, Pacific Northwest Research Station. 122 p., 351.
[54] Minor, E. S. and Urban, D. L. (2008). A graph-theory framework for evaluating landscape connectivity and conservation planning. Conserv. Biol. 22 297-307.
[55] MØller, J. and Waagepetersen, R. P. (1998). Markov connected component fields. Adv. in Appl. Probab. 30 1-35. · Zbl 0908.60035
[56] Papaïx, J., Adamczyk-Chauvat, K., Bouvier, A., Kiêu, K., Touzeau, S., Lannou, C. and Monod, H. (2014). Pathogen population dynamics in agricultural landscapes: The ddal modelling framework. Infect. Genet. Evol. 27 509-520.
[57] Poggi, S., Papaïx, J., Lavigne, C., Angevin, F., Le Ber, F., Parisey, N., Ricci, B., Vinatier, F. and Wohlfahrt, J. (2018). Issues and challenges in landscape models for agriculture: From the representation of agroecosystems to the design of management strategies. Landsc. Ecol. 33 1679-1690.
[58] Power, A. G. (2010). Ecosystem services and agriculture: Tradeoffs and synergies. Philos. Trans. R. Soc. Lond. B, Biol. Sci. 365 2959-2971.
[59] Ricci, B., Franck, P., Toubon, J.-F., Bouvier, J.-C., Sauphanor, B. and Lavigne, C. (2009). The influence of landscape on insect pest dynamics: A case study in southeastern France. Landsc. Ecol. 24 337-349.
[60] Saura, S. and Martinez-Millan, J. (2000). Landscape patterns simulation with a modified random clusters method. Landsc. Ecol. 15 661-678.
[61] Sciaini, M., Fritsch, M., Scherer, C. and Simpkins, C. E. (2018). NLMR and landscapetools: An integrated environment for simulating and modifying neutral landscape models in R. Methods Ecol. Evol. 9 2240-2248.
[62] Sirami, C., Gross, N., Baillod, A. B., Bertrand, C., Carrié, R., Hass, A., Henckel, L., Miguet, P., Vuillot, C. et al. (2019). Increasing crop heterogeneity enhances multitrophic diversity across agricultural regions. Proc. Natl. Acad. Sci. USA 116 16442-16447.
[63] Stoehr, J. (2017). A review on statistical inference methods for discrete Markov random fields. Preprint. Available at arXiv:1704.03331.
[64] Urban, D. and Keitt, T. (2001). Landscape connectivity: A graph-theoretic perspective. Ecology 82 1205-1218.
[65] Urban, D. L., Minor, E. S., Treml, E. A. and Schick, R. S. (2009). Graph models of habitat mosaics. Ecol. Lett. 12 260-273.
[66] van Lieshout, M. N. M. (2000). Markov Point Processes and Their Applications. Imperial College Press, London. · Zbl 0968.60005
[67] van Lieshout, M. N. M. (2019). Theory of Spatial Statistics: A Concise Introduction. CRC Press, Boca Raton, FL. · Zbl 1462.62003
[68] Varin, C., Reid, N. and Firth, D. (2011). An overview of composite likelihood methods. Statist. Sinica 21 5-42. · Zbl 05849508
[69] With, K. A. and King, A. W. (1997). The use and misuse of neutral landscape models in ecology. Oikos 79 219-229.
[70] Zamberletti, P., Papaïx, J., Gabriel, E. and Opitz, T. (2021). Supplement to “Markov random field models for vector-based representations of landscapes.” https://doi.org/10.1214/21-AOAS1447SUPP
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.