Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Disentangling the Formation of Contrasting Tree-Line Physiognomies Combining Model Selection and Bayesian Parameterization for Simulation Models

Isabel Martínez, Thorsten Wiegand, J. Julio Camarero, Enric Batllori and Emilia Gutiérrez
The American Naturalist
Vol. 177, No. 5 (May 2011), pp. E136-E152
DOI: 10.1086/659623
Stable URL: http://www.jstor.org/stable/10.1086/659623
Page Count: 17
  • Download PDF
  • Add to My Lists
  • Cite this Item
Disentangling the Formation of Contrasting Tree-Line Physiognomies Combining Model Selection and Bayesian Parameterization for Simulation Models
We're having trouble loading this content. Download PDF instead.

Abstract

AbstractAlpine tree-line ecotones are characterized by marked changes at small spatial scales that may result in a variety of physiognomies. A set of alternative individual-based models was tested with data from four contrasting Pinus uncinata ecotones in the central Spanish Pyrenees to reveal the minimal subset of processes required for tree-line formation. A Bayesian approach combined with Markov chain Monte Carlo methods was employed to obtain the posterior distribution of model parameters, allowing the use of model selection procedures. The main features of real tree lines emerged only in models considering nonlinear responses in individual rates of growth or mortality with respect to the altitudinal gradient. Variation in tree-line physiognomy reflected mainly changes in the relative importance of these nonlinear responses, while other processes, such as dispersal limitation and facilitation, played a secondary role. Different nonlinear responses also determined the presence or absence of krummholz, in agreement with recent findings highlighting a different response of diffuse and abrupt or krummholz tree lines to climate change. The method presented here can be widely applied in individual-based simulation models and will turn model selection and evaluation in this type of models into a more transparent, effective, and efficient exercise.

Notes and References

This item contains 88 references.

Literature Cited
  • ['Albert, C. H., W. Thuiller, S. Lavorel, I. D. Davies, and E. Garbolino. 2008. Land-use change and subalpine tree dynamics: colonization of Larix decidua in French subalpine grasslands. Journal of Applied Ecology 45:659–669.']
  • ['Alftine, K., and G. P. Malanson. 2004. Directional positive feedback and pattern at an alpine tree line. Journal of Vegetation Science 15:3–12.']
  • ['Améztegui, A., L. Brotons, and L. Coll. 2010. Land-use changes as major drivers of mountain pine (Pinus uncinata Ram.) expansion in the Pyrenees. Global Ecology and Biogeography 19:632–641.']
  • ['Batllori, E., and E. Gutiérrez. 2008. Regional tree line dynamics in response to global change in the Pyrenees. Journal of Ecology 96:1275–1288.']
  • ['Batllori, E., J. J. Camarero, J. M. Ninot, and E. Gutiérrez. 2009. Seedling recruitment, survival and facilitation in alpine Pinus uncinata tree line ecotones: implications and potential responses to climate warming. Global Ecology and Biogeography 18:460–472.']
  • ['Batllori, E., J. J. Camarero, and E. Gutiérrez. 2010. Current regeneration patterns at tree line in the Pyrenees indicate similar recruitment processes irrespective of past disturbance regime. Journal of Biogeography 37:1938–1950.']
  • ['Bella, I. E. 1971. A new competition model for individual trees. Forest Science 17:364–372.']
  • ['Bellman, R. E. 1957. Dynamic programming. Princeton University Press, Princeton, NJ.']
  • ['Brown, D. G. 1994. Predicting vegetation types at tree line using topography and biophysical disturbance variables. Journal of Vegetation Science 5:641–656.']
  • ['Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference: a practical information-theoretic approach. 2nd ed. Springer, New York.']
  • ['Butler, D. R., G. P. Malanson, S. J. Walsh, and D. B. Fagre, eds. 2009. The changing alpine treeline: the example of Glacier National Park, MT, USA. Developments in Earth Surface Processes 12. Elsevier, Amsterdam.']
  • ['Cale, W. G., Henebry, G. M., and J. A. Yeakley. 1989. Inferring process from pattern in natural communities: can we understand what we see? BioScience 39:600–605.']
  • ['Camarero, J. J., and E. Gutiérrez. 1999. Structure and recent recruitment at alpine forest-pasture ecotones in the Spanish central Pyrenees. Écoscience 6:451–464.']
  • ['———. 2004. Pace and pattern of recent tree line dynamics: response of ecotones to climatic variability in the Spanish Pyrenees. Climatic Change 63:181–200.']
  • ['Camarero, J. J., E. Gutiérrez, and M. J. Fortin. 2000. Spatial pattern of subalpine forest-alpine grassland ecotones in the Spanish central Pyrenees. Forest Ecology and Management 134:1–16.']
  • ['Camarero, J. J., E. Gutiérrez, M. J. Fortin, and E. Ribbens. 2005. Spatial patterns of tree recruitment in a relict population of Pinus uncinata: forest expansion through stratified diffusion. Journal of Biogeography 32:1979–1992.']
  • ['Cantegrel, R. 1983. Le pin à crochets pyrénéen: biologie, biochimie, sylviculture. Acta Biologica Montana 2:87–330.']
  • ['Carreras, J., E. Carrillo, R. M. Masalles, J. M. Ninot, I. Soriano, and J. Vigo. 1996. Delimitation of the supra-forest zone in the Catalan Pyrenees. Bulletin de la Société Linnéenne de Provence 46:27–36.']
  • ['Casella, G., and R. L. Berger. 2001. Statistical inference. 2nd ed. Duxbury, Pacific Grove CA.']
  • ['Chamberlain, T. C. 1897. The method of multiple working hypotheses. Journal of Geology 5:837–848.']
  • ['Clark, J. S., C. Fastie, G. Hurtt, S. T. Jackson, C. Johnson, G. A. King, M. Lewis, et al. 1998. Reid’s paradox of rapid plant migration. BioScience 48:13–24.']
  • ['Clark J. S., M. Silman, R. Kern, E. Macklin, and J. HilleRisLambers. 1999. See dispersal near and far: patterns across temperate and tropical forests. Ecology 80:1475–1494.']
  • ['Csilléry, K., M. G. B. Blum, O. E. Gaggiotti, and O. François. 2010. Approximate Bayesian Computation (ABC) in practice. Trends in Ecology & Evolution 25:410–418.']
  • ['DeAngelis, D. L., and W. M. Mooij. 2003. In praise of mechanistically rich models. Pages 63–82 in C. D. Canham, J. J. Cole, and W. K. Lauenroth, eds. Models in ecosystem science. Princeton University Press, Princeton, NJ.']
  • ['———. Individual-based modeling of ecological and evolutionary processes. Annual Review of Ecology, Evolution, and Systematics 36:147–168.']
  • ['Duboz, R., D. Versmisse, M. Travers, E. Ramat, and Y. J. Shin. 2010. Application of an evolutionary algorithm to the inverse parameter estimation of an individual-based model. Ecological Modelling 221:840–849.']
  • ['Dullinger, S., T. Dirnböck, and G. Grabherr. 2004. Modelling climate change-driven tree line shifts: relative effects of temperature increase, dispersal and invasibility. Journal of Ecology 92:241–252.']
  • ['Ellner, S. P., B. A. Bailey, G. V. Bobashev, A. R. Gallant, B. T. Grenfell, and D. W. Nychka. 1998. Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. American Naturalist 151:425–440.']
  • ['Fogel, L. J., A. J. Owens, and M. J. Walsh. 1966. Artificial intelligence through simulated evolution. Wiley, New York.']
  • ['Frontier, S., and D. Pichod-Viale. 1993. Écosystèmes: structure, fonctionnement, évolution. Masson, Paris.']
  • ['García-Ruiz, J. M. 1988. La evolución de la agricultura de montaña y sus efectos sobre la dinámica del paisaje. Revista de Estudios Agro-Sociales 146:7–37.']
  • ['Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2003. Bayesian data analysis. 2nd ed. Chapman & Hall/CRC, Boca Raton, FL.']
  • ['Gilks, W. R., G. O. Roberts, and S. K. Sahu. 1998. Adaptive Markov chain Monte Carlo through regeneration. Journal of the American Statistical Association 93:1045–1054.']
  • ['Grace, J., F. Berninger, and L. Nagy. 2002. Impacts of climate change on the tree line. Annals of Botany 90:537–544.']
  • ['Gray, S. T., J. L. Betancourt, S. T. Jackson, and R. G. Eddy. 2006. Role of multidecadal climate variability in a range extension of pinyon pine. Ecology 87:1124–1130.']
  • ['Greene, D. F., and C. Calogeropoulos. 2002. Measuring and modelling seed dispersal of terrestrial plants. Pages 3–23 in J. Bullock, R. Kenward, and R. Hails, eds. Dispersal ecology. Blackwell, Oxford.']
  • ['Greene, D. F., C. D. Canham, K. D. Coates, and P. T. Lepage. 2004. An evaluation of alternative dispersal functions for trees. Journal of Ecology 92:758–766.']
  • ['Grimm, V., and S. F. Railsback. 2005. Individual-based modeling and ecology. Princeton University Press, Princeton, NJ.']
  • ['Grimm, V., K. Frank, F. Jeltsch, R. Brandl, J. Uchmanski, and C. Wissel. 1996. Pattern oriented modelling in population ecology. Science of the Total Environment 183:151–166.']
  • ['Grimm, V., E. Revilla, U. Berger, F. Jeltsch, W. M. Mooij, S. F. Railsback, H.-H. Thulke, J. Weiner, T. Wiegand, and D. L. DeAngelis. 2005. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991.']
  • ['Grimm, V., U. Berger, F. Bastiansen, S. Eliassen, V. Ginot, J. Giske, J. Goss-Custard, et al. 2006. A standard protocol for describing individual-based and agent-based models. Ecological Modelling 198:115–126.']
  • ['Harsch, M. A., P. E. Hulme, M. S. McGlone, and R. P. Duncan. 2009. Are treelines advancing? a global meta-analysis of treeline response to climate warming. Ecology Letters 12:1040–1049.']
  • ['Hilborn, R., and M. Mangel. 1997. The ecological detective: confronting models with data. Princeton University Press, Princeton, NJ.']
  • ['Hobbs N. T., and R. Hilborn. 2006. Alternatives to statistical hypothesis testing in ecology: a guide to self teaching. Ecological Applications 16:5–19.']
  • ['Holtmeier, F.-K. 2009. Mountain timberlines: ecology, patchiness, and dynamics. Advances in Global Change Research 36. 2nd ed. Springer Science + Business, Heidelberg.']
  • ['Iman, R. L., J. C. Helton, and J. E. Campbell. 1981. An approach to sensitivity analysis of computer models, part 1. Introduction, input variable selection and preliminary variable assessment. Journal of Quality Technology 13:174–183.']
  • ['Jeltsch, F., K. A. Moloney, F. M. Schurr, M. Köchy, and M. Schwager. 2008. The state of plant population modelling in light of environmental change. Perspectives in Plant Ecology, Evolution and Systematics 9:171–189.']
  • ['Johnson, J. B., and K. S. Omland. 2004. Model selection in ecology and evolution. Trends in Ecology & Evolution 19:101–108.']
  • ['Kendall, B. E., C. J. Briggs, W. W. Murdoch, P. Turchin, S. P. Ellner, E. McCauley, R. M. Nisbet, and S. N. Wood. 1999. Why do populations cycle? a synthesis of statistical and mechanistic modeling approaches. Ecology 80:1789–1805.']
  • ['Kirkpatrick, S., C. D. Gelatt Jr., and M. P. Vecchi. 1983. Optimization by simulated annealing. Science 220:671–680.']
  • ['Komuro, R., E. D. Ford, and J. H. Reynolds. 2006. The use of multi-criteria assessment in developing a process model. Ecological Modelling 197:320–330.']
  • ['Körner, C. 1998. A re-assessment of high elevation tree line positions and their explanation. Oecologia (Berlin) 115:445–459.']
  • ['———. 2003. Alpine plant life: functional plant ecology of high mountain ecosystems. 2nd ed. Springer, Heidelberg.']
  • ['Kullman, L., and L. Öberg. 2009. Post-Little Ice Age tree line rise and climate warming in the Swedish Scandes: a landscape ecological perspective. Journal of Ecology 97:415–429.']
  • ['Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943–1967.']
  • ['Lloyd, A. H., and L. J. Graumlich. 1997. Holocene dynamics of tree line forests in the Sierra Nevada. Ecology 78:1199–1210.']
  • ['Malanson, G. P. 1997. Effects of feedbacks and seed rain on ecotone patterns. Landscape Ecology 12:27–38.']
  • ['Marjoram, P., J. Molitor, V. Plagnol, and S. Tavaré. 2003. Markov chain Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences of the USA 100:15324–15328.']
  • ['Martínez, I., and F. González-Taboada. 2009. Seed dispersal patterns in a temperate forest during a mast event: performance of alternative dispersal kernels. Oecologia (Berlin) 159:389–400.']
  • ['Marucco, F., and E. J. B. McIntire. 2010. Predicting spatio-temporal recolonization of large carnivore populations and livestock depredation risk: wolves in the Italian Alps. Journal of Applied Ecology 47:789–798.']
  • ['McIntire, E. J. B., and A. Fajardo. 2009. Beyond description: the active and effective way to infer processes from spatial patterns. Ecology 90:46–56.']
  • ['McKay, M. D., R. J. Beckman, and W. J. Conover. 1979. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245.']
  • ['Monserud, R. A., and H. Sterba. 1999. Modeling individual tree mortality for Austrian forest species. Forest Ecology and Management 113:109–123.']
  • ['Ninot, J. M., E. Carrillo, X. Font, J. Carreras, A. Ferré, R. M. Masalles, I. Soriano, and J. Vigo. 2007. Altitude zonation in the Pyrenees: a geobotanic interpretation. Phytocoenologia 37:371–398.']
  • ['Noble, I. R. 1993. A model of the responses of ecotones to climate change. Ecological Applications 3:396–403.']
  • ['Paruelo, J. M., S. Pütz, G. Weber, M. Bertiller, R. A. Golluscio, M. R. Aguiar, and T. Wiegand. 2008. Long-term dynamics of a semiarid grass steppe under stochastic climate and different grazing regimes: a simulation analysis. Journal of Arid Environments 72:2211–2231.']
  • ['Piou, C., U. Berger, and V. Grimm. 2009. Proposing an information criterion for individual-based models developed in a pattern-oriented modelling framework. Ecological Modelling 220:1957–1967.']
  • ['Platt, J. R. 1964. Strong inference. Science 146:347–353.']
  • ['Purves, D. W., J. W. Lichstein, N. Strigul, and S. W. Pacala. 2008. Predicting and understanding forest dynamics using a simple tractable model. Proceedings of the National Academy of Sciences of the USA 105:17018–17022.']
  • ['Reynolds, J. H., and E. D. Ford. 1999. Multi-criteria assessment of ecological process models. Ecology 80:538–553.']
  • ['Ribbens, E., J. A. Silander, and S. W. Pacala. 1994. Seedling recruitment in forests: calibrating models to predict patterns of tree seedling dispersion. Ecology 75:1794–1806.']
  • ['Robert, C. P., and G. Casella. 2004. Monte Carlo statistical methods. 2nd ed. Springer, New York.']
  • ['Russell, S., and P. Norvig. 2010. Artificial intelligence: a modern approach. 3rd ed. Prentice Hall, Upper Saddle River, NJ.']
  • ['Schwinning, S., and J. Weiner. 1998. Mechanisms determining the degree of size asymmetry in competition among plants. Oecologia (Berlin) 113:447–455.']
  • ['Shiyatov, S. G. 2003. Rates of change in the upper treeline ecotone in the polar Ural Mountains. PAGES News 11:8–10.']
  • ['Slatyer, R. O., and I. R. Noble. 1992. Dynamic of montane tree lines. Pages 346–359 in A. J. Hansen and F. di Castri, eds. Landscape boundaries: consequences for biotic diversity and ecological flows, Springer, New York.']
  • ['Smith, W. F., M. J. Germino, D. M. Johnson, and K. Reinhardt. 2009. The altitude of alpine treeline: a bellwether of climate change effects. Botanical Review 75:163–190.']
  • ['Stoyan, D., and S. Wagner. 2001. Estimating the fruit dispersion of anemochorous forest trees. Ecological Modelling 145:35–47.']
  • ['Tranquillini, W. 1979. Physiological ecology of the alpine timberline: tree existence at high altitudes with special reference to the European Alps. Springer, Berlin.']
  • ['Van Oijen, M., J. Rougier, and R. Smith. 2005. Bayesian calibration of process-based forest models: bridging the gap between models and data. Tree Physiology 25:915–927.']
  • ['Wardle, P. 1981. Is the alpine timberline set by physiological tolerance, reproductive capacity, or biological interactions? Proceedings of the Ecological Society of Australia 11:53–66.']
  • ['Watt, A. S. 1947. Pattern and process in the plant community. Journal of Ecology 35:1–22.']
  • ['Wiegand, T., F. Jeltsch, I. Hanski, and V. Grimm. 2003. Using pattern-oriented modeling for revealing hidden information: a key for reconciling ecological theory and application. Oikos 100:209–222.']
  • ['Wiegand, T., E. Revilla, and F. Knauer. 2004a. Dealing with uncertainty in spatially explicit population models. Biodiversity and Conservation 13:53–78.']
  • ['Wiegand, T., F. Knauer, P. Kaczensky, and J. Naves. 2004b. Expansion of brown bears (Ursus arctos) into the eastern Alps: a spatially explicit population model. Biodiversity and Conservation 13:79–114.']
  • ['Wiegand, T., J. J. Camarero, N. Rüger, and E. Gutiérrez. 2006. Abrupt population changes in tree line ecotones along smooth gradients. Journal of Ecology 94:880–892.']
  • ['Wilson, J. B., and A. D. Q. Agnew. 1992. Positive-feedback switches in plant communities. Advances in Ecological Research 23:263–336.']
  • ['Wood, S. N. 1997. Inverse problems and structured-population dynamics. Pages 555–586 in S. Tuljapurkar and H. Caswell, eds. Structured-population models in marine, terrestrial, and freshwater systems. Chapman & Hall, New York.']

Supplements