Critical desertification transition in semi-arid ecosystems: The role of local facilitation and colonization rate

Abstract In this work we study the effect of two different ecological mechanisms on the desertification transition in arid or semi-arid ecosystems, modeled by a stochastic cellular automaton. Namely we consider the role of the facilitation mechanism, i.e. the local positive effects of plants on their neighborhood and of colonization factors, such as seed production, survival and germination probabilities. Within the model, the strength of these two mechanisms is determined by the parameters f and b , respectively controlling the rates of the recovery and colonization processes. In particular we focus on the full desertification transition occurring at increasing value of the mortality rate m and we discuss how the values of f and b affect the critical mortality m c , the critical exponents β and γ σ ′ , determining the power-law scaling of the average vegetation density and of the root-mean-square deviation of the density fluctuations, and the character of the transition: continuous or abrupt. We show that m c strongly depends on both f and b , a dependence which accounts for the higher resilience of the ecosystems to external stresses as a consequence of an increased effectiveness of positive feedback effects. On the other hand, concerning the value of the exponents and the character of the transition, our results point out that both these features are unaffected by changes in the strength of the local facilitation. Viceversa, we show that an increase of the colonization factor b significantly modifies the values of the exponents and the order of the transition, changing a continuous transition into an abrupt one. We explain these results in terms of the different range of the interactions characterizing facilitation and colonization mechanisms.

[1]  S. Ruffo,et al.  Non-Gaussianity of resistance fluctuations near electrical breakdown , 2003 .

[2]  Piero Lionello,et al.  Simple statistical approach for computing land cover types and potential natural vegetation , 2010 .

[3]  S. Finnegan,et al.  Climate Change and the Past, Present, and Future of Biotic Interactions , 2013, Science.

[4]  M. Scheffer,et al.  Slowing Down in Spatially Patterned Ecosystems at the Brink of Collapse , 2011, The American Naturalist.

[5]  M. Rietkerk,et al.  Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems , 2007, Nature.

[6]  T. Downing,et al.  Global Desertification: Building a Science for Dryland Development , 2007, Science.

[7]  J. Pinton,et al.  Universality of rare fluctuations in turbulence and critical phenomena , 1998, Nature.

[8]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[9]  Todd M. Scanlon,et al.  Positive feedbacks promote power-law clustering of Kalahari vegetation , 2007, Nature.

[10]  Gregory P. Asner,et al.  The rate and spatial pattern of treefall in a savanna landscape. , 2013 .

[11]  Christopher B Field,et al.  Environmental and community controls on plant canopy chemistry in a Mediterranean-type ecosystem , 2013, Proceedings of the National Academy of Sciences.

[12]  Sonia Kéfi,et al.  Evolution of Local Facilitation in Arid Ecosystems , 2008, The American Naturalist.

[13]  A Vespignani,et al.  Avalanche and spreading exponents in systems with absorbing states. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  G. Ódor.  Universality classes in nonequilibrium lattice systems , 2002, cond-mat/0205644.

[15]  S. Carpenter,et al.  Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns , 2014, PloS one.

[16]  Elizabeth Pennisi.  Geography. Worth a thousand words. , 2013, Science.

[17]  N. Shnerb,et al.  Facilitation, competition, and vegetation patchiness: from scale free distribution to patterns. , 2008, Journal of theoretical biology.

[18]  Steven T. Bramwell,et al.  The distribution of spatially averaged critical properties , 2009 .

[19]  J. Escós,et al.  Association between competition and facilitation processes and vegetation spatial patterns in alpha steppes , 2006 .

[20]  Maxime Clusel,et al.  Criterion for universality-class-independent critical fluctuations: example of the two-dimensional Ising model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  J F Reynolds,et al.  Biological Feedbacks in Global Desertification , 1990, Science.

[22]  Marten Scheffer,et al.  The interplay of facilitation and competition in plant communities , 1997 .

[23]  S. Carpenter,et al.  Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data , 2012, PloS one.

[24]  Christensen,et al.  Universal fluctuations in correlated systems , 1999, Physical review letters.

[25]  Gregory P. Asner,et al.  LiDAR measurements of canopy structure predict spatial distribution of a tropical mature forest primate , 2012 .

[26]  S. Carpenter,et al.  Rising variance: a leading indicator of ecological transition. , 2006, Ecology letters.

[27]  Cecilia Pennetta,et al.  Desertification Transition in Semi-arid Ecosystems and Directed Percolation , 2015 .

[28]  Christopher B. Field,et al.  Changes in Ecologically Critical Terrestrial Climate Conditions , 2013, Science.

[29]  Nadav M Shnerb,et al.  Origin of Pareto-like spatial distributions in ecosystems. , 2008, Physical review letters.

[30]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[31]  Hugo Fort,et al.  Early Warnings for Catastrophic Shifts in Ecosystems: Comparison between Spatial and Temporal Indicators , 2010, Int. J. Bifurc. Chaos.

[32]  Osvaldo E. Sala,et al.  Competition, facilitation, seed distribution and the origin of patches in a Patagonian steppe , 1994 .

[33]  E. Meron,et al.  Diversity of vegetation patterns and desertification. , 2001, Physical review letters.

[34]  L. Walker,et al.  Competition and facilitation: a synthetic approach to interactions in plant communities , 1997 .

[35]  Sonia Kéfi,et al.  Local facilitation, bistability and transitions in arid ecosystems. , 2007, Theoretical population biology.

[36]  Marten Scheffer,et al.  Spatial correlation as leading indicator of catastrophic shifts , 2010, Theoretical Ecology.

[37]  S. Carpenter,et al.  Anticipating Critical Transitions , 2012, Science.

[38]  S. Ruffo,et al.  Non-Gaussian resistance noise near electrical breakdown in granular materials , 2004 .

[39]  Roberta E. Martin,et al.  Forest Canopy Gap Distributions in the Southern Peruvian Amazon , 2013, PloS one.

[40]  Rosa Lasaponara,et al.  1/fα fluctuations in the time dynamics of Mediterranean forest ecosystems by using normalized difference vegetation index satellite data , 2006 .

[41]  David Niemeijer,et al.  Ecosystems and Human Well-Being: Desertification Synthesis , 2005 .

[42]  David E. Knapp,et al.  Automated mapping of tropical deforestation and forest degradation: CLASlite , 2009 .

[43]  Peter Grassberger,et al.  Are damage spreading transitions generically in the universality class of directed percolation? , 1994, cond-mat/9409068.