Stochastic Desertification

Abstract

The process of desertification is usually modeled as a first order transition, where a change of an external parameter (e.g. precipitation) leads to a catastrophic bifurcation followed by an ecological regime shift. However, vegetation elements like shrubs and trees undergo a stochastic birth-death process with an absorbing state; such a process supports a second order continuous transition with no hysteresis. We present a numerical study of a minimal model that supports bistability and catastrophic shift on spatial domain with demographic noise and an absorbing state. When the external parameter varies adiabatically the transition is continuous and the front velocity renormalizes to zero at the extinction transition. Below the transition one may identify three modes of desertification: accumulation of local catastrophes, desert invasion and global collapse. A catastrophic regime shift occurs as a dynamical hysteresis, when the pace of environmental variations is too fast. We present some empirical evidence, suggesting that the mid-holocene desertification of the Sahara was, indeed, continuous.

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Cited by in corpus (8)

• Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states
• Finite-size scaling for discontinuous nonequilibrium phase transitions
• Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition
• Demographic noise can promote abrupt transitions in ecological systems
• Dispersal-induced resilience to stochastic environmental fluctuations in populations with Allee effect
• Impact of food distribution on lifetime of a forager with or without sense of smell
• Neural models for prediction of spatially patterned phase transitions: methods and challenges
• Front propagation and effect of memory in stochastic desertification models with an absorbing state