Ergodic to Non-ergodic Behavior Transitions and Hysteresis in Ecosystem Models

Pietsch, S. ORCID: https://orcid.org/0000-0001-6431-2212 & Bednar, J.E. (2015). Ergodic to Non-ergodic Behavior Transitions and Hysteresis in Ecosystem Models. In: Systems Analysis 2015 - A Conference in Celebration of Howard Raiffa, 11 -13 November, 2015, Laxenburg, Austria.

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Abstract

A widely used concept in natural sciences is the ergodic principle stating that the temporal average state of system equals the average of single states of an ensemble of the system. Originally formulated by Boltzmann to describe the physics of an ideal gas, the ergodic principle was and still is applied in, for example, the assessment of developmental aspects of individuals, but also in the growth series concept of whole ecosystems.
Hysteresis on the other hand describes the observable contrary of the ergodic principle, that is, that the current state of a system strictly depends on the individual temporal development steps, or that individual history is unequivocally important.
This work will provide evidence for ergodic to non-ergodic transitions in the application of biogeochemical ecosystem models using the showcase of Congo Basin rainforests. Using a climate gradient from west to east, ergodic model behavior is shown for a virgin forest refuge, non-ergodic behavior for a current forest savannah mosaic and ergodic behavior again for large open savannahs. Additionally, the occurrence of hysteresis related to the prevailing initial vegetation will be demonstrated, whereby the non-ergodic phase along the climate gradient is shown to be more extensive if rainforest was the original vegetation, as opposed to rainforest establishing on non-forest sites.
The combination of ergodic to non-ergodic transitions—sometimes referred to as catastrophic shifts in ecosystems—will be put into context with the changing distribution patterns of rainforest and savannah over the course of the Holocene.

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