The shade avoidance syndrome: a non-markovian stochastic growth model

Plants at high population density compete for light, showing a series of physiological responses known as the shade avoidance syndrome. These responses are controlled by the synthesis of the hormone auxin, which is regulated by two signals, an environmental one and an internal one. Considering that the auxin signal induces plant growth after a time lag, this work shows that plant growth can be modelled in terms of an energy-like function extremization, provided that the Markov property is not applied. The simulated height distributions are bimodal and right skewed, as in real community of plants. In the case of isolated plants, the theoretical expressions for the growth dynamics and the growth speed excellently fit experimental data for Arabidopsis thaliana. Moreover, the growth dynamics of this model is shown to be consistent with the biomass production function of an independent model. These results suggest that memory effects play a non-negligible role in plant growth processes.

💡 Research Summary

The paper presents a novel stochastic model of plant growth that explicitly incorporates memory effects, challenging the conventional Markovian assumption that the future state depends only on the present. The biological motivation stems from the shade‑avoidance syndrome (SAS), a suite of responses triggered when plants experience reduced red‑to‑far‑red light ratios in dense stands. SAS is mediated by the hormone auxin, whose synthesis is driven by two distinct signals: an environmental cue (the light environment created by neighboring plants) and an internal circadian‑like cue. Crucially, experimental evidence shows that auxin accumulation does not translate into elongation instantaneously; instead, there is a finite time lag (τ) between auxin production and the activation of growth mechanisms.

To capture this delay, the authors formulate a non‑Markovian stochastic differential equation for the height (h_i(t)) of each plant (i). The growth rate is derived as the gradient of an energy‑like functional (\mathcal{F}) that depends on the delayed states of all plants:

\