Synthetic soil crusts against green-desert transitions: a spatial model

Semiarid ecosystems are threatened by global warming due to longer dehydration times and increasing soil degradation. Mounting evidences indicate that, given the current trends, drylands are likely to expand and possibly experience catastrophic shifts from vegetated to desert states. Here we explore a recent suggestion based on the concept of ecosystem terraformation, where a synthetic organism is used to counterbalance some of the nonlinear effects causing the presence of such tipping points. Using an explicit spatial model incorporating facilitation and considering a simplification of states found in semiarid ecosystems i.e., vegetation, fertile and desert soil, we investigate how engineered microorganisms can shape the fate of these ecosystems. Specifically, two different, but complementary, terraformation strategies are proposed: Cooperation-based: C-terraformation; and Dispersion-based: D-terraformation. The first strategy involves the use of soil synthetic microorganisms to introduce cooperative loops (facilitation) with the vegetation. The second one involves the introduction of engineered microorganisms improving their dispersal capacity, thus facilitating the transition from desert to fertile soil. We show that small modifications enhancing cooperative loops can effectively change the location of the critical transition found at increasing soil degradation rates, also identifying a stronger protection against soil degradation by using the D-terraformation strategy. The same results are found in a mean field model providing insights into the transitions and dynamics tied to these terraformation strategies. The potential consequences and extensions of these models are discussed.

Methods
This is the code of the cellular automation

半干旱生态系统正面临全球变暖的威胁，其表现为脱水时长延长与土壤退化加剧。越来越多的证据表明，按照当前发展趋势，旱地面积或将持续扩张，甚至可能经历从植被覆盖态向荒漠态的灾难性状态转变。本研究基于生态系统改造（ecosystem terraformation）理念，探讨了一项新近提出的解决方案：利用合成生物（synthetic organism）抵消引发这类临界点（tipping points）的部分非线性效应。本研究采用纳入了物种促进作用的显式空间模型，并对半干旱生态系统的三类典型状态（植被覆盖态、肥沃土壤态与荒漠土壤态）进行简化，以此探究工程化微生物（engineered microorganisms）如何影响这类生态系统的存续命运。

具体而言，本研究提出两种互补的改造策略：基于协同作用的C型改造（C-terraformation），以及基于扩散能力的D型改造（D-terraformation）。第一种策略通过土壤合成微生物，构建与植被之间的协同循环（即促进作用）；第二种策略则通过引入工程化微生物以提升其扩散能力，进而促进荒漠土壤向肥沃土壤的状态转变。

研究结果表明，仅需对协同循环进行小幅强化，即可有效改变土壤退化速率提升时的临界转变阈值；同时还发现，采用D型改造策略可对土壤退化提供更强的抵御能力。通过平均场模型（mean field model）也得到了一致结果，该模型可帮助我们理解与这类改造策略相关的状态转变与动态过程。本研究最后还讨论了这些模型的潜在应用场景与拓展方向。

方法
以下为元胞自动机（cellular automation）的实现代码。